analele - “Ovidius” University Annals of Constanta

Transcription

“OVIDIUS” UNIVERSITY OF CONSTANTZA
UNIVERSITATEA „OVIDIUS” CONSTANŢA
“OVIDIUS” UNIVERSITY ANNALS CONSTANTZA
Year IX
(2007)
Series: CIVIL ENGINEERING
Volume 1
ANALELE
UNIVERSITĂŢII „OVIDIUS”CONSTANŢA
ANUL IX
(2007)
Seria: CONSTRUCŢII
Volumul 1
Ovidius University Press
2007
Ovidius University Annals Series: Civil Engineering
Volume 1, Number 9, 2007
SECTION I
Structural Analysis and Reliability
The influence of the water level variation in reservoirs upon the earth dams strain state
Virgil BREABAN
Sunai GELMAMBET
The generalized eigenvalues method in the nonlinear dynamics analysis
Gheorghe PICOL
Mircea IEREMIA
Rotation Capacity of Reinforced Concrete Elements
Bogdan HEGHEŞ
Cornelia MĂGUREANU
Assessment of the Potential for Progressive Collapse in RC Frames
Adrian IOANI
Liviu CUCU
Călin MIRCEA
Cracking of Reinforced Concrete Elements
Laura- Catinca LEŢIA
A Short Introduction to Load Carrying Capacity for High Strength Concrete
Cornelia MĂGUREANU
Dumitru MOLDOVAN
Studies on the Modalities of Use of Sludge Resulting From the Lime Milk Neutralization of
Acid Waters Derived From the Pickling of Wire Obtained At S.C. Mechel Câmpia Turzii
Daniela MANEA
Claudiu ACIU
Ofelia CORBU
Energy Conservation, an Essential Factor in Sustainable Construction
Daniela MANEA
Claudiu ACIU
Sustaining Systems for Underground Parking in Cluj - Napoca
Augustin POPA
Nicoleta Maria ILIEŞ
The Rayleigh Quotient, the Vector Iteration With Shift and the Rayleigh Product
Daniela PREDA
Florin MACAVEI
Calculation of deformation estimated value for protection harbor construction to seismic
application shaped through stationary random process
Isabella STAN
Dragos VINTILA
ISSN-1584 - 5990
7-14
15-22
23-28
29-36
37-44
45-52
53-58
59-64
65-70
71-76
77-80
© 2000 Ovidius University Press
180
Table of Contents / Ovidius University Annals Series: Civil Engineering 9, 179 - 181 (2007)
SECTION II
Fluid Mechanics and Hydraulic Structures
Reactive centrifugal rotor – the analytical study of two applications
Victor BENCHE
Radu ŢÂRULECU
Stelian ŢÂRULECU
Analogical electro hydrodynamic research on installations for launch subsonic constant
density jets
Victor BENCHE
Virgil-Barbu UNGUREANU
The Safety of Concrete Structures from the Water Supply System, Undermined by the Errors
and Careless in Design and Execution
Olimpia BLAGOI
Bogdan PATRAS
Maricel GEORGESCU
Marinela BARBUTA
Modeling, Simulation and Regulation of an Industrial Installation Intended for Field
Irrigation Using Attenuant Wastewater
Adrian BOLMA
Marian DORDESCU
Phased Execution of the Coastal Protection Works in the Southern Area of the Romanian
seashore
Romeo CIORTAN
A possible recovery system of the potential energy for the rain water
in the case of high buildings
Ovidiu Mihai CRĂCIUN
Radu ŢÂRULECU
The Analysis of the Impact of Storage Lake on Environment Using the Chemical
Characterization of the Water Resources. Case Study Bahlui Basin River
Ion GIURMA
Ioan CRĂCIUN
Catrinel-Raluca GIURMA
The Multicriterial Decisional Management Within Irrigation Arrangements
Gheorghe IORDACHE
Marian DORDESCU
Protection Measures on the Algerian Coastline of the Mediterranean Sea
Khoudir MEZOUAR
Shoreline Variation and Protection Measures on the Romanian Coast Line of the Black Sea –
A Case Study for Mamaia Beach
Khoudir MEZOUAR
Romeo CIORTAN
83-86
87-92
93-98
99-106
107-112
113-118
119-124
125-130
131-136
137-144
Table of Contents / Ovidius University Annals Series: Civil Engineering 9, 179 - 181 (2007)
Explanatory Aspects of the Research Concerning the National Land Reclamation Digital
Data Fund (FNDDIF)
Irina STATE
Tudor Viorel BLIDARU
Hydraulic Checking of a Sewerage Collector
Gabriel TATU
The Increase of Strong Rainfall Concentrated on Small Areas as an Effect of Climatic
Changes
Marius TELIŞCĂ
Catrinel-Raluca GIURMA-HANDLEY
Petru CERCEL
Energetic improvement of joinery embrasures
Analysis of heat exchangers obtained by division or multiplying of units
Neculae ŞERBĂNOIU
Maria MUREŞAN
181
145-150
151-154
155-160
161-168
169-176
Volume 1, Number 9, May 2007
The influence of the water level variation
in reservoirs upon the earth dams strain state
a
Virgil BREABAN a
Sunai GELMAMBET a
”Ovidius” University of Constantza, Constantza, 8700, România
__________________________________________________________________________________________
Rezumat: În această lucrare este studiată şi prezentată influenţa variaţiei nivelului apei în lacul de acumulare
asupra deformaţiilor barajelor de pământ. Pentru aceasta au fost realizate o serie de simulări numerice privind
efectele unor variaţii bruşte sau lente ale nivelurilor în lacul de acumulare asupra stării de deformaţii şi eforturi în
corpul barajelor de pământ. Analizele numerice s-au efectuat în ipoteza comportării neliniare a materialelor din
corpul barajului, cu ajutorul programului cu elemente finite Cosmos 2.6. Compararea rezultatelor numerice cu
măsurătorile din amplasamente validează modelele de calcul folosite şi permit evaluarea efectelor fenomenului
studiat asupra siguranţei barajelor de pământ. În final, în urma analizei rezultatelor obţinute sunt prezentate o
serie de concluzii cu privire la influenţa variaţiei nivelului apei în lac asupra deformaţiilor barajelor de pământ.
Abstract: In this paper is presented and studied the influence of the water level variation in the reservoirs upon
the earth dams strain state. For that there have been realized a series of numeric simulations about the effect of
sudden or slow variations of the levels in the reservoir over the state of strains and stress in the body of the earth
dams. The numerical analysis has been done in the hypothesis of nonlinear behaviour of materials in the dam
body, using the finite element program Cosmos 2.6. Comparison between the numerical results and the local
measurements made on dam validates the computational models used and allows the effects estimation upon the
earth dams’ safety. Finally, are presented a series of conclusions about the influence of the variations of the water
level in the reservoir over the earth dams strain state.
Keywords: the variations of the water level in the reservoir, strains, earth dam.
__________________________________________________________________________________________
1. Introduction
Earth dams represent the most common and
the oldest category of all the dams. Almost 70% of
the 46000 of great dams that are in the ICOLD
system are embankment dams [3].
With all the spread and the age of earth dams,
with all the remarkable scientific and technologic
progresses realised in this domain, especially in the
last five decades, the knowledge of the behaviour of
the earth dams at sudden variations of the water
level in the reservoir is not totally understood.
Because of these reasons, in this work is
represented and studied with the help of numeric
methods based on MEF [2], [6], the nonlinear
behaviour of earth dams and the sudden variations
of levels in the reservoir, adding to a better
knowledge of the studied phenomena, the rise in
performance and safety in the use of earth dams [1].
ISSN 1584 - 5990
For the analysis of the state of stress and strains
is important to take in consideration the hypothesis of
sudden variation of water level in the reservoir. This
sudden variation can appear in the situation in which is
necessary of a rapid empting or the case of a flood
wave [3]. The rapid empting of the dam may appear
necessary for reasons of safety of the dam, urgent
needs of the use of the water in the reservoir or other
special situations.
2. Numerical Simulation
The numerical simulations for the case of sudden
rise of the water level in the reservoir were done for
Dopca dam., a lest affluent of the river Olt, at a
distance of 1,5 km upstream of the town Dopca, a
village in the town of Hoghiz, in the county of Brasov.
The Dopca dam is made of fillings, made of
embankment from the materials extracted from the
8
The influence of the water … / Ovidius University Annals Series: Civil Engineering 9, 7-14 (2007)
lake ditch, with a reinforced concrete face, with a
surface of 7800 m2, made on the upstream face with
the maximum height of 18,0 m and the length at the
top of 175,0 m
Fig.1 The section of Dopca dam
The numerical simulations over the dam have
been done for two cases so that later, by comparing
the results we can see the effect of the sudden
variations of water in the lake. In both cases, the
simulations have been done with the help of the
program of finite elements COSMOS 2.6 [4], [5]. The
analyses done in the two cases have been nonlinear
analysed and was used the Drucker-Prager model [8].
Fig.2 The section of Dopca dam, with the difference of the water level
In the case of the first simulation there has been
considered a rise in water level in the lake of
1m/day and in the second case a rise of 3m/day.
The difference of level considered in the case of the
sudden variation was of 10m and is presented in the
fig. 2.
For the first case when the rise of level of water
level was considered of 1m/day the filling had
taken place in 10 days meaning 864000 seconds,
and in the second case the filling had taken place in
3,33 days meaning 288000 seconds.
To be sure that the results obtained represents a
behavior close to the behavior of the real dam, the
results have been compared with the real behavior of
the dam in time.
The results that were obtained from the simulations
in the two cases, in order to be seen and compared
more easily were presented in the following drawings.
V. Breaban , S. Gelmambet / Ovidius University Annals Series: Civil Engineering 9, 7-14 (2007)
9
Fig.3. The numbering of nodes
Fig.4 The variation of the displacement in the y
direction in node 1 in the case of sudden
variation(cm)
direction in node 1 in the case of no sudden variation
(cm)
variation(cm)
direction in node 9 in the case of no sudden
variation(cm)
10
variation(cm)
direction in node 18 in the case of no sudden
variation(cm)
Fig.10 The variation of the stress σx in node 26 in
the case of sudden variation (Pa)
Fig.11 The variation of the stress σx in node 26 in the
case of no sudden variation (Pa)
Fig.12 The variation of the stress τxy in node 26 in
the case of sudden variation (Pa)
Fig.13 The variation of the stress τxy in node 26 in the
case of no sudden variation (Pa)
Fig.14 The diagram of stress τxy at step 100 in the case of sudden variation (Pa)
Fig.15 The diagram of stress τxy at step 100 in the case of no sudden variation (Pa)
Fig.16 The diagram of εx strains at step 100 in the case of sudden variation
11
12
Fig.17 The diagram of εx strains at step 100 in the case of no sudden variation
Fig.18 The situation schematics of the dam with disposal landmarks for the following in time
In the following figures are presented the data
obtained from the study in time of the dam are
presented.
In fig. 18 is presented the plan of dispersion of
the landmarks for the following in time of the
Dopca dam is presented.
The landmark 41 coincides with node 1 of the finite
elements mesh.
elements mesh.
elements mesh.
The marked values are form 1 Oct 2001 when the
flow of water was 1m/day.
The settlement for node 1 from the calculations
shown in fig 5 is -5,75 mm.
13
The settlement for node 9 from the calculations shown
in fig 7 is -3,27 mm.
The settlement for node 18 from the calculations
shown in fig 9 is -6,16 mm.
Fig.19 The values of settlement necessary for the comparison
In fig. 20 are presented the differences between the settlement obtained by the calculation and the settlement
obtained by the measurement.
Fig.20 The comparison graphics between the calculation values and the measured values
14
3. Conclusions
We can see that in the case of sudden variations,
the movements and strains on the horizontal of the
dam modify significantly and are not to be
neglected. For dams with reinforced concrete face,
a problem is the deformation of the reinforced
concrete face under the action of sudden variations
of the level of water in the reservoir. Because of
these movements (strains) modification appears to
the profile of transversal sections and even
longitudinal fissures witch can influence the
resistance of the dam (infiltrations).
In the case of dams with reinforced concrete
face, the effect of the sudden variation of water
consists in the fact that the plastic strains are
extremely big, especially in the center zone of the
dam. The reinforced concrete face follows the
strains of the filling of the dam produced by the
pressure at the filling of the lake and it’s pulled to
the center of the dam. Because of this the vertical
ends of the central area of the reinforced concrete
face have a tendency to close and the ends of
perimeter areas open very much. In the case of the
perimeter area there are three distinct components
of the displacements: settlement on the normal face
of the reinforced concrete face, openings on the
normal direction of the end and displacements that
form a tangent parallel.
Following the comparison of the results in the
two cases, we can se that the influence of sudden
variation of the water level over the results is very
important. We can se that de difference of the
displacement on the y (vertical) direction are very
small, but the differences on the x (horizontal)
direction are important and cant be ignored.
In the case of the stress we can see an increase
of the values in the case of sudden variation in
especially in the case of the stress σx and τxy. By
comparing the results of the strains that are specific
we can se that in the case of the strains the εy
differences are very small like in the case of the
displacements. The more important differences
appear in the case of the strains εx and in the special
cases of strains γxy.
We also see that the horizontal strains can be
registered at the ½ the height of the dam on the
upstream prism. Therefore the biggest strains will be
produced in the central area of the upstream prism.
The complex nature of the phenomena of behavior
of embankment dams at the first filling of the reservoir
imposes a careful study of them on the full period of
the filling as well as in the first years of using. The
comparison of the data obtained from the measures
about the calculation from the design, the making of
post analysis tests make the most direct methods for
the understanding of the phenomena and the
preventing of incidents or accidents.
4. References
[1] Dibaj,M., Penzien, J., Nonlinear seismic response
of earth structures, Report No. EERC 69-2 , Univ. of
California, Berkeley, 1974.
[2] Popovici, A., Dynamic analisys by numerical me
thods, 1978, I.C.Bucuresti..
[3] Popovici, A., Dams for water accumulation, Vol.II,
2002, Editura Tehnică Bucuresti.
[4] Gelmambet, S., Dam-foundation seismic
interaction analysis, Simpozionul Concepţii Moderne
în ingineria Amenajărilor Hidrotehnice, 13 mai 2005,
Timişoara, Buletinul Ştiinţific al Universităţii
„POLITEHNICA” din Timişoara, Seria Hidrotehnică,
Tomul 49 (63), Fascicola 1, pag.46-53, Editura
Politehnica, România 2005;
[5] Gelmambet, S., Dam-reservoir seismic interaction
analysis, The XXXth National Conference of Solid
Mechanics Mecsol 2006 , 15-16 septembrie 2006,
Constanta, Vol.9 pag.251-258.
[6] Zienkiewicz, O.C. The finite element method in
engineering science, McGraw-Hill, London, 1971.
[7] Zienkiewicz,O.C., Bettess,P. Fluid-structure
Dynamic interaction and wave forces; an introduction
to numerical treatement, Int.J.Num.Meth.in Engng.,
Vol.13, 1978.
[8] *** Cosmos/M Manual Teoretic, Structural
Reasearch Corporation, Santa Monica USA, 1996.
The generalized eigenvalues method in the nonlinear dynamics analysis
a
Gheorghe PICOL a
Mircea IEREMIA a
Technical University of Civil Engineering Bucharest, Bucharest,020396, România
__________________________________________________________________________________________
Rezumat: În analiza dinamică liniară, în condiţiile în care modelul de calcul are o lege constitutivă liniarelastică, se poate folosi proprietatea de ortogonalitate a vectorilor proprii pentru rezolvarea ecuaţiilor de echilibru
seismic. În acest caz, vectorii proprii sunt ortogonali în raport cu matricea maselor şi matricea rigidităţilor. Dacă
se consideră amortizarea de tip Rayleigh, relaţia de ortogonalitate este valabilă şi pentru matricea de amortizare.
Din punct de vedere matematic, sistemul de ecuaţii care caracterizează fenomenul se transformă în “n” ecuaţii
decuplate , câte una pentru fiecare mod propriu de vibraţie.
În efectuarea unei analize dinamice incrementale neliniare, matricile maselor, de rigiditate şi de amortizare
nu mai sunt neapărat matrici simetrice.În consecinţă relaţia de ortogonalitate a vectorilor proprii în raport cu
matricile de rigiditate şi de amortizare nu mai este verificată şi ca urmare formele proprii de vibraţie nu se mai
pot decupla.Se recurge la metoda numerică de rezolvare a valorilor şi vectorilor proprii generalizaţi.
Abstract: In the linear dynamics analysis when the computation model has a linear-elastic constitutive law, it
can be used the orthogonality property of the eigenvectors to solve the seismic equilibrium equations. In this
case, the eigenvectors are orthogonal with respect to the mass matrix and stiffness matrix. If one considers the
Rayleigh type damping, the orthogonality relationship holds for the damping matrix too. From the mathematical
point of view the system of equations characterizing the phenomena becomes a set of “n” uncoupled equations,
one equation for each mode.
The achievement of a nonlinear dynamics analysis assumes the mass, rigidity and damping matrices are not
necessary symmetric. Consequently, the orthogonality relationships of eigenvectors with respect to the rigidity
and damping matrices are no longer true and the inner forms of vibrations cannot be decoupled. In this case one
uses the numerical method of generalized eigenvalues and generalized eigenvectors.
Keywords: Dynamic,damping, eigenvalues, generalized eigenvectors.
__________________________________________________________________________________________
1. The problem-Generalitys
In the linear dynamics analysis when the
computation model has a linear-elastic constitutive
law, the orthogonality property of the eigenvectors
can be used to solve the seismic equilibrium
equations. In this case, the eigenvectors are
orthogonal with respect to the mass matrix and
stiffness matrix. One neglects usually the damping
matrix; if the damping is taken into account then
the Rayleigh model is used where the damping
matrix is a linear combination between the mass
matrix and the stiffness matrix. Within these
conditions the orthogonality relation is also true for
the damping matrix. From the mathematical point
ISSN 1584 - 5990
of view the system of equations of free or forced
vibrations becomes a set of
“n” independent
equations, one equation for each mode.
The characteristics of an incremental nonlinear
dynamics analysis are the following:
-the history of the used excitation should be
considered;
- the numerical models must consider the rheological
properties of real materials: elasticity, plasticity,
viscosity ;
- for the linearization, “stress- strain” curve is
replaced by a polygonal line ;
- for a material with different loading and unloading
rigidity, the variation of rigidity is given by the
variation of the modulus of elasticity/plasticity with
16
The generalized eigen. meth…/ Ovidius University Annals Series: Civil Engineering 9, 15 -22 (2007)
respect to strain value(elastic-plastic) at the
corresponding moment of time ;
- the damping effect which modifies the
eigenfrequency of the damaged structure needs to
be considered;
- the stiffness matrix and the damping matrix are
not constant anymore, they are functions of the total
specific deformation; they are continuously
degrading when loading ;
- the mass, stiffness and damping matrices are non
necessary symmetric ;
- the orthogonality relatiohships of the eigenvectors
with respect to the stiffness and damping matrices
are not necessary true and as consequence the inner
forms of vibrations cannot be detached; one uses
the numerical method of generalized eigenvalues
and generalized eigenvectors with solutions arising
in the real field from the complex field.
In the sequel M, K are the mass matrix and
the stiffness matrix of a model respectively , with N
dynamical degree of freedom (DOF) and C the
damping matrix; P(t) is the vector of loads. The
•
••
unknowns are u, u and u - the vector of
displacements, velocities and accelerations. Then
the dynamic response of the body to an external
excitation is modeled by a system of differential
eqs. (1.1) .
••
•
••
•
M ⋅ u + C ⋅ u + K ⋅ u = P(t )
(1.1)
One considers both the homogenous viscous
damped associated model and the homogeenous
nondamped associated model, defined by eq.(1.2) and
(1.3) respectively:
M ⋅ u + C ⋅ u+ K ⋅ u = 0
••
M⋅ u+ K ⋅u = 0
•
[B]⋅ ⎧⎨X(t )⎫⎬ − [A]⋅ {X(t )} = { 0 }
⎩
⎭
(2.2)
Looking for particular exponential solutions
of (2.2) one gets the relationships (2.3) and (2.4).
det(β[A]-α[B])=0
(2.3)
(β[A]-α[B]){V}={0}
(2.4)
(1.3)
The initial conditions of the dynamic response
are given by the eqs.(1.4):
•
u (0) = u 0 ; u (0 ) = v 0 ,
(1.4)
where u0 şi v0 are the vectors of the initial displacements and the initial velocities.
To solve the equations (1.1)÷(1.4), there are
several methods, each of them proceeding in several
steps and some steps are common for two or more
methods; each method has its own hypotheses,
advantages and drawbacks.
2. Generalized eigenvalues method
2.1. The response in free vibrations with initial data
The system of homogenous differential eq.(1.2)
by the transformations (2.1):
⎧⎪ • ⎫⎪
[M ] [0] ⎤
⎡ − [C] − [K ]⎤
{X(t )} = ⎨u (t )⎬ , [B] = ⎡⎢
, [A ] = ⎢
⎥
⎥,
[
]
[
]
⎣ 0 − K⎦
⎣− [K ] [0] ⎦
⎪⎩u (t )⎪⎭
becomes equivalent with the system of differential
equations of the first order
(1.2)
the
(2.1)
The eq. (2.3) is called the characteristic equation,
(α( j), β( j)) ∈ C 2 − { 0} and the
pairs
{ }
vectors V j ∈ C n − {0} , which satisfy (2.3) and (2.4)
are called generalized eigenvalues and generalized
eigenvector. With no loss of generality one assumes
β ∈ R , β ≥ 0. Usual eigenvalues is λ given by:
λ = α/β
(2.5)
The part α(j) of the generalized eigenvalue of
(2.4) has the form (2.6).
P. Gheorghe and M.Ieremia / Ovidius University Annals Series: Civil Engineering 9, 15 -22 (2007)
α(j) = αR(j)+i αI( j),
with
αR(j) ,
(2.6)
α I ( j) ∈ R.
As the roots of the
characteristic equation are real or not we denote:
I1 = {j 1 ≤ j ≤ n , α I ( j) = 0 }
(2.7)
I 2 = {j 1 ≤ j ≤ n , α I ( j) > 0 }
If j ∈ I1 , then the generalized eigenvector is
a column of [VR ]∈ M n (R ) .
17
If j ∈ I 2 , then the real part and the imaginary part
of the generalized eigenvector are two columns of
[VR].
Using the eqs. (2.1), and the initial data (1.4) one
gets the coeficients μj from (2.8).
[VR ] ⋅ {μ j } = {v 0 , u 0 }T
(2.8)
The solution of the problem (1.2)÷(1.4) is given
by (2.9), for any s, 1 ≤ s ≤ p:
u s (t ) = ∑ e λ R ( j)⋅t ⋅ ((μ j ⋅ VR (p + s, j) + μ j+1 ⋅ VR (p + s, j + 1)) ⋅ cos(λ I ( j) ⋅ t ) +
(μ
j∈I 2
j+1 ⋅ VR (p + s, j) − μ j ⋅ VR (p + s, j + 1)) ⋅ sin (λ I ( j) ⋅ t )) + ∑ μ j ⋅ VR (p + s, j) ⋅ e
λ j ⋅t
,
(2.9)
j∈I1
Here the generalized eigenvalues are λ(j):
λ( j) = λ R ( j) + λ I ( j) ⋅ i, λ R ( j) ∈ R , λ I ( j) ∈ R
The functions e
sin (λ I ( j) ⋅ t ) ⋅ e λ R ( j)⋅t
eigenfunctions.
λ j ⋅t
(2.10)
, cos(λ I ( j) ⋅ t ) ⋅ e λ R ( j)⋅t and
from
(2.9)
are
called
2.2. The response in forced vibrations with
piecewise linear exciting force
One assumes that{u(t)} is a solution of (1.1)
and that the sequence of timestamps ti are ordered
ascendingly, ti<ti+1. Let {P(ti)}= {fi},with known fi .
The exciting force {P(t)} on the segment[ti<ti+1 ] is
(2.11).
{P(t )} = (1 − (t − t i ) (Δt )) ⋅ {fi } + (t − t i ) (Δt ) ⋅ {fi +1} (2.11)
with t i ≤ t ≤ t i +1 , Δt = t i+1 − t i .
The following relationships are given on the
generic interval [t0, t1] and they are the same on any
other interval. For simplicity we do not use the
indexes of the vectors.
Let (2.12) at the beginning of the interval.
⎧•
⎫
(2.12)
⎨u (t 0 ) = v 0 ⎬
⎩
⎭
From the linear expression of the exciting force
on the interval we get first the vectors {A d } and {Bd } :
{u (t 0 ) = u 0 } ;
{A d } = ({f1 }− {f 0 }) (Δt )
{B d } = (t 1 ⋅ {f 0 }− t 0 ⋅ {f 1 }) / (Δt )
(2.13)
Then one computes the vectors {α d } and {β d } .
{α d } = [K ]−1 ⋅ {A d } ;
{β d } = [K ]−1 ⋅ ({A d }⋅ t 0 + {B d }− [C]⋅ {α d })
(2.14)
The displacement solution u(t) of (1.1) with
restrictions (2.12), is:
{u (t )} = {u c (t − t 0 )} + {αd }⋅ t − {αd }⋅ t 0 + {βd }
(2.15)
The displacement uc(t) is obtained using the
results from §(2.1), because it verifies the homogenous
eq. (1.2) associated to (1.1) with the initial data (2.16):
{u c (0)} = {u 0 } − {β d } ;
⎧•
⎫
⎨u c (0)⎬ = {v 0 } − {α d }
⎩
⎭
(2.16)
18
3. The structural response in displacements,
velocities and frequencies
Various significant cases from practice
emmphisized the influence of structural damping,
of the particularities of the chosen model and of the
number of dynamical degrees of freedom.
In practical engineering applications we used
the procedures DGGEVX and DGESV from
LAPACK, DVOUT and DMOUT from ARPACK.
3.1. The undamped structural response
The frame with one opening of a bulding with
two floors is considered . The mass of the frame is
supposed to be concentrated at the floor level and
the floors move rigidly. The degree of freedom was
indicated on figure. The response of the structure to
the problem is required (1.1)÷(1.4) where the initial
conditions are null and the matrices [M],[C],[K] and
the vector of forces {P} are given by:
[M]
2.D0 0.D0
0.D0 1.D0
[C]
[K]
0.D0 0.D0 3.D0 -1.D0
0.D0 0.D0 -1.D0 1.D0
{P}
0.0D0
2.0D0
The exact displacements are given by (3.1).
{u(t )} = ⎜⎜1 + cos(
)
( )
(
(
)
)
2 t / 3 − 4 ⋅ cos t / 2 / 3 ⎞⎟
⎟
⎝ 3 − cos 2 t / 3 − 8 ⋅ cos t / 2 / 3 ⎠
⎛
(3.1)
Table 1.Comp. btw. the analytic and DGGEVX freq.
Analytic
Fortran90(DGGEVX)
.141421356D+01
2 = 1.4142135624...
.707106781D+00
1/ 2 = 0.7071067812
Table 2. Comparison between the analytic coefficients of the eigenfunctions and those obtained with DGGEVX
Eigenfunctions
GLD1, DOF1
GLD2,DOF2
Analytic
Fotran90(DGGEVX)
Analytic
Fortran90(DGGEVX)
1
− 1/ 3
3.3333333333333D-01
-3.3333333333333D-01
1/ 3
2
0
0.0000000000000D+00
0
0.0000000000000D+00
− 4/3
3
-1.3333333333333D+00
-2.6666666666667D+00
−8/3
4
0
0.0000000000000D+00
0
0.0000000000000D+00
One can see from these tables that the
approximation is as good as possible.
3.2. The effect of damping in modal analysis
One considers the system from fig. 1 in the
case of free and forced vibrations with initial data.
⎫
⎡0.5D0 0.0D0 0.0D0⎤
⎢
⎥
[M] = ⎢0.0D0 1.0D0 0.0D0⎥ , ⎪⎪
⎪⎪
⎢⎣0.0D0 0.0D0 0.5D0⎥⎦
⎬
0.0D0⎤ ⎪
⎡ 2.0D0 − 1.0D0
[K ] = ⎢⎢ − 1.0D0 4.0D0 − 1.0D0 ⎥⎥ ⎪⎪
⎢⎣ 0.0D0 − 1.0D0
2.0D0⎥⎦ ⎪⎭
{ v 0 }= {0}; { u 0 }= ⎧⎨− 16 ,− 13 ,− 76 ⎫⎬
⎩
Fig.1. Free vibrating system with initial data
For undamping vibrations one considers the
matrices [M] , [K] and the vectors of the initial data
{v0} and {u0}, given by (3.2) ,(3.2’).
⎭
(3.2)
(3.2’)
In the damping case one considers the damping
matrice (3.3) also.
19
The vectors of the initial data are the same in both
cases.
0
.
1
0
0
⎡
⎤
The analytic displacements are given by (3.4)
[C] = ⎢⎢ 0 0 0 ⎥⎥
(3.3)
⎢⎣ 0 0 0.5⎥⎦
(
)
(
)
⎧− (1 6) ⋅ cos 6 ⋅ t − (1 2) ⋅ cos 2 ⋅ t + (1 2) ⋅ cos(2 ⋅ t )⎫
⎪
⎪
{u (t )} = ⎨
(1 6) ⋅ cos 6 ⋅ t − (1 2) ⋅ cos 2 ⋅ t
⎬
⎪− (1 6) ⋅ cos 6 ⋅ t − (1 2) ⋅ cos 2 ⋅ t − (1 2) ⋅ cos(2 ⋅ t )⎪
⎭
⎩
(
)
(
)
(
)
(
)
(3.4)
Table 3. Comparison between the analytic angular frequency and that obtained with DGGEVX
Analytic
DGGEVX(undamped)
DGGEVX(damped)
.2449490D+01
.238949058D+01
6 = 2.4494897428...
.1414214D+01
.145441134D+01
2 = 1.4142135624 ...
2
.2000000D+01
.195127286D+01
Table 4. Comparison between the undamped and damped eigenfunctions ( obtained with the proc. DGGEVX)
Undamped
Damped
kcos(.2449490D+01*t)*exp(.1857943D-14*t)
cos(.2389491D+01*t)*exp(-.1093876D+00*t)
sin(.2449490D+01*t)*exp(.1857943D-14*t)
sin(.2389491D+01*t)*exp(-.1093876D+00*t)
cos(.1414214D+01*t)*exp(.4906539D-15*t)
cos(.1454411D+01*t)*exp(-.1449880D+00*t)
sin(.1414214D+01*t)*exp(.4906539D-15*t)
sin(.1454411D+01*t)*exp(-.1449880D+00*t)
cos(.2000000D+01*t)*exp(.0000000D+00*t)
cos(.1951273D+01*t)*exp(-.3456244D+00*t)
sin(.2000000D+01*t)*exp(.0000000D+00*t)
sin(.1951273D+01*t)*exp(-.3456244D+00*t)
Table 5. Comparison between the coefficients of the undamped and damped eigenfunctions
Eigen. Func.
DOF
Analytic
Undamped
Damped
−1 6
1
1
-1.6666666666667D-01
-1.5324453745705D-01
16
1.6666666666667D-01
1.2964861943519D-01
2
−
16
3
-1.6666666666667D-01
-2.2799097435107D-02
2
1
0
6.9854441481544D-17
9.4031423163675D-02
2
0
-2.0789052147676D-17
-8.4284668222341D-02
3
0
8.9480597215092D-17
1.1683391713828D-01
−1 2
3
1
-5.0000000000000D-01
-5.2811581389712D-01
−1 2
-5.0000000000000D-01
-4.8113345857307D-01
2
−1 2
-5.0000000000000D-01
-2.8695203010525D-01
3
4
1
0
3.7946038233531D-16
-2.2049260920957D-01
2
0
6.0827000183804D-17
-2.4145570810675D-01
3
0
2.9464341431205D-16
-4.4256711285042D-01
12
5.0000000000000D-01
5.1469368468751D-01
5
1
2
0
2.0004455055537D-16
1.8151505804552D-02
−1 2
3
-5.0000000000000D-01
-8.5691553912631D-01
6
1
0
6.5959487396052D-18
9.2532881133750D-02
2
0
2.8818226857972D-30
2.5791898163980D-01
3
0
-6.5959487396111D-18
1.2418385824861D-02
20
3.3. The dynamic structural response to time
variable loads
The linear variation of the applied force is shown in
figure 3. We have 9 DOF. In Table 6 a comparison
between the first two DOF is shown.
The dynamic response is considered of the
frame from fig. 2, discretized with 4 beam elements.
Fig.2. Frame modelled with 4 beam elements
Time,(s)
0.00
0.03
0.04
0.05
---
Fig.3. The force function at node 2
Table 6. Comparison between displacements on the first two DOF
Displ.DOF1(cm)
Displ. DOF2(cm)
Paz,Leigh
DGGEVX
Paz,Leigh
DGGEVX
0
0
0
0
0.12346
0.11855
-0.02569
-0.03626
0.16516
0.18429
-0.05606
-0.05369
0.20431
0.22177
-0.09073
-0.09270
---------
3.4. Extreme values of the structural response for
forced vibrations. The damping and undamping
case
Within the framework of the dynamics
analysis we propose to compute the frequencies, the
structural response and the extreme values of the
response for the sheared building with two floors
from fig. 4. The structure is subjected to a force of
10kN applied suddenly to the second floor. We assume
the elastic behaviour of the structure and we consider
two kinds of damping:
a)no damping;
b) 10% of the critical damping for each mode
Table 7.Comparison between the angular frequencies
Paz,Leigh
Fortran90
11.827
.1179679D+02
32.901
.3296284D+02
Fig.4. Frame with 2 levels subject to lateral forces
Table 8. Comparison between the first two DOF
Time(s)
Time(s)
Displ.DOF1(cm)
Displ.DOF2(cm)
Paz,Leigh
DGGEVX
Paz,Leigh
DGGEVX
0.00
0
-.6938894D-17
0.00
0
.1387779D-16
0.01
2.05E-05
.2057270D-04
0.01
0.00753
.7533334D-02
0.02
3.24E-04
.3251518D-03
0.02
0.02963
.2963100D-01
0.03
0.00161
.1612764D-02
0.03
0.06485
.6483580D-01
0.04
0.00493
.4953161D-02
0.04
0.11093
.1108797D+00
0.05
0.0116
.1165484D-01
0.05
0.16501
.1649071D+00
------------0.39
0.40966
.4159244D+00
0.39
0.52246
.5298873D+00
21
Table 9. Comparison between the eigenfunctions
Undamped
Damped 10%
cos(.1179679D+02*t)*exp(.0000000D+00*t) cos(.1173733D+02*t)*exp(-.1182954D+01*t)
sin(.1179679D+02*t)*exp(.0000000D+00*t)
sin(.1173733D+02*t)*exp(-.1182954D+01*t)
cos(.3296284D+02*t)*exp(.0000000D+00*t) cos(.3279819D+02*t)*exp(-.3290506D+01*t)
sin(.3296284D+02*t)*exp(.0000000D+00*t)
sin(.3279819D+02*t)*exp(-.3290506D+01*t)
Next the maximum and minimum of the displacements and velocities are presented as well as the moments
when they are reached depending on DOF.
a) Undamped
Dir, DOF umin
1
-.69D-17
2
.00D+00
at t
umax
.00D+00 .68D+00
.00D+00 .11D+01
at t
vmin
.24D+00 -.49D+01
.28D+00 -.69D+01
at t
.39D+00
.35D+00
vmax
.60D+01
.60D+01
at t
.14D+00
.70D-01
at t
umax
at t
vmin
.00D+00 .59D+00 .25D+00 -.29D+01
.00D+00 .92D+00 .28D+00 -.38D+01
at t
.39D+00
.36D+00
vmax
.48D+01
.54D+01
at t
.14D+00
.60D-01
b) Damped
Dir, DOF umin
1
.00D+00
2
.00D+00
Conclusions:
1. It is noted that the extreme values of the
displacements and , respectively , the velocities, are
reached at close moments of time in the case of the
undamping vibrations , on the direction of the same
degree of dynamic freedom.
2. It is noted that the spectral values of the
displacements decrease by aprox. 13% and those of the
velocities by aprox.30% in the case of the damping
vibrations compared to the undamping vibrations.
22
4. References
[1]
ANDERSON.E.,
Z.BAI,
C.BISCHOF,
S.BLACKFORD, J.DEMMEL, J. DONGARRA,
J.DU
CROZ,
A.GREENBAUM,
S.HAMMARLING,
A.
MCKENNEY
and
D.SORRENSEN, Lapack User’s Guide, Third
Edition, SIAM, Philadelphia, 1999.
[2] ATANASIU, G.M., Structural dynamics and
stability , Iaşi, 1995
[3] BATHE, K. J. Finite Element Procedures,
Prentice Hall., Engl.Chiffs, New Jersey, 1996.
[4] GHEORGHE, P Tehnica alegerii pivotului în
eliminarea gaussiană, Lucrările sesiunii ştiinţifice
a catedrei de matematică, Universitatea Tehnică
de Construcţii Bucureşti, 26 mai 2001
[5] GHEORGHE P., IEREMIA M., Numerical
computation of the response of a structure in free
vibrations with inital data , Constanta Maritime
University , MECSOL ,9,2006
[6] GHEORGHE , P. Contribuţii la determinarea
numerică a modurilor proprii de vibraţie ale unor
structuri inginereşti de mari dimensiuni în analiza
dinamică liniară şi neliniară , Teză de doctorat,
UTCB, 13.12.2006
[7] LEHOUCH, R., SORRENSEN, D.C., VU, P.A.
ARPACK: Fortran subroutines for solving large scale
eigenvalue problems, Release 2.1.
[8] MOLER, C.B. & STEWART, G.W. An Algorithm
for Generalized Matrix Eigenvalue Problems, SIAM J.
Numer. Anal. 10, pp.241-256 1973
[9] PAZ, M, , LEIGH,W. Structural Dynamics,
Theory and Computation, Kluwer Academic
Publishers, Boston-Dordrecht-London, 2004
Volume 1, Number 9, May. 2007
Rotation Capacity of Reinforced Concrete Elements
a
Bogdan HEGHEŞ a
Cornelia MĂGUREANU a
Technical University Cluj Napoca, Cluj Napoca, 400027, Romania
__________________________________________________________________________________________
Rezumat: Ductilitatea este o proprietate importantă pentru redistribuţia eforturilor şi prevenirea colapsului.
Lucrarea prezintă o comparaţie între valorile de calcul ale ductilităţii şi cele obţinute utilizând valorile
experimentale ale unor caracteristici de deformare. Elementele experimentale în număr de nouă, sunt grinzi
încovoiate simplu armate realizate din betoane de înaltă rezistenţă de clasă C80/90. Ductilitatea a fost exprimată
prin rotirea plastică a unui element în momentul formării articulaţiei plastice.
Abstract: Ductility is an important property for redistribution of forces and prevention of progressive collapse.
The ductility of structural members can be improved by confinement. For high strength concrete this is
especially important due increased brittleness. This paper summarizes results from nine reinforced beams of high
strength concrete. Ductility was explained by plastic rotation of the element, when in critical sections of the
beams plastic hinges appear.
Keywords: rotation capacity, high strength concrete, ductility.
__________________________________________________________________________________________
1. Introduction
The paper presents a comparison between the
calculus values obtained through several standards
codes and experimental values of the authors.
2. Experimental program
tested at bending. The beams were realized with
concrete class of C80/90, with constant length of
L=3200mm and the section of 125×250mm. The
longitudinal percentage of reinforcement was between
2.033-3.933%, and the transversal reinforcement was
the same for all the beams, with stirrups Ø6/300mm.
All the beams were tested with an hydraulic press
and loaded with two concentrated loads. (see Fig. 1).
The experimental program contained a
number of nine simple reinforced concrete beams,
Fig. 1. Schema de încărcare a grinzilor
Both ends of the beams were free to rotate
under loading. At each increment of the forces, the
ISSN 1584 – 5990
strain on multiple heights of the section and the flexure
of the beam were recorded. In Table 1 the compressive
24
Rotation capacity … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 23-28 (2007)
strength of the concrete is presented at the date of
the testing.
Table 1. Compressive strength of the concrete
Beams
FT5.1-1
FT5.2-1
I1-1, I1-2
I2-1, I2-2
I3-1, I3-2
I4-1
Compressive strength
fc,cube (MPa)
78
91
92.4
85.1
84.9
89.9
The longitudinal reinforcement percentage is
presented in Table 2. The longitudinal reinforcement
was with steel type PC52 and the transversal
reinforcement (stirrups) with steel type OB37.
Table 2. Longitudinal reinforcement percentage
Beams
FT5.1-1, FT5.2-1
I1-1
I1-2
I2-1
I2-2
I3-1, I3-2
I4-1
p (%)
2.033
2.621
2.654
3.072
2.990
3.357
3.933
The differences between the beams of the
same series (i.e. I1-.., I2-.. ) came through the
transversal dimensions deviations.
Plastic rotation capability
The plastic rotation capability θpl, is defined
by the difference between the total rotation θtot and
elastic rotation θel: θpl =θtot – θel. (See Fig. 2)
Fig. 2. Total rotation
The following definitions are adopted, which
apply universally to reinforced and prestressed
concrete members:
• The total rotation θtot is taken as the "sum of
angles made by the difference in tensile steel elongation
and shortening of outermost compressive concrete fiber,
where a section reaches nominal strength".
• The elastic rotation θel is taken as the "sum of
angles made by the difference in tensile steel
elongation and the shortening of the outermost
compressive fibre for which neither the reinforcement
nor prestress has reached its elastic limit."
• The plastic rotation θpl is taken as the "sum of
additional deformations along the beam after yielding
of either the ordinary or prestressed reinforcement and
until a section reaches nominal strength" or, as
previously shown, as the difference of the total rotation
and the elastic rotation.
The plastic theory uses the reserves of plastic
hinges of static undetermined structures which are
capable of forming plastic hinges in the most stressed
areas, and to redistribute the efforts at less stressed
areas. This hypothesis presumes that the elements have
sufficient plastic deformation capabilities.
To check the deformation capacity the required
rotation Θreq has to be compared with the plastic
rotation Θpl as follows:
Θ nec ≤ Θ pl
(1)
CEB-FIB Model Code 1990
The plastic rotation according to MC90:
Θ pl = ∫
l pl
0
⎛ σ ⎞
⋅ ⎜1 − sr1 ⎟ ⋅ (ε s 2 − ε sy )da
d − x ⎜⎝
f yk ⎟⎠
δ
(2)
where:
lpl – length of plastic hinge
δ – the coefficient which taking into account the form
of the stress-strain curve of the reinforcement in the
inelastic range (δ ≈ 0,8)
x – the depth of the compression zone
d – the efficient height of the cross-section
σsr1 – the steel stress in the crack the steel stress in the
crack when the first crack forms as the characteristic
concrete tensile strength is reached
B. Hegheş and C. Măgureanu / Ovidius University Annals Series: Civil Engineering 9, 23-28 (2007)
25
fyk – the characteristic steel yield stress
εs2 – the steel strain of the cracked section
εsy – the steel yield strain
a – the abscissa
In order to facilitate practical applications, the
abscissas Θpl and x/d represent the design values of
the normalized neutral axis depth (Fig. 3)
Fig. 4. Plastic rotation according Eurocode2
Fig. 3. Plastic rotation according CEB-fib MC90
Eurocode 2
DIN 1045-1
Dependent on the ductility class of steel,
normal (N) or high (H), the plastic rotation can be
taken from Fig. 4. It can be seen that the plastic
rotation Θpl for x/d ≤ 0,16 is limited for H-steel to
Θpl = 20 mrad and for N-steel to Θpl = 10 mrad.
Θ pl = 20 mrad for x / d < 0.16
1.8
⎡
x⎞ ⎤
⎛
Θ pl = ⎢5.8 + ⎜ 6.22 − 11.5 ⎟ ⎥ mrad
d ⎠ ⎥⎦
⎝
⎢⎣
0.16 ≤ x ≤ 0.5
d
Simplified relationships for the Θpl.cap are drawn
up in Fig. 3 and Fig. 4 for different reinforcement
types and are valid for a slenderness ratio of l*/d = 6
(l* is the distance between two consecutive zero
moment points on either side of the support). The
rotation capacity can be multiplied by for other values
of l*/d.
(2)
pt.
(3)
The curvature may be used for all variations
of material and geometrical parameters. Eq. 2 and 3
describes the admissible plastic rotation (Fig. 4)
using only the compressive depth (x/d) as input
parameter. Material and other geometrical
parameters are not taken into account.
DIN 1045-part 1 (2001) gives both detailed and
simplified expressions for the available rotation
capacity.
Simplified relationships for the plastic rotation
capacity are divided into concrete grades C12/16 to
C50/60 and the high strength class C100/115. The
relationships are reproduced in Fig. 5.
The difference between Eurocode2 and DIN
1045 procedures to calculate the plastic rotation is that
eq. (4) and (5) considers the slenderness of the
system λ = l / d . The plastic length is estimated by lpl
= 1.2 · h.
The simplified expression reads:
Θ pl = 20 ⋅
λl
20
mrad, for x
d
< 0.16
(4)
1.8
⎡
x ⎞ ⎤ λl
⎛
Θ pl = ⎢5.8 + ⎜ 6.22 − 11.5 ⎟ ⎥ ⋅
mr
d ⎠ ⎥⎦ 20
⎝
⎢⎣
ad, for 0.16 ≤ x ≤ 0.5
(5)
d
26
The plastic rotation capacity can be obtained
form Fig. 5.
Figure 5 is obtained for λ=3. For different values
of λ, the rotation capacity Θ is multiplied by
λ / d.
Plastic rotation due to bending
The plastic hinge can be simulated with a single
beam and a single load. The length of the beam is
determined by the length of the area with negative
moment over the support.
The plastic rotation due to bending may be
calculated as follows:
aq
Θ pl = 2 ∫ k ( x ) dx
(7)
0
where:
Fig. 5. Plastic rotation according DIN 1045-1
a q = 0.2 ⋅ λ ⋅ d and
The simplified expression reads:
Θ pl ,cap = β n β s
ε su∗ − ε sy
1− x
λ /3
(6)
d
The integration of the plastic area (grey area in
Fig. 6) is expressible in the form:
where:
βn = 22.5
βs = 0.074
λ – shear slenderness; the distance between
M=0 şi Mmax after redistribution
ε*su – steel strain at ultimate:
- steel failure:
(0.4 ⋅ x d + 0.13)ε
uk
/ βc
- concrete failure:
1.8( x / d )
0.7
k - the curvature at cracking, yielding and
ultimate.
(1 / (x / d − 1)) ε
εsy – characteristic steel yield strain (=0.0025)
εuk – characteristic steel strain at ultimate load
(= 0.05 – for high ductility steel)
εcu – characteristic concrete strain at ultimate
load (=0.035 – for <C50)
⎡ ⎛My
⎞
− 1⎟⎟ +
⎢k cr ⎜⎜
⎠
⎢ ⎝ Mu
⎢
⎛M
M
Θ pl = 0.2 ⋅ λ ⋅ d ⋅ ⎢+ k y ⎜ cr − cr
⎜
⎢
⎝ M y Mu
⎢
⎢
⎛ My ⎞
⎟
⎢+ ku ⎜⎜1 −
M u ⎟⎠
⎝
⎣
⎤
⎥
⎥
⎞ ⎥
⎟ +⎥
⎟ ⎥
⎠ ⎥
⎥
⎥
⎦
(8)
B. Hegheş and C. Măgureanu / Ovidius University Annals Series: Civil Engineering 9, 23-28 (2007)
27
Fig. 6. Model for calculating the plastic rotation due to bending and model for a plastic hinge
3. Results and interpretation
The experimental program consisted in testing
at bending of nine reinforced concrete beams.
In Table 3 the experimental data on the beams is
shown.
Table 3. Experimental results
FT 5.1-1
FT 5.2-1
I 1-1
I 1-2
I 2-1
I 2-2
I 3-1
I 3-2
I 4-1
p%
kcr
ky
ku
x/d
Θpl_nec
(mrad)
Θpl EC2
(mrad)
Θpl DIN
(mrad)
Θpl MC90
(mrad)
2.033
2.033
2.621
2.654
3.072
2.990
3.357
3.357
3.933
0.00394
0.00120
0.00124
0.00046
0.00078
0.00073
0.00088
0.00088
0.00076
0.00394
0.00438
0.00528
0.00455
0.00590
0.00555
0.00496
0.00496
0.00577
0.03314
0.02867
0.03137
0.03036
0.04177
0.03854
0.04379
0.03970
0.04767
0.1355
0.1162
0.1475
0.1493
0.1877
0.1827
0.2057
0.2057
0.2274
2.5167
3.3649
2.1653
1.9335
1.8745
1.2982
2.2194
2.2198
3.2794
20.0000
20.0000
20.0000
20.0000
18.2633
18.5805
17.1449
17.1449
15.8541
15.7800
15.7800
15.7800
15.7800
16.2220
16.5040
15.2290
15.2290
14.0825
15.8178
14.5266
16.4929
16.5665
16.6596
16.4065
15.2868
15.2868
14.4795
28
4. Conclusions
5. Bibliography
The comparison between the experimental
values and theoretical values is shown in Table 3.
The data obtained from this experiment and the
results of from the other authors leads us to the
conclusion that actual standard codes are much to
permissive regarding the plastic rotation.
The lack of an integrated and consistent
concept for the development of non-linear
calculation prevents a simplified calculation model
for all kinds of concrete.
The number of experimental results is rather
insufficient to compare the described models with
the real structure behavior.
The future studies in our Reinforced and
Prestressed Concrete Departement will be axed on a
comparison of the same beams realized with steel
type S500, others reinforcement percentage and
beams with multiple openings.
[1] Magureanu Cornelia, Hegheş B, Experimental
Study on Ductility Reinforced Concrete Beams Using
High Strength Concrete, fib Congress, 2006, Napoli
[2] Mark Rebentrost, Deformation Capacity and
Moment Redistribution of Partially Prestressed
Concrete Beams, PH.D. Thesys, 2003
[3] Carsten Ahner, Jochen Kliver, Development of a
New Concept for the Rotation Capacity in DIN 1045,
Part 1, Lacer 1998, pp 213-236
[4] DIN 1045-1, Tragwerke aus Beton, Stahlbeton und
Spannbeton, Teil 1
[5] Eurocode 2, Design of reinforced and prestressed
concrete structures.
Assessment of the Potential for Progressive Collapse in RC Frames
Adrian IOANI a
Liviu CUCU a
Călin MIRCEA a
a
__________________________________________________________________________________________
Rezumat: În lucrare sunt discutate preocupările actuale ale inginerilor structurişti pentru evitarea şi, în special,
pentru reducerea riscului de cedare progresivă a structurilor supuse la sarcini catastrofice (anormale sau
neobişnuite). Ca şi în proiectarea antiseismică, se urmăreşte ca structurile de beton armat să aibă un nivel adecvat
de continuitate structurală, redundanţă, robusteţe şi ductilitate, astfel încât în condiţiile „pierderii” (cedării) unui
element structural, să existe alte căi de transfer ale solicitării. Este prezentată metodologia de evaluare a riscului
de cedare progresivă a unei structuri de beton armat dezvoltată de U.S. GSA (2003) şi rezultate care confirmă
capacitatea intrinsecă a unei structuri proiectate antiseismic de a rezista la fenomenul de cedare progresivă.
Abstract: In the paper, the concerns of structural engineers to avoid, and especially to mitigate the potential for
progressive collapse of structures subjected to abnormal loads is discussed. As in the seismic design, reinforced
concrete structures should be provided with an adequate level of structural continuity, redundancy, robustness
and ductility, so that alternative load transfer paths can develop, following the loss of an individual member. The
methodology developed by U.S. GSA (2003) for assessing the vulnerability of existing RC framed structures, as
well as results that confirm the inherent capacity of such structures, seismically designed, to resist progressive
collapse are presented.
Keywords: RC frames, abnormal loads, progressive collapse, seismic design, assesememt of vulnerability.
__________________________________________________________________________________________
1. Introduction
Many structural collapses of important
buildings concived in various structural solutions,
tionalities and height regimes were registered in the
last fifty years. Some of them had a local character,
while other spread progressive to the scale of the
full structure or large parts of it.
The main causes leading to a structural
progressive collapse of buildings, seen as a chain
reaction of failures that propagates throughout a portion
of structure, disproportionate to the original local
failure[1], are: fire, wind gusts, floods and human
errors, impact by vehicles, but especially major
earthquakes and blasts[2].
The concerns of the structural engineers to
prevent or to mitigate the potential for progressive
collapse have to be seen in correlation with the
structural effects of the abnormal loads [1].
Considering the definition given in Section 2 of
the GSA Guidelines [3], abnormal loads are: “other
than conventional design loads (dead, live, wind,
ISSN 1584 - 5990
seismic) for structure, such air blast pressures generated
by an explosion or an impact by vehicles, etc.” The
design philosophy of structures subjected abnormal loads
is to prevent or mitigate damage, not necessarily to
prevent the collapse initiation from a specific cause. This
approach is similar to the concept adopted in any modern
earthquake-resistant design codes.
If the progressive collapse prevention is
associated to certain structural characteristics as an
adequate level of continuity, redundancy and ductility
so that alternative load transfer paths can develop
following the loss of an individual member or a local
failure, then it is obvious that these requirements are
found in seismic design as well.
Structural response to blast, for instance, is
related to the large variety of possible scenarios
regarding the location of the detonation point, charge
and design details. Due to the high intensity of the air
pressure exerted in fractions of second, the localized
failure of the direct exposed members (i.e., columns,
walls, girders, floor systems) is most like to occur.
30
Assessment of … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 29-36 (2007)
For this reason, in the assessment methodology
for the potential progressive collapse, engineers
should consider the loss of portions of the structure
using different “missing column” or “missing beam”
scenarios. Such checks are required, though the
cause is not always specified (natural hazard or manmade hazard), in the currently used design codes for
the reinforced concrete structures.
Thus, in the beam design, Section 15.4.2.1.5 of
EC2 [4] requires that “reinforcement used should be
continuous and able to resist accidental positive
moments (settlement of the support, explosion etc.)”.
The most recent Romanian Seismic Design Code P
100-1/2004 - Art. 4.1.1.2 [5], explicitly demands that
“seismic design should provide the building structure
with an adequate redundancy. In this manner, it is
ensured that the failure of one single element or the
failure of a structural link does not expose the
structure to the loss of stability”.
Consequently, it seems natural at present for
the engineers to use their creativity to find costeffective solutions that make structures more
resilient to both natural hazard (e.g. earthquakes)
and man-made hazards (e.g. bomb blast, impact by
vehicles) and, in consequence, the designed
structural system will satisfy, at the same time, the
requirements of lateral-load resistance and those of
the prevention of the progressive collapse.
The study presents the methodology
developed by U.S. GSA [3] for assessing the
vulnerability of existing RC framed structures, as
well as, results that confirm the inherent capacity of
such structures seismically designed, to resist
progressive collapse.
Fig. 1. Possible blast behavior of frame structures:
a) earthquake resistant design b) gravity-load design.
As presented in Fig.1b, after the removal of an
exterior column (“missing column” scenario) by the
blast effect, the lack of bottom continuous
reinforcement generates the flexural failure of the
newly resulting two-bay frame beam. The potential of
brittle failure by shear could also be induced by the
lack of closely spaced stirrups at the ends of the frame
beam (Fig. 1b).
This was the case of the Murrah Building, a nine
story building with Ordinary Moment Frames designed
for gravity loads [6]. When the blast effect abruptly
removed column G20 by brisance, the transfer girder,
which lost its support was unable to support the
structure above the third floor. The type of damage that
occurred and the resulting collapse of nearly half of the
building indicate that progressive collapse extended
the damage beyond that caused directly by the blast
effect (Fig. 2) [6].
2. Progressive collapse of RC frames
It is known that the structures provided with
interior core structural walls for lateral–load
resistance and ordinary moment frames (frames
designed for gravity-loads) or flat-plate structures
with interior core walls and, in general, ordinary
moment frame structures have a limited capacity to
redistribute loads and prevent progressive collapse.
Such a situation represents a consequence of
the fact that gravity-load designed systems are not
adequately reinforced and detailed to develop
alternative load paths when a vertical support is
removed due to a blast or an impact [1].
Fig. 2. Failure boundaries of floor slabs in Murrah
Buildings [6].
A. Ioani et. al. / Ovidius University Annals Series: Civil Engineering 9, 29-36 (2007)
The report [6] underlined that the use of
Special Moment Frames (SMF) rather than
Ordinary Moment Frames would not completely
eliminate the loss of some portions of the building,
but the losses would be greatly reduced.
For this reason, an Executive Order of GSA
(EO 12699/1990) has required that “new Federal
buildings be designed to meet seismic requirements”
and consequently, “these new buildings in areas of
high seismicity may already provide suitable
ductility for blast resistance at no additional cost by
satisfying seismic design requirements” [6].
3. Assesement of the potential for progressive
collapse
3.1 Progressive collapse analysis
The U.S. General Services Administration
(GSA) has developed the “Progressive Collapse
Analysis and Design Guidelines for New Federal
Office Buildings and Major Modernization
Projects” – June 2003 [3] to ensure that the
potential for progressive collapse is addressed in
the design and construction of new buildings and
major renovation projects. These guidelines provide
a detailed methodology for minimizing the
potential for progressive collapse in the design of
new buildings and for assessing the vulnerability of
existing buildings to progressive collapse.
Using a flow-chart methodology the
Guidelines determine whether the building under
consideration might be exempt from detailed
analysis for progressive collapse. For example, a
structure which:
- does not contain single point failure
mechanism,
- does not possess atypical structural conditions,
- is not over ten stories,
- has public areas or parking areas controlled with
proper security systems, is designed consistently with
at least Seismic Zone 3 or Seismic Design Category D
or E requirements (see UBC – 1997 and IBC- 2000),
is a candidate for automatic exemption from the
consideration of progressive collapse.
If the existing construction is determined not
to be exempt from further consideration for
progressive collapse, the methodology presented in
Section 4.2 or 5.2 [3] is applicable and shall be
31
executed, and the potential for progressive collapse
determined in this process – whether low or high –
must be quantified.
3.2 Missing column scenarios
The typical RC structural configuration, framed
structures or flat plate structures, shall be considered
individually in the following analysis scenarios:
1. The instantaneous loss of column for one floor
above grade (1 story) located at or near the middle of
the short side of the building - case C1, at or near the
middle of the long side - case C2, and located at the
corner of the building - case C3 (Fig. 3).
2. For facilities that have underground parking
and/or uncontrolled public ground floor areas, the
instantaneous loss of an interior column would also
have to be considered.
Fig. 3. Missing column scenarios for exterior columns.
3.3 Loading assumptions
In the static analysis of each case, the vertical load
applied downward to the structure is:
Load = 2(D + 0.25L)
(1)
where D is the dead load and L the live load.
In the GSA criteria, live load is reduced to 25 %
of the full design live load, admitting that the entire L
value is less probable. At the same time, by
multiplying the load combination by a factor of two,
the Guidelines take into account – in a simplified
approach – the dynamic amplification effect that
occurs when a vertical support is instantaneously
removed from the structure, and demands (QUD) in
structural components are determine in terms of
moments, axial forces, shear forces, etc.
The magnification effect of a static force when
dynamically applied is termed impact factor by Popov
32
(1976) [7] or dynamic coefficient by authors and it
is given by the expression:
⎛
2h
Pdyn = Pst ⎜⎜1 + 1 +
Δ st
⎝
⎞
⎟ = Pst ⋅ Ψ
⎟
⎠
(2)
If a load is applied to an elastic system
suddenly (instantaneously) and h = 0, Ψ is
equivalent to twice the same load statically
(gradually) applied, as in Eq. (2).
At the same time, strength increase factors are
applied to the material properties in order to
determine the ultimate strength capacity (QCE) of
structural members (beams, columns etc.) under
dynamic loads. The concrete compressive strength
and the tensile or yield strength of the reinforcing
steel are increased by a factor of 1.25, Table 4.2 of
the GSA Guidelines [3], to account for strain rate
effects and material over-strength.
3.4 Acceptance criteria
4. Results and commentary
The GSA Guidelines – Section 4.1.2.4 –
consider that local damage may occur and this is
acceptable with the instantaneous removal of an
exterior column, but the resulting structural
collapse shall be limited to a reasonably sized area.
In other words, the maximum allowable extents of
the collapse shall be confined to whichever is
smaller: the structural bays directly associated with
the instantaneously removed vertical element or
1800 ft2 (167 m2) at the floor level directly above
the removed vertical column.
Working with the results given by the linear
elastic analysis (moment, shear, axial force), engineers
shall identify the magnitude and distribution of
potential areas of inelastic demands and thus, they will
quantify the potential collapse areas.
The magnitude and distribution of these demands
will be given by the concept of Demand – Capacity –
Ratios defined as [3]:
DCR = QUD QCE
combined forces) and QCE - expected ultimate un-factored
capacity of the component or connection (Φ=1.0).
According to the GSA Guidelines, acceptance
criteria, the allowable DCR values for structural elements
are: DCR ≤ 2.0 for typical structural configurations and
DCR ≤1.5 for atypical structural configurations. Using the
DCR concept of linear elastic approach, structural
elements that have DCR values exceeding the allowable
magnitudes are considered to be severely damaged or
collapsed.
It is underlined that if the DCR for any member is
exceeded, based upon shear force, the member is to be
regarded as a failed member. In addition, if the flexural
DCR values for both ends of a member as well as the
span itself are exceeded (creating the classical three
hinged failure mechanism), the member is also to be seen
as a failed member.For continuous elements, the flexural
DCR value at an element section may exceed 1.0 because
in this case flexural demand can be redistributed along the
length of the element to sections that have reserve flexural
capacity [1].
(3)
where QUD - acting force(demand) in the component or
connection (moment, axial force, shear and possible
4.1 FEMA 277/1996 Report
In 1995, the Federal Emergency Management
Agency (FEMA) deployed a Building Performance
Assessment Team (BPAT) to investigate damage
caused the terrorist attack against the Alfred P. Murrah
Federal Building in Oklahoma City. From visual
inspection and analysis of the damage that occurred in
the Murrah Building as a result of a blast caused by a
truck bomb, it is concluded that progressive collapse
extended the damage beyond that caused directly by
the blast. The main findings and conclusions are [6]:
- the loss of three columns and portions of some
floors by direct effect of the blast accounted for only a
small portion of the damage;
- most of the damage was caused by progressive
collapse following loss of the columns;
- the nine-story frame type of the building was an
Ordinary Moment Frame (OMF), i.e., a frame designed
for gravity loads;
- if additional amounts and locations of reinforcing
steel as for Special Moment Resisting Frame (SMRF)
in seismic areas had been used, the Murrah Building
would have had enough strength and ductility that
about half of the damage would have been prevented;
- investigations to determine the cost of using
SMRF rather than OMF were conducted and
suggest that the average increase in cost is in the
range of 1 to 2 percent of the total construction cost
of the building;
- using reinforcement, connection and other
details required by the design of frame structures or
dual systems in areas of high seismic activity, will
provide similar toughness and ductility in face of
the blast;
- the most important aspect of using SMRF or
Dual Systems is the ductility detailing (e.g., closedhoop reinforcement to confine columns, continuous
bars for continuity, beam-to-column connections to
transfer forces through the joints, etc.);
- in areas of low seismic risk, incorporating the
seismic details required for regions of high seismic
risk can significantly improve the blast protection
of the buildings.
4.2 Other studies
In a study upon redundancy and robustness of
RC structures subjected to blast and earthquakes
Mircea (2006)[2] makes a critical review of
common structural types and shows that spatial
frame structures have more redundancy potential
than plane frame structures because more
possibilities for load transfer are provided.
In general, frame structures and flat slab
structures need supplementary lateral stiffness,
usually provided by shear walls or vertical
bracings. Even if walls are rigid and possess large
masses, Crawford at all., cited in [2], reported
significantly more column damage in blast tests on
structure with columns and infill walls, in
comparison with tests on structures without walls.
Baldrige and Humay (2003) conducted a
progressive collapse analysis on a 12-story RC
frame structure having five longitudinal bays of 7.3
m and three transversal bays of 7.3 m [1]. The
model was designed to the older requirements of
the Uniform Building Code (UBC-1991 edition).
The required strength U to resist to a combination
of dead load (D=2.0 kPa), live load (L= 2.4 kPa)
and earthquake effect (E), considers [8]- for UBC
Seismic Zone 2B (a moderate seismic zone)- a total
equivalent seismic force having the magnitude of
Ft* = 1.4 Ft = 1.4 ⋅ 0.0523G = 0.0732G .
33
The computer program ETABS was used to
generate a 3-D model; case 1 investigated the
structural effect of removal of an exterior column
along the long side of the building, and case 2
examined the removal of a corner column, also at the
ground floor. The removal of the column at the middle
of the long side doubles the beam span at the first floor
and the vertical forces of the magnitude 2(D+0.25L)
generate a maximum positive moment in beam, over
the removed column.
Following the GSA Guidelines, demands in
structural components are assessed in beams at midspan section and at column faces and the afferent DCR
values are computed. All of the DCR values are below
1.0, except at the mid-span of the beam over the
removed column (case 1) where a value of 1.02 for
flexure was reported; the maximum DCR value in
beams, for shear, was only 0.69.
Practically, the damaged structure remains in the
elastic stage, no other structural member is expected to
fail in shear or flexure and consequently, progressive
collapse is not expected to occur [1].
Obviously, the American model [1], is
seismically designed under similar or comparable
gravity and seismic forces as a typical RC frame
structure from Bucharest (Romania), where currently
the total equivalent seismic force for such structure is
F ≈ 0.08G. The study [1] shows that RC frames
designed for a moderate or high seismic intensity zone
do not experience progressive collapse when are
subjected to the removal of an external column.
4.3 Authors’ studies
In order to determine the inherent reserve capacity to
progressive collapse of a RC structure erected in a high
seismic zone of Romania, an investigation was conducted on
a 13-story RC frame building designed according to the older
requirements of the Romanian Seismic Design Code P100–
92 [9]. One expects that for new buildings designed
according to the provisions of the new P 100-1/2004, this
analysis will be conservative.
The structure consists of five 6.0 m bays in the
longitudinal direction and two 6.0 m bays in the
transversal direction and has a story height of 2.75 m,
except for the first two floors that are 3.60 m high [10]. In
the design at the Ultimate Limit State, the Special
Combination of loads according to the Romanian
Standard STAS 10107/0A-77 (1977) is:
34
D+0.4L+E
(4)
meaning, for the design of the analyzed building, a
combination of dead load D=2 kPa, live load L=2.4 kPa
with a load factor of 0.4, and the earthquake effect (E).
The seismic analysis is performed for Bucharest,
a seismic area of degree VIII on the MSK Intensity
Scale (zone C on the Romanian zonation map with
ks=PGA/g=0.2). For Romania, the seismic coefficient
ks varies from 0.08 to a maximum value of 0.32. The
magnitude of total equivalent seismic force S that
enters the load combination given by Eq.(4) is
calculated as follows [9]:
S = α ⋅ k s ⋅ β (T ) ⋅ψ ⋅ ε ⋅ G = 0.0945G
(5)
In the progressive collapse analysis according to
the GSA Guidelines provisions, the expected ultimate,
un-factored, capacity of the structural elements was
determined with the help of the characteristic (unfactored) values for the strengths, multiplied by the
strength increase factor of 1.25 (Table 1).
Table 1. Strengths of materials for the model (MPa).
Seismic
design
Material
Concrete
Bc20
Rc = 12.5
Rt = 0.95
Rtk = 1.43
1.78
PC52
Ra = 300
Rak ( f y ) = 345
431
Steel
•
•
Fig. 4. ROBOT Millennium model of a 13-story
RC building: missing column scenarios.
The structural response of the model under the
Special Combination of loads, and the behavior of
the damaged structure (case C1, C2, C3 of the
“missing column” scenarios) is determined with the
3-D linear
elastic model, created and analyzed in the FEA
program ROBOT Millennium, Version 19.0 (2006).
The model generated by this computer program is
shown in Fig. 4.
The material properties are given in Table 1.
In the seismic design of the model, design values
for strengths have been used.
Design
values *
Progressive collapse
analysis
Characteristic
With
un-factored
1.25
values
factor
Rck ( f c' ) = 16.6
20.75
Rak ( f y ) = 255
OB37
Ra = 210
318
Rc (Rt) = design value of the compressive (tensile)
strength of concrete;
Ra = design value of the yield strength of
reinforcement.
The removal of the column (Fig. 4) at the middle
of the short side – case C1 – doubles the beam span at
the first floor and the vertical forces of the magnitude
2(D+ 0.25L)- see Eq.(1)- generate a maximum positive
moment over the removed column, of 537.1 kNm (Fig.
5). If the bottom reinforcement in the beam is not
continuous through the column joint as in the gravityload designed frames, the positive moment capacity is
limited to the cracking strength of the section and the
failure in this case will be abrupt, leading to a brittle
collapse (Fig. 1b).
In contrast, seismically designed frames used in the
analyzed model having a large amount of bottom
longitudinal reinforcement (As=9.64 cm2) in the beam,
that means a reinforcement ratio ρ=0.0084, provides a
positive flexural capacity over the “missing column”, and
consequently, the beam has enough ductility to develop
alternate load paths (Fig 1a).
The new bending moment and shear force diagrams
generated in the damaged structure by the removal of the
column (case C1) are shown, for the exterior transversal
frame, in Fig. 5 and Fig. 6, respectively.
Following the GSA Guidelines (2003), demands
in structural components (QUD) –see Eq. 3, assessed in
beams at mid-span and at column faces (Fig. 5), are
compared to the expected ultimate beam capacities
(QCE) from Eq. 3.
Following the procedure presented above,
DCR values for significant beam sections are
represented in Fig. 5 and Fig. 6, in brackets.
All of the DCR values for flexure are below
1.0, except at the mid-span of the beam over the
removed column (Fig.5).
35
The DCR values based upon shear (Fig. 6) are
well below 1.0, the maximum value being 0.67.
The author’s results are similar with the results of
Baldrige & Humay (2003) [1] who reported a
maximum DCR value for flexure of 1.02 and for shear
of 0.69.
Even the differences between the computed
deflections are small, being of only 26% [10], if one
takes into consideration the differences between the
models regarding the span length (6.0 m vs. 7.30 m)
and beam dimensions (35×70 cm vs. 55.6×45.7 cm for
the American model [1] ).
5. Conclusions
This study is in line with the trends of the
specialized reference literature that aims at assessing the
vulnerability of the existing structures subjected to
abnormal or catastrophic loads produced by natural
hazard (e.g. earthquakes) or by man-made hazards
(terrorist attacks, impact by vehicles, bomb blast, etc).
The following conclusions can be reached based
on this study:
Fig. 5. Damaged structure (case C1): bending
moments and DCR values ( ) in beams.
Because this value is only 1.015 and satisfies
the GSA Guidelines criteria (DCR≤2), the beam
will have adequate reserve ductility for an efficient
redistribution of loads and consequently, the
flexural demand that exceeds 1.0 is redistributed to
sections that have reserve flexural capacity .
Fig. 6. Damaged structure (case C1): shear forces
and DCR values ( ) in beams.
1. Practically, due to economic constraints, it is
impossible to design an overall structure and each
structural member individually so as to resist to
abnormal loads or to prevent collapse initiation from a
specific cause. More important is to stop or to limit the
progression of the collapse and to reduce the extent of
the damage and this should be the design philosophy
assumed by engineers.
2. Many design codes (ACI 318, EC-2, P100-92,
P 100-1/2004) require an adequate level of continuity,
redundancy and ductility for the selected structural
system. Interagency Security Committee (ISC)
Security Criteria clearly requires all new constructed
facilities to be designed with the intent of reducing the
potential for progressive collapse, and the existing
facilities to be evaluated to determine the potential for
progressive collapse [3].
3. The GSA Guidelines [3] offer a realistic
approach and performance criteria for these
determinations.
4. The concept of DCR offers to engineers a
valuable tool to identify the magnitude and distribution
of potential areas of inelastic demands and thus, the
extension of potential collapse zone can be evaluated
and compared to the maximum allowable collapse area
36
resulting from the instantaneous removal of an
exterior or interior column.
5. A typical medium-rise building (13 stories)
having RC frames, seismically designed for the
Bucharest – a zone of high seismic risk- does not
experience progressive collapse [10] when subjected
to different “missing column” scenarios, according
to GSA Guidelines (2003). Similar results have been
found by Baldrige & Humay (2003) [1] for a 12story RC framed structure seismically designed for a
moderate (Zone 2B) or a high seismic risk zone
(Zone 4), according to the requirements of a Uniform
1.
Building Code (UBC-1991 edition).
6. For the Romanian zones of high seismic
risks as the zone C (ks=0.20), zone B (ks=0.25) and
zone A (ks=0.32) [9], further analyses will be
developed by authors in order to determine the
vulnerability to progressive collapse of other types
of structural systems, including existing reinforced
concrete frame structures of 7 to 9 story high,
designed to the older requirements of Romanian
Design Code P100-92 [9].
6. Acknowledgements
Part of this work is based on different
2.
technical materials (books, reports, design
codes)
provided with generosity by the U.S. Federal
Emergency Management Agency. The support of
3.
this organization is gratefully acknowledged.
7. References
[1] Baldrige, S. M., and Humay, F. K., Preventing
Progressive Collapse in Concrete Buildings,
Concrete International, vol. 25, No. 11, Nov. 2005,
pp. 73-79.
[2] Mircea, C., Risk factors in the redundancy and
robustness of RC structures subjected to blast and
earthquakes, ”Concrete Solutions”- Proceedings of
The Second International Conference on Concrete
Repair, St. Malo, June 2006, pp.782-792.
[3]. U.S. General Services Administration (GSA),
Progressive Collapse Analysis and Design Guidelines
for New Federal Office Buildings and Major
Modernization Projects, June 2003, 119 pp.
[4]. European Committee of Standardization,
EUROCODE 2: Design of Concrete Structures,
Brussels, 1997, 160 pp.
[5]. Ministry of Public Works, P 100-1/2004, Seismic
Design Code for Buildings (in Romanian), Bucharest,
2005, 410 pp.
[6]. FEMA-277, The Oklahoma City Bombing:
Improving Building Performance Through MultiHazard Mitigation, Federal Emergency Management
Agency, Aug. 1996, 98 pp.
[7]. Popov, E. E., Mechanics of Materials - second
edition; Prentice/Hall International, Inc., London,
1976, 590 pp.
[8]. ACI Committee 318, Building Code Requirements
for Structural Concrete (ACI 318M-99) and
Commentary (ACI 318RM-99), American Concrete
Institute, Farmington Hills, Mich., 1999, 319 pp.
[9]. Ministry of Public Works, P100-92, Seismic
Design Code for Buildings (in Romanian), Bucharest,
1992, 152 pp.
[10]. Ioani, A., Cucu, L.,and Mircea, C., Seismic
design vs. progressive collapse :a reinforced concrete
framed structure case study, Proceedings of the
International Conference ISEC-4, Melbourne, Sept.
26-28, 2007 (in press).
Cracking of Reinforced Concrete Elements
a
Laura- Catinca LEŢIA a
__________________________________________________________________________________________
Rezumat: Sunt prezentate relaţiile de calcul prevăzute în diferite norme, privind calculul deschiderii şi distanţei
între fisuri, cu referire la betonul armat, realizat cu beton de înaltă rezistenţă. Se fac comparaţii cu valorile
experimentale obţinute pe elemente de beton armat având ca variabilă procentul de armare.
Abstract: There are presented the evaluation formulae from different norms, regarding the estimation of crack
opening and spacing, which is referred to the reinforced concrete with high strength concrete. It is compared
with the experimental results obtained on reinforced elements having as variable the reinforcement amount.
Keywords: crack opening, crack spacing, high strength concrete.
__________________________________________________________________________________________
1. Foreword
Cracking of reinforced concrete elements is a
complex phenomenon; the causes of crack
formation are different.
Assuming that under the loads action (such as
tension, compression, torsion, bending, and share
force) the crack formation in practically inevitable,
the present norms are seeking mostly to confine this
phenomenon to some values that are not affecting
the behavior of the element or of the structure in
service in a significant manner. The crack opening
limitation has to take in account the cost of it,
related to the concrete strength and the
reinforcement yield point.
The studies and researches on high strength
concrete (HSC) elements made until nowadays are
showing that the north American and European
norms, that allows us to estimate the crack opening
and distance, are consistent for regular concrete, but
they can not offer a correct image on the crack
behavior of HSC elements. The cracking behavior
for HSC is mostly influenced by the tension and
compression strength, contraction and bond, etc.
2. The experimental program
The experimental program is based on
bending tests of eleven beams (three beams FT5
and two for each I beam). All beams had a width of
ISSN 1584 - 5990
125 mm, height of 250 mm and span length L0=3000
mm.
The concrete strength at the day of testing is
about 90 N/mm2 (C80/90).
The physical and mechanical characteristics of
reinforcement are listed in Table 1.
Table 1. Mechanical characteristics of reinforcement
Reinforcement
Longitudinal
Transversal
type
reinforcement reinforcement
Nominal
12, 14, 16
6
diameter (mm)
Yield point, fym
320
210
(MPa)
The longitudinal reinforcement is made from
PC52 steel PC52. The transversal reinforcement (the
stirrups) is made from OB37.
The longitudinal and transversal reinforcement
coefficients are listed in Table 2.
Table 2 The reinforcement coefficients
FT
I
The element
5
1
2
3
ρl=Asl/bw·d
2.06 2.59 3.03 3.40
(%)
ρw=Asw/bw·s
0.152
(%)
4
3.83
38 Cracking of Reinforced / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 37-44 (2007)
The loaing scheme is presented in Figure 1.
Fig. 1. The loading scheme
All the beams were tested using hydraulic
testing system and loaded with the two equal
concentrated loads, F. The distance between the two
concentrated loads was kept equal to L1=1000 mm.
Both ends of the beam were free to rotate and
translate under load. At each load increment, the
mid-span deflection and all strain reading were
recorded and the developing crack patterns marked
an the beam surface. The concrete maximum
compressive strain is recorded at the mid-span by
strain gauges glued are placed on one of the beam
side in the tensile zone. Beams are submitted to a
growing monotonic loading until failure. The
monotonic loading is applied 1/10 of the failure
calculated force.
3. Formulas to estimate the crack opening and
spacing
Sarkar, Adwan, Munday[2] researches show that
at the reinforcement level the crack opening and
spacing depend on the concrete strength and on
reinforcement coefficient.
Generally, the first crack appear immediately
after overtaking the I stage, when the cracks became
visible, and their opening depend on the loads nature
and intensity[9]. The estimation is compute in the IInd
stage of service, because under this (service) loads
action the elements are working in the cracked II stage
[10].
The design of reinforced concrete elements is
assuming that the concrete between two cracks is
capable to undertake strain and it is uncracked [10].
The European norms (EC2, CEB- FIP) and the
north American norms (ACI 318), but the Australian
(AS 3600-Part2) and the Romanian norms
(STAS10107/0-90) too recommend different relations
to evaluate the crack behavior. The Romanian (STAS
100107/0-90) and rhe European (EC2) norms establish
constructive conditions for crack control, such as the
limitation of reinforcement bars spacing and/or
diameter.
Fig. 2 Crack formation under load
L. C. Leţia / Ovidius University Annals Series: Civil Engineering 9, 37- 44 (2007)
EUROCODE 2 [3]
The crack control is analyzed in the 7.3
section of EC2, considering the Serviceability Limit
States (SLS).
Taking in account the Exposure Class and
type of element (reinforced concrete and
prestressed elements with bonded or unbounded
tendons) are established the maximum crack
opening. The crack formation of reinforced
elements subject to bending or shear is considered
as being normal, but it cannot affect the normal
behavior of the element or structure, or to create
any discomfort.
The European norms establish a minimum
reinforcement areas for crack control, denoted with
As and witch depends on the mean value of the
tension strength fct,eff= fctm [or it may be less,
meaning fctm(t), if t<28days], estimated just when a
first crack appears, and when the maximum
reinforcement strain σ s , the concrete areas within
the tensile zone Act, considering the effect of nonuniform self equilibrating stress, k, and the stress
distribution immediately prior to cracking and of
the lever arm, kc.
The values for fctm are given in a table for
concrete reaching the class C90 or it can be
determined as it follows:
( 2 / 3)
f ctm = 0,30f ck
(1)
for ≤ C50 / 60
f ctm = 2,12 ⋅ ln(1 + f cm / 10)
(2)
for > C50 / 60
where
fcm - the mean concrete compressive strength at 28
days.
fck the characteristic compressive cylinder
strength of concrete at 28 days.
39
For the crack control without special calculation,
EC2 establishes the maximum diameters and spacing
of reinforcement.
The crack spacing is calculated using the
equation:
w k = S r , max (ε sm − ε cm ) ;
(3)
where: ε sm − ε cm the difference between the mean
reinforcement strain under the relevant combination of
loads and the mean concrete strain between cracks, it
may be computed using the formulas:
σs − k t
ε sm − ε cm =
f ct , eff
ρ p, eff
(1 + α e ⋅ ρ p, eff )
Es
σ
≥ 0,6 s (4)
Es
where: σ s - the stress in the tension reinforcement
assuming a cracked section.
A s + ξ12 A p '
ρ p, eff =
A c, eff
(5)
where: ξ1 - for the pretension elements, it represents
the ratio the bond strength taking in account the
different diameters of prestressed and reinforcing steel.
Ap’ – aria of pre or posttensioned
As - the reinforcing area within the tension zone
Ac,eff - the effective area of concrete in tension
surrounding the reinforcement
kt - factor depending on the duration of the load,
taking the value 0,6 for short term loading, and 0,4 for
long term loading.
α e - the ratio Es/Ecm (equivalence coefficient)
Schematic the concrete area that is surrounding
the reinforcement area within the tensile zone may be
represented as it follows:
x
h
εt=0
d
A
Level of steel centroid
B
Effective tension area, Ac,eff
A
hct,eff
εt
B
Fig. 3. Effective tension area
To determine the maximum spacing between
cracks, Sr,max , if the bar spacing is less or equal to
5(c + φ / 2) , it may be used the following
expression:
S r , max = k 3c + k1k 2 k 4
φ
ρ p, eff
(6)
where: φ - the bars diameter, that may be
considered an equivalent diameter φ eq , when the
bars have a different diameters.
c – the cover to the longitudinal reinforcement
k1 – the coefficient that takes account of the
bond properties of the bonded reinforcement
=0,8 high bond bars
=1,6 for bars with an effectively plain surface
k2 – the coefficient that takes in account the
strain distribution
=0,5 for bending
=1,0 la pure tension
k3,k4 – coefficients that are specified in the
national annexes of each country, and it may have
the recommended values between 3,4, respectively
0,425.
If the bars spacing is greater than 5(c + φ / 2) ,
the maximum crack spacing shall be:
S r ,max = 1,3(h − x )
(7)
CEB 1997 [6]
CEB 1997[6] imposes a series of limitations
regarding the reinforcement strain, the bars
diameter and spacing, and the reinforcement ratio.
The values for the concrete tension strain up to
C100 are considered as having the value:
0.6
f ctm = 0.315f cm
(8)
where fcm – the mean concrete compression
strength.
The mean crack opening is estimated using the
formula:
w m = S rm (ε sm − ε cm ) =
4
L t ⋅ (ε s 2 − β ⋅ ε sr 2 )
3
(9)
wher: Lt – the transmission length
The maximum crack opening is computed as it
follows:
w k = l s, max (ε sm − ε cm − ε cs )
(10)
where: ε sm - the mean reinforcement strain for
the segment length ls,max
ε sc - the mean concrete strain for the segment
length ls,max
ε sr - the concrete strain due to the shrinkage
The length ls,max on witch it is registered the slip
between concrete and reinforcement, and it may be
computed as it follows:
l s, max = 2 ⋅
(σ s2 − σ s1 ) φ
(4τ bk )
s
(11)
where: σ s 2 - the reinforcement strain at the
crack
σ s1 - the reinforcement strain at the point
where the slip is
φ s - the bars diameter or the equivalent
diameter, when the bars have different diameters
τ bk - the smallest value of the mean bond stress,
that may be equal to 1.8fctm(t);
where fctm(t) – the mean value of the concrete
tension strength when the cracks appear
For the stabilized faze, the expression may be
considered:
l s, max = σ s 2
φs
2τ bk (1 + nρ s, ef )
(12)
where: n – the ratio Es/Ec.
ρ s, ef - the effective reinforcement ratio
As/Ac,ef
As – the reinforcement area
Ac,ef – the effective concrete tensile area,
A c,ef = b[2.5(h − d )]
(13)
where:b, h – the dimensions of the cross
section of the concrete element, the width and the
height
d – the effective distance from the compress
fiber to the tensile zone centroid
ACI 224R-01 [7]
The crack estimation at the concrete beams in
ACI, suppose using formulas that allow
determining the crack opening having a probability
of almost 90%.
Starting with ACI 318-95, the estimation of
crack opening begins from certain conclusions
obtained after completed research:
- the steel stress is the most important variable
- the concrete cover thickness is also an
important variable, but not just from the geometric
point of view.
- the
concrete
aria
surrounding
the
reinforcement bars are important from the
geometric point of view
41
- the ratio between the surface crack opening and
the one at the reinforcement level is proportional to the
ratio between the surface deformation and the one at
the reinforcement level.
According to ACI 224R-01 the crack opening
can be determined using the expression:
w max = 0.011 ⋅ f s 3 d c A ⋅ 10 −3
(14)
where dc – the distance from the bars centroid to
the tensile fiber, mm
A – the concrete aria symmetric to the bars
number, mm2
In ACI 318 the expression appears in a simplified
form:
z = fs 3 dcA
(15)
and the maximum allowed value for inside
elements is 30.6 MN/m and it correspond to a crack
opening of 0.41mm.For external elements the z value
is limited to 25.4 MN/m, an the crack opening cannot
overpass 0.33mm.
The crack opening for elements subjected to
bending with 10% smaller that the one of the tensile
elements, that is approximately 4 times the concrete
cover, for a rage of 30 up to 75 mm.
The last research (Frosh 1999) regarding the
crack formation of elements subjected to bending
showed that the crack opening estimation formula wmax
is not underestimated. For this reason, ACI 318-99
makes no difference between inside and outside
exposure conditions, but it indicates that for crack
control the spacing between beams and one-way deep
plates reinforcement has to be equal to:
s(mm)=[(95000/540fs)-2.5 cc
(15’)
but it cannot overpass 300(252fs)mm
where:fs – the reinforcement stress under service
loads.
cc – the concrete cover for the longitudinal
reinforcement
STAS 10107/0-90 [8]
Similar to the European norms, the Romanian
norms are restricting the crack opening such as this
will not affect the structure performance and the
element performance especially.
Taking in account that in the next future our
country will adopt the European norms previously
described, this paper will embrace only a few
mentions to the computation rules from STAS
10107/0-90.
STAS 10107/0-90 refers to the cracking limit
state and has some conditions regarding the mean
crack opening, cracks that are inclined or normal to
the element axes under service loads.
The maximum crack opening depends on the
exposure conditions of the element to different
aggressive substances, but it refers to the
impermeability conditions and the applied loads.
The values are in a range of 0,1 mm and 0,3 mm.
To estimate the crack spacing the following
relation is used:
λ f = 2 ⋅ (c + 0,1 ⋅ s ) + A ⋅
d
pt
(16)
explicitated the relation is:
λ f = 2 ⋅ (c + 0,1 ⋅ s ) + 25 ⋅ k 1 ⋅ k 2 ⋅
d
pt
(17)
where:k1 şi k2 – coefficients that are taking in
account the nature of the load and the bond
25 ⋅
Rt
= A = 25 ⋅ k1 ⋅ k 2 .
τ am
(18)
c- the concrete cover
s – the distance between the reinforcement
bars axes (mm), <15d
d – reinforcement diameter
pt – the longitudinal tension reinforcement
ratio,
pt =
Aa
⋅ 100
A bt
(19)
Abt – the concrete aria that involves the
reinforcement, considering for each bar a aria of
involving of maximum 7,5d.
When there are different diameters the ratio d/pt
will be computed as it follows:
A bt
d
=
p t 25 ⋅ ∑ π ⋅ d
(20)
where d – the reinforcement bars diameter.
As the Europeans norms due, the Romanians
norms are taking in account the participation of
concretre between cracks.
Therefore, considering the mean concrete strain
ε tm and of the reinforcement ε tm it may be written:
λ f ⋅ ε am = α f + (λ f − α f )ε tm
(21)
and the crack opening becomes:
αf =
(ε am − ε tm ) ⋅ λ f
(1 − ε tm )
(22)
If it is neglected the concrete strain ε tm the
relation for α f becomes:
α f = ε am ⋅ λ f
(23)
STAS 10107/0-90 recommend for crack opening
estimation:
σ
αf = λf ⋅ ψ ⋅ a
Ea
(24)
where the coefficient of the bond between concrete and
reinforcement in
ε
ψ = am
εa
considering: ε a =
(25)
σa
Aa
(26)
For the coefficient ψ the STAS indicates the relation:
A ⋅ R tk
ψ = 1 − β(1 − 0,5 ⋅ ν ) bt
Aa ⋅ R a
(27)
43
Where: ν − the ratio between the total service loads
(M,N) using the long term fraction of it, and the
total service loads (this are given in table 30, Anexa
C, STAS 10107/0-90)
β − the coefficient that takes the value 0,3 for
OB37 and 0,5 for PC52 and PC60.
σ a − the reinforcement stress for the cracked
section is the II-nd stage of service , that for usual
cases is:
A a , nec
σ a = 0,85 ⋅ R a ⋅
(28)
A a , ef
portion is made at the service limit state, when the
loads are less intens that in the ultimate limit state.
All this relations have been determined starting
from the idea of the uniform distribution of cracks,
with the distance between 15 and 30 mm, but in case
of reinforcement ratio less then 0,3% in case of
elements subjected to bending and 0,4% for those
subjected to tension have to be verified, considering
that the reinforcement has to be tied to the left and
right side of the crack with la.
4. The results of the experimental program and
debates.
Aa,nec/Aa,ef – the ratio between the necessary aria
that is a result of the ultimate limit state of strength
and the effective used aria.
Rtk – the caracteristic concrete tension strength, that
is underlining the fact that the analysis af that
Table 3 synthetically presents the experimental values
and the estimation of the cracking characteristics of the
experimental elements.
Crack opening
Experimental
values
Beam:
wymed1
Crack spacing
Theoretical values
Ratio
αf,
Theoretical values
Sr,mar
λf
cf. EC2
cf. STAS
10107
6
7
8
1.06
1.00
85.0007
110.5857
1.280
1.079
1.15
1.26
1.07
0.98
85.0007
85.0007
109.0906
84.8155
1.382
1.053
1.15
0.88
85.0007
82.7903
1.382
1.108
1.38
1.11
85.0007
87.8908
1.200
1.382
1.131
1.15
0.94
85.0007
91.1292
1.300
1.380
1.149
1.06
0.88
85.0007
95.9569
wk
for the
etire
beam.
wymed2
constant
bending
moment
zone
EC2
STAS10107
[0,1mm]
[0,1mm]
[0,1mm]
[0,1mm]
[cm]
[cm]
0
1
2
3
4
5
FT5.1-1
FT5.6-1
I4-2
I4-1
I3-1
I2-1
I1-1
1.100
1.300
1.379
1.297
0.900
0.900
1.200
1.100
1.379
1.382
0.900
1.200
0.800
1.000
0.900
0.900
w k ,EC2
w ymed2
α STAS10107
w ymed2
Table 3. Experimental and theoretical values to estimate the crack opening and
The section cracking takes place when the
tension in concrete reaches the value of the rupture
modulus.
Using the CEB+EC2 model, the moment
when a beam cracks does not depend only by the
reinforcement ratio. The explication consists in the
fact that the great part of the reinforced concrete
element cracks during their service life (this are the
effects due to the tension stress from the early
shrinkage of the concrete).
The results obtained show that the value of the
experimental bending moments is greater that the one
determined according to CEB+EC2 and STAS
101017/0-90.
The formulas that are estimating the crack
opening presented in EC2 overestimates the crack
opening. On the other hand the STAS 101017/0-90
underestimates them.
5. Conclusions
Increasing the longitudinal reinforcement
ration the cracking bending moment increases [13].
The crack opening experimentally determined
is greater that the values obtained applying the
STAS10107/0-90 relations, but they are less that
the values obtained using EC2/92.
Once the reinforcement ratio is increased the
crack opening decreases [13].
The analysis of the theoretical and
experimental values regarding the crack opening
and the crack spacing constitute a permanent
preoccupation of the author, and in the future (in
the next articles to be published) will be completed
with relations and norms, considering that HSC has
a different crack behavior that normal concrete.
6. Bibliografie
[1] Mãgureanu, C. – „Betoane de înaltã rezistenţã şi
performanţã” – Ed. UT PRES, Cluj-Napoca, 2003
[2] Sarkar, S., Adwan, O, Munday, J. G. L. – „High
strength concrete an investigation of the flexural
behavior of high strength RC beams”, The
Structural Engineers, Vol. 75, April 1997, pp. 115121
[3] EUROCODE 2: Design of concrete structures –
Part 1-1: General Rules and Rules for Buildings, EN
1992-1-1; December 2004, pp. 118-126
[4] EUROCODE 2: Proiectarea structurilor de beton –
Partea 1-1: Reguli generale şi reguli pentru clãdiri, SR
EN 1992-1-1; December 2004, pp. 118-126
[5] Manuel du CEB Fissuration et Deformations –
Prepare Par le Comite Euro-International du
Beton (CEB), 1983
[6] CEB Bulletin d’Information No 235 –
Serviceability Models – Behavior and modelling in
serviceability limit state including repeated and
sustained loads, April 1997
[7] ACI Manual of Concrete Practice 2005- Part 2ACI 224R-01 to ACI 313R-97
[8] STAS 10107/0-90 Calculul şi alcãtuirea
elementelor structurale din beton, beton armat şi beton
precomprimat
[9] Nicula, I., Oneţ, Tr. – „Beton armat”, Ed Didacticã
şi Pedagogicã, Bucureşti 1982, pp. 66-85
[10] Cadar, I., Clipii, T., Tudor, A. – „Beton
Armat”ediţia a II-a, Ed. Orizonturi Universitare,
Timişoara, 2004, pp. 279-300
[11] Wittmann, F.H. –„High Performance of Cementbased Materials”- WTA report series No 15,
Aedificatio Publisher
[12] Shah, S. P., Ahmad, S.H.- „High Performance
Concretes and Applications” – pp.1-60
[13] Magureanu, C., Leţia, C. - Cracking behavior at
bending of reinforced high strength/ high performance
concrete beams - Concrete: Construction’s Sustainable
Option - Dundee, 4 – 6 September 2007 – în curs de
publicare
A Short Introduction to Load Carrying Capacity for High Strength Concrete
Cornelia MĂGUREANU a
Dumitru MOLDOVAN a
Tehnical University of Cluj-Napoca, Cluj-.Napoca, 400027, Romania
a
__________________________________________________________________________________________
Rezumat: În prezenta lucrare se vor face consideraţii cu privire la comportarea la rupere a betoanelor armate
realizate cu betoane de înaltă rezistenţă, supuse la moment încovoietor. Ecuaţia de referinţă pentru calculul
capacităţii portante este cea propusă de Hognestad şi alţii, în anii 1950, în urma experimentelor pe care echipa sa
le-a efectuat. Codurile de proiectare actuale consideră pentru parametrii independenţi care apar în relaţia de
calcul diferite valori, dependente de stadiul datelor experimentale disponibile la vremea respectivă. Deoarece
actualmente aceste date sunt mult mai numeroase se impune o actualizare a acestor parametrii pentru a evita
supraevaluarea capacităţii portante a elementelor realizate cu betoane de înaltă rezistenţă. Se vor face de
asemenea şi unele consideraţii cu privire la procentul de armare longitudinal. Armarea transversală nu pare a
avea efecte cu privire la creşterea capacităţii portante a elementelor întocmai ca şi la betoanele obişnuite.
Abstract: This work presents some results obtained by the authors regarding concrete behavior near collapse,
under flexure, in the case of high strength concrete. A brief history on the mathematical apparatus involved in
the computing of the capable bending moment is presented, based on the initial proposal of Hognestad et al., in
the early 1950’s. Various national design codes use different values for the coefficients involved in this
computing. Since experimental studies provide now sufficient data, it is necessary to adjust the values of those
coefficients as not to over estimate the load carrying capacity for high strength concrete. Some observations on
the longitudinal reinforcement ratio will be presented. It seems that transversal reinforcement does not have
influence on the capable bending moment as it is the case for classic concrete.
Keywords: high strength concrete, flexure, collapse, projection codes, reinforcement.
__________________________________________________________________________________________
1. Introduction
High strength concrete (HSC) is recently one
of the most used worldwide materials in the
construction industry mainly due to their high
performance properties. When compared to classic
strength concrete (CSC) HSC may be used for
greater spans, has a higher resistance in time to
various destructive agents, uses less mixture
components, a cast requires less concrete volume
and therefore less self-weight which in turn means
smaller foundations, a cut on cost for maintenances,
in one word, a better sustainability.
The mathematics used to project HSC is
based on the one used for CSC. Since nowadays
experimental studies do not yet provide a full
coverage of various factors that may arise in a
particular cast, it is understandable why more than
one value is used for a given coefficient to compute
this result, depending on the national design code
utilized.
ISSN 1584 - 5990
2. Factors that influence the load carrying capacity
of HSC
a) Compressive strength and ultimate strain
It is well known for CSC that as compressive
strength increases so does the load carrying capacity.
HSC is no exception to this rule
σ − ε diagram, compressive strength and ultimate
strain may vary with: the ratio between different
components in the concrete matrix, type of cement and its
structure, type and kind of aggregates, admixtures, storage
conditions, age when loaded, tests conditions, etc. Some
of the above have a major influence on the concrete’s
behavior, e.g. type of aggregate is most important for E,
elasticity modulus of the concrete.
When presented in a chart, one can notice an
increase in the linearity of the σ − ε diagram, an
increase in strain value as the peak stress is reached a
steeper slope both on the ascending and on the
descending portion on the diagram.
46 A short introduction … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 45-52 (20067)
Fig.1.
σ −ε
diagram for different compressive strengths
As expected the ultimate strain values
decrease as the capacity increases. According to
different national design codes the value for the
ultimate strain is:
- ACI : 0.003
- British codes : 0.0036, for a compressive
strength of 12 MPa, with a decrease to 0.0028, for a
compressive strength of 50 MPa
- Other codes ( Belgium, Sweden, Germany,
Canada, etc.) : 0.0035
b) Elasticity modulus
The elasticity module of concrete does not
increase proportionally to the increase of compressive
strength.
Fig.2. Elasticity modulus of concrete for different compressive strength
47
C. Măgureanu and D. Moldovan / Ovidius University Annals Series: Civil Engineering 9, 45-52 (2007)
MPa, Carrasquillo et. al. ( 1981) 0.97 ⋅
c) Poisson’s ratio
Test results published until now suggest for
Poisson’s ratio values from 0.2 to 0.28, for
compressive strength from 55 MPa up to 80 MPa.
The most important influence on those values
seems to have the water-cement ratio.
'
f c MPa for
ompression strength of up to 83 MPa. Russell et. al. (
2003) proposed a lower bound of 0.62 ⋅
upper bound of
0.97 ⋅
fc
'
'
f c and an
MPa for compressive
strength of up to 103 MPa.
d) Rupture modulus
3. Design of HSC members
Cracking moment is influenced by rupture
modulus
and
the
minimum longitudinal
reinforcement that is required to prevent sudden
failure under bending moment. A review of the
Ultimate strain distribution as a function of
compressive strength is given in Fig. 3.
The generalized stress distribution and the
rectangular stress distribution for the compressed area
of a concrete member under flexure is given in Fig. 4.
literature suggests values of 0.62 ⋅
fc
'
to
fc
'
Fig.3. Ultimate strain vs. compressive strength
Fig.4. Generalized stress distribution and rectangular stress distribution
The parameters that define the sectional
values at rupture are:
k1, the ratio of the average compressive stress
to the maximum compressive stress
k2, the ratio of the depth of the resultant
compressive force to the depth of the neutral axis
k3, the ratio of the maximum compressive stress
force at the mid-depth of the assumed rectangular
stress block, as follows:
α1 =
k1 ⋅ k3
2 ⋅ k2
(2)
β1 = 2 ⋅ k 2
'
to the compressive strength of the cylinder f c .
In the 1950’s, Hognestad et. al. proposed this
parameters based on the eccentric bracket tests they
performed. The k1 ⋅ k3 value and the k 2 value can
The flexural resistance can be shown as:
Cu această substituţie ecuaţia (1) devine:
be obtained from the equilibrium of the external
and internal forces as follows:
M n = α 1 ⋅ β1 ⋅ f c ⋅ b ⋅ c ⋅ ⎜ d −
M n = k1 ⋅ k3 ⋅ f c ⋅ b ⋅ c ⋅ ( d − k 2 ⋅ c ) +
'
'
(
+ A s ⋅ f su ⋅ d − d
'
'
)
(
+ A s ⋅ f su ⋅ d − d
'
(1)
The three-parameter stress block can be
reduced to a two-parameter equivalent rectangular
block, by keeping the resultant of the compression
'
)
⎛
⎝
β1 ⋅ c ⎞
2
⎟+
⎠
(3)
A comparative review of different national
design codes and the values it use for α1 , β1 is given
in Fig.5.
Fig.5. α1 , β1 values as given by national design codes
Fig.6. α1 , β1 values as given by literature
49
Tabel 1. Tested beams parameters
Member
fc, cube (MPa)
FT5.1-1
91
I1-2
92.44
I2-1
85.10
I 3-1
84.88
I 4-1
89.92
4. Experimental study and results
Experimental case involved a number of 10
beams of of 125 x 250 x 3200 mm , with a designed
and achieved concrete class of C80. Reinforcement
consisted of PC 52 steel bars. The two point loadtest for the specimens were conducted in a static
test setup described schematically in Fig. 7.
Parameters of the beams are given in Tab. 1.
ρ1 (%)
2.061
2.586
3.03
3.401
3.829
Fig. 7. Two-point load specimens test setup
For all tested specimens the loading task was
1/10 of the calculated rupture force. Near collapse
the loading task was reduced to 1/20.
The values monitored were: strains for three
characteristic sections – in the simetry axis, and
under the applied forces, buckling (δ) of the
element,cracking development, strains of stretched
reinforcement.
Terms between the loading task and buckling
F
(
− δ ) is given in Fig. 8.
Fu
1.000
F/Fu
0.900
0.800
p=2.061%
0.700
p=2.586%
0.600
p=3.030%
0.500
p=3.401%
0.400
p=3.829%
0.300
0.200
0.100
0.000
0
100
200
300
400
500
600
Buckling δ [0.1 mm]
Fig.8. Terms for F
Fu
−δ
700
800
900
The value of l/200 for buckling was recorded
= 0.5 .
for a loading task greater than F
Fu
Terms between rupture buckling δr and
reinforcement ratio ρ , is given in Fig. 9.
Rupture buckling is decreasing with the
increase in reinforcement ratio as aspected. For an
increase in reinforcement ratio of about 2 times, the
rupture buckling seems to decrease for about 2 times as
well. The increase of reinforcement ratio conducts to
an increase of the rupture force Fr, as given in Fig. 10.
Rupture buckling δr [mm]
100
95
90
85
80
75
70
65
60
55
50
45
40
35
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
Reinforcem ent ratio ρ [%]
Fig. 9. Terms between rupture buckling δr and reinforcement ratio ρ
17000
16000
15000
Fr
14000
13000
12000
11000
10000
9000
1.000
1.500
2.000
2.500
51
3.000
3.500
Reinforcem ent ratio ρ [%]
Fig. 10. Rupture force Fr
4.000
4.500
5.000
6. Conclusions
7. Bibliografy
As a result of the tests conducted the main
conclusion arisen is that for an increase in
reinforcement ratio there is a clear decrese in
buckling. The tests will continue with the
computing of HSC members while considering the
stress distribution for the compressed area of a
member section.
[1] Măgureanu C., Hegheş B., High strength concrete
– ductility of members under flexure. 2007, BIR,
Bucharest, Romania
[2] Nilson N.H., D. Dolan C.W., Design of concrete
structures. 2003, 13th ed., Mc-Grawhill, USA
[3] Mausar, Chin M. A., Wee M.S. , T.H., Flexural
behavior of high strength concrete. 1997, ACI
Structural Journal, vol. 94, p. 663-674
[4] Hognestad E., Study of combined bending and axial
load in reinforced concrete members. 1951, University
of Illinois, Engineering Experimental Station, Bulletin
Series No. 399, Bulletin No.1
Studies on the Modalities of Use of Sludge Resulting From the Lime Milk Neutralization
of Acid Waters Derived From the Pickling of Wire Obtained At S.C. Mechel Câmpia
Turzii
Daniela MANEA a
Claudiu ACIUa
Ofelia CORBU a
Tehnical University of Cluj-Napoca, Cluj-.Napoca, 400027, Romania
a
__________________________________________________________________________________________
Rezumat: În prezent omenirea se confruntă cu probleme deosebite atât în ceea ce priveşte problema resurselor
materiale cât şi poluarea mediului înconjurător. În acest context, o problemă deosebită o constituie deşeurile
rezultate în urma unor procese tehnologice, atât din punct de vedere al asigurării spaţiului de depozitare cât şi din
punct de vedere al poluării. Din acest motiv se impune găsirea unor soluţii viabile pentru reutilizarea acestora.
Un astfel de caz a apărut la 1 ianuarie 2007 în cadrul societăţii S.C. MECHEL Câmpia Turzii, la care în urma
procesului de fabricaţie a sârmelor se obţine ca produs secundar 400 t/lună de şlam, ca rezultat al neutralizării cu
lapte de var a apelor acide provenite din decaparea sârmelor. Lucrarea de faţă prezintă rezultatele programului
experimental realizat în cadrul laboratorului, având ca scop găsirea unor soluţii de reutilizare a şlamului prin
obţinerea unor materiale de construcţii ecologice.
Abstract: Mankind is currently confronted with special problems both in terms of raw materials and
environmental pollution. In this context, a particular problem is represented by the waste material resulting from
technological processes, both from the point of view of ensuring a storage space and from the point of view of
pollution. This is why viable solutions for the reuse of waste material need to be found.
Such a case appeared on 1 January 2007 at the S.C. MECHEL Câmpia Turzii company, where following the
manufacture of wire, 400t sludge/month are obtained as a secondary product, resulting from the lime milk
neutralization of acid waters derived from wire pickling. This study shows the results of the experimental
program carried out in the laboratory, aiming to find solutions for the reuse of sludge for obtaining ecological
construction materials.
Keywords: raw materials, environmental pollution, waste material, sludge, ecological construction materials.
__________________________________________________________________________________________
1. Introduction
Since 1 January 2007, 400 tons of
sludge/month has been available at the MECHEL
Câmpia Turzii Commercial Company. This result
from the lime milk neutralization of acid waters
derived from wire pickling. Sludge has a pH = (7 –
8.5), a density ρ = 1.3 g/cm3, and a chemical
composition Fe 24.4; Ca 7.2; Cu 0.05; P 1.0; Zn
0.4; Si 3.1, according to the analysis bulletins
drawn up by the specialists of the company’s
laboratories.
Sludge is known in the literature as a mixture
of water and fine mineral matter particles in
suspension, resulting from the mechanical wet
processing of ore or coal.
ISSN 1584 - 5990
The studied sludge respects this definition, but is
derived, as it was shown above, from the lime milk
neutralization of acid waters resulting from wire
pickling.
In Romania, there are commercial companies that
produce waste material such as galvanic sludge, which
is considered dangerous. Among these companies, the
following can be mentioned: SC Romlux SA
Târgoviste, SC Steaua Electrica SA Fieni, SC Uzina
Mecanica SA Mija, SC Cromsteel SA Târgovişte, etc.
SC UPET SA produces phosphating sludge as a waste
material. Another category of sludge is produced by oil
equipment belonging among others to SNP Petrom SA;
this is oil sludge, resulting from the extraction of crude
oil. It can be estimated that the studied sludge is
similar to that produced by SC Oţelinox SA Târgovişte
54
Studies on the … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 53-58 (2007)
and to that of SC COS SA Târgovişte, due to the
production object.
One of the strategic objectives of
environmental protection in Romania is the use of
waste material.
The management of waste material aims to
use processes and methods that should not:
a) involve risks for the population, water, air, fauna
or vegetation;
b) produce phonic pollution or unpleasant smell;
c) affect the landscape or the protected areas.
At national level, this becomes an essential
concern, so that there are already studies and results
in this sense. The team including Crăciunescu L.,
Şerban L., Popescu M., Matei V. can be mentioned,
who proposed the use of bauxite sludge for the
obtaining of natural colored concrete, artificial
aggregates, and bauxite sludge bricks.
variables were the addition percentage: 20%, 30%, and
50%, and also the cement dosage II A-S 32.5R: 320,
346, 360 kg/m3.
2.2. Sand granulometry, drawing of the sand
granularity curve
The aggregate used is river sand, with a (0 – 7)
mm granularity, of two sorts: (0 – 3) mm and (3 – 7)
mm, having the granularity curve presented below, in
Fig. 1.
Following the experimental program, the results
are shown in Table 1, and the values of passages
expressed in percentage represent the granularity curve
drawing data shown in Fig. 1.
No.
2. Experimental program
1.
2.
3.
4.
5.
6.
According to the annex to the contract, we
started an experimental program in order to try to
use the sludge obtained following the lime milk
neutralization of acid waters derived from wire
pickling at MECHEL Câmpia Turzii S.A.
The studies performed aimed to identify the
physical-mechanical characteristics of sludge, so
that this could be used in as high amounts as
possible in construction.
Sludge was tested in order to check if it can
be used as an aggregate or as an addition for the
preparation of mortars, the amount resulting after
the carrying out of experiments being a percentage
of the amount of cement used for obtaining a cubic
meter of material (cement dosage).
Fig. 1. The granularity curve of the sand used
2.1. Determination of the composition of mortar
Given the chemical analysis bulletin of
sludge, we considered it risky to recommend it for
the obtaining of plaster or masonry mortar. Its
strong color might penetrate the plaster and
painting, affecting the quality of finishing.
This inconveniency cannot occur when sludge
is used in an auger bit.
For this purpose, 9 recipes were elaborated for
a material in which sludge represents an addition, a
percentage of the cement dosage used. The chosen
Table 1. Sand granularity curve
Residue Passages Passages
φ
[g]
[g]
[%]
[mm]
7
50
950
95
3
363
587
58.7
1
250
337
33.7
0.2
309
28
2.8
tray
28
1000
-
-
Of the nine recipes:
three recipes propose a cement dosage of
kg/m3 and a sludge addition of 20%, 30%
50%, with an A/C ratio = 0.6;
50%, with an A/C ratio = 0.6;
50%, with an A/C ratio = 0.75; 0.8.
Table 2 shows all these recipes.
320
and
346
and
360
and
D. Manea et. al. / Ovidius University Annals Series: Civil Engineering 9, 53-58 (2007)
Recipe 1
Recipe 2
Recipe 3
Recipe 4
Recipe 5
Recipe 6
Recipe 7
Recipe 8
Recipe 9
Table 2. The mortar recipes of the experimental program
Sludge
Cement II A-S
Aggregate [Kg]
A/C
32.5R [Kg/m3]
%
(0-3)
(3-7)
[Kg]
320
64
20
0.6
1030.4
809.6
320
96
30
0.6
1030.4
809.6
320
160
50
0.6
1030.4
809.6
346
69
20
0.6
994.0
781.0
346
104
30
0.6
994.0
781.0
346
173
50
0.6
994.0
781.0
360
72
20
0.75
892.1
700.9
360
108
30
0.75
892.1
700.9
360
180
50
0.80
865.2
679.8
2.3. Preparation and manufacture of (4x4x16) cm
prismatic and cubic test pieces
According to STAS 2634-80, for the
determination of tensile bending strength and
compressive strength, the test pieces should be
prismatic, (4x4x16) cm in size. Their minimum
number is three, of which two are tested and one is
the control.
The fresh material was poured into
dismountable metal molds, the three prism case,
according to STAS 2320-79. The molds were filled
in two layers. Each layer was compacted by 10 hits
with a mallet. The mortar in excess was removed
by smoothing with a metal ruler. The case mold
was placed on full bricks and was stored until
demolding, covered with a glass plate. At 24 hours
Recipe 1
Recipe 2
Recipe 3
Recipe 4
Recipe 6
Recipe 7
Recipe 9
55
from casting, the prisms were demolded and kept until
the age of 7 days in water, at a temperature of 20 ±
4°C, and then in rooms with a temperature of 20 ± 4°C
and humidity of 65 ± 5%.
3. Results and interpretation
3.1. Determination of bending strength
The determination of bending strength and
compressive strength was performed in the cast prisms
and cubes both at the age of 7 days and 28 days.
Of each recipe, two prisms were tested in order to
determine bending strength. The results were recorded
in Table 3 for the age of 7 days and in Table 4 for the
age of 28 days.
Table 3. Results of the experimental program at 7 days
Determination of compressive strength
Determination of bending
strength
4 x 4 x 16 cm prisms
Cubes
test piece 1 test piece 2
test piece 1
test piece 2
test piece
test piece
1
2
P2 [daN]
P1 [daN] P2 [daN] P1 [daN] P2 [daN]
P1 [daN]
P2 [daN]
P1 [daN]
1.400
1.450
1500
1450
1420
1460
4300
4200
2.000
1.950
1800
1700
1750
1640
7400
7450
1.275
1.125
1100
1150
950
1200
2900
2750
2.770
2.500
2800
2700
2750
2750
4700
4500
1.900
1.700
2400
2600
2500
2500
3700
3550
1.800
1.890
1800
1900
1850
1800
5300
5400
1.700
1.660
1550
1700
1600
1650
4350
4200
3.2. Determination of compressive strength
The prism halves were submitted to the action
of the hydraulic press and compressive resistance
was determined. The breaking forces indicated by the
dial of the press were recorded in Table 3 for the age
of 7 days and in Table 4 for the age of 28 days.
56
Recipe 1
Recipe 2
Recipe 3
Recipe 4
Recipe 6
Recipe 7
Recipe 9
Tabel 4. Results of the experimental program at 28 days
Determination of compressive strength
Determination of bending
strength
4 x 4 x 16 cm prisms
Cubes
test piece 1 test piece 2
test piece 1
test piece 2
test piece
test piece
1
2
P2 [daN]
P1 [daN] P2 [daN] P1 [daN] P2 [daN]
P1 [daN]
P2 [daN]
P1 [daN]
2.670
3.200
1830
1840
1680
1640
5400
5500
3.530
3.420
1970
1840
1850
1870
14100
14000
2.065
2.350
1120
1160
1140
1150
3300
3950
3.955
4.110
2560
2970
3500
3650
9700
9600
2.880
2.970
2320
1960
2320
2160
6300
6250
3.725
3.210
1900
2180
1750
2050
7500
7450
2.765
2.750
2540
1850
1960
1920
4900
5100
The brand of the material is indicated by the
Table 6 indicates the values of tensile bending
compressive resistance value obtained in the prism
strength and compressive strength at the age of 28
halves, at 28 days.
days.
Table 5 indicates the values of tensile bending
strength and compressive strength at 7 days.
Table 5. Strength of mortar at 7 days
2
Rc [daN/cm2]
Rc [daN/cm2]
Rti [daN/cm ]
prism halves
cubes
Rc1,2 Rc1 med Rc2,1
Rc2,2 Rc2med Rcmed
Rc1
Rc2
Rcmed
Rti1 Rti2 Rtimed Rc1,1
93.8
90.6
92.2
88.8
913
90.0
91.1
87.8
85.71
86.73
Recipe 1 19.6 20.3 19.9
Recipe 2 28.0 27.3 27.7 112.5 106.3 109.4 109.4 102.5 105.9 107.6 151.0 152.0 151.5
68.8
71.9
70.3
59.4
75.0
67.2
68.8
59.2
56.12
57.65
Recipe 3 17.9 15.8 16.8
91.83
93.87
Recipe 4 38.8 35.0 36.9 175.0 168.8 171.9 171.9 171.9 171.9 171.9 95.9
72.45
73.97
Recipe 6 26.6 23.8 25.5 150.0 162.5 156.3 156.3 156.3 156.3 156.3 75.5
Recipe 7 25.2 26.5 25.8 112.5 118.8 115.6 115.6 112.5 114.1 114.9 108.2 110.2 109.2
96.9
106.3 101.6 100.0 103.2 101.6 101.6
88.8
85.71
87.24
Recipe 9 23.8 23.2 23.5
Rti1
Rti2
Rtimed
Table 6. Strength of mortar at 28 days
Rc [daN/cm2]
prism halves
Rc1,1
Rc1,2 Rc1 med Rc2,1
Rc2,2 Rc2med
37.4
49.4
28.9
55.4
40.3
52.2
38.7
44.8
47.9
32.9
57.5
41.6
44.9
38.3
41.1
48.7
30.9
56.5
41.0
48.6
38.5
114.4
123.0
70.0
160.0
145.0
118.8
158.8
2
Rti [daN/cm ]
Recipe 1
Recipe 2
Recipe 3
Recipe 4
Recipe 6
Recipe 7
Recipe 9
115.0
115.0
72.5
185.0
112.5
136.3
115.6
114.7
119.0
71.3
172.5
133.0
127.5
137.2
4. Conclusions
Following the experimental program, the diagrams
of Fig. 2 and Fig. 3 were drawn up, which represent
102.5
115.6
71.3
218.0
145.0
109.3
122.5
103.1
116.8
71.8
228.0
135.0
128.2
120.0
102.7
116.2
71.5
223.0
140.0
118.8
121.3
Rcmed
108.7
117.6
71.3
198.0
136.5
123.1
129.2
Rc [daN/cm2]
cubes
Rc1
Rc2
Rcmed
110.2
140.0
67.3
1980
128.0
153.0
100.0
112.2
141.0
80.6
196.0
127.0
152.0
104.0
111.2
140.5
73.9
197.0
127.5
152.5
102.0
compressive strength at 7 days and at 28 days,
depending on cement dosage and on the percentage of
the added sludge in the recipe: 20%, 30%, 50% of the
amount of cement II A-S 32.5R.
57
D. Manea et. al. / Ovidius University Annals Series: Civil Engineering 9, 53-58 (2007)
36
0
36
0
34
6
32
0
32
0
350
32
0
34
6
400
300
250
501
01
.5
6
11
4.
84
20
20
50
10
7.
65
50
68
.7
5
50
30
20 9
1.
09
100
15
6.
2
150
5
17
1.
8
7
200
0
Recipe 1
Recipe 2
Recipe 3
Cement [kg/mc]
Recipe 4
Sludge [%]
Recipe 5
Recipe 6
Recipe 7
Rc [daN/cmp]
36
0
34
6
32
0
32
0
350
32
0
34
6
400
36
0
Fig.2. Variation in mortar strength depending on dosage and addition, at 7 days
300
12
3.
12
13
6.
5
20
50
50
50
71
.3
11
7.
6
20
50
30
100
20
150
10
8.
69
200
12
9.
2
19
8
250
0
Recipe 1
Recipe 2
Recipe 3
Cem ent [kg/m c]
Recipe 4
Recipe 5
Sludge [%]
Rc [daN/cm p]
Recipe 6
Recipe 7
Fig.3. Variation in mortar strength depending on dosage and addition, at 28 days
58
The following conclusions can be drawn:
- the highest strength values are obtained for a
cement dosage of 346 kg/m3 and 20% sludge;
- in the case of an increase in cement dosage: -from
320 kg/m3 to 346 kg/m3, for 20% added sludge,
compressive strength increases from 108.7 daN/cm2
to 198.0 daN/cm2;
- from 346 kg/m3 to 360 kg/m3 for 20% added
sludge, compressive strength decreases from 198.0
daN/cm2 to 123.1 daN/cm2;
- from 320 kg/m3 to 346 kg/m3 , for 50% added
sludge, compressive strength increases from 71.3
- from 346 kg/m3 to 360 kg/m3 for 50% added
sludge, compressive strength decreases from 136.5
So, a cement dosage of 346 kg/m3 is more
effective for the obtaining of an auger bit
equivalent to mortar M100. This observation is also
true for tests performed in test pieces at 7 days.
For weaker mortars, a cement dosage of 320
kg/m3 with a sludge addition of 20%, 30%, even
50%, can be used, because Rc > 50 daN/cm2.
At the age of 28 days, the material prepared
according to the recipes enclosed can be indicated
for the casting of some auger bits, having a strength
equivalent to mortar M100, using:
- a cement dosage of 320 kg/m3, with a sludge
addition of 20%, 30%;
addition of 20%, 30%;
addition of 20%, 30%.
It is found that regardless of the cement
dosage, 320, 346, 360 kg/m3, for a sludge addition
of 50%, a reduction in compressive strength occurs.
For a cement dosage of 346 kg/m3 and 360
3,
kg/m for a sludge addition of 50%, compressive
strength values higher than 100 daN/cm2 (10
N/mm2) are found, which is equivalent to mortar
M100.
Recommendations:
In order to obtain mortar M100, a cement dosage
of 346 kg/m3 and 360 kg/m3 with a sludge addition of
50% is recommended.
of 320 kg/m3 with a sludge addition of 50% is
recommended.
of 320 kg/m3, 346 kg/m3 and 360 kg/m3 with a sludge
addition of 20%, 30% is recommended.
We recommend sludge to be used after drying,
for the obtaining of auger bits, and less as plaster and
masonry mortar, due to the chemical composition
indicated in the analysis bulletin. The research could
continue in order to obtain pavements, in which case
sludge would also play the role of a pigment. For this
purpose, wear resistance and frost resistance should be
determined.
Another idea is to use sludge as an aggregate, for
the manufacture of auger bits, alone, without a river
aggregate. The use of fluidizing and super-fluidizing
additives, which would also increase workability and
reduce the A/C ratio, would also have a beneficial
effect on compressive strength.
5. Bibliography
[1] Manea D., Netea Alex., Materiale de constructii şi
chimie aplicată, 2006, Ed. Mediamira, Cluj-Napoca.
[2] Craciunescu L., Serban L., Popescu M., Agregate
artificiale si cărămizi pe bază de bauxită, Materiale de
construcţii, 1991, pag.81.
[3] Craciunescu L., Serban L., Popescu M., Matei V.,
Beton aparent cu parament colorat cu şlam de bauxită,
Materiale de construcţii, 1990, pag.203.
Energy Conservation, an Essential Factor in Sustainable Construction
a
Daniela MANEA a
Claudiu ACIUa
__________________________________________________________________________________________
Rezumat: În prezent omenirea se confruntă cu probleme deosebite atât în ceea ce priveşte problema resurselor
materiale cât şi poluarea mediului înconjurător situaţie survenită ca o consecinţă a industrializării, a exploziei
demografice, a globalizării şi dezvoltării accelerate pe toate continentele. Din acest motiv dezvoltarea durabilă
este o soluţie care se impune pentru rezolvarea acestei probleme. Aceasta înseamnă ca nevoile actuale să fie
satisfăcute fără a periclita pe cele ale generaţiilor viitoare şi că mediul înconjurător natural trebuie protejat prin
măsuri reparatorii. Dezvoltarea durabilă este un concept apărut ca o consecinţă a crizei energetice, a epuizării
materiilor prime şi nu în ultimul rând datorită necesităţii de protejare a mediului. Lucrarea prezintă una din
soluţiile adoptate în construcţii în acest scop şi anume refolosirea deşeurilor; fapt care are menirea de a contribui
în primul rând la valorificarea acestora şi protejarea mediului şi în al doilea rând la rezolvarea problemei privind
resursele energetice şi reducerea costurilor de producţie în domeniul construcţiilor.
Abstract: Mankind is currently confronted with special problems regarding both material resources and
environmental pollution, as a result of industrialization, demographic explosion, globalization and accelerated
development on all continents. This is why sustainable development is required for the solution to this problem.
This means that current needs should be satisfied without endangering the needs of future generations and
natural environment should be protected by reparatory measures. Sustainable development is a concept that has
appeared as a result of the energy crisis, of the exhaustion of raw materials and, last but not least, due to the need
for environmental protection. This study presents one of the solutions adopted in construction for this purpose,
namely the reuse of waste material, which is intended to contribute in the first place to its valorisation and
environmental protection, and in the second place, to the solution of the problem of energy resources and the
reduction of production costs in the field of construction.
Keywords: sustainable development, raw materials, reuse of waste material, environmental protection.
__________________________________________________________________________________________
1. Introduction
The ”oil shock” of the '70s has drawn the
attention of the whole world to the potential
exhaustion of natural and energy resources of the
globe. This is why a number of international events
have marked the appearance and substantiation of
the concept of sustainable development.
Thus:
- the World Conference on Environmental
Protection - June 1972 – can be considered the
first international manifestation in this sense. The
Declaration on Environment adopted here poses,
among others, the problem of the conservation of
natural sources.
ISSN 1584 - 5990
- the Report of the World Commission for
Environment and Development (the Brundtland
Report) – 1987 represents a new important event that
marks the evolution of the concept of sustainable
development.
- the United Nations Conference on
Environment and Development - Rio de Janeiro,
June 1992, approached the global environmental
problems with which the planet is confronted.
The documents adopted on environment and
development include the Rio Declaration and Agenda
21. The Declaration is focused on economic and
social
objectives,
required
for
sustainable
development. Agenda 21 is a global action program
intended for the implementation of the Rio
Declaration.
60
Energy conservation, … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 59-64 (2007)
- the Kyoto Agreement of 1997 – one of the
most important sustainable development events was ratified in 2005 by 123 states, among which
Romania.
This agreement stipulates for each country the
maintenance of greenhouse gas emissions below
the level of the year 1990.
- the World Conference on Sustainable
Development, from Johannesburg – September
2002, showed that progress in the implementation
of sustainable development was extremely
disappointing, and that the state of poverty of the
population
and
environmental
degradation
worsened. The most important document of the
Conference is the Implementation Plan, which
contains the main objectives of sustainable
development.
- in March 2003, in Brussels, the European
Council defined a set of priorities regarding
development, in order to implement the documents
adopted at the Johannesburg Conference and to
establish the European Union Strategy regarding
Sustainable Development.
In order to achieve these objectives, the
European Council established a number of
measures:
-economic growth, with emphasis on the use
of regenerable energy sources;
-stopping environmental degradation;
-reduction of gas emissions by the
development of new fuels and technologies;
-adoption of the program ”Intelligent energy
for Europe”;
-introduction of a system of sanctions,
including penal sanctions, against pollution acts.
- the International Conference on Energy
Consumption and Greenhouse Gas Emissions
(UNCCC) – 28 Nov.-9 Dec. 2005, Montreal –
emphasizes the fact that over the next years,
emissions will be increasing on the globe and
consequently, climatic changes will be increasingly
important, and that the Kyoto Agreement will need
to be replaced by another agreement that should
include the high energy consumer countries
(U.S.A., China, India, Brazil, South Africa,
Australia).
Romania’s concern about sustainable
development results from the governmental actions
taken over the past years. Thus, the “Medium term
national
strategy”
(2001-2004)
adopted
by
Governmental Decision establishes measures for
efficient energy management.
The creation in 1997 of the National Center for
Sustainable Development, financed by the United
Nations Program for Development, was an important
step initiated by Romania in sustainable development,
aiming at the elaboration of the National Strategy for
Sustainable Development and the National Action
Plan, regarding the implementation of Local Agenda
21 in Romania.
In the field of energy conservation in buildings,
the Romanian Governmental Order no. 29/2000 on
the thermal rehabilitation of existing buildings and the
stimulation of thermal energy saving is mentioned.
This stipulates the obligation to perform the
rehabilitation and thermal modernization of buildings
and attendant services, to ensure the reduction of
seismic risk, as well as the necessity of the delivery of
an energy certificate for buildings. In this sense, a
number of norms were elaborated.
However, the sustainable development strategy
for the energy sector in Romania does not include as a
priority the development of regenerable sources, which
could increase the differences between Romania and
the developed EU countries. This might have a
negative impact in the long term, when regenerable
sources might have a major contribution to the energy
sector, creating new dependencies on imports for
Romania, this time of technological and cognitive
nature.
In the context of the elaboration of laws that will
support the development of this energy sector, the
market of regenerable energy sources will certainly
develop, as Romania has a high cognitive level and
many specialists that can successfully work under the
conditions of a liberalized energy market.
2. Sustainable construction
In construction, the concept of sustainable
development can be seen as a modality by which this
sector acts for the current and future improvement in
the quality of life, having as a starting point the
definition given by Ch. Kilbert at the International
Conference on Sustainable Construction (Tampa,
1994): “the creation and the responsible management
of a healthy environment, based on the efficient use of
resources and ecological principles”.
D. Manea and C. Aciu / Ovidius University Annals Series: Civil Engineering 9, 59-64 (2007)
In this context, the “International Board for
Research and Documentation in Civil Engineering”
(CIB – Conseil International du Bâtiment)
published the Agenda 21 for Sustainable
Construction, offering a detailed picture of the
concepts and problems of sustainable construction.
The elements considered are:
- the reduction in the use of fossil fuel energy
sources and the use of regenerable sources;
- the conservation of natural areas and
biodiversity;
- the insurance of the quality of the built
environment and the management of a healthy
indoor environment.
In the same spirit, in December 2002, the
European Parliament adopted the Directive
2002/91/EC on the energy performance of
buildings. The aim of this Directive is the
promotion of the increase in the energy
performance of buildings on the territory of the
Community, taking into consideration the climatic
and local outdoor conditions, as well as indoor
temperature requirements and economic efficiency.
At present, this law is also adopted in Romania.
The obligation to apply the European
Directive 2002/91/EC, called “Energy efficiency
of buildings” in all EU countries starting with
January 2006 has a special impact on the thermal
rehabilitation of buildings.
In Romania, the stage of sustainable
construction is closely connected to the economic,
social and political conditions.
In the first place, the existing buildings need
rehabilitation works in order to align to the
European energy performance level, and the
development policy requires the design and
building of new constructions that should integrate
in the concept of sustainable development.
The norm “regarding the design of dwelling
buildings, based on performance requirements”
elaborated in 1995 by IPCT – Bucharest, establishes
the minimum quality requirements for a dwelling.
These requirements are in accordance with those
stipulated in the “European directives on building
products and interpreting documents”, approved by
the Permanent European Committee in 1995.
For the thermal rehabilitation of existing
buildings, as well as for the insurance of an
optimum comfort level of new buildings, the
61
respect of the Quality in Construction system provided
by Law no. 10/1995 is extremely important.
3. Reuse of waste material, an important factor in
sustainable construction
The reuse of waste material is part of the
integrated approach to problems of economic growth,
population health, education, protection of energy
sources, environmental protection.
This is one of the solutions adopted at
international level which is intended to contribute in
the first place to the valorization of waste material and
environmental protection and in the second place to the
solution of the problem of energy sources and the
reduction of production costs in the field of
construction.
In civil engineering, concrete is a very frequently
used material. This is obtained using incorporated
energy which is found in the highest proportion in
Portland cement. As it is shown in Table 1, although
its proportion in the recipe is only 12%, the energy
incorporated in it is as high as 92% of the energy
required for the manufacture of concrete.
Table 1. Energy required for the manufacture of
concrete
Component
Percentages by
Energy %
weight
Portland cement
12%
92%
Sand
34%
2%
Crushed stone
48%
6%
Water
6%
0%
For the production of each ton of cement, ~ 1 ton CO2
is produced
Given this, the attention of specialists has
focused on two aspects: finding substitutes for Portland
cement and finding solutions for the manufacture of
cement with an as low as possible energy consumption,
without affecting environment.
A solution in this sense is the use of waste
material as an alternative fuel for the manufacture of
cement.
In Belgium, 40%-45% of the fuel used for
burning in the ovens of cement factories is of
alternative origin. In Czechia, where authorities and
society have adopted a proactive position, the use of
alternative fuels has reached 60%.
62
The percentage of the use of alternative fuels
in Romania is low, maximum 5%.
3.1 Aspects regarding the reuse of waste
material for the manufacture of cement
The manufacture of cement results in
important CO2 emissions, which are both direct, by
the burning of fuel and the decarbonation of the raw
material mixture, and indirect, by the electrical
energy consumption of technological equipment.
The main strategies for the reduction of CO2
emissions are aimed at the improvement of energy
efficiency, the replacement of fossil fuels by
alternative fuels (fuel waste material), the use of
waste materials as raw material substitutes or as
additions in cement grinding.
The secondary or alternative fuels used
include used tires, various solid or liquid waste
materials, plastic materials, as well as waste derived
biological fuels.
Although there are apparently no technical
constraints to prevent the replacement of coal by
alternative fuels, the secondary fuel amount should
be accurately established in order to maintain the
balance of processes inside the oven, as well as the
quality of the clinker.
3.2 Some waste materials
manufacture of cement
used
for
the
The processes and fuels used for the
manufacture of the cement clinker differ depending
on the regional tendencies in cement production.
Chloride
Cadmium
Mercury
Lead
Zinc
The raw material consists of a well
homogenized, finely ground mixture of 77-75%
limestone and 23-25% clay, as well as siliceous
(diatomite), aluminous (bauxite), and ferruginous
(pyrite ash) additions.
The waste materials that can be burned in
cement ovens are extremely varied:
- liquid energy waste materials: used oils, colorants,
dyes, organic compounds from the drug industry, etc;
- viscous energy waste materials: sludge, muds, tars
from the oil, iron industry, water treatment, etc.;
- solid energy waste materials: used tires, wood,
paper, plastic materials, etc.;
- non–energy waste materials: pyrite ash, thermal
power station ash, sludge, etc.
In the cement oven, due to an extremely high
temperature (about 1400 degrees C), any kind of
waste material can be eliminated. This is decomposed
and burned, residual energy being used as a fuel, and
minerals become clinker components and are
incorporated in the resulting product – cement.
The evaluation of a fuel also depends on its
composition; this influences both the quality of
cement and emissions that can be toxic. Thus, the
high zinc content in tires can be a restrictive factor
because zinc concentrations higher than 500 ppm
(parts per million) in cement increase water
requirements. The quality of cement is not affected
when zinc concentrations in the clinker vary between
200-500 ppm.
Table 2 shows the concentration of some elements of
various secondary fuels compared to that of solid
coal:
Table 2. Concentration of some elements of various fuels (mg/kg in 1998)
Solid coal
Used tires
Plastic
Oil and solvent Paper fiber
materials waste materials
residues
1500
2000
10800
3000
340
1
5
6
6
1.5
0.5
0.001
0.6
0.1
0.3
80
250
92
200
12
85
16000
114
500
200
More than 25% of the fuel requirements can
be satisfied by using waste tires as a secondary fuel
in furnaces with coal as a main fuel.
Used tires are waste materials with an
extremely high energetic potential, similar to that of
Powder of
animal origin
6000
<0.7
<0.1
<0.5
-
coal. The main fuel can be replaced in a 15-20%
proportion by rubber, without the burning process, the
final product or environment being affected.
The compressive strength of mortars prepared
from the cement obtained from two clinkers (coal and
D. Manea and C. Aciu / Ovidius University Annals Series: Civil Engineering 9, 59-64 (2007)
coal mixed with shredded tires) showed no
significant difference. After 28 days, the lowest
63
values were approximately 50 N/mm2, significantly
above the required limit, as Table 3 also shows.
Table 3. Comparison of the characteristics of the clinker using oil coke and used tires as a
secondary fuel (Giugliano et al., 1999)
Compressive strength (kg/cm2)
100% oil coke
16 – 36% used tires
1 day
20
19.8
2 days
30.5
30.5
28 days
54.5
54.4
Free CaO
1.1
0.9
SO3, wt%
1.8
1.9
The only effect on the quality of the clinker at
a 15-20% replacement rate of the main fuel by tirederived fuels was due to the significant increase in
zinc, resulting from the metal part of the used tires.
This caused the extension of the beginning of the
setting time from 165 minutes to 194 minutes and
of the end of the setting time from 210 minutes to
252 minutes.
Consequently, it is recommended that the
replacement of the conventional fuel content by
tire-derived fuels in cement ovens should not
exceed 25% in order to avoid the negative effects of
zinc on the setting time.
Plastic waste material is used all the more so as
there is an increasing number of sorting centers for
household waste material. As long as plastic material
can be separated from the other waste materials, it can
be burned directly in the oven, without any other
changes. Plastic materials can cover up to 50% of the
energy resulting from fossil fuels.
Profuel is a fuel prepared in Great Britain
from paper, plastic waste material, and residues
from the textile industry. These are secondary
products and are hard to recycle, the majority
ending up in dumps.
The caloric capacity of “Profuel” is similar to
that of coal and it could be used in a proportion of
40% in the preheater and 50% in the calciner.
In the majority of the European countries,
chemical waste material is burned in cement
ovens, instead of being burned in incinerators.
Industrial chemical waste materials are
increasingly used as waste oils, solvents, diluters
and petrochemical residues. In Great Britain,
“Cemfuel” is a fuel obtained by mixing several
waste materials. Its special formula includes
secondary products from the pharmaceutical and
chemical industry, solvents, dyes, oils and substances
resulting from the manufacture of inks. Cemfuel is
perfectly compatible with the burning process and does
not participate in chemical reactions that occur during
the formation of the clinker. Its production is
controlled and it has a low inflammability point, like
petrol. In the oven, it burns completely, the resulting
elements remaining in the clinker, except for mercury.
Canal mud is used as an alternative fuel
especially in Japan, Netherlands and Great Britain. In
Netherlands, dry canal mud that has an energy value of
12 kJ/kg represents 5-35% of fuels. – 275 kg mud can
replace 193 kg inferior coal or 81 kg crude oil.
Animal residues and fat are increasingly used
as an alternative fuel. In 2000, in France, 10% of the
fuel used in the majority of the ovens was of animal
origin – in total 200 kt. In 2001, an increase of up to
450 kt occurred.
The amount of animal residues that can be used
is limited by the phosphate amount that reaches the
clinker and by the chlorides that appear during
combustion. Thus, animal residues have an energy
value similar to that of brown coal. This type of fuel is
successfully used in the Retznei cement factory in
Austria, in a 15% proportion.
3.3 Influences of the use of alternative fuels
The emissions resulting from the cement industry
are controlled by rigorous laws. The use of alternative
fuels in Europe is the object of Directive 2000/76/EC
of 28 December 2000 on the burning of waste material.
CO2 emissions
The production of cement releases CO2
64
emissions due to the calcination of limestone
(54%), the burning of coal (34%) and 12% due to
emissions related to the use of electricity
(depending on the production technology – thermal
power stations). For the production of each ton of
cement, 0.83 tons CO2 are released.
Some measures for the reduction of CO2
emissions include:
- the improvement of the energy efficiency of
the production process by the use of more efficient
ovens and by their adequate maintenance and the
control of CO2;
- the replacement of fuels by alternative fuels;
- the partial replacement of limestone.
As it was shown, tires have a higher energy
content than coal, so 1 kg tire-derived fuel can
replace 1.25 kg coal. The replacement of coal by
tires does not result in a significant reduction in
CO2 emissions.
SO2 emissions
The main measures for the reduction of SO2
emissions involve the optimization of the burning
process and the insurance of the quality of raw
materials and fuel.
Tires have a sulfide content similar to that of
coal and do not usually affect SO2 emission in
cement production.
The replacement of 15-20% coal by used tires
had no significant results on SO2 emission, which
were 193 mg/m3 for coal and 187 mg/m3 for coal
and tires.
4. Conclusions
Under the impact of climatic changes, of the
continuously ascending price of fuels, of alarming
signals regarding the exhaustion of natural energy
sources, construction plays a decisive role.
An efficient cement production by the use of
waste material as an alternative fuel essentially
contributes to sustainable construction.
The cement industry offers a partial solution
to the major problem with which Romania is
confronted – waste material. Its use is a solution
with major beneficial results, which can transform
this industry from a polluting into a depolluting
industry. Some Romanian factories have already
acquired technologies that allow them to use waste
material as alternative fuels.
In 2002, Carpatcement Holding inaugurated the
first automated line in Romania that processes
alternative fuels for the production of cement, at the
Deva factory (June), and in August, a similar
installation at the Bicaz factory.
In its turn, Lafarge mounted at the Medgidia
factory an installation for the cutting of plastic
materials used as alternative fuel. The total value of the
environmental investments made by Lafarge since
1998 amounts to more than 40 million dollars. The
sum represents approximately one third of all industrial
investments made by Lafarge.
Holcim (Romania) invested in the modernization
of the cement production lines of its factories from
Câmpulung (Argeş) and Aleşd (Bihor), in order to
allow the co-processing of more than 100 waste
material types. The waste materials that can be burned
in the ovens of the Holcim cement factories (Romania)
include oil waste materials (from used oils and their
emulsions to tars and contaminated soil), plastic,
paper, cardboard, textile, leather, package waste
(industrial waste material or waste material derived
from the sorting of household waste), rubber waste
(including used tires), wood waste, organic compounds
resulting from the chemical industry, muds derived
from water treatment, etc.
5. Bibliography
[1] H. HANSEN, A. ZÖLD: Ecobuild –
Environmentally friendly construction and building.
Project co-ordinator Horsens Polytechnic, 2001.
[2] Cristian UNGUREANU – Contributii la
proiectarea constructiilor civile în cadrul conceptului
de dezvoltare durabila, Iasi, 2006
[3] George ŢĂRANU, Sesiune Nationala de
Comunicari Stiintifice Studentesti, Cluj-Napoca,
Editura U.T. PRES, 2006.
[4] SMITH I. – Co-utilisation of coal and other fuels in
cement kilns 2003.
[5] NETEA A., MANEA D. – Chimie si materiale de
constructii. Cluj-Napoca, 2004.
Volume 1, Number 9, May2007
Sustaining Systems for Underground Parking in Cluj - Napoca
a
Augustin POPA a
Nicoleta Maria ILIEŞa
Technical Univesity of Cluj - Napoca, Cluj - Napoca, 400027, Romania
__________________________________________________________________________________________
Rezumat: Problemele referitoare la parcajele din zonele centrale ale marilor oraşe reprezintă în ultimii ani o
problemă stringentă a administraţiilor locale şi bineînţeles a inginerilor. La fel ca şi alte mari oraşe şi municipiul
Cluj – Napoca se confruntă cu o asemenea problemă, care este cu atât mai delicată cu cât zona centrală este una
cu clădiri vechi sau monumente istorice. Necesităţile de parcare din zonele centrale ale municipiului Cluj Napoca
au impus realizarea unor parcaje subterane multietajate. Lucrarea va prezenta două parcaje subterane, cu două şi
respectiv trei niveluri subterane, executate în vecinătatea unor construcţii vechi, care au două şi respectiv trei
niveluri prezentând soluţiile tehnologice adoptate.
Abstract: Problems concerning parkings in central areas of large cities are a stringent problem for local
authorities and also for the building engineers. As other large cities, Cluj – Napoca has the same problem, wich
is more delicate because in the central area of the city there are a lot of old buildings or historical buildings.
Requirements of parking in the central area of Cluj Napoca imposed the achivement of multilevel underground
parkings. This paper will present two underground parkings, with two respectively three underground levels,
executed in the nearby old buildings having two respectively three levels. In this paper are presented some
technological solutions used in execution.
Keywords: parkings, old buildings, buried walls, secant piles.
__________________________________________________________________________________________
1. Introduction
The increse number of vehicles in Cluj –
Napoca imposed the necesiy of underground and
overhead parking. The most difficult problems
appear on executing underground parkings in the
central built - up areas of the city. Execution of
excavations in the vicinity of old buildings, with
high ground water table, impose some
consolidation solutions for those and the
achivement of excavation without jeopardize the
stability of the nearby construction.
This paper presents some technical solutions
used for sustainig structures for underground
multilevel parkings excavations located in the
central area of Cluj – Napoca.
and it is bordered by two buildings, withe more than 80
years old, both having G+F / S+G+F, Fig. 1.
2. Site description
Both analized works are located in the central
area of Cluj – Napoca. The first one Beyfin Hotel –
is located on the west side of Avram Iancu Square
ISSN 1584 - 5990
Fig. 1. Sections position.
66
Sustaining systems … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 65-70 (2007)
The building has a plane surface of
14,00x30,69m, having two underground floors
(parkings), ground level, attic and four floors. The
superior excavation level is +0,00, and the inferior
one -6,80, considered as level ±0,00 of the building.
Foundation soil examination has been made
by two geotechnical drillings, in the extremity of
the building and by dynamic penetration tests
(DPH). Geotechnical characteristics have been
established using penetration tests according to
EUROCODE 7 – EN 1997 - 2 (Cen, 2005a)
(Table 1).
Table 1. Stratification and geotechnical characteristics.
γ
cu
ϕ’ c’
Stratification
[kN/m3] [o] [kPa] [kPa]
Filler of ground
0,00with clay,gravel
4,00
and bricks and
17
Gravel with sand
4,00and boulder
5,00
stone, rammed
19
Gravel with sand
5,00- and boulder
10,00 stone, medium
rammed
19
10,00- Marly clay, gray,
16,00 stiff.
19.9
10
4
Table2. Stratification and geotechnical characteristics.
γ
cu
ϕ’ c’
Stratification
[kN/m3] [o] [kPa] [kPa]
Filler of
ground with
rock and
brick.
Gravel with
sand and
3,00(3,30)- boulder and
9,90(12,00) silty bond,
yellow, gray,
rammed
Marly clay,
blue,russet,
hard, with
9,90(12,00)some
14,60
decimetric
levels of
rammed sand.
0,00-3,00
(3,30)
16,9
10
4
19
34
19
10 34
80
Ground level table appear at 3,50m depth.
Underground water has chimical agresivity to
concrete: very low carbonic agresivity and very low
sulphatic agresivity.
45
3. Technical solutions [1]
34
10 34
50
Soil level 0,00 coincide to the level -0,80 of
the building. Ground water table is located at 4,50m
unto the ground level (street level).
The second work is a building for offices
located on No. 18-20 Dorobanţilor Street, having
three underground levels (parking), ground floor
level and 5 – 7 floors. The building is located in the
vicinity of some S+G / G buildings. The plane
surface is 26x45m. The superior level of excavation
is 0,00, and the inferior one is -11,10m.
Foundation soil examination has been made
by three geotechnical drillings executed until
14,00m and two dynamic penetration tests (DPH),
until 12,00m depth. Ground stratification and
design geotechnical characteristics are given into
Table 2.
Beyfin Hotel[2].
Construction of the new hotel has been made onto
an old building site (No. 3 Avram Iancu Square),
between two old building (No. 2 and No. 4 Avram Iancu
Square). Height regime of the demolished building was
S(partial)+G+F, like the nearby constructions. Buildings
were made in 1920 and they have a brick masonry with
metalic beams floor and arch bricks structure. On the
north side (No. 4) and on the south side (No. 2)
buildings have partial subsoil (Fig. 1).
Depth of foundation of nearby buildings is -2,10
- -2,70m (level ±0,00 – level of hotel ground floor).
The level of the second subsoil is -5,70m.
To sustain the excavation for both levels of
underground parking it was necessary an buried
bearing wall. Considering foundation solution for
nearby buildings, there were adopted three sections for
the execution of buried bearing walls, Fig. 2. The level
of superior part of the bearing wall was between -0,70
- -2,50m. The inferior level of the second underground
level was -5,70m. Unlike section 1, in section 1’ it has
been kept the same level for the beam – raft foundation
67
A. Popa and N. M. Ilieş / Ovidius University Annals Series: Civil Engineering 9, 65-70 (2007)
(-2,50m) and between -2,50m and -0,10m levels
excavation are sustained by a piles wall (Φ300mm).
+0.45
+0.30
+0.30
±0.00
+0.30
+0.30
-0.10
-2.30
-0.70
-2.50
-2.70(3.05)
-2.10
-2.30
-3.60
-3.00
-2.30
-2.90
-3.20
3.70
-5.70
-6.70
VAR = 8.55-13.05m
-5.70
-6.80
-6.70
Fig.2. Existing foundations consolidation details.
VAR = 8.55-13.05m
-6.80
Considering the site position, it wasn’t possible
to locate any derrick outside the building area.
Therefore, it was imposed to execute a buried bearing
wall between levels -0,70 - -2,50m and -6,80m
(excavation level). To help on excavation stability and
to reduce it’s displacements, during the excavation
execution there were utilized ground slopes near buried
wall (Fig. 3).
+0.45
+0.30
+0.30
±0.00
-3.00
-2.50
-2.70(3.05)
-2.70(3.05)
-3.00
-3.00
-3.00
Fig. 3. Excavation execution details.
-5.70
-6.70
VAR = 8.55-13.05m
-6.80
Buried walls were executed by secant piles:
primary piles, without steel, of low resistance material
and secondary piles, with resistance role, of reinforced
concrete. Piles had 620mm diameter and variable lenght
L=8,55 – 13,05m, located at 0,90m interax (Fig. 4).
68
- Anchor dead wall by welding to floor elements,
- Consolidate dead wall by welding with metalic
profiles (U), anchorated to floor elements,
- Repairing the walls by grouting, etc.,
- Executing an reinforced plastering (#Φ6/10),
anchorated by floor elements, for dead wall and
foundation, with connectors.
Offices building [3].
Fig. 4. Piles disposal.
On the inferior part it was executated an
1,00m height raft foundation where the walls were
fixed by baring of the steel and welding with steel
from secondary piles. The interior resistance
structure was made by cast in place reinforced
concrete frames. On the superior part piles were
tied by an reinforced concrete beam, section
80x100cm, with different levels for fixing concrete
diaphrgm wall (-0,70 - -2,50m).
Resistance structure for superstructure was
made by concrete diaphragm walls (18cm) which
were directed to an inferior raft foundation.
To eliminate water infiltration during
execution of vertical diaphragms it was made a
vertical hydro – insulation by pinting.
Considering poor technical state of nearby
buildings, before executing the sustaining area it
was necesary to execute some consolidation works.
There were made some interventions:
- Underpining nearby buildings foundations, on
variable heights (0,60 – 1,00m), function of
fundation quality and nearby building walls,
- Foundation consolidation by underpining and
ground ancorages (where adjacent building
foundation have fallen),
- Grouting consolidation with binding material
under existing foundations,
- Excavation consolidation to A. Iancu Square, by
an minipiles wall (Φ300mm) on 2,30m height,
Also it was executated consolidation for
adjacent buildings dead walls:
- Φ20 ancorages located along the wall or in the
areas where has been showed / have existed
vertical cracks,
Offices building (Fig. 5) have been made over an
old building site with height regime of subsoil(partial)
and ground floor. On one side there is one floor
building, having rock stone foundations, without
mortar and on the east side there is also an one floor
building. On the south side there is Dorobantilor Street
and on the north side –one floor plant and an interior
court. Considering buiding area and personnel number
had been imposed three levels undergroung parking.
Building structure is reinforced concrete frames for
3S+G+8F.
For excavation has been proposed an enclosure,
covering four sides with walls, accomplished by secant
piles Φ62cm, tied with 80x100cm reinforced concrete
beam on superior part. Inferior level for piles is 14,50m, providing fixing condition for piles into the
base layer and 1.50m fixing lenght into the gray, hard
marly clay layer.
Abutment wall was made by primary concrete piles
(Φ62cm/90cm) and secondary reinforced concrete
piles (Φ62cm/90cm). For the enclosure excavation has
been made stageed (Fig. 6):
A. Popa and N. M. Ilieş / Ovidius University Annals Series: Civil Engineering 9, 65-70 (2007)
Fig. 5. Subsoil – Offices building.
69
70
±0.00
-3.75
-3.75
-3.75
-3.75
-3.75
-7.05
-7.05
-7.05
-7.05
-11.05
-11.05
-11.05
-11.50
-12.05
Fig.6. Excavation stages.
- Stage I: excavation in large spaces, until -3,75m
level and ground evacuation by dump car;
casting floor above subsoil S2 on ground
(casting have been made on 10cm aqalization
concrete and polyethylene foil),
- Stage II: ground excavation under the floor until
-7,05m level, casting floor above subsoil S3 on
ground. Acces has been made by an acces ramp,
casted in the same stage like excavation.
Excavation has been made ensuring adjacent
ground slopes for interior walls.
- Stage III: ground excavation under the floors
until -11,05m level, casting raft foundation on
ground for subsoil S3.
- Stage IV: coating execution for piles along
subsoil perimeter and for elevations starting
subsoil S3 until subsoil S1.
- Stage V: stiffening beam and level -0,30m floor
execution.
Considering technical foundations and dead wall
state it was necessary to make some structural
interventions to consolidate old buildings:
- Underpinning rock stone foundation,
- Wall consolidation by:
•Air placed reinforced concrete (Φ5/10),
anchorated to adjacent building floor,
•Consolidation by anchoring tie – rod
located along the wall (2Φ20),
•Consolidation by metalic profiles.
4. Conclusions
Achivement of some new buildings in central
area of Cluj – Napoca is difficult because old buldings
concentration and because chaotic infrastructure.
Excavtions near existing buidings is also difficult
because they can affect old buildings stability. One
second important element is high ground water level.
To ensure stability and protection against infiltrations
it is necessary to adopt protection walls to be part of
the infrastructure resistance structure. In this paper
there are presented two execution technologies for
multilevel infrastructures, with solutions imposed by
the real site conditions.
5. Bibliografy.
[1] Ernst et Sahr, Grundbau Taschenbuch,. 1992,
Berlin.
[2] Popa A., Technical design – Beyfin Hotel, A. Iancu
Square, Cluj – Napoca, 2004.
[3] Popa A., Ilieş N., Technical design – Offices
building, orobanţilor Street, Cluj - Napoca, 2005.
The Rayleigh Quotient, the Vector Iteration With Shift and the Rayleigh Product
a
Daniela PREDAa Florin MACAVEIa
Technical University of Civil Engineering Bucharest,Bucharest, 020396,Romania
__________________________________________________________________________________________
Rezumat: Se prezintă câteva rezultate obţinute de autori în domeniul modurilor proprii de vibraţie ale sistemelor
dinamice structurale. În lucrare se îmbină catul Rayleigh, iteraţia inversă cu translaţie şi produsul Rayleigh. O
atenţie deosebită se acordă valorilor proprii multiple sau numeric egale, caracteristice structurilor spatiale. Se
propune o metodă practică pentru minimizarea produsului Rayleigh.
Abstract: This work presents some results obtained by the authors in the field of eigenvalues and eigenvectors
of the dynamic structural systems. The Rayleigh quotient, the inverse vector iteration with shift and the Rayleigh
product are joined. A particular attention is paid to multiple eigenvalues or numerically equal, characteristic to
space structural systems of the constructions. A practical way for the minimization of the Rayleigh product is
presented.
Keywords: Rayleigh quotient, vector iteration, Rayleigh product.
__________________________________________________________________________________________
1.
Introduction
In the references [1], [2], [3], the Rayleigh
quotient is studied. If an eigenvector {φ}i is
approximated with an error ε , then the error of the
corresponding eigenvalue, λ i , is of order ε 2 [1].
This approximated eigenvalue is given by the
Rayleigh quotient, according to the Rayleigh
principle regarding the stationary value of the
eigenperiod
and the eigenfrequency in the
neighbourhood of the corresponding eigenvector.
The direct vector iteration method [1], [3],
converges to the first eigenmode in a flexibility
formulation and to the last eigenmode of the
dynamic model in a stiffness formulation. The
inverse vector iteration converges to the first
eigenmode in a stiffness formulation.
The inverse iteration with shift converges to
the eigenmode with the eigenvalue nearest the shift
[1]. For a multiple eigenvalue, the convergence
occurs to a vector in the eigensubspace
corresponding to the eigenvalue.
The space steel structures [4], [5], [6], several
multiple
eigenvalues
and
corresponding
eigensubspaces may have. In this paper the sets of
the multiple eigenvalues and of the corresponding
ISSN 1584 - 5990
eigensubspaces, using the “Rayleigh product” are
analysed.
The Rayleigh product in the reference [2] was
introduced. Several developments of this scalar
function of vectorial variable, in references [3], [7]
and [8] are presented. By minimization of the
Rayleigh product, the nearest eigenvector to a given
vector can be determined. In reference [8], for this
minimization, the elimination form of the inverse is
used. In the present paper the Cholesky
decomposition is used. Moreover, a practical way
of sliding on the gradient of the Rayleigh product is
proposed.
2. The Rayleigh quotient
Lord Rayleigh published in 1877 the work
“The Theory of Sound” where he stated a principle
which was to bear his name: “ The vibration
pulsation of a conservative system is stationary in
the neighbourhood of eigenshapes”.
Let be a square, real, positive definite matrix
[A] and the associate eigenproblem
[A]{φ} = λ{φ}
(1)
72 The Rayleigh Quotient, … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 71-76 (2007)
where the matrix [A] was obtained reducing the
general eigenproblem represented by the stiffness
matrix [K] and the mass matrix [M] of the dynamic
model of the structural system. Let be
λ 1 ≤ λ 2 ≤ ... ≤ λ i ≤ ... ≤ λ n
(2)
the eigenvalues of the matrix [A] and
{φ}1 , {φ}2 ,.., {φ}i ,.., {φ}n
the corresponding
eigenvectors.
For any vector {x}, the Rayleigh quotient is:
QA =
{x}T [A ]{x}
{x}T {x}
(3)
Premultiplying both sides of Eq. (1) by transposed
vector {φ} , it follows that for
T
{x} = {φ}i
(4)
it results
QA = λi
(i= 1, 2,…n)
(5)
where
λ i = ω i2
(6)
Here ω i is the i th eigenpulsation of the structure.
The Rayleigh quotient lies between the lowest
and the highest eigenvalues of the matrix[A]:
λ1 ≤ Q A ≤ λ n
3. The inverse vector iteration with shift
The direct vector iteration applies Eq. (1):
[A]{x}(k ) = {y}(k +1) = λ(k +1) {x}(k +1)
where k is the step of iteration.
The iterative process converges towards the
maximum eigenvalue and the corresponding
eigenvector.
In the inverse vector iteration, the iterative
process converges towards the minimum
eigenvalue and the corresponding eigenvector.
A powerful procedure is the vector iteration
with shift. This procedure is based on Dirac’s
theorem [3]. Namely, if {φ} is an eigenvector of the
matrix [A] and the corresponding eigenvalue is λ ,
then {φ} is an eigenvector of the matrix [A]- μ[I ]
and the corresponding eigenvalue is λ − μ . Here
μ is shift and [I] is the unit matrix.
For the general eigenproblem the inverse
iteration is made with the matrix:
[K ] = [K ] − μ[M]
*
(9)
and the iteration converges to the eigenmode whose
eigenvalue is nearest to μ [1]. The procedure is
used for determining the eigenvector, when the
eigenvalue has been determined by another method
which produces only eigenvalues. The inverse
iteration with shift may also be used when the
computed eigenvalue is approximate. An
approximate eigenvalue can be obtained using the
Rayleigh quotient and an approximate eigenvector
{x} :
(7)
Rayleigh’s principle states that for an
eigenvector the Rayleigh quotient is stationary.
From Eq.(7) it follows [8] that for the first
eigenvector Q A is a minimum and for the last one,
a maximum.
For i ≠ 1 and i ≠ n the Rayleigh quotient is
only stationary.
(8)
μ=
{x}T [K ]{x}
{x}T [M ]{x}
(10)
For distinguishing eigenvalues, if
{x} = β{φ}i −1 + (1 − β){φ}i +1
(11)
where β is a scalar close to 0.5, that is {x} is a
combination between the eigenvectors {φ}i −1 and
{φ}i +1
D. Preda and F. Macavei/ Ovidius University Annals Series: Civil Engineering 9, 71-76 (2007)
73
, the inverse iteration with the shift (10) may
converge to the eigenvector {φ}i , even if {φ}i is
not included in the combination (11).
The same observation is valid for any pair of
different eigenvectors in Eq. (11). Also, it is valid
for more different eigenvectors.
4. Multiple eigenvalues
Numerically equal eigenvalues may occur for
space structural systems. In Fig. 1 a steel column
for electrical network is represented [4] and in Fig.
2, a storied structure.
Fig.2 Storied building
Also, each dynamic system has torsional
eigenvibrations. If two or three eigenperiods are
equal, then instead an eigenvector the dynamic
structural system has an eigensubspace, and any
non-zero vector of this subspace is an eigenvector
of the system. That is, the translations in one plane
may be coupled to the translations in the other
plane and, moreover, the torsion may be included.
Using the inverse iteration with shift equal to
the multiple eigenvalue, it is determined one
eigenvector of the subspace, but the corresponding
eigenshape is not necessary in a plane of vibrations
corresponding to the other eigenvalues or a
torsional eigenshape.Using the Rayleigh product we
can determine the nearest eigenvector to a given
vector.
5. The Rayleigh product.
The Rayleigh product. of a matrix [A] is the
product between the Rayleigh quotient of the
matrix [A] and the Rayleigh quotient of the inverse
matrix, [A ] :
−1
Fig.1. Steel column for electrical network
Each type of structure has two vertical
orthogonal planes in which the eigenvibrations are
produced.
P = Q A ⋅ Q A −1
(12)
The Rayleigh product of a matrix equals the
Rayleigh product of its inverse matrix. Therefore
the Rayleigh product characterizes a structure rather
than a matrix.
The Rayleigh product has several important
properties [2], [8]:
• For an eigenvector, the Rayleigh
product is stationary.
• For all the eigenvectors, the stationary
value of the Rayleigh product equals
the unit.
• For an eigenvector, the Rayleigh
product has a minimum value
(separation theorem). Hence, around
each eigenvector there is a concavity
of the product P.
We make here the observation that for a
multiple eigenvalue, the Rayleigh product has the
value one on the eigensubspace, except for origin.
Indeed, any non-zero vector of this subspace is an
eigenvector of the dynamic structural system.
It is named “eigendepression i ” the zone of the
unit radius hipersphere around the eigenvector {φ}i ,
which has the property that, starting from any its
points, by the Rayleigh product minimization one
arrives to the eigenvector {φ}i
. The
eigendepression includes the concavity of that
eigenvector.
The following notations will be used:
(13)
a = {x} [A ]{x}
T
(14)
b = {x} [B ]{x}
(15)
c = {x} {x}
(16)
T
{g} of the vectors {x} and grad P, so that
c=1
(19)
Instead the vector grad P, it may be considered
a half of it:
{g} = b[A ]{x}+ a[B]{x}− 2P{x}
The Rayleigh product P becomes
ab
P= 2
(17)
c
and its gradient is:
2
4ab
grad P = 2 (b[A ]{x}+ a[B ]{x}) − 3 {x} (18)
c
c
(20)
Let be “k” a step of iteration. The expression of
the vector {x} will be:
{x}(k +1) = {x}
(k )
{}
− αk g
where α k is a positive constant.
Starting from the unit vector
following operations are performed:
•
[B] = [A ]−1
{}
One may work with the unit vectors x and
•
6. A practical procedure
T
It is not necessary the explicit expression of the
inverse matrix, [B].We only multiply this matrix by
the vector {x}.
•
•
(21)
{x}( ) ,
k
the
the constants a and b (Eqs. 14 and 15)
and the product P( Eq. 17) are
determined;
the vector {g} (Eq. 20) and the unit
{}
vector g are computed;
the constant α k is modiefied until- on
the support of the vector grad P- the
minimum value of P is obtained (Eq.
21);
(k +1)
the unit vector x
is determined.
{}
A simple way of determining the solution
α k consists in increasing this constant in steps of
equal sizes, sufficiently small to ensure the desired
accuracy.
But a fast way is to return to the previous
value of the constant if the solution α k is
surpassed and the step is diminished, ten times, for
example (Fig.3).
D. Preda and F. Macavei/ Ovidius University Annals Series: Civil Engineering 9, 71-76 (2007)
75
Fig. 3 Determining the constant α k
The problem is to compute [B]{x}, where [B]
is the inverse of the matrix [A]. In order to do this,
it will be used Cholesky decomposition of the
matrix [A].:
[A] = [T]T [T]
[T]
(22)
where [T] is an upper- triangular matrix and
Since [T]
T
{ }
a 12
t 11
……………………………….
a12 = t 11 t 12 hence t 12 =
Generally, the following recurrence relations
are obtained:
0 ,5
(23)
(24)
[T]{z} = {z * }
(28)
is a low-triangular matrix, the
7. Conclusions
•
•
•
Let be
that is
and
unknowns z may be computed by substitution,
starting with the first equation. Since[T] is an
upper- triangular matrix, the unknowns {z} may be
computed by substitution, too, starting with the last
equation.
From the relations (23) and (24) it results that
if [A] is a banded matrix, then [T] is also a banded
matrix with the same bandwidth. This fact is
important for storage requirement.
2
a 11 = t 11
hence t 11 = a11
{z} = [B]{x} = [A]−1 {x}
(27)
*
T
j−1
⎛
⎞
t ij = ⎜ a ij − ∑ t ki t kj ⎟ / t ii , (j>i)
k =1
⎝
⎠
[T]T [T]{z} = {x}
[T]T {z * }= {x}
is its transpose.
The elements of the triangular matrix [T] can
be determined in terms of the initial matrix [A]
elements, identifying the result of the product
j−1
⎡
2 ⎤
t ii = ⎢a ii − ∑ t ki
⎥
k =1
⎣
⎦
(26)
The system of equations (27) may be solved
in two stages:
T
[T] [T] element by element, namely
[A]{z} = {x}
or
(25)
It may outline the following conclusions:
The inverse iteration with shift, using the
Rayleigh quotient, converges to the
eigenmode with the eigenvalue nearest the
shift.
Starting from a given vector, the nearest
eigenvector is determined by Rayleigh
product minimization.
For multiple eigenvalues of the space
structural dynamic system, using Rayleigh
product, the nearest eigenshape to a given
shape can be determined.
8. References
[1] Bathe K.I., Wilson E.L. Numerical
Methods in Finite Element Analysis, 1976, PrenticeHall, Englewood Cliffs, New Jersey.
[2]Macavei F., A Method for Eigenvectors
Separation, Buletinul Inst. Politehnic Iasi, 1988,
Tomul XXVI (XXX), fasc. 1-2, pag. 23-27.
[3]Macavei F., Poterasu V.F. , Complemente
de dinamica structurilor, 1994, Ed. Virginia, Iasi.
[4] Dalban C., Juncan N., Serbescu C., Varga
A., Dima S., Constructii metalice, 1983, Ed.
Didactica si Pedagogica, Bucuresti.
[5]Chesaru E., Preda D., Expertizarea si
consolidarea structurilor metalice,1998, Ed.
CONSPRESS, Bucuresti.
[6] Preda D., Elemente structurale din otel.
Studiu- sinteza in domeniul stabilitatii generale a
elementelor comprimate si incovoiate, 2007, Ed.
Tehnica, Bucuresti.
[7] Macavei F., Procedeu numeric pentru
determinarea independenta a oricarui vector
propriu de vibratie, 1998, Al VI-lea Simpozion
National de Informatica in Constructii, Timisoara
[8]Macavei
F.,
Eigendepressions
of
Structures, 1996, Third European Conference on
Structural Dynamics, EURODYN ’96, pag. 409413, Florence, Italy.
Calculation of deformation estimated value for protection harbor construction to
seismic application shaped through stationary random process
Isabella STAN a
Dragos VINTILA b
Sport Department of Constantza, Constantza, 900669, Romania
b
”Ovidius” University of Constantza, Constantza, 900524, Romania
__________________________________________________________________________________________
a
Rezumat:
Scopul acestui studiu de caz este de a dezvolta procedee de analiză bazate pe o simulare stohastică a acceleraţiei
seismice a terenului. Această acceleraţie se modelează ca proces aleatoriu staţionar (zgomot alb sau zgomot alb
filtrat). Modelul dinamic utilizat pentru structură este determinist.
Abstract:
The purpose of this case study is to develop analyze processes based on a stochastic simulation of the seismic
acceleration of the soil. This acceleration it’s shaped as a random stationary process (white noise or filtered
white noise). For the structure the dynamic model used is necessitarian.
Keywords: stochastic process, seismic movement, harbor constructions
__________________________________________________________________________________________
1.
Introduction
The most frequently used stochastic
representation of the seismic movement of the soil
it’s based on the potential spectral density of the
seismic acceleration and on a equivalent period of
the earthquake, accordingly to the powerful part of
soil movement. This kind of wording problem,
based on a necessitarian dynamic system submitted
to a random model of the excitation, allows the
processes development to obtain the response
statistic
parameters,
such
as
variance,
autocorrelation function or potential spectral
density. Once obtained these parameters, ought to
formulate the existing relationships between them and
the extreme response of the system. This analysis
requires to solve the problem from the response first
phase through one limit, which is defined as the
searched extreme value.
It’s been developed analysis processes based
on a stochastic simulation for the soil seismic
acceleration. This acceleration it’s shaped as random
stationary process (white noise or filtered white noise).
For the structure the dynamic model used is
necessitarian. It’s developed the theory for single
freedom degree systems, which allows the calculation
of it’s estimated extreme response. [1,4]
Figure 1 – Single freedom degree model submitted to a random seismic excitation [1]
ISSN 1584 - 5990
78 Calculation of deformation…/ Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 77-80 (2007)
2.
Response stochastic spectrum
The way to obtain response stochastic
spectrum, which will be analyzed therefore, it’s
based on the response estimated extreme values,
concluded for single dynamic freedom degree
systems, submitted to seismic excitation shaped as
stationary stochastic process.
The main advantage of this process type to
define an action consist in manufacture suitable
design spectrums, based on realistic hypothesis,
general accepted, regarding the soil seismic
movement. As an additionally advantage it can be
mentioned the exigent of less process entrance
dates. These dates are available in most seismic
zones, including the ones with less seismic
recordings.
In case of a seismic excitation shaped as a
stationary stochastic process, te process time that is
significant seismic movement time it is a great
influence parameter of the results. So, spectral
ordinates are xe , to distinguish their dependence
the filter
average frequency.
To calculate the response estimated
extreme value of a single freedom degree system
submitted to a seismic excitation shaped as a
stationary stochastic process, we elaborated a
calculation program named STATRAN [1],
through C++ programming language, transcript in
Linux operating system.
3. Calculation of deformation estimated value
for protection harbor construction to seismic
application
In this case study we proposed for
stationary stochastic process with a potential
spectral density of 1500 gal2/Hz.
The structure has been reduced to a single
dynamic freedom degree structure, with proper
periods determinate through three analysis models
and with fraction values from damping.
We considered for the filter
parameter
ωg
1
H1 g
2
the next
values
which
characterize
it:
= 4.6rad / s and ν g1 = 0.6 , meanwhile for
2
are
ω g = 100.0rad / s
2
and
ν g = 0.3 . For the signal we admit a period of 120 s
2
in the end of which the process become really
stationary.
For STATRAN entrance dates we obtained the
estimated extreme values of deformation as given in
Tables 1. [2]
Tables 1
Model A
Estimated
Fraction
extreme
Graphic
from
values of
T[s]
critical
deformations
damping
xe [cm]
1
2
on process time. These can be calculated with:
⎛ θ ⎞
xe = σ x 2 ln⎜ te m ⎟ , where θ m - the process
⎝ π ⎠
H2g
3
0.05
0.10
0.15
2.604
3.68
2.61
2.13
0.05
0.10
0.15
1.733
3.34
2.31
1.85
0.05
0.10
0.15
1.605
3.23
2.22
1.77
Model B
Graphic
1
2
3
T[s]
Estimated
extreme
values of
deformations
xe [cm]
0.05
0.10
0.15
2.646
3.69
2.62
2.14
0.05
0.10
0.15
2.320
3.61
2.54
2.07
0.05
0.10
0.15
2.079
3.53
2.47
2.00
Fraction
from
critical
damping
I. Stan and D.Vintilă / Ovidius University Annals Series: Civil Engineering 9, 77-80 (2007)
Graphic
1
2
3
Fraction
from
critical
damping
Model C
Estimated
extreme
values of
T[s]
deformations
xe [cm]
0.05
0.10
0.15
2.364
3.62
2.56
2.08
0.05
0.10
0.15
1.949
3.48
2.42
1.95
0.05
0.10
0.15
1.789
3.38
2.34
1.88
Model A
Model B
79
In figure 2 we graphical represented the
variation of deformation estimated extreme value in
accordance with stationary stochastic process period
considered as a model of seismic signal.
We can observe that, as the proper period of
the structure is lower, so is the estimated extreme value
of deformation for the same fraction values from
critical damping.
80 Calculation of deformation…/ Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 77-80 (2007)
Model C
4. Conclusions:
These results led to identify some
advantages in response calculations to seismic
applications of protection harbor constructions,
such as:
- Usage of response spectrum, which represent a
customary way to define a soil seismic action for
the structures analysis, allows the describes of the
most important response characteristics, where the
excitation time history it’s useless;
- The response spectrum may be modified so it can
include the soil local conditions, when the
excitation process details are unknown;
- The use of calculation program allows to find out
the extreme estimated values of the response
movement for different dynamic characteristics
(proper periods) and for different values of
fractions from critical damping;
- The elaborated calculation program may be
modified so it can allow the calculation of
stochastic response
accelerations.
spectrum
in
velocities
and
5. References
[1] Barbat, A. H., Canet, J. M., „Estructuras sometidas
a acciones sismicas”, 2nd Edicion, CIMNE,
Barcelona, 1994.
[2] Breabăn, V., Pascale, D., Popa, M., „Dynamic
Modal Analysis of Harbor Protection Rock–Fill
Breakwaters”, Ovidius University Annals of
Constructions, Constanţa, 2002.
[3] Penzien, J., Liu, S.C., „Nondeterministic analysis
of nonlinear structures subjected to earthquake
excitations”, Proceeding of the Fourth World
Conference on Earthquake Engineering”, Santiago,
Chile, 1973 July 2005.
[4] Sandi, H., „Elemente de Dinamica Structurilor”,
Editura Tehnică, Bucureşti, 1983
Reactive centrifugal rotor – the analytical study of two applications
a
Victor BENCHE a
Radu ŢÂRULECU a
Stelian ŢÂRULECU a
“Transilvania” University , Eroilor Boulevardl, 29, Braşov, 500036, Romania
__________________________________________________________________________________________
Rezumat: În lucrare se prezintă principiul constructiv şi funcţional şi rezultatele unor calcule privind un rotor
fluidic rotativ reactiv, reprezentând o construcţie simplificată, fiabilă, cu preţ de cost redus, cu o execuţie nu prea
pretenţioasă, pentru puteri mici, în condiţiile valorificării unor energii fluidice disponibile, reziduale, stocate (aer
comprimat, abur, gaze arse, lichide sub presiune).Rotorul poate fi utilizat ca motor pentru antrenarea unor
cilindri rotitori din compunerea unor turbine de vânt, ca generator de vârtej inelar din compunerea unor eoliene,
exhaustoare – ventejectoare cu inel de vârtej depresiv etc.
Abstract: In the paper it is presented the constructive and functional principle and the results of some calculus
about a reactive fluidic centrifugal rotor, representing a simplified, reliable construction, with a low cost price
and with a simple execution, for small powers, in the conditions of some stocked residual energies valorization
(compressed air, steam, burned gases, under pressure liquids).The rotor can be used as an engine for the driving
of some revolving cylinders from some wind turbines, and as a generator of ring-shaped swirl for wind turbines
or for exhausters – wind ejectors with inner depressive swirl etc.
Keywords: Rotor, wind turbine, flow rate.
__________________________________________________________________________________________
1. Introduction
The authors have designed (summary) a
fluidic rotary reactive rotor, with a simplified
construction, for very small powers, for the
valorization of some fluidic residual energies
(compressed air, steam, burned gases, under
pressure liquids). As an engine it can be used for
some rotary pistons driving from wind turbines
(based on the Magnus effect); for a depressive
cylindrical drum driving inside an original
exhauster [1], [3]; and like a generator of ringshaped swirl inside on some concentrators for wind
turbines or for exhausters – wind ejectors with inner
depressive swirl. The specified applications are
original contributions of the authors [1], [2], [3],
[4], who know the principle of functioning for a
centrifugal filter presented in [5] and [6].
& n and overpressure
fluid, with the weight rate m
pm, through an inner pipe system Ci, with an
adjustment and closing valve Ra and some tubes of
reaction Tr solider with the rotor, which is spinning
around of a tubular axle As. The rotary cylinder Cr
is solider with the engine and sustained by the
central axle.
2. The centrifugal fluidic reactive engine
The centrifugal fluidic reactive engine, showed
in fig.1, is formed of a rotor Rr, feed with motor
ISSN 1584 - 5990
Fig.1. The centrifugal fluidic reactive engine
84 Reactive centrifugal rotor… / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 83-86 (2007)
After the launch from the tubes of reaction, the
motor fluid is took in the shell Cs and exhausted
through the tap Re (the liquids are returned into a
tank, and the gases can’t be recycled).
The reactive centrifugal rotor (with two
symmetrical tubes of reaction) represents an inertial
reference system in rotation, where we attach the
reference system 0xyz (fig.2). The tube of reaction
is formed from two by-passes at an angle of 90o.
For the flowing through the tube of reaction is
applying the Bernoulli equation for rotary systems
with the hydraulic local resistance coefficient ξ.
Fig.2. The tube of reaction
ω 2 ⋅ r22
pm
+
=
2g
ρm ⋅ g
2
⎡
⎛A ⎞ ⎤ 2
⎢1 + ξ − ⎜ 2 ⎟ ⎥ ⋅ w (1)
⎜ A ⎟ ⎥ 2g
⎢
⎝ 1⎠ ⎦
⎣
(
)]
M = ρm ⋅ Qm ⋅ r2 ⋅ w ⋅ sinα − r22 − r12 [N.m](2)
the total weight rate beaing:
& m = ρ m ⋅ Q m = ρ m ⋅ A 2 ⋅ w ⋅ z [kg/s]
m
πD 3 L
Mf = η
ω [N.m]
2j
(4)
The limit maxim rotary speed is obtaining from
M=Mf+Mcil.
The system from two equations, Bernoulli
theorem (1) and Euler torque theorem (2), helped
by the relations (3) and (4), represents a non-linear
system that permits the compute of two unknown
measures w and ω, that being the flow rate through
engine and the maxim rotary speed. In another way
is computed ωmax, and assess a wanted value
ω<ωmax and it’s computed the necessary pm and
& m.
m
A simplified, estimated model of computing
neglect the total friction torque and consider that
the maxim rotary speed its limited only of the
flowing resistance ξ through the tubes of reaction
and installation of motor fluid adding.
The equation system became:
2
⎡
⎛ A2 ⎞ ⎤
pm
2 2
⎟⎟ ⎥ ,
2
+ ω ⋅ r2 = ⎢1 + ξ − ⎜⎜
A
ρm
⎢
⎝ 1 ⎠ ⎥⎦
⎣
(
(3)
The moment M it’s consumed for the friction
surmounting from the rotor bearings Mf and
between the rotary cylinder and air Mcil, that one
having a small value.
If we note with D the diameter and with L the
total length of the two axles, with the bearing
clearance j and the coefficient of dynamic viscosity
Where sin α =
R
R 2 + l 22
And r1 = R − l1 , r2 =
(1’)
)
(2’)
,
(5)
r2 ⋅ w ⋅ sin α = ω r22 − r12 ,
The moment of reaction of z tubes is:
[
η of the lubricant, the friction moment is conform
to the Newton law for the viscous friction:
R 2 + l 22 , where from
can be computed w and ωmax.
The calculi, in the design of the engine for one
opportunity, are combining with the availabilities
(the motor fluidic source), with different
restrictions and options, following from successive
iterations.
There are defying:
- Reactive fluidic power N r = M ⋅ ω [W]
(6)
V. BENCHE et al. / Ovidius University Annals Series: Civil Engineering 9, 83-86 (2007)
- Motor fluidic power N m = p m ⋅ Q m [W] (7)
- Engine fluidic efficiency, degree of valorize at the
engine power, degree of conversion of the motor
fluidic power in reactive fluidic power.
ηf =
Nr
M⋅ω
= i din ⋅ i cin
=
Nm pm ⋅ Qm
(8)
There are noted the dimensional indicators:
dynamic idin, as a ratio of the dynamic measures M
and pm and cinematic as a ratio of the cinematic
measures ω and Qm. The energetic optimization
analysis have on the base η f → max ,
i din → 1 , i cin → 1 .
3. Numerical calculus results for the centrifugal
fluidic reactive engine
It was considered the compressed air as motor
fluid. The tube of reaction formed of two by-passes
having l1=l2=25mm, ended with a nozzle,
A1=81,5mm2, A2=Aaj.m=40mm2. Radius: R=0,5m,
r1=0,475m, r2≈0,5m, sinα≈1. Sum of the hydraulic
local resistance coefficients (pipe with valve,
interior pipes, pipe bend, and nozzle) is ξ=3.
85
R=17,3mm; for oil, with ρm=850kg/m3, R=18,8mm,
the centrifuging effect being considerable increase.
In fig.3 is showed also the consumed liquid curve
Qm=(0÷307)l/min for z=2 tubes of reaction.
In the rotary speed limit nmax=5000rot/min, for
z=2, are obtained: maximum reactive power
Nr,max=61,2W, maximum necessary motor power
Nm,max=214 W and fluidic efficiency ηf=0,35.
Table 2. Functioning parameters for the the
centrifugal fluidic reactive engine
n
500 1000 2000 3000
4000
5000
52,5 105
210
314
420
525
ω
w
6,6
14
28
41,5
55,5
64
Pcentr[Pa]
41,5 1660 6650 15000 26000 41500
Qair[m3/h]
1,9
4
8
12
16
18,5
Qliquid[l/min] 31,7 66,7 133
200
266
307
4. The reactive rotor used as a generator of ringshaped swirl
The reactive rotor used as a generator of ringshaped swirl for the wind ejector – exhauster is
showed in fig.4. There are supplementary noted: T
– fixed tube of circular section with inner radius rT;
Aasp – exhauster (aspirator); Cf – fuselage central
body, fixed, with radius r0; Cip – inner chamber of
pressure, fixed with the rotor; vj – ring-shaped
swirl. The motor nozzle Aj.m, shaped, has a
rectangular orifice of launching. The study of a
wind ejector with depressive ring-shaped swirl,
assisted by the Coanda effect, has be made by the
authors and presented in [6].
Fig.3. The characteristic curves
In fig.3 are showed the characteristic curves
obtained for values of pm=(0÷4,15).104Pa. It can be
obtain the rotary speed n=(0÷5000)rot/min for
Qaer=(0÷18,5)m3/h. The dimensions of the reactive
engine can be reduced using liquids as motor fluid,
there obtaining: for water, with ρm=1000kg/m3,
Fig.4. The reactive rotor used as a generator of
ring-shaped swirl
The circular motion have place with the speed
(velocity) w at radius rT, where from results a
depression
in
the
cross
86 Reactive centrifugal rotor… / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 83-86 (2007)
(
2
2
)
section A asp = π rT − r0 , square descendent
with radius (after a parabolic law) [6] of media
value:
p d ,med =
3
p d,max [Pa]
4
with p d ,max =
(9)
ρm ⋅ w 2
[Pa]
2
(10)
And the sucked flow rate:
Q asp = μ asp ⋅ A asp ⋅ 2
p d,med
ρ asp
[m3/s],(11)
μasp being the flow rate coefficient of the exhauster.
The fluidic induction coefficient, of driving
and ejection is:
u=
ρ asp ⋅ Q asp
&m
m
,(12)
And the fluidic efficiency of the ejector is:
ηej =
N asp
Nm
=
Q asp ⋅
ρ asp
2
2
⋅ v asp
&m
m
⋅ pm
ρm
=
2
v asp
⋅ u (13)
2p m
ρm
The definition (13) can be written under the
form:
2
⎛ v asp ⎞
⎟ ⋅ u , with vm=w
ηej = ⎜⎜
⎟
w
⎠
⎝
(14)
4. Numerical calculus results for the reactive
rotor
It is considered r2=rT=150mm, r0=50mm,
Aasp=6,28.10-2m2, r2=rT-l1=125mm, z=2 tubes of
reaction, compressed air.
It is results w=31,6m/s, pd,med=452Pa,
pm=6420Pa=650mm.col.water (value which can be
obtained with a centrifugal blower of high pressure,
for the pneumatic transport, or an air blower). We
also
obtain:
vasp=6,4m/s,
Qasp=24m3/min,
& m = 3,38kg / min , Nasp=105W, Nm=302W,
m
u=8,5, ηej=0,35.
Table 2. Functioning parameters for the reactive
rotor
500 1000 2000 3000 4000 5000 n [rot/min]
178 159
127 39,6 118
165
Nreactive=Nr
220 185
147
50
127
214
Nm
0,81 0,86 0,86 0,79 0,93 0,77 ηf=Nreact/Nm
5. References
[1] – Benche, V., Benche, L., - Ejector cu tambur
depresiv, Brevet OSIM RO88769;
[2] – Benche, V., Benche, L., - Eoliană turbionară
lentă, Universitatea Transilvania Braşov, Buletinul
Comisiei Inginerilor si Tehnicienilor, Brasov, 1988,
p. 11...14;
[3] – Benche, V., Benche, L., - Exhaustor cu
tambur depresiv, Buletinul Comisiei Inginerilor si
Tehnicienilor, Brasov, 1988, p. 39...44;
[4] – Benche, V., Ungureanu, B.V., - Eoliană
turbionară lentă cu cilindri rotitori cu efecte
combinate, Conferinţa Naţională de Termotehnică,
Galaţi, mai 2001;
[5] –Hara, V., Stan, M., - Mecanica fluidelor şi
maşini hidropneumatice, Editura TIPARG, Pitesti
2002;
[6] –Hara, V., Stan, M., - Mecanica fluidelor şi
elemente de acţionări hidropneumatice. Îndrumar
de laborator, Editura Universităţii din Pitesti 2005;
[7] – Benche, V., Ungureanu, B.V., - Ventejector
Coandă interior cu vârtej inelar.
Analogical electro hydrodynamic research on installations for
launch subsonic constant density jets
a
Victor BENCHE a
Virgil-Barbu UNGUREANU a*
__________________________________________________________________________________________
Rezumat: Se abordează energetica instalaţiilor de producere (lansare) a jeturilor fluide izodense subsonice libere
neînecate în baza unei analogii electrohidrodinamice, autorii propunând formule şi indicatori globali şi zonali. Se
creează o bază analitică ilustrată printr-o aplicaţie numerică de proiectare care permite calculul, estimarea
performanţelor, studii comparate, opţiuni, optimizări constructive şi funcţionale.
Abstract: The paper presents some energetic considerations on installations for constant density, subsonic and
free fluid jets launching, based on an electro-hydrodynamic analogy. The authors propose relations and global or
partial indicators. It is created analytical basis illustrated by a design numeric application that permits the
calculus, performances estimation, compared studies, options, constructive and functional optimisations.
Keywords: Hydraulic systems, fluid jets, electrohydrodynamic analogy.
__________________________________________________________________________________________
1. Introduction
There are presented some energetic
considerations on installations for free fluid jets
launching, based on an electro-hydrodynamic
analogy [1]…[3] and some contributions to the
economical calculus for pressurized fluid pipes
[5]…[7], the dynamic definition of the closing and
control valves [8] and there are proposed global and
partial indicators. It is created analytical basis
illustrated by a design numeric application that
permits the calculus, performances estimation,
compared studies, options, constructive and
functional optimisations.
Q = μ ⋅ Ao ⋅ 2 ⋅
ISSN 1584 - 5990
(1)
in which: Δp is the static pressure difference in
installation, being a promoter factor of the
movement; v apr - the velocity in the conduit with
the section area A ; Ao - geometric section of the
nozzle orifice, where the initial speed of the jet is
vo .
The flow coefficient μ can be defined:
2. Basic relations
An installation for launch a fluid jet includes
the source (generator, reservoir), a conduit for
transport having apparatuses of circuit, a fitting for
closing and control and the convergent-divergent
nozzle, converting the potential energy of pressure
in kinetic (dynamic) energy.
For constant density fluids ( ρ = const . ) the
flow rate can be written:
Δp
2
+ vapr
ρ
μ=
1
α tr + ζ inst.ech.
,
(2)
in which:
ζ instl .ech. = ζ tr.ech. + ζ arm. + Csec t. ⋅ ζ aj ,(3)
with:
88
Analogical electro hydro… / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 87-92 (2007)
ζ tr.ech. = ∑ ζ tr + λ ⋅
l
4 ⋅ Rh
and:
2
⎛ A ⎞
⎟⎟ .
Csec t. = ⎜⎜
⎝ ϕc ⋅ Ao ⎠
U = R ⋅ Ic ,
(4)
(5)
in which U is the electric voltage, I c - current
strength and R - electric resistance.
There are analogous the following pair
quantities:
N h ≈ N el , Δp ≈ U , Q ≈ I c
There are used notations: α - coefficient of
Coriolis, depending from the flow regime in the pipe
used for transport; ζ i (i = equivalent transport,
control fitting, convergent nozzle) - coefficient of
hydraulic local resistance ; Rh - hydraulic radius of
from which appear the necessity to define the
equivalent hydraulic resistance of the hydraulic
conductor R* ≈ R .
Thus, it can express the hydraulic power,
analogous to relation (8):
the transport conduit (particularly case 4 ⋅ Rh = d ,
N h = R * ⋅Q 2 [ W ]
for circular pipes A = π ⋅ d 2 4 ); λ - friction factor
in the conduit having the length l ; ϕc - coefficient
of contraction, ϕc = A jet Ao ≤ 1 .
(
)
Δp = R * ⋅Q .
(11)
Using the above relations it is defined:
p p = Δp = ρgz +
ρQ 2
2 ⋅ A2
[Pa ]
(6)
and hydraulic power of the pump:
N hydr. = Δp ⋅ Q [W ] ,
(7)
R* = k a ⋅
pump.
Expression (3) can have particularly aspects by
suppression two terms, which permitting the
particular study of the three zones of energetic
interest: pipe for transport, ( ζ inslt.ech = ζ tr.ech. ),
the control and closing fitting ( ζ arm. ) and the
convergent nozzle ( C m ⋅ ζ aj )
For an electric conductor is known the Joule’s
law for the dissipated power:
N el = U ⋅ I c = R ⋅ I c2 [W ]
(8)
⎡ N ⋅s⎤
m&
⎢
⎥,
2 ⋅ Ao2 ⎣ m 5 ⎦
(12)
& = ρ ⋅ Q is the mass flow rate and k a is
in which m
an original analogous dimensionless constant [3]:
ka =
z being the difference of level between nozzle and
and Ohm’s law:
(10)
and the drop pressure analogously to relation (9):
It is defined the output pressure of the pump:
+ (α tr + ζ instl.ech. ) ⋅
(9)
1
μ2
,
(13)
particular for different types of movements.
The equivalent hydraulic resistance, in the
expression (12) presents a non convenient structure,
presenting explicitly a linear depending of mass flow
rate:
R* = Cm ⋅ m& ,
(14)
in which:
Cm =
ka
2 Ac2
[m− 4 ].
(15)
V. Benche and V. B. Ungureanu / Ovidius University Annals Series: Civil Engineering 9, 87-92 (2007)
2
In the relation (1) the term vapr expressing
the kinetic energy of approach of the fluid (in pipe)
from the nozzle for jet launch presents values less in
comparison with the potential term (pressure
2 << 2 ⋅ Δp ρ that it can be
specific energy): vapr
2 ≅ 0 in technical applications.
neglected vapr
It can point out the hydraulic resistance with
help of main factors by introducing the criteria of
Reynolds (flow regime):
Re =
ρ⋅v⋅d
,
η
2 η ⋅ Re 2 η ⋅ Re
= ⋅
.
R* = k a
π
π μ2 ⋅ d 3
d3
(17)
(18)
and the impulse force:
= 2 ⋅ Ao ⋅
2
= 2 Ao ⋅ pdyn [N ].
(19)
It is expressed below the correspondent
correlation with R * .
It can obtain:
R* = Ci ⋅
I mp
Q
(
,
and noting the coefficient of proportionality:
)
R* = Ci ⋅ ρ ⋅ v jet ,
(22)
(ρ ⋅ v jet ) being the mass flow rate.
The relation (20) can be used that an
unpublished definition for the impulse forces:
I mp =
1
⋅ R * ⋅Q
Ci
(20’)
interpretable in the case of correspondent devices
that generates and utilise fluid jets in dynamic
purpose (actives or reactive).
There are defined two relations for conversion
the specific potential energy in specific kinetic
energy, for a unitary flow rate:
pdyn = k e ⋅ Δp
(23)
edyn = k e ⋅ e pot [m]
(24)
and
in which:
I mp = m& ⋅ v jet = ρ ⋅ Q ⋅ v jet =
ρv 2jet
(21)
3. Conversion coefficients
In case of fluid jets a practical application
importance has the dynamic impact, expressed by
the dynamic pressure (of stand, impact):
ρ 2
⋅ v jet [Pa ] .
2
[ ]
ka
m−2 ,
2 ⋅ Ao
relation (20) can be arranged in the form:
(16)
in which it is considered the circular section, average
velocity in the section v = Q A , η - fluid
dynamic coefficient of viscosity.
It is obtained a new expression:
pdyn =
Ci =
89
(20)
ke =
1
ka
(25)
is a coefficient of proportionality, dimensionless,
under unity, proposed, original.
The coefficient ke can be used like an
indicator of energetic conversion having the
signification of conversion efficiency, taking in
consideration specific hydraulic energy loss by
hydraulic resistance.
It is remarked that the overall specific energy
of a fluid flow in a section is defined by:
90
e= z+
p v2
+
= e pot + ekin ,
ρg 2 g
• increase of the flow section area of the pipe
(26)
the first two components: geometric height z and
the pressure height p (ρ ⋅ g ) being static
(potential) and the 3rd, v 2 (2 ⋅ g ) being kinetic
(dynamic).
The fluid flow power in section is:
N h = G& ⋅ e = m& ge = ρgQe [W ] .
(27)
& g is the gravimetric flow
in which G& = ρgQ = m
rate.
In the case of constant density fluids (non
compressible), the case of liquids, gases and vapours
in industrial installation spreads with technical
velocities relatively small (under 50 m/s), variations
of potential energy of position and of kinetic energy
are less sometimes negligible versus the variation of
potential energy of pressure, preponderant being the
pressure potential energy Δp (ρg ) , that justifies
relation (7).
The first component of the hydraulic power is
the pressure - the dynamic component (that
generates the force), the second being cinematic
(volume flow-rate, Q ). It is interpreted pressure that
a specific hydraulic power (for a unit of flow rate).
Relations (25) and (24) are specific hydraulic
power balances, relation (23) for a unit volume flow
rate Q and relation (24) for a unit gravity flow-rate
G& . In the case of steady state flow of constant
density fluids, flow rates appear in both terms of
equations and they are simplified.
The energetic optimisation analytic sustained
by the present study, can be obtained by adequate
measures just in the design phase but also by
interventions in the exploitation phase.
It is desired the minimisation of the hydraulic
resistance R * by:
&;
• minimisation of the mass flow-rate m
however, generally this is imposed or also, the jet
velocity and the fluid, this fact permitting to
consider some options for the flow section area Ao ;
A , the influence being overwhelming (diameter is
at numerator and has the exponent 4);
It is pursued to minimise the coefficient k a
and to approach of 1 the energetic coefficient k e ,
thus the maximisation of the flow coefficient
( μ → 1 ). This appears at the 2nd power in the
denominator of relation (13), with sub unitary value,
thus, its influence is important.
In the case of relations (2)…(5) it is pursued
minimisation of expressions (3) and (4), thus
λ → min ,
l → min ,
d → great value ,
∑ ζ → min .
About the Coriolis coefficient, in laminar flow
α = 2 and in turbulent flow, α = 1.03...1.01 . It is
desired to obtain the smooth turbulent regime when
value of α approach to unity and λ is minim
(determined for example with Blasius correlation).
The present study can facilitate solution for
two categories of problems: design and exploitation.
In the design case it is imposed the fluid and
the launch speed; it can be realised a combined
optimisation ( k a → min , k e → 1 ). The algorithm
can be iterative (successive approximations).
In the case of exploitation problems, the
system is known and it is desired to obtain the
correlation launch velocity – flow – rate – pressure hydraulic resistance.
It can utilise the relation (11) too, but arranged
in the form:
Δp ⎡ m 3 ⎤
Q=
⎢
⎥ (11’)
R* ⎢ s ⎥
⎣
⎦
It can be emphasised with help of expressions
or R * the main factors and adequate measures.
4. Application
It is exemplified a design case. It is imposed to
obtain a free water jet having: Q = 10 l s with
v jet = 50 m s . For beginning, it can use an
adduction conduit of 2” (50mm), a valve with
ζ arm. min = 4 and a convergent nozzle for jet
launch having ζ aj = 2...3 .
V. Benche and V. B. Ungureanu / Ovidius University Annals Series: Civil Engineering 9, 87-92 (2007)
From
calculus
results:
m& = 10 kg s ,
A = 2 ⋅10 −3 m 2 ,
Ao = 2 ⋅10 −4 m 2 ,
v = 5.1 m s , fully roughness turbulent flow regime
(
)
(
)
( α ≅ 1 , λ ≅ 0.02 , ρ ⋅ v jet = 5 ⋅10 4 kg m 2 ⋅ s ,
pdin = 7.5 bar , I mp = 500 N .
In the case of a known schema of installation
with bends, contractions and high ( z > 0 ),
emplacement of the water pump, results
ζ instl.ech. = 50 .
From calculus results: μ = 0.14 , k a = 0.51 ,
k e = 1.96 ⋅10 −2 ,
R* = 6.37 ⋅ 109 N ⋅ s m 5 ,
C m = 6.37 ⋅ 108 m −4 and Δp = 392 bar which
corresponds to a hydraulic power N h = 382 kW .
The pump pressure and power are very high,
however realisable with cu plunger pumps. But it
can not utilise a current industrial pipe of 2”
diameter; it is imposed to realise a high thickness of
the wall pipe.
It is necessary to study an optimised variant.
There are accepted measures: decreases the
installation length (approach pump from the nozzle);
using a smooth pipe having a less value of λ ;
decrease hydraulic local resistances and reduce to
minimum the apparatus of circuit; using a high
performance control valve and convergent nozzle
(having small local loss coefficient).
The installation equivalent hydraulic resistance
reduces considerable R* = 7.45 ⋅ 108 Ns m 5 for
ζ instl.ech. = 5 (at the technical limits).
It
is
calculated:
C m = 7.45 ⋅ 10 7 m −4 ,
μ = 0.41 , k a = 5.95 . The energetic coefficient is
considerable improved: k e = 0.168 .
Δp = 44.6 bar
and
It
results:
N h = 44.6 kW acceptable values, which can be
realised with normal pumps.
5. Conclusions
This energetic analysis method can be used for
installations in that flow constant density fluid,
91
being used for subsonic and free jets launching. The
method is based on an electro-hydrodynamic
analogy. There are proposed global and partial
indicators, being created analytical basics for an
energetic analysis. The method is illustrated by a
design numeric application that permits: calculus,
performances estimation, compared studies, options,
constructive and functional optimisations.
6. References
[*] [email protected].
[1] Benche V., Craciun O.M., Ungureanu V.B.
Electrodynamic analogy regarding the hydraulic
rezistence and the debit module in the effluent flows.
Proceedings
of
International
Conference
TEHNONAV 2004, Ovidius University of
Constanta, Faculty of Mechanical engineering, 27th30th May 2004, ISSN 1223-7221.
[2] Benche, V., Ungureanu, V.B. Consecinţe şi
interpretări energetice la o analogie electrohidrodinamică.
Revista
Recent
(Universitatea
Transilvania din Braşov), vol. 3. (2002), nr. 1 (6),
mai 2002, p. 14…17, ISSN 1582-0246.
[3] Benche, V., Ungureanu, V.B. Noi definiţii şi
corelaţii fluidoenergetice. Revista RECENT,
(Universitatea Transilvania din Braşov), an 5 (2004),
nr. 1 (10), martie 2004, ISSN 1582-0246, p. 22…25.
[4] Benche, V., Ungureanu, V.B., Crăciun, O.M.
Contribuţii la studiul analitic optimizator al
instalaţiilor de transport fluide energetice. Susţinută
la Conferinţa naţională de energetică industrială,
Milenium, CNEI 2000 şi publicată în volumul
"Perspectivele energeticii în pragul mileniului III şi
impactul acesteia asupra dezvoltării umane", Bacău,
10-11 nov. 2000, p. 106...109, ISBN 973-99703-4-6.
[5] Benche V., Ungureanu V.B. O abordare
economică a conductelor sub presiune din punct de
vedere al debitului optim. A Treia Conferinţă a
Hidoenergeticienilor din România « Dorin Pavel »,
Universitatea Politehnica din Bucureşti, Facultatea
de Energetică, Catedra de Hidraulică şi Maşini
Hidraulice, 28-28 mai 2004., p. 33…38.
[6] Benche, V., Ungureanu,V.B. Contributions to
the analytical study of the improvement of carrying
installations for gaseous fluids. Buletinul Institutului
Politehnic Iaşi, editat de Universitatea Tehnică
Gheorghe Asachi, Iaşi, Tom XLV (IL), Fasc. 5C,
1999, p. 45...48, ISSN 0258-9109.
92
[7] Benche, V., Ungureanu, V.B. Contributions to
the Generalization of the Economical Calculus for
Pressurized Fluid Pipes. Ovidius University Annals
of Constructions, Vol. I, Number 3,4, April, 2002, p.
229…232. ISSN 1223-7221.
[8] Benche, V., Ungureanu, V.B. Contributions to
the Dynamic Definition of the Closing and Control
Valves for Fluids in Pressurized Pipes. Proceedings
of the Science Conference with International
Participation Inter-Ing 2003 “Petru Maior”
University, Faculty of Engineering, Târgu Mureş, 67 November 2003, vol. I, p. 39…44, ISBN 9738084-82-2.
The Safety of Concrete Structures from the Water Supply System, Undermined by the
Errors and Careless in Design and Execution
Olimpia BLAGOI a Bogdan PATRAS a Maricel GEORGESCU b Marinela BARBUTA a
a
Technical University “Gh. Asachi” Iassy, Iassy, 700050, Romania
b
S.C. APA GRUP Botosani, Romania
__________________________________________________________________________________________
Rezumat: Funcţionarea îndelungată şi continuă afectează construcţiile din sistemul de alimentare cu apă prin
condiţiile tehnologice, condiţiile de mediu, calitatea exploatării şi din cauza modului de proiectare şi execuţie.
Autorii prezintă evoluţia şi starea construcţiilor de beton dintr-un sistem de alimentare cu apă cu longevitate
mare, cu studiu de caz la sistemul regional de alimentare cu apă Botoşani. S-a identificat că eroarea inginerească
este cauza primară a degradărilor, în urma procesului de inventariere, analiza şi evaluare a condiţiilor specifice în
care au funcţionat şi funcţionează fiecare tip de construcţie din beton armat. Principalele cauze prezentate sunt:
nerespectarea prevederilor tehnice de turnare a betonului; erorile de proiectare şi de execuţie; nerespectarea
tehnologiei de montaj, a tehnologiei de etanşare, a tehnologiei de finisare; viciile tehnologice iniţiale.
Abstract: The constructions with long-time and continuous working are degraded by the specific technological
conditions, environmental conditions and by the quality of exploitation.
The authors present the evolution and state of concrete constructions from the water supply systems with high
longevity, and a case study on the Botosani water supply system. After reviewing, analysing and evaluating the
specific operating conditions for each type of reinforced concrete structure, the authors have tried to find out
whether the engineering error is the first cause of the degradations. The main presented causes are: nonobservance of technical stipulations concerning the concrete pouring; design and execution errors; nonobservance of montage technology, of tightness technology, of finishing technology; initial technological vices.
Keywords: engineering errors, design errors, concrete pouring, ex-filtrations.
__________________________________________________________________________________________
1. Introduction
The increasing of water consumption and the
danger of pollution of water sources are preoccupying
the specialists and the authorities from the domain for
ensuring a normal functioning of hydraulic systems of
water supply. The majority of constructions that form
these systems are realized of concrete. The concrete is
subjected to degradations due to specific technological
conditions, environmental conditions and quality of
exploitation, that action independent or synergetic,
also to natural aging processes. The water supply
systems must have a big longevity, because of that the
preliminary studies, projection and execution must be
extremely rigorous. The engineering errors lead to
financial and material losses, dissatisfaction of
beneficiary, environment degradation, even the
collapse of the construction or human life losses.
ISSN 1584 - 5990
These errors constitute the origin of causal chain of
degradations.
The problem has been studied during 15 years on
reinforced concrete constructions from a regional
system of water supply, very complex, executed and
developed gradually on a period of over 100 years.
The evolution of materials, of design, prospecting
and technological conditions during one century had
left the mark on the functional state of constructions.
2. Non-respecting
concrete pouring
of
technical
provisions
of
The development of Bucecea treatment plant is
beginning in 1968-1972; the plant treats the water
captured from the Bucecea accumulation lake, on the
Siret River.
94
The safety of … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 93-98 (2007)
The pumping station is built between the 500
m3 storing basin serving the filters executed in the
first stage and the 1,500 m3 basin that serves the
filters executed in the second and third stage of
developing. Because of the construction deficiencies,
the wall of the 1,500 m3 basin has numerous zones of
ex-filtrations. The water infiltrated in the pumps hall
makes dangerous the electrical force installation and
the stability of construction. This fact imposes the
daily evacuation of infiltrated water using the
dewatering pumps, therefore supplementary costs.
The walls and the floor were poured without
concrete vibration and presented areas with
segregations, unprotected reinforcements and
without protection plaster.
The filters from stages II, III are placed in the
same hall with the first, having in common the
gallery for the hydraulic equipment of filters, the
1,500 m3 basin that collects the filtrated water etc.
The pouring of concrete from the walls and floor of
pipes gallery was done with special deficiencies.
The concrete was not vibrated, there are
segregations, and the reinforcements are
discovered. Through the wall of 1,500 m3 reservoir
there are strong ex-filtrations (Fig. 1).
The wet acidic atmosphere has excessively
corroded the reinforcements from the walls and floor
of the filters hall (Fig. 2). The discovered
reinforcement had swelled and had exfoliated, thus
they do not ensure the strength of concrete members
and there is the danger of collapse (Fig. 3).
Fig. 2. Concrete segregation, corrosion and
swelling of reinforcement.
(Technological gallery from the filters station,
stages II-III Bucecea)
Fig. 1. Wall with points of ex-filtration. Detail.
(Reservoir of 1,500 m3)
Fig. 3. Segregation in slab, steel corrosion.
(Technological gallery from the filters station,
stages II-III Bucecea)
O. Blăgoi et. al. / Ovidius University Annals Series: Civil Engineering 9, 93-98 (2007)
The no. 4 reservoir of 10,000 m3, placed in
Catamaresti, is a cylindrical construction, overground, of pre-stressed concrete, having D=45 m
and H= 9 m.
The foundation raft is monolith and the floor
is made of prefabricate caissons, supported at
exterior on the reservoir wall and in interior on
concentrically circular beams, built on the superior
ends of supporting columns from inside the
construction.
The foundation raft was neglectful executed
and so important water infiltrations are producing
in the adjacent valve chamber (Fig. 4), from where
it must periodically been evacuated.
95
So, the clarifier with mud recirculation for Q=500
l/s, made of prefabricated concrete units, with D=34 m
and H=6.7 m present serious non-observances of
concrete pouring technology. Parts of columns and walls
present concrete segregation, cracks in prefabricated
units, exfoliations of interior waterproof plaster.
Fig. 5 Floor with corroded steel
(Reservoir no. 2 of 10,000 m3)
3. Errors of designing
Fig. 4. Ex-filtration zone in valve chamber.
(Reservoir no. 2 of 10,000 m3)
The floor is affected very much by the wet
atmosphere, charged with chloride vapours used for
water disinfection. The neglectful pouring of floor
caissons, with concrete segregation and not
ensuring the concrete cover layer for the
reinforcement had resulted in high steel corrosion
and swelling. The reinforcement has become
crushed and exfoliates (Fig. 5). The caissons
without inferior rebar can collapse, especially in
winter under the snow load.
The technological errors continue in the
development
stage
(1987-1991),
without
considering any previous experience.
The period 1968-1972 is the first stage of
Bucecea treatment plant developing that began to use
captured water from the Bucecea accumulation lake on
Siret River.
The penstock with Dn 500 mm and L=19 km
realized of steel, transports water from the Bucecea
station to the 5,000 m3 reservoir from Catamaresti.
There were not complete geological and hydrological
studies for the pipe route that passes through
aggressive soils. The chemical action of long duration
had perforated the pipe in a lot of sections.
The operating interruptions and repeated repairs
produce supplementary costs and dissatisfaction of
beneficiary.
The errors of designing and superficiality of
preliminary studies had continued in the next stages.
Thus, in the period of extension of water supply
system Botosani (1987-1991), the raw water pipe of
Dn 1,200 mm was made of PREMO type tubes (50%)
and steel (50%). Geological and hydrological studies
96
were insufficient so that the hillside pressure near
the Sitna River, the variable level of river waters
and the slipping of the right side of the Sitna River
on 500 m length were not considered in design.
water will be treated with chlorine for disinfection were
not considered, thus ignoring the provisions from the
“Code of protection for concrete, reinforced concrete
and pre-stressed concrete” C21/85 and C 130/78. The
internal protection plaster was not designed as anti-acid
type, but for normal conditions of exploitation, at neutral
pH, the mortar was not prepared with cement that resists
at chemical aggressively, the used aggregates had no
anti-corrosion properties. In consequence, after 5 years
of operating, first cracks occurred in the inner plaster of
the reservoir. These cracks were the origin of the exfiltrations. In the present 80% from the prefabricated
units are cracks. The vertical cracks have 0.5 ÷ 3 m
lengths (Fig. 7) and are located in the middle third that
corresponds to the medium level of the water from the
reservoir. The cracks occurred in the convex part of
prefabricated units and to the joints among units. In the
road towards exterior, the water washes the metallic
tendons used for post-tensioning of the reservoir.
Fig. 6. River bank caving near a pipe support
The consequences were the collapse of a pipe
support in aerial zone, the danger of loosing the
stability of underground pipes Dn 1,000 mm and
Dn 500 mm parallel with the first (Fig. 6). There
were registered horizontal displacements of 25 ÷ 30
cm, vertical displacements of 3 ÷ 7 cm, the
displacement speed of 0.75 ÷ 1 cm/day, the stability
coefficients have unlimited values, the depth of
slipping plane is 5 ÷ 6 m.
The clarifier with mud recirculation was
designed
neglecting
the
eutrophication
phenomenon of the storage lake water during the
summer. The consequences are gravely and
irreparable because the eutrophication imposes
water pre-chlorination and so the increase of
chlorine concentration from the water intensifies
the corrosion of settling tanks.
The no. 4 reservoir of 10,000 m3, cylindrical
construction with D=45 m and H=9 m was executed
from 68 prefabricated reinforced concrete units,
placed on the perimeter of a monolith reinforced
concrete foundation raft. The tightness was made by
rubber strip. To the reservoir designing, the fact that
Fig. 7. Interior cracks. Detail.
(Reservoir no. 4 of 10,000 m3 Catamarasti)
The pre-existed corrosion state of the pretensioning tendons is aggravated in time. The
tensioned cables are at risk to collapse, at the
maximum level of water from the reservoir or at the
seismic action, leading to irreparable damages of the
reservoir and putting in danger the life of inhabitants
from that area.
O. Blăgoi et. al. / Ovidius University Annals Series: Civil Engineering 9, 93-98 (2007)
The waste pipe from the treatment station
Catamaresti is seriously affected by the designing
errors. The fact that the trace crosses agricultural
terrains was not took into account, so the vibrations
and loads given by the agricultural machines will
produce a dynamic fatigue in the pipe.
The dynamic and supplementary loads that
were not considered in design, produced the
cracking and crumbling of the pipe vault, collapse
and washing of the soil on 200 m length in the
vicinity of the railway. In consequence, the stability
of railway bridge is jeopardizing and the big debit
of wastewater intensely degraded the environment
(Fig. 8).
97
degradations and defects from this reservoir are caused
principally by numerous errors of execution. Until the
placement in 1993, the metallic cables were deposited 2
years in the air without any protection against corrosion.
In consequence, they were corroded in the moment of
placement.
5. Non-respecting of mounting technology
In the period 1972-1975, the raw water pipe Dn
1,000 mm and L=20 km was made of steel tubes (30%)
and PREMO type tubes (70%).
The non-respecting of mounting technology led
to important consequences in service. The sand layer
on which the pipe had to be placed was not entirely
made. Though in appearance minor, this technological
negligence had the following consequences
accompanied by big material losses: unequal
settlements, wresting from joints of PREMO tubes,
breaking of welding joints of steel tubes.
The isolation of steel was badly executed, thus
the chemical aggression of the soil corroded the pipe.
6. Initial technological vices
Fig. 8. Environment degradation by neglecting
of dynamic loads on the wastewater pipe of
plain concrete Dn 800 mm
In the period 1987-1991 of extension of Water
Supply from Botosani, the raw water pipe Dn 1,200
mm in PREMO concrete tubes (50%) and steel (50%)
was executed.
The concrete section with L=12 km was bad built
and so 8 PREMO tubes were replaced because of
irreparable deterioration.
4. Errors of execution
The pumping station of drinking water in the
no. 3 and no. 4 reservoirs of 10,000 m3 functions
continuously of about 20 years. The construction
has an underground level with the concrete walls,
where are placed the pumps and a ground level of
masonry where are placed the supervision platform.
The underground part was not well isolated and the
concrete was negligible poured. In consequence,
the walls have numerous defects through which the
rainwater passes, degrading the interior plaster.
The no. 4 storing reservoir with the volume of
10,000 m3 is a cylindrical construction, posttensioned with D=45 m and H=9 m. The
Fig. 9. Neglecting of soil chemical aggression
(Tendon collapse to PREMO tube Dn 1,200 mm)
98
cover was insufficient. As it follows the reinforcement
were in direct contact with the aggressive soil (Fig. 9).
The long soil action had corroded the transversal pretensioned tendons and so finally collapsed (Fig. 10).
7. Non-respecting of tightness technology
To the clarifier with mud recirculation, made of
prefabricated concrete units with D=34 m and H=6.7
m, the tightness among the units was not executed.
Consequently, there are grave ex-filtrations with
damages in winter (Fig. 11).
8. Non-respecting of finishing technology
Fig. 10. Absence of concrete cover
(Tendon corrosion in PREMO Dn 1,200 mm pipe)
To the clarifier with mud recirculation, after the
concrete pouring, there were not executed finishing
works on exterior and the defects of concrete pouring
were not repaired. Consequently, the water losses from
the clarifier are important.
9. Observations
The study was opportune timely because on its
base there are adopted feed-before measures
(prevention, protection and repair).
Near the monitoring data there is an important
archive of photo-documents from which some are
presented in this paper.
References
Fig. 11 Non-respecting of tightness technology.
(Clarifier with ex-filtration points, winter)
It has observed that all replaced tubes had
pouring vices that means: in exterior the mortar
[1] Blagoi O., Georgescu M., et al., The Efficiency of
Aluminium Sulphate on Small and Medium Water
Treatment Plants. 2001, Buletinul Institutului
Politehnic din Iasi, Tom XLVII (LI), Fasc. 1-4
Hidrotehnica, pag.193–201
[2] Georgescu, M., Studii si cercetari privind siguranta
in exploatare a constructiilor din beton din sistemul
hidrotehnic de asigurare cu apa a localitatilor
(Botosani). 2006, Ph.D Thesis, Universitatea Tehnica
„Gh. Asachi” Iasi
[3] Patras M., Patras B.M., Siguranta constructiilor
hidrotehnice din beton armat exploatate timp
indelungat. 2002, Buletinul Institutului Politehnic din
Iasi, Tom XILVII (IL), Fasc. 5, pag. 75-82
Modeling, Simulation and Regulation of an Industrial Installation Intended for Field
Irrigation Using Attenuant Wastewater
a
Adrian BOLMA a
Marian DORDESCU a
National Company of Land Reclamatin RA , Dobrogea, Constanta, Romania
__________________________________________________________________________________________
Rezumat: In această lucrare, este prezentată o abordare multicriteriaiă a tehnicilor de conducere automată a
unor instalaţii industriale de irigare a terenurilor agricole folosind apele uzate în diluţie, cu efecte deosebit
pozitive în rezultatele economice ale întregii amenajări de irigaţii. Alegerea soluţiei de conducere automată cu
sistem multivarialbil cu regulatoare independente (SMRI) este rezultatul etapelor de analiză, modelare şi
simulare a proceselor hidrodinamice ce au loc în instalaţia de irigare pe fiecare echipament în parte şi în
întregul ei. Alegerea regulatoarelor este determinată de specificitatea fiecărei variabile supuse controlului,
astfel încât să contribuie la îmbunătăţirea exploatării echipamentelor instalaţiei de irigare şi totodată să
constituie un important punct de plecare pentru alegerea celor mai bune metode de modernizare a amenajărilor
de irigaţii. Lucrarea prezintă o analiză şi oferă o soluţie de conducere automată a instalaţiei de irigare cu apă
uzată în diluţie.
Abstract: In this study, it is presented a multicriterial approach of the automatic management techniques of
industrial installations for fields irrigation by using attenuant wastewater. This has an extremely positive effect
on the economical results of the entire irrigation equipment. Choosing the automatic management by a
multivariable system with independent regulators (MSIR) is the result of several stages of analysis, modelling
and simulation of hydrodynamic processes that take place within the irrigation installation on each equipment
and in its integrity. The regulators choice is established by the specificity of every variable subject to control, so
that it contributes to a better exploitation of the irrigation installation’s equipments and at the same time to
represent an important start point for choosing the best methods for modernization of the irrigation equipments.
The study exposes an analysis and offers a solution of automatic management of the installation of irrigation
using attenuant wastewater.
Keywords: hydraulic system, wastewater, multivariable regulation system.
__________________________________________________________________________________________
1.Introduction
The technological installation mentioned
before is intended for the distribution of wastewater
on fields through the irrigation system. The water
comes from a pig breeding farm near Constanta.
The research made by experts had shown
that wastewater in dilution with clear water can be
used directly to irrigate the fields. The irrigation
system using wastewater in dilution was
conceived and technically implemented so that:
•It ensures the achievement of technical-economical
parameters registered on the hydraulic installation
•It ensures that the hydraulic installation of transport
and distribution of wastewater will run for a long
time; it also ensures the achievement of high
efficiency.
ISSN 1584 - 5990
•It enhances the fruitfulness level of the irrigated soils
and as a result, the yield.
The main purpose of this project was to identify
the ways in which can be ensured high reliableness and
long-lasting efficiency.
The implementation of a command and automatic
control system of the hydrodynamic processes that
appear in the transport and distribution of wastewater
installation has as a main goal the efficiency of
exploitation by:
•ensuring hydraulic conditions that are necessary for
the running.
•perfectioning the functioning power of the hydraulic
installation achieving and maintaining the water quality
parameters through controlled dilution of wastewater.
100
Modeling, Simulation … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 99-106 (2007)
Wastewater properties after decantation in the
physical stage are specified in table 1. They will
Nr.crt.
1
2
3
4
5
6
7
8
9
Parameters
pH
Rude suspension
Fix residue
Total nitrate
Total phosphorus
Total potassium
Ammonium
Nitrate
Carbolic
2.The experiment
1.The modellation of the irrigation installation
and the selection of the regulator
The modellation of the hydraulic installation,
change after the dilution with conventionally clear
water.
Table 1. Wastewater properties
UM
Range of variation
6,8…8,0
mg/l
1900…2100
mg/l
1500…3250
mg/l
270…620
mg/l
25…95
mg/l
180…260
mg/l
172…185
mg/l
0,55…0,575
mg/l
0,02…0,03
shown in Fig. 1 and modellation equivalence sche-me
in Fig.2, intended for the irrigation process of fields
aims to establish a characteristic equation useful for
setting up an automatic control management system.
Fig. 1 Hydraulic installation scheme
A. Bolma and M. Dordescu / Ovidius University Annals Series: Civil Engineering 9, 99-106 (2007)
101
TC – concentration traductor
TDP – pressure and debit traductor
SPAC – conventionally clear water pumping unit
SPP- pumping unit and pressurising
RDIS – water distribution network on the wet field
Fig.2 Modellation equivalence scheme
In the final stage of the installation it is
required a debit Qr and pressure pr, both necessary
for the irrigation of the fields.
On this installation, we have the equations:
hydraulic balance Qu + Qc = Qn , where Qn = Qr
massic balance
QuCu + QcCc = QnCn , where Cn,
the concentration of the mix obtained in the mixing
tank must be maintained within the limits
mentioned in table 1. For the regulation a nd
maintainance of the concentration, the conventionally clear water debit shall be modified.
The adjustments of the installation are made
through:
1.debit (flow) adjustments (Qc) to maintain the concentration (Cc)within the parameters
2.adjustments to the variable speed system that
carries the variable debit pump to ensure the debit
and pressure required by the distribution system.
The principles of mathematical modelling:
1.in a physical system analysis it is required the
formation of a conditioned system: the number of the
equation and the number of X’s are equal
2.the value of the physical constants in the system
must be correct and justified physically
The pressure in the recipient is constantly
maintained at the level of the clear water circuit.
In the hydraulic installation we have:
pc<pu – wastewater is injected in the mixing recipients
pa<pc – the pressure from the mixing tank is smaller
than the pressureof the injected clear water
pa<pu – this pressure imbalance will allow the injection
of the wastewater
Due to the different pressure values, the
following can be said:
Q u = K 1 p u − p a for the wastewater debit
102
Qc = K 2
p c − p a for conventionally clear
water debit
Qn = K 3
p a − p n for mixed water debit
K1, K2, K3 are debit constants of the induction apertures.
The equation of debit variation is influenced by
the variation of the pressure in time.
If the division of debits in the mixing recipient is
taken in consideration, the following equation can be
written:
Fig.3 Calculation scheme
A dp a
= Qu + Qc − Qn
γ a dt
(1)
Upsetting debit is : Q r = K 4
Where γa is the specific weight of the
wastewater and clear water mix expressed in the
following equation:
⎛
γ n = γ u C + γ c (1 − C ) = γ c ⎜⎜1 +
γ c (1 + aC )
⎝
Δp – KQn2, where Δp is contribution of pressure pump.
γu −γc ⎞
C ⎟⎟ =
γc
⎠
Qu, Qc, Qa – are time functions and A is constant
– the transversal section of the mixing recipient.
Therefore, the following can be said:
A dp a
= Q u + Q c − Q n = f (t ) ,function
γ a dt
conti-nnue in time.
There can be a slow variation for pressure pr =
pr(t) and also Qn = Qn(t). The pressure is : pr = pa +
p r − p at
If in equation 1 the debits are replaced, the
following is obtained:
A dpa
= K1 pu − pa + K2 pc − pa −K3 pa − pn
γa dt
or if Qr is replaced :
A dpa
=K1 pu −pa +K2 pc −pa −K4 pr −pat ,
γa dt
in which the law of variation of the lifting pressure in
time can be introduced. For example, it is considered
the necessity of decreasing the lifting pressure and
implicitly the debit in time (at daytime the debit is
bigger and in the evening it can be continously
decreased until shut-down). This will lead to a
continous reduction of energy, therefore to an efficient
exploitation.
In equation 1 the specific weight of the mix can
be inserted and the result is a differential equation
that connects the three elements: the debit, the
concentration and the pressure. It obtains:
103
dp a
1
= γ c (1 + aC ) .
Q u + Q c − Q n dt
Fig.4 Functional scheme for regulation system
To obtain more command measures necessary
to achieve the action of automatic adjustment of the
multivariable technological installation it is
obligatory that the automatic regulator is
multivariable, meaning that he must receive more
error measures, reshaping them after fixed laws,
and to ensure the achievement of more command
measures.
The achievement of more error measures
requires the evaluation of more reference measures
and the comparison of these with the final measures
transmitted to the comparison elements through
several principal negative reactions.
The results is a multivariable adjustment system
which has multiple transmition channels.
2. The numeric simulation of the multivariable
system
The result of the matrix method is the numeric
simulation of the analysed system diagram using the
simulation method Matlab-Simulink, present in fig. 5.
The simulation data can be found in the
programme date.m.
104
Fig.5 Numeric simulation scheme using Simulink
3. Results and interpretations
The results of the numeric simulation are
represented in fig. 6 and 7.
Variatia presiunii ( pr ) in conducta de irigare
2
1.8
1.4
1.2
1
0.8
0.6
0.4
Parametrii regulator presiune
Krp=20
Tip=0,1
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Timp (secunde)
Fig.6 Variation of pressure pr in irrigation tube
Variatia concentratiei ( Cn ) in rezervorul de amestecare
140
C o n c e n tra tia C n a a m e s te c u lu i (m g /l)
P re s iu n e a p r (m H 2 O )
1.6
120
100
80
60
40
Parametrii regulator concentratie
Krc=35
Tic=1,6
20
0
0
5
10
15
20
Timp (secunde)
Fig.7 Variation of concentration Cn in mixed tank
25
105
106
4. Conclusions:
•By adjusting the accord parameters of the
automatic regulators, a stabile reserve can be
ensured
•The performances of the multivariable system
depend on the measures of the accord parameters.
By choosing correctly these measures it is possible
to maintain the performances within the required
limits
•The simulation diagram has a general character
and it can be used for every adjustment structure
belonging to this category, mentioning that the
automatic process has to be appropriately modelled.
•The implementation of the adjustment structure
with numeric process regulators allows the
distribution of the management and supervising
functions for other measures in the process.
5. Bibliography
[1] Robescu, Dan., Lanyi, Sz., Robescu, Diana,
Constantinescu, I., Verestoy, A., Wastewater
treatment. Technologies, installations and equipment.
Editura tehnică, Bucureşti, 2001.
[2] Robescu, Dan., Lanyi, Sz., Robescu, Diana,
Verestoy, A., Fiabilitatea proceselor,instalaţiilor şi
echipamentelor pentru tratarea şi epurarea apelor.
Editura tehnică, Bucureşti, 2003.
[3] Robescu, Diana, Robescu, Dan. On the advanced
wastewater treatment. Al VIII-lea Simpozion
Tehnologii, instalaţii şi echipamente pentru
îmbunătăţirea calităţii mediului, 9-12 noiembrie 1999.
[4] Cox, Earl Fuzzy logic for business and industry.
Charles River Media, Rockland, Mass., 1995.
Cussler, E.L. Diffusion. Mass transfer in fluid systems.
Cambridge University Press, 1984.
Phased Execution of the Coastal Protection Works in the Southern Area of the
Romanian seashore
Romeo CIORTANa
I.P.T.A.N.A. Bucharest, Bucharest, 010867, Romania
__________________________________________________________________________________________
a
Rezumat: In prezent litoralul romanesc al Marii Negre cunoaste un intens proces de eroziune din cauza scaderii
aportului de nisip transportat de curentul N-S, a prezentei unor amenajari hidrotehnice, a poluarii etc. Pentru
stoparea eroziunii sunt necesare lucrari care trebuiesc concepute diferit in lungul litoralului. Se au in vedere si
solutii de etapizare a acestora pentru a esalona efortul finaciar si a adapta solutiile dunctie de necesitati.
Abstract: Presently, the Romanian shore of the Black Sea is subject to an intense erosion process due to the
reduction of the sand input drifted by the N-S current, to the presence of some hydrotechnical facilities, to
pollution, etc. For stopping the erosion process, certain works that should be conceived in different ways have to
be executed along the shore. There are also considered certain solutions for phasing such works, in order to
space out the financial effort and to adopt the measures as they become necessary.
Keywords: coastal erosion, groins, sand fill.
__________________________________________________________________________________________
1. Introduction
The Romanian shore of the Black Sea
stretches over a length of approx. 240 km, from the
Chilia Channel of the Danube, in the North, to the
Bulgarian border, in the South.
From the geomorphologic and genetic points
of view, two areas can be distinguished:
the area north of the Midia Cape, belonging
to the Danube Delta and the Razelm – Sinoe
lagoon complex, which is 165 km long. This
area is represented by low littoral strips
overtopped by the sea waves during storms,
which consist of sand of Danubian origin and
organogeneous material (shell fragments).
The area south of the Midia Cape, up to
Vama Veche, which is 75 km long and includes
two subunits: Midia Cape – Singol Cape and
Singol Cape – Vama Veche. This area is
characterised by the presence of cliffs,
alternating with littoral strips that separate the
sea from the seaside lakes. The source of
formation of these littoral strips and beaches is
prevailingly
oraganogeneous,
other
less
significant sources being cliffs’ erosion, coastal
drift and erosion of sea bottom rocks.
ISSN 1584 - 5990
Presently the entire Romanian shore of the
Black Sea is subject to an intense and continuous
process of degradation by marine erosion, which
has been noticed on about 60-70 % out of the
shoreline length. (fig. 1)
108
Phased execution of … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 107-112 (2007)
The marine erosion processes are also
favoured by the global climatic changes, the sea
level alteration and the intensification of the total
wave and current energy.
Many countries consider the problem of the
shore erosion processes to be of national
importance. Beach erosion results in territory
losses, it compromises the coastal ecosystems and
the social and economical value of the tourist
coastal area, inflicting important losses to the
national economy and a huge loss to the future
generations.
2. The coastal erosion along the shoreline
In the north side, the shoreline has drawn back
on variable distances from one shore sector to
another, with values of up to 10 m/year. On certain
sections, where the littoral strip is narrower, the sea
covers the shore entirely during storms, and
sometimes it creates breaches, connecting the sea
with the seaside lakes and affecting the specific
ecosystems of such lakes.
Southwards, the surface water infiltrations
and the sea action have generated landslides and
important damages to the cliffs, in some sections a
draw back of the coast line of approx. 0.5 m/year
has been noticed, this process being an intermittent
one.
The negative evolution of the Romanian
shore, in the sense of erosion intensification, is
caused by the unbalance created by natural and
artificial causes regarding the available quantity of
sediments in the seashore area in relation to the
wave and current energy.
The unbalance was created by some human
activities, and particularly by:
the anti-erosion works, breakwaters and
outflow take-offs executed in the countries
located in the Danube basin, which have resulted
in a reduction of the overall drift rate in the
Danube by more than 50%; the Danube is the
main source for the alluviums supplied to the
seashore;
the changes occurred during the last century
in the Danube Delta, which have altered the
conditions of river drift towards the sea, and
particularly the regulation of the Sulina Channel.
In relation to this objective, two breakwaters
were executed in order to protect the fairway at
the outlet into the sea, which gradually acquired
a length of 7.5 km, thus relocating offward the
drift unloading point, so that the not all the
alluviums return to the alongshore drift circuit;
these breakwaters and the bar that is formed
constitute an obstacle for the northerly drift,
particularly that of the Chilia Channel;
the construction of protection breakwaters
in the ports of Midia, Constanta and Mangalia,
which fragmented the shoreline, and the
configuration of which, although intended to
produce the least negative impact on the coastal
area, intercepts and directs offwards the already
diminished alluvium flow that should be drifted
by waves and currents along the shore;
the extraction of sand from the bed of the
Danube and its tributaries and even from the
beaches, in order to use it as construction
material;
- the polluting effect of certain activities.
3. The integrated management of the coastal
area
Nationally, the management of the Romanian
coastal area is mainly governed by the Law of
Waters (no. 107/1996) the Environmental Law (no.
137/1995) the Law for Institution of the “Danube
Delta” Biosphere Reservation (no. 82/1993) and the
Emergency Ordinance regarding the integrated
management of the coastal area (no. 202/2002).
The Government Decision no. 981/1998
regarding the institution of the National Company
“Apele Române” (“The Romanian Waters”) S.A.,
provides, inter alia, that “The surface waters
belonging to the public domain, including their
minor beds, the lakes’ banks and basins, their
natural resources and the exploitable energetic
potential, the surface waters, the ground waters the
sea cliffs and beaches” are leased to the National
Company “Apele Române” S.A.
The Black Sea shore will witness the
development of the tourism, but it also includes
industrial zones and, for this reason, there is
necessary to elaborate a unique, integrated
prospective development plan.
The coastal erosion has to be considered in
the global context of an integrated management and
R. Ciortan / Ovidius University Annals Series: Civil Engineering 9, 107-112 (2007)
109
the strategy has to be organized consequently,
because the erosion process will be still as active.
For this reason, the strategy has to get through
several steps, namely:
identifying the problems of the coastal area
by evaluating the evolution trends of each
geomorphological component;
quantifying the erosion causes;
establishing a long-term prospective
programme regarding the protection and
rehabilitation actions;
phasing the measures to be taken in order to
achieve the proposed objectives;
actions’ planning by the relevant
administrative bodies;
implementing the actions; at the
implementation level, the decision making
factors have to apply the strategy established for
the coastal area, elaborating the actual action and
investment plans.
The coastal area integrated management
(CAIM) is a dynamic, continuous and interactive
process, conceived to promote the sustainable
management of the coastal area. It seeks to balance
on the long term the benefits of the economical
development and the human exploitation, the
benefits from protecting, maintaining and
rehabilitating the coastal area, from mitigating the
losses related to human lives, properties and public
facilities, while maintaining the natural soil water
and air conditions.
CAIM is based on the co-operation and
participation of all interested parties, on the
evaluation of the social objects in the relevant
coastal area and on the initiation of the necessary
actions to achieve the objectives.
The “Dobrogea – Littoral” Water Directorate
has initiated and implemented such an integrated
management with the assistance of the Dutch
company Haskoning.
At national level, there has been provided the
institution of a Committee charged with the
supervision of the seashore development, as shown
on the informative chart below.
4. Projects for stopping the coastal erosion
In order to reduce and even remove the
negative effects of the coastal erosion on the
Romanian shore of the Black Sea, different studies
and execution projects must be accomplished, as
follows:
studying the driving to the South of the
inferior delta of the Chilia Channel and the
measures for alluviums’ passing to the South;
quantifying the effect of the Sulina Channel
jetties on alluviums’ circuit on the North –
South direction;
including the permanently dredged sand
from the bar of the Sulina Channel into the
alongshore drift circuit;
maintaining the width of the littoral strips
that separate the lakes from the Black Sea in the
Razelm – Sinoe area and protection of such
strips against waves’ action and level variations;
assuring the necessary depths in the sea
ports, by executing dragage works in the basins
and the fairway, and using the resulting
appropriate sand in the South adjacent areas;
execution of beaches, also by sand fill, and
maintenance of such beaches for tourism
purposes and for shore protection as well;
re-evaluation of the existing groins in order
to increase their efficiency by providing
110
completion works as well as the execution of
overflow dams;
assuring the stability of the cliffs;
improvement of Sf. Gheorghe Channel’s
outlet into the sea;
organizing the waste water outlets into the
sea so as to achieve the most efficient dilution of
the discharge;
drifting southwards, in Mamaia area, of the
sand stored to the North of the Midia Port;
environmental pollution mitigation by
adopting appropriate operating technologies and
efficient
interventions
on
the
aquatic
environment (artificial reefs).
During the last five decades, there have been
built a number of beach protection dikes, especially
at those intended for recreation purposes, related to
the development of the seaside resorts. Between
Mangalia and Midia Cape, more than 50 such
works have been carried out, relying on many site
and laboratory studies, and in accordance with the
information available at that time.
Many of these dykes require repair and
completion works to increase their efficiency.
5. Solutions for protecting the south coast area
The studies that were produced have led to
some solutions that, in the main, provide transversal
and longitudinal dykes and sand fill.
The dykes are intended to stabilize the shore
and to create areas where the waves stirring and the
currents effect are smaller. Thus, their negative
effect, that of carrying off the beach sand, is much
diminished. The dykes can also contribute to the
formation of material deposits in the sheltered
areas.
The sand supply is necessary to compensate
for the deficit, as the currents are bare of alluvium.
In this respect, in order to assure the required beach
width, there is provided the transport of a sand
mass, that will be further protected by the
dykes.(fig.2)
6. Phasing the coastal protection measures in the
south area
The shore study has pointed out the areas
where protection works must be urgently carried
out.
The high price of these improvements
requires works’ phasing, resulting in a more
rational staging of the investment. Therefore, there
can be provided protection works that would make
possible the independent execution of some
improvements.
The so-called protection “cells” with 200 –
300m width and 500 – 800m length will be carried
out according to the final solution. They will be
made of transversal dykes and other dykes parallel
with the shore, above and below the water level.
Sand deposits will be created between these dykes.
(fig.3)
R. Ciortan / Ovidius University Annals Series: Civil Engineering 9, 107-112 (2007)
111
Another aim of this phasing is checking at
natural scale the effect of the proposed solution.
The observations will be made both on the existing
constructions and on the interaction with the
adjacent coastal area. These observations must be
made during several seasons, in order to assess the
morphological changes caused by waves and
currents on shore’s new configuration. The result of
these observations will allow improvement of the
constructive and overall solutions, therefore
increasing their efficiency.
7. Solutions for the north area
Eforie
After analyzing the area hydraulic aspects,
one of the solutions provides the execution of
longitudinal sand banks that would assure the
downstream “discharge” of the current, without
creating other inverse currents that cause erosions .
This solution can be also taken into
consideration at Sulina channel (fig 4.1) and at Sf.
Gheorghe channel (fig 4.2).
8. Conclusion
Venus
Eforie
The coastal protection of the Romanian shore
of the Black Sea is imperative, considering the
irreversible evolution and the extent of the erosion
process.
112
level, where sand fills will be performed. For the
Northern area, it is recommendable to conceive an
alongshore route, assuring the currents uniform
flow, without erosion.
The chosen alternative allows the works’
phasing, with positive effects on investment’s
staging and a better knowledge of their effect.
By elaboration of a unique, well-substantiated
and coordinated plan for research, design and
execution of a protection and rehabilitation system,
concurrently with a permanent analysis of the water
quality, an attractive seaside, profitable for all its
customers, will be achieved.
9. Bibliography
The studies to be performed must provide
solutions according to the causes of such erosions.
The Southern area of the seashore is low in
sand, which results in narrow beaches and therefore
a reduced touristic value.
To rehabilitate this area, there is provided the
execution of some “cells” consisting of transversal
and longitudinal dykes, above and below the water
[1] Bonnefille R., Cours d'hydraulique Maritime,
1992, 3o edition - Ed. MASSON.
[2] Bruun Peer, Port Enginerring, 1995, fourth
edition, Gulf Publishing Company, Huston.
[3] Centre of civil Engineering Research and Code,
Manual of the use of rock in hydraulic engineering.
[4] Chapon J., Travaux Maritime, 1978, Ed.
Eyrolles, Paris.
[5] Djunkovskii N.H., Porti i portavae soorujnia,
1967, Sfroizdat, Moskva.
[6] Larras J., Cours d'hydraulique maritime et de
travaux maritime, 1961, Ed. Dunod, Paris.
[7] *** Studii de hidraulica, 1992, Institutul de
Cercetari pentru Ingineria Mediului, Bucuresti.
[8] JICA-Japonia, The Study on protection and
reabilitation of the southern romanian Black Sea
shore in Romania, 2006.
[9] Japan Society of Civil Engineers, Design
Manual for Coastal Facilities, 2000.
A possible recovery system of the potential energy for the rain water
in the case of high buildings
a
Ovidiu Mihai CRĂCIUN a
Radu ŢÂRULECU a
__________________________________________________________________________________________
Rezumat: Lucrarea prezintă un sistem hydraulic cu trei variante constructive, utilizabil în vederea recuperării de
energie potenţială a apelor pluviale, la clădirile multietajate prevăzute cu terase având suprafeţe mari. Energia
hidraulică recuperată poate servi la pomparea apei potabile într-un rezervor plasat la ultimul nivel al clădirii sau
poate fi transformată în energie electrică stocată în baterii (acumulatori), fiind folosită în diverse scopuri.
Abstract: In the paper is presented a hydraulic system useable for the recovery of the rain water hydraulic,
energy in the case of the high buildings (with eight or more levels). The potential energy of the accumulated rain
water volume can be used for the conversion into electric energy, stored in battery accumulators or for other
practical applications, without energy consumption.
Keywords: Hydraulic system, energy, high buildings.
__________________________________________________________________________________________
1. Introduction
For the multi-level buildings over 8÷10 levels,
which have large terraces (surfaces over 500m2), is
becoming
advantageous
the
rain
water
accumulation resulted from rainfalls (over 20 l/m2
in 24 hours).
This rain water accumulation can be made into
a tank placed at the highest level of the building for
an ulterior usage of the collected water volume in
different purposes, without energy consume.
2. The propose installation presentation
At the designing and building of the multilevel buildings with large terraces, it must have in
view that the water provided from rain or snow
melting, to be directed to a large tank (10÷12m3)
placed at the highest level of the building, like in
figure 1.
The rain water or the water provided from rain
or snow melting, will be directed through pipe 10
into the tank 1 where have place the impurities
ISSN 1584 - 5990
sedimentation. At the reaching of some degree of
fullness, the water will pass through a metallic strainer
3 placed on the dividing wall in compartment 2 of the
collector tank.
The tank 2 has a drain pipe 12, which for the
situation when the electro-valve 5 is opening, the
hydraulic engine 6 (turbine type or hydraulic engine
with piston having an alternative rectilinear
movement), can be fill up with under-pressure water.
The electric energy supply of the electro-valve 5
is commanded of an adequate electric circuit, by a float
from the tank 2. This float 4 can shut or open the
electric energy supply of the electro-valve 5, in
function of the water level in tank 2. When the water
level attained to maximum height, the electro-valve
will be opening and the water will drain, in some time
interval, through the hydraulic engine 6, and into the
draining pipe 12. At the reaching of a minimum level
of the water in tank 2, the float 4 commands the
closing of the electro-valve5. After the passing through
the hydraulic engine, the water flows into the draining
pipe 18.
114 A possible recovery system… / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 113-118 (2007)
Fig.1. The proposed recovery system
When the under-pressure water passing
through the hydraulic engine will drive the pomp 7
mounted on an axle joined with the turbine. The
pomp 7 will realize the fresh water pumping from
the lower tank 13 into the upper tank 9 placed at the
final level of the building, where will be stocked a
certain volume of fresh water without energy
consume. Between the pump7 and tank 9, on the
pipe 16 will be mounted a one-way sense valve
witch allows the water flowing only from the pomp
to tank 9. The tank 9 is closed at the upper part,
having a short pipe with an air tap 19. When the air
tap 19 is closed, the tank 9 works like a water
supply plant with air cushion, which is allows
filling only with a limited volume of water. This
tank 9 can supply with water the people from the
building only on short intervals of time through
pipe 13, if it’s opening the tap 17.
For the tank 1 cleaning, at some time intervals is
opening the flow control device 11 mounted on the
pipe 14, the water from tank being evacuated along
with the bottoms to the duct 18. Also, is made the tank
1 and metallic strainer 3 cleaning.
Another possibility is the direct mounting of an
energy generator on the turbine axle 6 who will supply
with energy a set of batteries bounded in parallel. In
this case the stoked electric energy can be used to the
illumination of the building staircase or basement.
In figure 2 is showed an example of the proposed
system where the water flowing from the tank 2 has
place automatic without any electric energy consume.
When the clean water level exceeds the highest part of
the hydraulic drain trap 4, this is self-induces and the
water is draining through pipe 12.The water draining
from tank 2 have placed until when its level decreases,
reaching the altitude of the left inferior end drain trap
pipe 4.
O. Crăciun and R. Târulescu / Ovidius University Annals Series: Civil Engineering 9, 113-118 (2007)
115
Fig.2. The proposed system where the water flowing from the tank 2 has place automatic without any
electric energy consume
The component parts for the scheme from
figure 2 are:
1 - decantation-sedimentation
tank
of
the
impurities;
2 - tank with rain water;
3 - metallic strainer mounted on the dividing wall
of tanks 1 and 2;
4 - drain trap pipe;
5 - tap
6 - hydraulic engine (turbine type or hydraulic
engine with piston having an alternative rectilinear
movement);
7 - mechanic droved pump if at 5 component exists
a turbine;
8 - one-way valve;
9 - tank with air cushion;
10 - pipe for the rain water;
11 - sluice valve for quick exit;
12 - draining pipe of water from tank 2;
13 - pipe with fresh water;
14 - draining-cleaning pipe for the tank 1;
15 - tank with water from the network;
16 - filling pipe for the tank 9;
17 - tap;
18 - tank bounded to the duct;
19 - short pipe with air tap;
Hg - level difference between the tank 2 base and the
horizontal plan where the hydraulic engine axle 6 is;
ΔH - difference between the maximum and minimum
level of water in tank 2.
If in place of turbine 6 from figure 2 is using a
linear hydraulic engine, the scheme will be like is
showed in figure 3.
For pressure increasing to the piston pump
droved of the hydraulic engine is choosing a piston
diameter smaller comparing with diameter D of the
linear hydraulic engine.
Fig.3. The scheme for a linear hydraulic engine usage
The component parts for the scheme from
figure 3 are:
1 - linear hydraulic engine cylinder with alternative
rectilinear movement;
2 - cylinder of the mechanic droved pump;
3 - hydraulic engine piston rod;
4 - slide valve with four ways and two positions;
5 - hydraulic engine piston of diameter D;
6 - pump piston of diameter d;
7 - pump suction pipe;
8 - pump repression pipe;
9 - suction valve;
10 - repression valve;
11 - oscillatory link box;
12 - fixed hinge;
13 - sliding hinge;
14 - oscillatory rigid bracket around the hinge 12;
15 - slide valve command arm;
16 - safety valve;
17 - by-pass pipe, between the suction and
repression of the pump.
In this case under pressure water entering in the
slide valve 4 is bounded to the pipe 12 (figure 2)
and the output is bounded to the draining duct.
The pistons running are the same for the
hydraulic engine and pump, but having in view the
smaller diameter of the pump piston it can be
accomplish a highest pumping pressure, which
allows the fresh water tank to be placed at a highest
altitude. The pressure limitation on the pump
repression pipe is realize because of the by-pass
pipe where is mounted the safety valve.
3. Theoretical considerations
As following the rain water accumulation in
the tank 2, (figure 2), at its filling up till the drain
trap priming level, results a liquid volume V.
The potential energy of this water volume can
be written in this way [1]:
E h = ρ ⋅ g ⋅ V ⋅ Hg
(1)
where:
Eh – potential energy of this water volume
accumulated in the tank 2;
ρ - water density;
g – gravity acceleration;
V – water volume accumulated in the tank 2 at
the complete filling;
O. Crăciun and R. Târulescu / Ovidius University Annals Series: Civil Engineering 9, 113-118 (2007)
Hg – level difference between the tank 2 base
and the horizontal plan where the hydraulic engine
axle is, from stop siphoning moment of the drain
trap 4 (figure 2).
Q = v⋅
πd 2
4
[m3/s]
117
(5)
The charging losses on the pipe 12 ways can be
written [2]:
For relation (4) is admits that this draining pipe
12 has a constant diameter. The recovered effective
capacity can be written:
∑ h p = ∑ h pi + ∑ h pl
Nu =
(2)
where:
∑ h pi
- sum of local charging losses (bent
pipes, section enlargement or diminution for the
pipe 12 etc);
∑ h pl - sum of linear charging losses on the
pipe parts having different diameters;
∑ h p - total sum of charging losses on the
pipe 12.
Having these elements it can be determined the
real charge of the flowing:
H = Hg − ∑ h p [m]
(3)
Using the real charge value H is determined the
flowing speed through 12:
v=
2⋅g⋅H
[s]
j=n
i=m
li
1 + ∑ ζ j + ∑ λi ⋅
di
j=1
i=1
(4)
η⋅ρ⋅g ⋅Q⋅H
1000
[kW]
(6)
where:
Nu – recovered effective capacity at the
turbine;
Q – flow rate [m3/s];
H – flowing real charge [m];
η – turbine efficiency.
For determination of the time interval when is
actuated the turbine for a single priming of the
hydraulic drain trap 4 we use the relation:
Δt a =
V
Q
[s]
(7)
where:
Δta – time interval when the turbine is actuated
at a single emptying of the tank 2;
V – accumulated water volume in the tank 2 at
the complete filling;
Q – flow rate through the pipe 12 calculated
with relation (5).
The recovered useful energy at a single
emptying of the tank 2 is[3]:
v – the flowing medium speed through 12;
j= n
∑ζj
- sum of local charging losses
E hu = Nu ⋅ Δt a
(8)
j=1
coefficients, for all the hydraulic local resistances;
i =m
∑ λi ⋅
i =1
li
- sum of products between the
di
local charging losses coefficients and pipes parts
lengths reported to their diameters.
Having the flowing speed established, it
determines the flow rate through pipe 12:
Fig.4. The considerate distances for the system
Considering the figure 4, it can be express the
pressure losses through a random section at a
distance n* in ratio with the tank 2 base (figure 4).
Applying the Bernoulli equation into a halfpermanent movement between section (1) and
some other section situated lower at distance n*, it
can be write:
α ∗ ⋅ v 2∗ p ∗
α1 ⋅ v12 p1
∗
n + n +
+
+n = n
2g
ρg
2g
ρg
(9)
∗
1 n 2 ∂v
+ ∫ β⋅
⋅ dS + h ∗
pn
g n1 ∂t
where:
α1 , α
and n*;
v1 , v
*
n∗
- speeds in the same sections;
n
the same sections;
β - Boussinesq coefficient, β =
pn ∗
p
n∗
− p1 = Δp n , results the pressure
loss in some section placed at distance n* at the tank
base:
n∗ ∂v
*
Δp * = ρ ⋅ g ⋅ n − ρ ⋅ ∫ β ⋅ − ρ ⋅ g ⋅ h ∗ (11)
pn
n
∂t
0
or
∗
1 n
∂v
Δp * = ρ ⋅ g ⋅ ( n * − ⋅ ∫ β ⋅
− h ∗ ) (12)
pn
n
g 0
∂t
4. Conclusions
- Coriolis coefficients in sections n1
n∗
n - distance from the tank base to the random
considerate section;
p1 , p ∗ - static pressures at the pipe wall in
h
Noting
α+2
;
3
- charge loss between the tank base and
the random considerate section at distance n*
(figure 4).
Applying the continuity equation in situation
when α1 = α ∗ = 1 , namely a speeds uniform
n
distribution in that sections, results the speeds
equality v1 = v ∗ . In this conditions, the relation
n
(9) can be written:
∗
p ∗ − p1
∂v
1n
*
n
= n − ∫ β⋅
−h ∗
pn
ρg
∂t
g 0
(10)
The proposed installation in this paper
demands a large volume of initial investments,
about the different design accountable to normal
buildings and supplementary spending for tanks,
turbine, pump, etc.
But, for entire time of building exploitation,
can be recovered considerable quantities of energy
used for fresh water pumping or for free electric
energy obtaining.
The large dimensions of the tanks (10÷15m3)
can attenuate the horizontal oscillations in case of
quake, because of the water inertia, stabilizing the
building in a shorter time interval.
With lowest costs of maintenance, the
installation brings important energetic benefits on
the total life duration of the building.
5. References
[1] – Ionescu, D., Mecanica fluidelor şi maşini
hidraulice, Editura Didactică şi Pedagogică,
Bucureşti 1983;
[2] – Crăciun, O.M., Mecanica fluidelor şi maşini
hidraulice, Editura Universităţii Transilvania
Braşov, 2000;
[3] – Crăciun O., Ţârulescu R., A possible energy
recovery system used at auto-trucks which moves
whitout effective load, Conferinţa naţională de
energetică CNEI 2005, Ediţia a V-a, Bacău, 2005.
The Analysis of the Impact of Storage Lake on Environment Using the Chemical
Characterization of the Water Resources. Case Study Bahlui Basin River
Ion GIURMA a
, Ioan CRĂCIUN a
Catrinel-Raluca GIURMA a
a
__________________________________________________________________________________________
Rezumat: Lucrarea abordează problematica influentei sistemului de monitorizare a calităţii apelor în domeniul
impactului acumulărilor complexe asupra mediului. Sunt prezentate elemente privind organizarea sistemului de
monitorizare pe bazine hidrografice si particularizări pentru Bazinul Râului Bahlui.
Abstract: This work presents the monitoring system influence in the field of the environmental impact of
storage lakes on environment. Are presented elements regarding the organization of the monitoring system on
Bahlui basin river and a case study for Podu Iloaiei storage lake using the LakeWatch software.
Keywords: water quality monitoring system, complex storage lake, environmental impact.
__________________________________________________________________________________________
1. Presentation of Bahlui River Basin
The catchments area of Bahlui river basin
(Figure 1), belonging entirely to the county of Iaşi,
is about 1,917 km2.
The
complex
storage
lakes
are
hydrotechnical structures used for managing the
water resources. In the same time this lakes
changing the environment regarding the
geographical, ecological and socially aspects. The
evaluation of environmental impact elements
represent solutions for minimizing the negative
effects and finding solutions for the future in the
context of durable development.
The length of the Bahlui river between its
spring and the confluence with Jijia river is about
119 km. Bahlui river ends in the Jijia about 6 km
before the latter flows into the Prut river, 390 km
upstream from the confluence of the rivers Prut
and Danube. Jijia river is channelized between the
confluence with Bahlui river and the confluence
with the Prut river. The old river bed called Jijia
Veche unsually contains only a small amount of
mostly stagnant water [2].
Bahlui river is, like Jijia and Prut, a rain fed
river, with a relatively small discharge most of the
ISSN 1584 - 5990
year, and a few short periods of high waters, usually
in early spring, when snow melts and most rainfall
occurs. Most of the time about 75% of Bahlui river
discharge of at the confluence with Jijia is
represented by the effluent of
Waste Water
Treatment Plant (WWTP) of Iaşi town, entering
Bahlui 3 km upstream from the confluence.
As much as 17 reservoirs are in operation in
Bahlui basin. Dams construction took place between
1965 and 1980. Initially the reservoirs were designed
for flood control in downstream areas, especially for
Iaşi town protection. The reservoirs are also used for
urban and industrial water supply, commercial
fishing, irrigation and recreation.
The mass balance study concerns Bahlui river
downstream the reservoir Pârcovaci, a short stretch
of Jijia river between the monitoring stations
upstream and downstream the confluence with Bahlui
river and the only monitored tributary of Bahlui - the
strongly polluted Bahlueţ brook. The most affected
reservoirs by pollution are the reservoirs Tansa and
Podu Iloaiei situated on Bahlui, respectively Bahlueţ
water courses [2].
120
Study on the use … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 119-124 (2007)
Figure 1 Iaşi County water quality monitoring system
2. Monitoring water quality programme and
monitoring stations
3. Mass balance analysis of the pollutants in Bahlui
basin river
The surface water quality monitoring
programme of the National Administration
Romanian Waters (NARW) Iaşi Branch includes
river monitoring stations of first and second level,
with a measuring frequency of 12 times a year,
respectively 4 times a year,. At first level stations
three samples are taken with a time step of 8 hours
at 8.00 h, 16.00 h and 24.00 h; the average values
of three analyses are reported. From monitoring
stations of the second level just one sample is
taken. The reservoirs are also given a first level or
second level monitoring status. The first level
reservoirs are monitored four times a year, while
the second level reservoirs only twice near the dam.
Furthermore, waste water discharges are monitored
by NARW Iaşi Branch with a frequency of 2 to 12
times a year, depending on their potential or
expected degree of pollution (Table 1).
A mass balance compares the amount (named
load) of a substance entering and leaving a certain part
of a water system. The load of a substance in a stream
is computed by multiplying the water discharge by the
concentration of the substance. The time interval for
which the discharge (m3/s) is expressed becomes the
time interval for the load (g/s) [2, 8].
The average loads of the river were computed for
the years 1995, 1996 and 1997, corresponding to
different hydrological regimes. The instantaneous
loads get a weighting factor proportional to the
discharge (Figure 2). The average load Lav is [2]:
n
Lav =
∑ (qi ⋅ ci ) / n
(1)
i =1
Table 1
D. Drăgan, C. Mârza and R. Dardai / Ovidius University Annals Series: Civil Engineering 9, 119-124 (2007)
Reservoirs
Pârcovaci reservoir
Tansa reservoir
Podu Iloaiei reservoir
Plopi reservoir
Sârca reservoir
Cucuteni reservoir
∗ two samplings per year; ∗∗ four sampling per year
where qi is the measured discharge, ci the
concentration of the monitored parameter and n the
number of the chemical measurements.
The average weighed-discharge Lav, Q is
computed as [8]:
⎛ n
⎜
ci qi
⎜
⎜
=
1
i
Lav , Q = k ⎜
⎜ n
⎜
qi
⎜⎜
⎝ i =1
∑
∑
⎞
⎟
⎟
⎟
⎟⋅q
⎟
⎟
⎟⎟
⎠
(2)
where k is a conversion factor considering the
drawing frequency and the units used for
concentration and discharge; q is the average
discharge computed on the basis of daily
registrations.
The considered water systems are Jijia river
downstream the confluence with Bahlui, the river
Bahlui including the storage lake Tansa and its
main tributary Bahlueţ including the storage lake
Podu Iloaiei. Mass balance were established for
those substances exceeding the limits defined in
Romanian standard STAS 4706-88 considered as
problematic parameters and for other substances
needed for the interpretation of the mass balance of
the problematic parameters: chemical demand
(COD, determined with permanganate), biological
oxygen demand (BOD5, oxygen consumption
during 5 days), oxygen (O2), ammonium (NH4+),
nitrate (NO3-) and phosphorus (P) [2].
121
∗∗
Loads leaving Tansa reservoir are computed using
concentrations of samples taken near the spillway,
close to the water surface. This point is located 58 km
downstream the springs of the Bahlui ∗∗
Loads leaving Podu Iloaiei reservoir are computed
using concentrations of samples taken near the
spillway, close to the water surface, 37 km
downstream the springs of Bahlueţ river ∗∗
∗
∗
∗
The load decrease of the effluents from WWTP
Iaşi in order to fulfill the quality requierements at the
confluence of Bahlui river with Jijia (Chipereşti
section) can be analyzed according two scenarious,
considering that the pollution from the existent sources
remains at the same level:
a) framing in the Ist category at Chipereşti; this
category cannot be achieved only by improving the
operation at WWTP Iaşi, being necessary to diminish
the pollution at all the other sources.
b) framing in the IInd category in the same section; the
necessary concentration at Victoria (Jijia) and Bahlui
upstream WWTP Iaşi is: 15 mg O2/l COD, 7 mg O2/l
BOD5, 3 mg/l ammonium.
According to the mass balance at Jijia-Bahlui
confluence, the WWTP charges must be diminished as
per Table 3 in order to fit into the Ist, IInd and IIIrd
category [5, 6].
4. Chemical characterisation of the storage lakes
The global characterization of the water quality
in the reservoirs may be performed in two ways:
a) in agreement with the standards, considering the
reservoirs as static eco-systems and operating with
constant values of the parameters to frame the quality
into the four categories;
b) considering the reservoirs as dyamic eco-systems
and operating with average values of the quality
parameters for a given period.
From the reservoirs of first level monitoring
status studied between 1998-2006, considering the
phosphourous concentration two of them, Chiriţa and
122
Pârcovaci belong to the Ist quality category, while
the rest to the IInd and IIIrd category. The trend of
the global quality shows that five reservoirs of the
second level monitoring status have a negative
evolution, four of them have a positive evolution,
and three tend to preserve the present quality. From
the analyzed parameters, 29 % had an improving
trend, 37% a decreasing trend, and 34% preserve
the present quality.
Generally, the reservoirs of second level
monitoring status fit into the IIIrd and D category,
which shows a bad water quality both from
chemical and biological point of view. The siltation
of these lakes as well as the increased pollution
during the past years led to the quality
deterioration.
4.1. Podu Iloaiei Reservoir
Podu Iloaiei reservoir, built on Bahlueţ river,
has at the normal water level a surface of 2.1 km2,
and a volume of 2.5 million m3. Some of the water
users (fishery, irrigation) need a water of the II
category; the lake has in the same time a touristic
potential imposing thus for the swimming water the
Ist category. However, the levels of COD and
BOD5 fall in the categories III and degraded; the
lake has too high bacteriological pollution and
phytoplankton blooms, those of bluegreen algae
being the most problematic. The oxygen levels
registered in 1995 to 1997 were mostly in the Ist
category (six value in the Ist category; one value in
the IInd category).
Phosphorus concentrations measured in 1995
and 1996, 2002-2005 exceeded the STAS standard
value corresponding to category III, which was not
the case with the values measured in 1997. Due to
the limited number of measurements (2 in 1995, 3
in 1996 and 2 in 1997), the conclusion that the
phosphorus load entering the lake decreased would
be premature. Moreover, the lower values of 1997
year could be the effect of algae blooms, which can
convert almost all dissolved phosphate (orthophosphate) into algae-bound phosphate, which is
not included in phosphorus determination by
NARW Iasi. Water samples are filtered, removing
thus algae and particulate matter to which phosphorus
can bind.
Also the nitrogen compounds appear to reflect
uptake by algae. Two values of ammonium measured
in 1995, in samples taken in January and early March,
indicated a degraded water, while the five values
measured in the spring and summer of 1996 and 1997
were much lower, corresponding to the category I and
II. Algae blooms lower also the concentration of
nitrate, especially because the uptake of ammonium by
algae cuts off the nitrate production by nitrification.
All nitrate levels measured between 1995 to 1997 were
outside the limits of the Ist category. Measuring of
Kjeldahl-nitrogen in unfiltered samples could confirm
whether the nitrogen is indeed taken up by algae.
A case study basing the chemical data from
NARW Iasi for the storage lake Podu Iloaie are make
using the LakerWatch v.1.0.0.2. software regarding the
prognosis trend of storage. Are used the data collected
between 0 and 0.5 m depth of water and chlorophyll
concentration (Chla), NO3 (nitrate) and NH4
(ammonia) on mg/l. The period of analysis are MayJuly 2005. This analysis indicate that the Podu Iloaiei
lake trend is eutrophically (figure 2) [7].
Understanding the pollution mechanisms of Podu
Iloaiei reservoir and possible measures to improve the
water quality require: a monitoring station immediately
upstream from reservoir; a higher monitoring
frequency of the reservoir and accurate discharge
registration; measurement of total phosphorus and
Kjeldald-nitrogen in unfiltered samples [1, 2].
The Framework Directive 2000/60/EC and the
Decision No 2455/2001/EC of the European
Parliament and of the Council in the field of water
resources foresaw a new monitoring strategy under an
integrated monitoring concept of the waters (a triple
integration) which must be applied in the Bahlui basin
river if we want a good quality of the environment: of
the investigation areas at the basin level: natural
surface waters, artificial surface waters and effluent
protected areas; of the investigated areas: water,
sediment integrated with the biological components; of
the quantitative and qualitative monitored elements:
biological, hydro geomorphological, physical and
chemical [3, 8].
D. Drăgan, C. Mârza and R. Dardai / Ovidius University Annals Series: Civil Engineering 9, 119-124 (2007)
123
100
90
80
70
Depth
60
Chla
50
NO3
40
NH4
y = 10.476Ln(x) + 0.0403
30
Log.
(NH4)
20
10
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18
Figure 2
5. Conclusions
The improvement of the water quality on
Bahlui hydrographic basin and particullary for
storage lakes and our environmental impact can be
accomplished by:
- connected to the public sewage system;
- replacing the hydraulic evacuation of the
zootechnical dejection by dry evacuation systems;
thus, a lower volum of dejections results, their
nutritive potential being capitalized;
- monitoring the pollutant charges of the
effluent creeks, including monitoring campaigns
nearby the confluence;
- representative samples of the discharged
waste waters for the analyzed system;
- extending the analysis programmes to
the phosphour measurement in blank samples and
azote Kjeldahl measurements on the same type of
samples for storage lakes;
- installing monitoring sections nearby
upstream storage lakes and completing the database
by increasing the monitoring frequency and the
quality of the data as well as the measure of the
total phosphour and azote Kjeldahl on unfiltered
section as well as of focus azote and phosphour from
the suspension matter – in order to understand the
phenomenon which affects the quality of the Podu
Iloaiei and Tansa reservoirs;
- better monitoring of the heavy metals and
organic micro-pollutants, especially pesticides; in this
respect, for some of the pollutants with a high level of
toxicity the sampling is restricted to some significant
locations with a lower frequency (once a year, for
instance);
- elaborating monitoring program for the
pesticides which can affect the groundwater resources;
- compiling a GIS environmental database
which should identify the areas with the risk of
affecting the water quality;
- application of the environmental protection
legislation and the financial measures to protect the
water quality;
- ellaborating a policy of reduction the
pollution, as well as immediate and long term
measures and necessities;
- inventorying the discharge points and
diffused sources.
124
6. Reference
[1] Crăciun, I., Drobot R., Wasserqualitätsanalyse
der
Stauseen
im
Bahluibecken
durch
Mathematikmodellierung, The Buletin of P.I. of Iaşi,
Tom XLVII(LI), Fasc. 1-4 (II), Hidrotehnics, vol. II,
pg. 13-16, IIIrd Section "Env.Engineering", 22-24
nov., 2001
[2] Crăciun, I., Contributions to the water quality
management of the Bahlui gegraphical basin,
Doctoral Thesis, Technical University of Civil
Engineering, Bucharest, 2003
[3] European Parliament - Directive 2000/60/EC and
the Decision No 2455/2001/EC for surface waters
quality
[4] Giurma-Handley C.R., Giurma I., Crăciun I., (2006)
Modeling of the Environmental Impact of Complex
Storage
Lakes,
International
Conference
of
Environmental Engineering ICEEM03, Iasi, pg. 44-49
[5] Giurma I., Water Management Systems, (in
romanian) ,Ed. CERMI, Iasi, 2000.
[6] Giurma I., Craciun I., Giurma C.-R., Hidrology, Ed.
Politehn ium, Iasi, 2006.
[7] Scisoftware, LakeWatch v.1.0.0.2. software, Lake
Monitoring Analysis and Control
[8] Varduca, A.,- Integrated monitoring of water
quality, En gineering of Waters Resources, HGA Ed.,
Bucharest, 1999
The Multicriterial Decisional Management Within Irrigation Arrangements
a
Gheorghe IORDACHE a
Marian DORDESCU a
National Company of Land Reclamatin RA , Dobrogea, Constanta, Romania
__________________________________________________________________________________________
Rezumat: In această lucrare, este prezentată o abordare multicriterială a tehnicilor de decizie, utilizate în
managementul amenajărilor de irigaţii. Analiza economică a fost realizată utilizând metoda Electre III în cadrul
căreia se cuantifică importanţa relativă a criteriilor considerate. Alegerea pragurilor este determinată de
specificitatea fiecărui criteriu, astfel încât să reflecte preferinţa factorului de decizie. Prin relevarea zonelor cu
eficienţă economică scăzută, analiza realizată contribuie Ia îmbunătăţirea deciziilor care trebuie luate, constituind
un important punct de plecare pentru alegerea celor mai bune metode de modernizare a amenajărilor de irigaţii.
Lucrarea prezintă o analiză a unor importante criterii de evaluare a eficienţei sistemelor de irigaţii în Sistemul
hidrotehnic „Nicolae Bălcescu", component al amenajării pentru irigaţii Valea Carasu, judeţul Constanţa.
Abstract: In this study presents a multi-criteria approach for decision techniques used in irrigation system
management. Economical analysis was made using Electre III method which counts the relative importance of
the considered criteria. Choosing levels is determined by every criteria individuality particularity. By showing
low economic efficiency areas, the analysis upgrades the decisions, and by doing that we have an important
starting point for choosing the best modernizing methods for irigations devices. This study reaveals the analysis
of the most important criteria evaluation of the irrigation system eficiency for Nicolae Balcescu hydrotechnical
System which is part of Valea Carasu's irigation system.
Keywords: multi-criteria decisions tehniques, optimizing, irigation system.
__________________________________________________________________________________________
1. Introduction
1. Generality
The great changes that came in Romanian
agriculture after 1989 had an impact on the
irrigation system activity therefore reducing the
irrigated areas percentage. The recovery of this
activity is bound of assuring the efficiency of water
distribution through a rigurous cost analysis also
considering field and environment conditions,
irrigation method, pumping levels.
In [7] is shown the efficiency irrigation
criteria analysis such as the energetical one, the
economic-financial
and
irrigation
water
distribution, from a water provider point of view,
using the ELECTRE (Elimination et Choix
Traduisant ia Realite). By showing the critical
areas, with low economic efficiency, this kind of
analysis is improving the decisions that have to be
made for the irigation system administration. It’s
also a very important starting point for making the
ISSN 1584 - 5990
best modernizing choices.This study works with
ELECTRE III version to syntetize the relative
importance of the considered criteria.
ELECTRE was initially developed to estimate
the uncertainty of the decision process by using the
preference and indifference levels. ELECTRE is a noncompensating method - a low grade for a certain
criteria cannot be compensated with better grades for
other
criteria.
ELECTRE
models
allow
incomparability. This element appears between A and
B alternatives when there is no relevant evidence for A
or B. There are interesting applications of this method
in multi-criteria decisions theory [3,4]. Main
ELECTRE method concepts are: thresbolds and
ranking. First preordonation Zt descending filtration
process. The ascending filtration is made in the same
way except for the fact that the low quality projects are
restrained at the beginning. The result will be a prearrangement Z. In the same group the projects are
equally arranged.
126 Multicriterial Decisional… / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 125-130 (2007)
2.Considerations of the Electre method implementation
The following types of criteria are taken into
consideration:
Composed criteria: economical; hydro;
energetical.
Primary
criteria:
modernization
and
readaptation costs, maintenance and repair costs,
irrigation efficiency, the importance of the grantsin-aid, water volumes, lost volumes of water;
improved area; contracted area; active/reactice
energy consumption; specific consumption.
To be able to define a set of policies that
includes economical, hydro and energetical aspects,
a series of factors have been defined, factors that
can be subject to exterior influences and can be
modified according to the purpose of the analysis
and the requirements of the system. These are: the
method of setting up the irrigation system (A), the
cost of the water (B), the irrigation stages (C)that
has a strong influence on the energy consumption
andthe lost volume of water, crops planning (D),
the irrigation system (E), grants-in-aid (F).
2. Experiment
Total area of 28 125 ha, the irrigation system
„Nicolae Balcescu”, built in four energetical stages:
stage 1 (Hpumping = 65 Mca, Surface = 3310 ha); stage 2 (Hp = 91mCA, s = 4560 ha); -stage 3 (Hp =
113Mca, S = 16640 ha); -stage 4 (Hp = 143 Mca,
S= 358 ha).
Disposing the irrigable surfaces in the four
energetical stages makes one think that the
irrigation system „Nicolae Balcescu” is a major
energy consumer, having an impact on the
economical indicators of A.N.I.F. R.A. Constanta
which delivers water to the consumers.
The water distribution for plants is done by
means of affusion on 24.049 ha (86%) and on
furrows of 4.076 ha (14%). A surface of 21.990 ha
is improved with underground pipes, and the
surface of 6.135 ha with external pipes.
The amount of water necessary for this was
calculated according to a crops planning in which
the corn crop is dominant – 40% of the total
surface, followed by cereal crops – 30%, sunflower and alfalfa – 8%, soya – 7%, sugar beet –
3%, vegetables, vineyards and fruit trees – 2%.
For the evaluation of the chosen factors, the
following qualifications habe been used: A = excellent,
B= good, C= medium, D= sufficient, E = insufficient,
and for the evaluation of the criteria were used
numbers from 5 (=A) to 1 (=E).
a.Estimating the irrigations. The first method is
surface leaking. Economically speaking, this type of
irrigation gets a „C” for modernization and
readaptation costs, because only 14% of the surface of
the system considered is fit out using this method. Still,
the costs of this investment won’t be high compared to
other methods. The maintenance and repair works
were qualified with a „B”, because this type of
arrangement doesn’t require a high qualified work for
the maintenance and repair of the sewers. Profit wise,
it gets a „C”. Regarding the hydro criteria the method
gets a „C”, taking into consideration the equipped and
precontracted surfaces , and for the energetical criteria
it receives an „A”.The affusion method was qualified
with a „B” profitwise, because the costs of
modernization and readaptation are „excellent” (86%
of the surface is already arranged for affusion) and the
maintenance and repair expenses are relatively big (C).
A „B” for the hydro criteria and for the energetical
criteria the result is a „D”.
b.The price of the water. After estimating the
price of the water, the result was a „B” for the current
price, which is fair both to the water distributor and the
grower. In the case of cutting off the subventions, an
assumption has been made which is based on
increasing the price of water with 150%. In such a
case, it is qualified with an „E”.
c.Pumping stages. The qualifications were
bestowed for the maintenance cost in direct ratio to the
pumping stage, according to the length of the sewers
and the construction and technological characteristics of
the repumping units. Stage I received a”B” and stage IV
got an „E”. As for the importance of the grants-in-aid,
the grades were in indirect ratio to the pumping stage, an
„E” for stage I and for the fourth stage an „A”. The lost
water volume was considered „excellent” on stage I and
„insufficient” in stage IV. Energy consumption was also
proportional to the stages of the energy.
d.Crops planning. There were considered four
scenarios. The scenario according to the precontracts
takes into consideration the actual distribution of the
crops within the system. The grades were: „medium”
for the economical criteria, „B”for the hydro criteria
and „medium” for the energetical criterion. The haulm
G. Iordache and M Dordescu / Ovidius University Annals Series: Civil Engineering 9, 125-130 (2007)
127
scenario takes in consideration the fact that this
1. PECO = 0,6 / PHIDRO= 0,2 / PENG = 0,2;
kind of crops have a bigger resistance against
2. PEC0 = 0,2 / PHIDRO= 0,6 / PENG = 0,2;
drought, being the second most cultivated after
3. PECO = 0,2 / PHIDRO= 0,2 / PENG = 0,6;
corn.as a result, it received it was qualified as
4. PECO = 0,334 / PHIDRO= 0,333 / PENG = 0,333 .
„medium” economically, „sufficient” in what
concerns water consumption, and „medium”
The qualitativ matrix is the start point and it
energywise. The corn scenario got an „A” for the
highlights 6 groups of factors and their subdivisions
economical criterion and „B” for both hydro and
(18). According to this, there have been selected 3
energetical criteria. The sun-flower scenario
factors (actions) whose hefts double when it comes to
received a „B” for all criteria.
estimating the criteria. The results are: „B- the price of
e.The irrigation equipment. There are two
the water”, „C-the irrigation stages” and „E-irrigation
scenarios: the current situation and and the case in
equipment”. All these factors have been sorted and
which the necessary could be insured (without the
analyzed, resulting a set of alternative policies. From
renewing technologically). In the first case, we
the total we then obtain 18 realistic policies of interest.
have: „C” for economical criterion, „E” for the
The selection criteria are: the sorting method, named
hydro criterion and „C” for energy. For the second
the „screening method”; grading the global criteria: the
scenario , we have a „B” for economical, „A” for
profit, hydro criteria, energetical criteria: =B=C=0;
hydro and „B” for energy.
D=1; E=2; declaring 9 incompatible or irrational
f.Subventions. The subvention for the power
policies such as: incompatibility (A1) „Irrigation
that is necessary to deliver the water to the
through furrows”(D2) „Haulm crops”, incompatibility
beneficiary has a great importance on the criteria
B1 „current price of water” with F2 „cutting off the
mentioned before. For the current situation we have
subventions”. Still, in the process of choosing these 18
a „B” for economical criterion, „C” for hydro and
policies there are also elements taht are influenced by
„insufficient” for energy. In the second case, the
subjective decisions. The result is 8 final arrangements
one in which the subventions are cut off, we have
(Îd3, IdlO, Eco3, EcolO, Hidro3, Hidro 10, Eng3,
„E”, „C” and „B”.
EnglO).
There are four hypothesis influenced by each
decision factor:
Nr.
ID
ECO
HIDRO
ENG
Alternative
political
Id3
Id10
Eco3
Eco10
Hidro 3 Hidro10 Eng3 Eng10
1
111111
1
4
2
2
5
5
1
3
2
111321
3
6
1
6
4
8
3
9
3
12 1222
3
4
3
2
3
5
3
4
4
122422
5
6
4
4
5
7
5
7
5
123322
7
8
5
9
9
9
8
10
6
123422
3
2
4
2
4
3
3
4
7
121312
9
2
7
5
8
4
5
2
8
211121
2
3
2
2
3
5
1
1
9
211421
1
1
1
1
2
2
2
2
10
211521
1
1
1
1
1
1
1
1
11
221512
11
5
7
4
10
5
7
5
12
223212
8
3
6
3
9
4
7
6
13
2224 12
5
6
4
7
3
4
5
5
14
31132 1
10
2
8
3
7
3
6
3
15
322322
7
7
5
8
5
5
4
8
16
322222
6
5
3
6
4
3
6
7
17
323512
8
7
6
9
6
6
6
10
18
323322
4
4
3
8
2
2
4
9
Electre maintains the diversity of the three
criteria so that even if a strategy has a great
performance within a criterion and a low
performance within another criterion, they’re both
taken into consideration. Although policies 9 and
10 are on the first position, the method reveals
interesting things about ranks 2,3 and 4.
a).ECO 10 : the decision factor: peco = 0,6 /
PHIDRO= 0,2 / PENG =0,2 (0.1/0.2/0.1/0.2
0.1/0,04/0.04/0.02 0.1/0.1);
Tabel 2
Nr.
crt.
1
2
3
4
Number
politic
P9
P10
P1
P8
P12
P14
P4
P11
Alternative
ABCDEF
211421
211521
111111
211121
223212
313321
122422
221212
The institutional frame is not modified: the
subventions are the same (F1); the irrigation stage
is the most favorable (C1). The economical
criterion predominating over, leads to an opposition
towards progress and modernization. The method
of irrigation through affusion is well positioned and
her spreading can be seen on the entire surface.
From a crops planning perspective, each of the
proposed strategies are present here.
b)-HIDRO 10-the decision factor involving the
distribution of water: PEC0 = 0,2 / PHIDRO= 0,6 /PENG=0,2
(0.04/0.06/0.04/0.06/0.3/0.12/0.12/0.06/ 0.1/0.1).
Tabel 3
Alternativ
ABCDEF
Nr.
crt.
Number
politic
1
P10
211521
2
P9
P18
P6
P14
P16
P7
P12
P13
211421
323322
123422 3
1132 1
322222
121312
2 2 3 2 12
2 2 2 4 12
3
4
P18 is surprisingly ell positioned. It’s a policy of
changes in all departments, therefore, within this action
there is nothing left from the initial state. A strong
intervention
is
necessaryin
the
following
directions:increasin the price of the water with 150%,
establishing a strict consumption of water, cutting off
the subventions which leads to the minimalization of
the irrigated surfaces. Even if the effect of the
consequences on this is positive this policy can’t be
taken into consideration.
P16, the policy that achieved the best position in
this scenario involves giving up grants-in-aid, doesn’t
have an appliable effect and this shows how
insegnificant is a singular action within the whole
estimating policy.
c).ENG 10: the decision factor involving the
energy: PEC0=0,2/PHIDRO= 0,2 / PENG = 0,6
(0.04/0.06/0.04/0.06 0.1/0.04/0.04/0.02/ 0.3/0.3 ).
Tabel 4
Nr.
crt.
1
3
Number
politic
P8
P10
P9
P7
P1 P14
4
P3 P6
2
5
P11
P13
Alternati
ABCDEF
211121
211521
211421
12 1312
111111
31 1 3 2 1
12 1 2 2 2
123422
22 12 12
222412
The criteria comprise aspects about specific
consumption and the energy consumption. It is clear
that the most favorable criterion is the first stage of
pumping (C1 = stage 1), and giving up subventions is
aut of question(F1). The irrigation by dripping method
(A3), that would have saved energy can’t be
considered, requiring a great financial and
technological effort.
d) ID 10: the decision factor involving all three
criteria PECO=0,33/PHIDRO=0,33/ PENG = 0,34 ( 0.06
/0.1/0.06/0.11 0.17/0.07/0.06/0.03/0.17/0.17).
The decision factor has to choose between many
alternative policies: some of them are not suggesting
radical changes, for example, best arrangement method
is the affusion which has the majority in this case. The
crop plan includes all strategies, mostly corn which is
G. Iordache and M Dordescu / Ovidius University Annals Series: Civil Engineering 9, 125-130 (2007)
till now the predominant culture, but also sunflower and vegetable + potatoes, which act very
good during irigation. As for the increasing water
price, 60% of the versions maintain the actual one,
same for subventions. Medium politics dominance
reflects the multiple problems from which the
decision factor has to choose.
3 Results
PI - 1 1 1 1 1 1 -: „Actual state" (clasifications:
IdlO: 4 / EcolO: 2 / HidrolO: 5 / EnglO: 3)
Most of the 1 criteria reflects the actual state
from the studied system. PI has a good evaluation
considering the economic point of view, but a low
classification from the hydro-energetical point of
view because it's considering only the I stage.
Overall, the 4-th place obtained considering
policies is not satisfying.
129
water price(B2), but working on the IIT scale (C3)
leads to a high hydro-energetical cost so , eventually,
the strategy gives us unsatisfactory classification.
P13-222 4 1 2-: „Revolution”( IdlO: 6 / EcolO: 7
/HidrolO: 4 /EnglO: 5)
This strategy implies too many changes – even
changes at an institutional level: cutting off
subventions, the semnificative growth of the price of
the water. Although is very efficient for the hydro
criterion, economically it’s eutopic.
P17 - 3 2 3 5 1 2 -: „Pro vegetables + potatoes"
(cotări: Id 10: 7 / Eco 10: 9 / HidrolO: 6 / EnglO: 10)
This strategy also implies important changes at
an institutional level, but it’s not acceptable due to
high economical and energetical costs.
4.Conclusions
P4 -1 2 2 4 3 2-: „No subventions, in favor for
sun-flower (clasifications: IdlO: 6/EcolO:
4/HidrolO: 7/EnglO: 7)
This very liberal strategy ( cutting off the
subventions and rising the water price) has a high
cost not only from the economic reasons but also
energetic ones, with no compensations for a hidro
level. Theese are the reasons for low clasifications
in each sharing system.
P9 - 2 1 1 4 2 1 -: „Compromises" (clasifications:
IdlO: 1 / EcolO: 1 / HidrolO: 2 / EnglO: 2)
Number 9 strategy provides compromises for
the economic, energetical and environmental fields
as to obtain best classifications in each share
system. Considering the arrangement, the option is
"affusion" (A2), suggest the expansion of sunflower culture(D4) and, of course, the proper
irrigation equipment (E2).
P12 - 2 2 3 2 1 1 -: „for the III-rd degree"
(clasifications: Id 10: 3 / Eco 10: 3 / HidrolO: 4 /
EnglO: 6)
First 2 2 pair is a proper strategy for water
saving: affusion irrigation system(A2), rising the
The way of approaching the decisional matter,
used in this study leads to achieving some orientative
results for the decision factor. The next step is
replacing the criteria with real facts, which makes it
more precise and easier to be interpreted.
As a conclusion, we can say that the best hydro
strategy is by far keeping things the way they are and
requiring major changes regarding the water volumes
(measurement, the impermeability of sewers and most
of the surfaces equipped with underground pipes), the
crops structure (advising the farmers to cultivate high
rated crops for irrigations and for the farmer itself), the
price of water and the subventions (maintaining the
current price by investments made for rehabilitating
the system).
5. Bibliography
[1] ARONDEL,C, P. GIRARDIN: Sorting Cropping
Systems on the Basis of their Impact on Groundwater
Quality. in: European Journal of Operational
Reasearch, 1998.
[2] CISMARU C, V. GABOR, T.V. BLIDARU, D.
SCRIPCARIU: Studii privind eficienţa lucrărilor de
reabilitare şi de modernizare a sistemelor de irigaţii
cu mai multe trepte de pompare, Ovidius University
Armals of Constructions Vol. 1, Nr. 2, 2000.
[3] CONSTANTIN N., S. DUMITRIU: Multimodel
Approach for Electrical Actuator Control. în: Proc.
4*Int. Conf. on Electromechanical and Power
Systems, SIELMEN, 2003, pp. 139-143.
[4] IORDACHE, GH., L. ROŞU, C. MAFTEI, C.
GHERGHINA: Cercetări privind eficienţa
sistemelor de irigaţii din zone colinare, în corelaţie
cu suprafaţa irigată pe trepte energetice şi studiu
de caz. în: Bul. Inst.Politehnic din Iaşi, Seria
Hidrotehnică, XLVII (LI), Fasc. 1-4, (II), Iaşi,
România, 2001, pp. 213-218.
[5] NICOLAESCU, I.: Bazele modernizării
sistemelor de irigaţii în România. Partea a II-a.
în:Rev.Hidrotehnica, nr. 10 ,1993, pp. 17-26.
[6] OEZELKAN, E.C., L. DUCKSTEIN:
Analysing Water Resources Alternatives and
Handling Criteria by Multi Criterion Decision
Techniques.
in:
Journal
of
Environmental
Management. 48, 1996, pp. 69-96.
[7] ROŞU, L, C. MAFTEI, C. GHERGHINA, L.
ŞERBAN, M. IOSIF: On a Method of the Major
Economic indicators Analysis in the Irrigation
Systems. in: Proc. of the Int. Conf. "Constructions
2003",Vol.3-Civil Engineering&Building Services,
Cluj-Napoca, România, 2003, pp. 411-418.
[8] ROŞU L, C. MAFTEI, M. DOBRE, A. ŞERBAN,
GH. IORDACHE: ELECTRE Method Used in the
Economical Analysis of Romanian Irrigation Systems.
In: 6th International Congress on Advancesing Civil
Engineering, 6-8 October, Istanbul, Turkey, 2004.
[9] ROY, B. The Outranking Approach and the
Foundations of ELECTRE Methods. în: Theory and
Decision,Volume 31, France, 1991, pp. 49-73.
Protection Measures on the Algerian Coastline of the Mediterranean Sea
Khoudir MEZOUARa
Institution of The Sea Science and The Management of The Litoral (ISMAL), Algeria
__________________________________________________________________________________________
Rezumat: În Algeria, situaţia coastei mării este atât de alarmantă încât mai mult de 60% din lungimea ei
este expusă procesului de eroziune.De-a lungul celor 1200 km,aproximativ 800 km se retrag cu aproximativ un
metru pe an. Anumite părţi, relativ rare, sunt expuse la un proces de acumulare.Există diferite zone care prezintă
o situaţie alarmantă : de exemplu coasta Bejaia cunoaşte un indice a retragerii de aproximativ 10m/an. Având în
vedere importanţa economică şi populaţia din zonă, eroziunea costală este considerată o faţă foarte periculoasă a
dimensiunii economice a spaţiului litoral, şi cu vulnerabilitatea populaţiei ce locuieşte aici,eroziunea costală
este privită astăzi ca un risc natural major. Pentru a minimaliza aceste efecte negative şi pentru a cauza doar mici
pagube ale ţarmului şi ale împrejurimilor,au fost schiţate mai multe soluţii noi şi puse chiar în aplicare în diferite
părţi ale lumii.
a
Abstract: In Algeria, the condition of the sea coast is rather alarming as more than 60% of its length is subject to
the erosion process. Along 1200 km, about 800 km is withdrawing by about one meter per year. Certain parts
that are relatively rare are exposed to an accumulation process. There are several areas showing an alarming
condition: for e.g. Bejaia coast knows an withdrawing rate of about 10m/ year.
Considering the economic importance and the population of the area, the coastal erosion is thus considered as a
major hazard face the economic dimension of littoral space and with the vulnerability of the populations which
reside at it, coastal erosion is regarded today as a major natural risk.
In order to minimize these negative aspects and in particular to cause only little damage to the shore and the
environment, various new solution have been outlined and even implemented in different parts of the world.
Keywords: Coastal erosion, Erosion process, Major natural risk, Shore.
__________________________________________________________________________________________
1.
Introduction
The importance of beaches as holiday resorts
and consequently the permanent growth of
touristical developments in coastal area increases
the claim of land and beach to the very limit of the
sea. This phenomenon was particularly evident in
the industrialized countries. Most of these coastal
development were planned without enough
consideration of possible negative consequences on
beach evolution and eroding capacities of the sea.
Several factors may cause beach erosion, most of
which are natural. Beaches are constantly moving,
building up here and eroding there, in response to
oceanographic factors (waves, winds, storms,
relative sea level change and supply fluctuation).
The hydraulic structures have a very
important influence on the morphological processes
of the coasts. However, the dikes, the water intakes,
the deepening of the river bed for navigational
ISSN 1584 - 5990
purposes, the excavation of sand and gravel from
the river bed (and even directly from the beaches)
reduce the bed load at the river mouth, and, as a
consequence, the supply of littoral sand. [8] The
execution of river mouth jetties, large harbours, or
even some transverse coastal structures foreseen for
protection of the shore, has a negative effect as
concerns the continuity of the littoral transport, in
the same way as groins cause upstream
accumulation and downstream erosion. In addition,
the water pollution may reduce the number of shells
and the organic sand supply of the beaches.
Hopping to stop drastically erosion induced
problems, local authorities or private developers
often build sea-walls, dams or other similar hard
defences which themselves provoke more erosion
due to phenomena, such as reflexion, currents,
overtopping, scouring, etc…
132
Protection Measures on… / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 131-136 (2007)
A feasibility study for coastal protection
works on the Algerian coast showed that beach
nourishment could be considered as an effective to
traditional building of detached breakwaters. Proper
sand qualities are required to contribute te
predominant longshore transport. Artificial
nourishment of beaches is the evident solution but
this is not possible everywhere or it is too
expensive; protection works are and will be in the
future more and more necessary.
2.
Intervention requirements
This section presents typical shore protection
measures with a discussion of site characteristics,
construction materials, design considerations,
maintenance requirements, advantages, and
disadvantages.
Researchers from the above mentioned,
specialized institutes declare that the minimum
requirements for the shore protection are the
following: [3]
- " Soft solutions", (Beaches’ artificial
nourishment, sand fences, dunes’ stabilization
planting beach grasses. In combination with
adequate beach strands, they provide an effective
measure of protection to upland properties against
the effect of waves.) for short and medium time
scale;
Beach nourishment is the replacement of sand
along the shoreline of an eroding beach. This
method of control takes advantage of the natural
protection that a beach provides against wave
attack. Beach nourishment may also be used in
combination with other methods of shore erosion
control such as groin fields and breakwaters.
Beach nourishment is appropriate where a
gently sloping shoreline is present. It is also
appropriate where the erosion rate is low. The sand
applied in a beach nourishment project should be
identical to the original beach. A coarser sand may
erode more slowly than a finer sand. The sand may
be dredged and pumped from offshore or
transported from upland sites by trucks and
dumped.
The erosion rate of the property is probably
the most important element in designing a beach
nourishment project. If the rate is high then beach
nourishment may not be appropriate.
The direction and rate of movement of sand
along the shoreline should be determined. Sand
may be placed directly along the eroded shoreline
or at a point up drift, allowing natural currents to
move sand down drift. The resulting shoreline
protects the area in back of it by sacrificing the
newly deposited sand. If the added materials are
eroded their eventual fate should be considered, to
avoid shoaling and filling of adjacent properties and
waterways.
Periodic replenishment of the beach using
appropriate size sand will help maintain the beach.
The need to replenish the beach depends upon the
rate of erosion at the particular site. Although the
original cost of the addition of sand may be low, the
cost of periodic replenishment may rival a more
permanent solution.
Beach nourishment provides effective
protection without altering the recreational values
or natural integrity of a shoreline. In providing
protection, beach nourishment benefits rather than
deprives adjacent areas. This option maintains
access along the beach for activities such as
swimming and fishing.
- " Hard solutions" ,common hard defences are
groins ( perpendicular to the coast), detached
breakwaters (parallel to the coast), sometimes
submerged, and se-walls. Each of these protective
structures has a specific function.
Groins are built to reduce the longshore sediment
transport in a certain beach area. [1] If not well
designed (length, height) they can cause at the leeside severe erosion, extending over several
kilometres along the coastline. The latter, n turn,
cause an elongation of the defence system over
more and more coastline.
Detached breakwaters are offshore barriers
intended to reduce wave action on the existing
coastline. This effect will not only reduce onshore –
offshore transport (especially during storm
conditions) but will, in certain circumstances
reduce littoral drift and create " tombolo’s " due to
wave diffraction effects. Under severe storm
conditions the water layer above
K. Mezouar / Ovidius University Annals Series: Civil Engineering 9, 131-136 (2007)
the crest will no longer abate the incoming waves,
which will continue to attack and erode the beach
area. Furthermore, the wave attack on the structure
is heaviest under these conditions.
Sea-walls are built to prevent to coastline from
further regression. On eroding beaches with
predominant longshore transport such defences will
no alter the longshore transport and beach erosion
in front of the sea-wall will continue. The latter
increases wave attack on the sea-wall and the
offshore transport. As a consequence: the stability
of the structure is undermined.
These solutions are applicable in medium and long
time scale.
Groins and breakwaters will only affect the
wave climate and sediment transport in the
immediate area. They do not create solutions for the
adjacent coastal areas where the sediment transport
capacities are unchanged. On the contrary, the may
cause a spectacular increase in sediment transport
on the lee-side of the construction causing new
coastal erosion. In fact the problem has been moved
from one area to another.
If recreational aspects are important, any
coastal structure one the beach should be avoided.
Furthermore, considerable sums of money have to
be spent on maintenance and repair due to storm
damage of the structures.
- " Non-structural ", the first three protection
measures mentioned above fall into this category.
The consideration of any of these methods requires
careful planning and design considerations to
withstand the erosive forces that may be
encountered on your property.
A property owner should first consider taking
no action. Often, a property owner's reaction to
shore erosion is to act immediately. The property
owner is advised to estimate the losses if no action
is taken, especially if the land is undeveloped or
relatively inexpensive structures are at risk. In some
circumstances, the property will have only a very
low erosion rate or experience erosion only during
major storms. It may be desirable under these site
characteristics to leave the shoreline in its natural
condition. If the encroachment of the water on the
property threatens valuable structures, then
relocation should be the next alternative considered.
133
Site characteristics: The shoreline is usually
flat. The exposure to the forces of erosion must be
minimal and the erosion rate low to nonexistent.
Sufficient land should also be present between the
water and any structures to withstand the erosion
rate during the lifetime of the structures.
The advantages of this option are saving
money and avoiding accelerating erosion on
adjacent properties. The relocation of any structures
could cost less than erosion control measures.
The disadvantages are: The loss of any
waterfront property maybe costly and this option
provides no protection from erosion. Relocation of
structures takes special equipment and technical
expertise and could cost as much or more than an
erosion control structure. The introduction of
sediment from uncontrolled erosion into the water
may also be harmful to fish and aquatic plants.
Actually, "soft solutions" or "do nothing"
solutions are considered optimum, in good
agreement with coastal mechanism dynamics and
natural processes. Usually, these methods have a
reduced impact on the beach environment and, they
require lower costs and reduced maintenance.
3.
Protection measure
Efforts were certainly authorized for the
safeguarding of the beaches, but compared to the
environmental and economic stakes, one notes
overall that it remains still much to make. We can
present in three shutters. The Algerian experiment
as regards rehabilitation of the beaches: systems of
coastal protection, the legal devices for protection
and methodological research for the integrated
management of the beaches.
The protection works used on the Algerian coast are
quite diverse.
3.1 Longitudinal works:
These ones can be encountered all aver the
central pert of Algeria (Boumerdes, Ain Taya,
Alger) and their purpose is to stop the sea progress.
These works constructed as vertical walls were
considered as the only means to protect the sea
coast because of their advantages: their area is
relatively restricted and they can stand against the
wave’s impact due to their massiveness. However
134
their efficiency is rather low due to their reflecting
power, and especially to the taking-over of power
of the frontal waves. Also they are not aesthetic.
3.2 Transversal works:
They are concentrated in the area of the towns
such as Alger, Boumerdes, Tipaza. They can also
be met along a great length of the coastal area
(AinTaya, Bordj El Kiffan, and Sidi Fredj) [2].The
main inconvenient lies in the fact that the alluvia
are deposited on the exposed side while the
continuous erosions can be noticed in the protected
area without sediments. In order to prevent the
extension of these erosions, the number of groins
has been enlarged.
Sometimes they are performed too close to the
shore and can absorb only a small part of the
wave’s power. Thus the protection works are not
adapted to the constant degradation type and
generally the same type has been used.
In the case of groins there can be noticed
erosions in the downstream and thus the solution
has to be analyzed. The protection walls are meant
to stabilize the high shores and to protect the
structures against the sea action, especially in case
of sea storms (Boudouau Marine, Bordj El
Bahri).The walls cease the alluvial change between
the high beach and the sea shore creating a
significant lack of balance of the waves power, and
thus an increase of the erosion.
4.
The new soft protection shore in the
Algerian littoral
For Algeria, the objective is to find a solution
not only economic but also which will be matched
with the durable development. The artificial supply
of the beaches is possible but it is needed a material
as close to the existing one (e.g. granularity).At
present this idea is under study as the borrowing
sources are rare. This solution is expensive but
efficient if the nature and granularity of the existing
sediments is satisfied. Also it is necessary to protect
the dunes as they are at the origin of the Aeolian
entrapping of the sediments.
The use of the sand of the Saharian Atlas
proposed for the concept of artificial nourishment.
[5]
The objective was double; to fight against the
projection of the desert while facing the marine
floods. It was necessary to confirm or cancel the
existence of a sand which must be imperatively
close to the littoral (Saharian Atlas) and also of a
texture (size) coarse or identical which answers the
climate of waves of the easily flooded dimensions
by applying the law of Krumbrein. [6]
R = ( Aφ a / Aφ n ) exp −
(Mφ n − Mφ a )2
(
2 A 2φ n − A 2φ a
)
(1)
Aφ e s tandard deviation of material of contribution
Aφ n standard deviation of natural material of the
shore
φ the Krumbein scale of Phi.
Mφ e median of material of contribution
Mφ n median of natural material of the shore
It is necessary that R borders 1,5.
The report/ratio obtained for the sand of the
source is equal to 1.63. The results confirm that the
sand of the atlas has very good quality (diameter
and morphoscopy) to feed the beach.
The loading of the dimensions by the sand of
the Saharian Atlas, an other objective was drawn up
which is the creation of the artificial see-weeds
which will have the role of attenuator of billows
and to protect the shore with a reasonable cost
compared to the riprap, groynes and breakwater
which are very expensive.
As example this technique could be
recommended on the Western beach of Sidi frej and
Bejaia plage or of the thousands of cubic meters of
sands gone up of the small funds is evacuated
backwards country because of the destruction of the
dunes or the sea does not cease advancing.
In many projects beach nourishment is
combined with the construction of hard defence
structures saw with soft defence, such as:
- Combination of artificial nourishment with
construction of groins battery of length (60 meters)
and decreasing in the direction of longshore.
- Combinations of beach fill with a set of long
jetties (artificial headlands) and a series of lowcrested, submerged breakwaters (artificial reefs).
Artificial headlands contain the sediment
K. Mezouar / Ovidius University Annals Series: Civil Engineering 9, 131-136 (2007)
movement within a coastal cell, limiting the
sediment transport across the headlands.
- Artificial seaweed is another technique. The
artificial seaweed is placed in the water in units of
1.3 m long. They reduce the speed of the current,
allowing sand to be deposited around and on top of
the seaweed units. The units are eventually buried
by an offshore sand bar, and the deposit protects the
beach from wave action
- Beach nourishment and rebuilt dune with buried
seawall/revetment. The soft alternative (beach and
dune with buried rock seawall/revetment) was
determined to be both environmental and
economically advantageous when compared against
an armored revetment for storm protection against
the 1 percent change storm event.
In the event of a major storm causing severe dune
erosion, the buried seawall will prevent storm
damage if a second major storm occurs in the same
season.
- Geotextile materials or filter fabrics have a long
history for foundation mats beneath rubble-mound
structures and, they have been used as silt curtains
to contain dredged materials in the water column.
They have also been formed into bags and long,
sausage-shaped cylinders (called Longard Tubes)
and filled with sand. They have been deployed as
revetments for dune protection, as nearshore
breakwaters, and as groins. The design life of a
geotextile filled bag depends on many factors. It is
generally less than properly designed rock
structures serving the same function. However, if
found to cause negative impacts to adjacent
shorelines, the bags can be cut open and removed
with the filled sand remaining on the beach. It is for
this reason that a soft groin field was permitted with
a beach nourishment project
- Slope grading and terracing: A shoreline bank
may be unstable due to the steepness of the slope.
Slope grading and terracing will reduce the
steepness, and therefore, decrease erosion caused
by waves striking a steep slope. The shoreline must
have a steep slope where erosion is present. No
additional materials are required for this type of
shoreline protection other than top soil, vegetation
and materials for surface/subsurface water
management such as ditches or drains.
135
If wave energies are high, the use of slope
reduction and terracing may not be enough to stop
erosion. The slope of the existing shoreline and the
desired one must be determined. A recommended
design is 5:1 (average for terracing), although a
slope of 3:1 is often satisfactory - especially if
combined with other methods of shore protection. It
is recommended that regraded banks be stabilized
with plants. The control of surface and sub-surface
runoff is necessary to maintain slope stability and to
prevent the destruction of any grading that is
performed on the site. Generally, the cost for this
procedure is low but varies. The cost rises
dramatically if materials need to be removed from
the site.
Maintenance Requirements: Periodic regrading
and replanting may be necessary depending upon
the erosion rate. The use of additional material may
also be necessary to maintain the proper slope.
Slope grading and terracing can result inland
that is more useful to the property owner and
provides access to the waterfront. The process can
also be combined with erosion control structures for
increased effectiveness at low additional cost.
Many non-traditional ways to armor, stabilize,
or restore the beach including the use of patented,
precast concrete units, geotextile-filled bags, and
beach dewatering systems have been tried in the
field. Their success depends on their stability
during storm events and durability over the
economic, design life. Their initial cost and cost for
removal if environmental impacts warrant can be
less than traditional methods, at some sites. These
new technologies often involve non-traditional
materials or shapes but are employed in a
traditional manner, e.g., nearshore breakwaters. [8]
5.
Conclusion
The constructions of hard coastal defences
(groins, detached breakwaters, sea-walls) are not
always the optimal solution for the prevention from
the beach erosion. They may even displace the
coastal erosion problem from one area to another.
The better understanding of coastal dynamics,
use of coastal morphological models verified and
calibrated with field measurements and the
evolution in dredging techniques and equipment
136
tends to postpone the need to construct new groins,
breakwater, etc…
The time won in delaying the implantation of the
hard solution gives more lee-way to investigate,
understand, and so manipulate the processes of
beach erosion. As a result one endsup questioning
the necessity for a hard solution in the first place; a
decision which may prove to have been unjustified.
Many coastal erosion problems can be solved by
proper sand suppletion as well as contributing much
better to any recreational aspect of the beach.
Examples of beach nourishements all over the
world show a progressive confidence in this matter.
In many projects beach nourishment is combined
with the construction of hard defence structures and
with soft defence.
Any beach nourishment project must always be
accompanied by a well defined observation
programme to monitor trends.
6.
Bibliography
[1] Bonnefille R., Cours d’hydraulique maritime,
1992 , 3° édition - Ed. MASSON
[2] Boutiba M.,. Etude en grandeur nature du mode
de fonctionnement des ouvrages de protection de la
plage Est de Sidi-Frèdj (Ouest algérois), 1996
Magister en géomorphologie et aménagement des
côtes. ISMAL, Alger, 123 p.
[3] Coman, C.and I. Postolach., Protection
Measures for Romanian Schore, proceedings of the
international conference on Coastal Zone
Management and Coastal Engineering,, 1997.Varn
Bulgaria. Pp. 104-109
[4] CERC, Shore protection projects. Civil
Engineering Research Center, Department of The
Army Corps of Engineers, 2001. Washington DC
part V,chap. 3, 92 p.
[5] Hemdane,Y., et Gater S., faisabilte des
rechargements, en algerie, des plages et petits fonds
incluant les produits geosynthetiques. Exemple
d’une plage de bejaia, 2000. Memoire d’ingenieurat
d’etat en protection des littoraux. Ismal. Alger.
[6] Krumbrein,W.C., A method for specification of
sand for beach fills, Beach Erosion Board, 1957.
Technical Memorandum N 102,Washington
[7] Paskoff, R., Cotes en danger. Coll de la
geographie, 1993. Masson ed, 247p
[8] US Army Corps of ingineers (1981): Low-cost
shore protection: A property owener’s quid; low
cost shore protection: A guide for local
government officials; Lows-cost shore protection:
A guide for Enginners and contractrs. Washignton,
D.C.
Shoreline Variation and Protection Measures on the Romanian Coast Line
of the Black Sea – A Case Study for Mamaia Beach
Khoudir MEZOUAR a
Romeo CIORTAN b
Institution of The Sea Science and The Management of The Litoral (ISMAL), Algeria
b
I.P.T.A.N.A. Bucharest, Bucharest, 010867, România
__________________________________________________________________________________________
Rezumat:Ţărmul românesc al Mării Negre este foarte variat ( plaje, faleze, lagune, delta…)existând şi un curent
litoral important de o comlexitate deosebită. Se pot observa zone de acumulări ca şi sectoare supuse eroziunii. In
acest articol se propune modelarea fenomenului de variaţie a coastei, bazată pe modelul UNIBEST. Se
calculează schimbările liniei ţărmului pe o perioadă lungă de timp şi pe o zonă întinsă. Acest model este foarte
utilizat în inginerie costieră.Eroziunile generale ale ţărmului românesc şi extinderea portului Midia sunt
principalele cauze ale pierderii de plaje în zona Mamaia. Modelarea evoluţiei liniei de coastă în Mamaia arată că
zona de sud este în principal afectată de eroziuni. În lucrare sunt recomandate unele lucrări de protecţie. Acestea
constau în principal în reabilitarea digurilor insulă şi aport de nisip.
a
Abstract: The Romanian Black sea coastline is very varied (beaches, cliffs, mudflats, delta,…) with important
and complex sedimentary drifts. We can see piles of sand which may disturb the economic activity as well as
subsiding sandy coasts subject to erosion. We propose in this paper an approach of modeling the phenomena of
coastline variation, based on UNIBEST model. There are already various models of coastal erosion but these
models always have difficulties because of the nature of the system considered or the method of resolution used.
UNIBEST models calculate changes in the shoreline position on long time periods and wide areas. They are very
used in coastal engineering. The general erosion of Romanian coast and the extension of the Midia harbour are
the main causes of the severe losses in the beach area at Mamaia. The modelling of the coast line evolution in the
Mamaia showed that there the southern zone is affected by erosion. Some protective solutions have been
recommended in this work. They consist either on the implantation of some sand bar and rehabilitation of
detached breakwaters.
Keywords: beaces, drift, coastal erosion.
__________________________________________________________________________________________
1. Introduction
Any coastal morphology is changing with the
hydrodynamic factors and with the alternations of
the boundary conditions throughout the year.
Longshore currents, wave actions, storm surges and
other hydraulic loads cause permanent changes to
the shore, some being quick, others becoming
evident only after years. If the shore is a flat beach,
there may be a balance of erosion and accretion
during the year and only storm surges may cause
severe loss of soil. In other places there is a threat
of permanent erosion, so defense works have to be
realized.
The Romanian Black sea zone has a total
length of 243 km and it can be divided into two
sectors from both geological and geomorphological
ISSN 1584 - 5990
points of view. The boundary between the sectors is
usually placed at Cape Midia. The northern sector
is placed in front of the Danube Delta and its
evolution is well correlated with that of the delta,
and the southern sector is characterized by the
presence of cliffs, interrupted in several zones
(Mamaia, Eforie, Costinesti and North Mangalia)
by littoral bars.
Field observations and measurements on
Romanian coastline have shown a strong
degradation evolution due to the beach erosion. If
one would not
counteract this structural erosion considerable parts
of the coastal region would be lost in time. In the
paper, the Romanian shoreline evolution is
analyzed. The reasons of seashore degradation and
the means for stopping these phenomena and for
138 Shoreline Variation … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 137-144 (2007)
beach rehabilitation, which were applied lately, are
described.
1.
Description of the model [5]
We present in this work, the evolution of the
shore of mamaia using the model UNIBEST.
In this study a short description is given of the
UNIBEST model. UNIBEST-TC stands for
uniform Beach Sediment Transport Time dependent
Cross-shore.
This
version
uses
vertical
extrapolation of the sediment transport across the
dry part of the profile as implemented by Gootjes
[6].
It is based on the discretization by finite
elements of the equations controlling the
propagation of the swell, the littoral current and
transport transversely and the line of coast. The
application of model UNIBEST is valid only under
certain assumptions:
- Morphological assumptions: the littoral must be
uniform, i.e. that the bathymetric lines are almost
parallel and that the relative transverse profile is in
balance.
- Sedimentological assumptions: granulometry must
be uniform and of the same dimension,
- Hydrodynamic assumptions: the hydrodynamic
factors such as the swell characterized by its period
T, its significant height Hs and its direction of
propagation compared to the transverse profile of
the coast, must be constant
Model UNIBEST is composed of three
dependent subprograms :(UNIBEST-LT) Uniform
Beach Sediment Transport-Longshore Transport;
(UNIBEST-TC)
Uniform
Beach
Sediment
Transport-Time Dependent Coastal profile model;
(UNIBEST-CL ) Uniform Beach Sediment
Transport-Coast-Line dynamics.
1.1. Formulation of UNIBEST-LT model
Program UNIBEST-LT has for role essential
to estimate the value of the littoral transit, for each
formula of transport, while being based on the
calculation of the littoral current due to the tide,
with the combined swell or their actions, all along
the transverse profile of the coast. It is formed with
the conservation equations of the energy of the
swell (1), quantity of movement according to the x
axis (3) and of the law of Snell (4).
d
dx
⎛
⎜⎜ C
⎝
E
Df
⎞
Db
cos α ⎟⎟ +
+
= 0
ωr
⎠ ωr
ωr
(1)
x : longitudinal axis, E: energy of the swell, C g :
g
speed of group, α: angle of incidence of the swell
D d :dissipation of the energy of the swell due to
the surge D f :dissipation of the energy of the swell
due to friction
ωr
(2)
ω r : relative frequency of the swell
= ω − KV . sin α
V : current velocity, K : wave of the swell in the
direction of the propagation numbers. ω Eigen
frequency of the swell (2π/T),
d
dx
(S
XX
) + ρ gh . d ξ
dx
(3)
= 0
k * sin α = C te
(4)
Sxx: shear stress according to the y axis, ξ:
unevenness of the sea level due to the action of the
swell, h : depth of water, g: the acceleration of
gravity, ρ: density of sea water, T: period of the
swell.
1.2. Equations of the longitudinal current
It is about the conservation equation of the
quantity of the movement projected on the axis of
the Y.
d
(S XY ) + ρ gh dh 0 + ρ g V .V tot = 0
dx
dy
C ch
(5)
Sxy: component, according to y axis of the tensor
of radiation, h0 : depth of water at rest,
C ch : coefficient of Chezy, Vtot : total speed, U rms :
orbital velocity of the water particles
2
V tot = V 2 + U rms
(6)
139
K. Mezouar and R. Ciortan / Ovidius University Annals Series: Civil Engineering 9, 137-144 (2007)
1.3. Equations of longitudinal transit [7]
In the model of transport of sediment six
empirical formulas of transport are programmed.
Formula of Van Rijn (1992), formula of Vander
Mer-Pilarczyk (1992), formula of CERC (1984),
formula of Baillard (1981), formula of EnglandHansen (1979), formula of Bijker (1971).
1.4. Mathematical
formulation
UNIBEST-TC model
of
UNIBEST-TC is designed to compute crossshore sediment transport and resulting profile
changes along a longshore uniform coast. Sediment
transport is calculated under the combined action of
waves, longshore currents and wind. These
boundary conditions can be either constant or
periodic, or can be given as time series.
The UNIBEST-TC model consists of five submodules, these are:
• Wave propagation module.
• Mean current profile module.
• Wave orbital velocity module.
• Bed load and suspended load transport module.
• Bed level change module.
It is formed with the conservation equations of the
energy of the swell (1), quantity of movement
according to the x axis (3) and of the conservation
of the momentum according to the y axis (5)
ρghiy
Dt
ω
K sin α = Aρ
1 + sin 2 α
π
f ω f c U1V (7)
i y : longitudinal gradient of the water level due to
the tide,
,
Dt :dissipation of energy due to turbulence
f c , f ω : factors of frictions, U 1 : amplitude
orbital velocity corresponding to Hrms, A
coefficient of chock.
Equations of the model of the rip current :
U 2K
D
τ = ρν t b sin (2 Kh ) + t
C
C
(8)
vt : turbulent viscosity, U b : amplitude of the
oscillatory speed near of the bottom, C propagation
velocity of the swell.
For the layer of medium and the layer of the
bottom, the conservation equations of the
momentum are given respectively by:
∂ ⎛ ∂U ⎞
∂
<U
⎜ν t
⎟=
∂Z ⎝
∂z ⎠ ∂x
(
2
> − <V
)
> + g
2
∂ < Zs >
∂x
(9)
∂ ⎛ ∂U ⎞ ∂
∂ < zs > ∂ < uw >
+
⎜ν t
⎟ = (< u2 > − < v2 >) + g
∂Z ⎝ ∂z ⎠ ∂x
∂x
∂z
(10)
U, w: components orbital velocity of the swell,
U: current secondary.
Equations of the morphological change of the
bottom:
The morphological changes of the bottom are
evaluated by using the conservation equation of the
mass. According to the transverse axis, this
equation is given by:
∂ z ∂ q tr
=0
+
∂ t ∂ xr
(11)
xr transverse coordinate, qtr transport, Z depth
of water.
1.5. Mathematical
formulation
of
UNIBEST-CL model
Model UNIBEST-CL has as a role to estimate
the evolution of the feature of coast and to observe
the impact of the works of protection established
along the coast while being based on the effect of
the gradient of the littoral transit evaluated by
model UNIBEST-LT and of the transport
transversely evaluated by unit UNI-TC. Model
UNIBEST-CL is composed of two units (SHOWTS
unit, STRUCT unit). It is based on the conservation
equation of the mass:
∂Q s
∂y
(12)
h
+
+ q = 0
c
∂t
∂x
b
Qs: longitudinal transport of sediment, hc: depth
activates transverse profile, qb source term or well.
The estimate of the feature of coast by
UNIBEST-CL is based on the conservation
equation of the mass in the longitudinal direction.
Each section is modeled only, by imposing
adequate conditions at each end. UNIBEST model
proposes three boundary conditions: the feature
evolution of coast parallel with itself
(∂σ / ∂t = 0 ) with (∂x / ∂y = 0 ) , the coast does
not evolve/move in the course of
time (∂ y / ∂ t = 0 ) , a variable littoral transit
according to the time.
1.6. Evaluation of the Mamaia shore
The shoreline evolution of Mamaia beach is
strongly influenced by the Midia harbour dikes. The
sand supply of the longshore drift is trapped
upstream of the Midia harbour dikes, causing
sediment starvation of the Mamaia beach and the
remainder of the Romanian southern coast, where
the other touristic beaches are located.
Field observations and measurements on
Romanian coastline have been made during the last
35 years. It was found a strong degradation
evolution due to the beach erosion. During 19621997, the sea has been advancing at an average rate
of approximately 25 m per year. From the total
length of the Northern Unit, of 128 km, as much as
57% is eroded, 36% is under accretion, and 7%
shows a relative constancy [3].
In the Southern Unit, Mamaia beach shows
accretion in its northern part and erosion in the
southern one. Mamaia beach shoreline retreated up
to 38 m, between 1978 and 1995, and it has been
registered an accumulation of 15 m (maximum
value) only in a small area. More then a half part of
the beach is protected by “hard” works consisting
of 6 breakwaters parallel to the shoreline and a
groin in the southern part.
Erosion Causes
- The rectification of Sulina branch of the Danube
delta and extension of jetties 8 km seaward
determined a constant migration of sediment
discharging points to areas of larger depths (> 15
m). However, this sediment load has a big role in
replenishing coastal sand bars from the southern
part of the coast, from Mamaia to Vama Veche.
-The seaward extension of the jetties for navigation
purposes, created a sediment trap for the sediments
discharged through Chilia branch. These sediments
contribute to a secondary delta of Chilia branch
north of Sulina in Musura.
- The Sahalin Island, a naturally formed littoral
sand bar and Midia, Constanta South.
- Agigea, Mangalia harbour dikes disturbed the
natural direction of the longshore drift, having
negative effects both on the littoral sediment budget
and the shoreline.
- Sea level rise and intensification of hydrodynamic
factors contribute to the erosion phenomenon.
1.7. Hydrodynamic data
Statistic tests of wind direction indicate also a
high value of the coefficient of stability during
storm situations with strong winds [2]. Mean
duration (about 30 hours) and maximal duration of
storms (more than 130 hours) are recorded for wind
from the North.
Maximum wind speed is about 40 m/s.
Maximum wave height during these storms is about
9.5 m and about 8 m near the shore. The NorthSouth orientation of the Romanian shore the
bathymetric contours determine the asymmetry of
wave propagation. Winds from West have a
confined fetch and wave crests run parallel to the
shoreline because refraction in the shallow water
near the shore. The highest values of the average
wave parameters are recorded for waves from the
East direction, perpendicular to the shore: length
(Lm) is about 34 m, height (Hm) about 1.2 m and
the period (Tm) about 5 sec.
1.8. Parameters of UNIBEST model
Depth of closing: It is the depth from which is held
indeed the phenomenon of transport. [4]
h f = 2 .28 H so − 68 .5
H so2
gT 2
(13)
h f : Depth of closing , H 50 : significant height of
the swell.
Profiles of balance: It depends on the
hydrodynamic conditions and the granulometry of
the medium
H
r
(xr ) =
A 1 xr
2/3
with A 1 = 0 . 067 W
0 . 44
s
(14)
∑ [H (xr ) − H (xr )]
∑ H (xr )
141
2
ε =
r
d
(15)
1
2
r
1
H r : depth of water to the transverse position
xr :compared to the coast, H d : depth of Dean to
The calibration related to the hydrodynamic
parameters, the coefficients of the formulas of
transport, limit of the dynamic zone xrb
corresponding to the height of closing and limit of
the zone of transport.
the position xr, Ws : falling speed of the particles.
2.
Diagram of Bonnefille [1] giving the height
and the period according to the characteristics of
the wind (lasted of action, speed, fetch)
Table 1: Results of the calibration of the model
Equation
parameters
T dom =
∑
∑P
Pi T i
i
i
i
α dom
,
⎡ ∑ Pi H T i ⎤
⎥
= ⎢⎢ i
⎥
T dom
⎢⎣
⎥⎦
2
si
H
sdom
⎡ ∑ Pi H si2 Ti sin α i
⎢
= Arctg ⎢ i
P H 2 T cos α i
⎢ ∑ i si i
⎣
1/ 2
⎤
⎥ (16)
⎥
⎥
⎦
T i : period of the swell n° I, T dom : period of the
dominant swell, pi : percentage of occurrence of
the swell, H si : Significant height of the swell,
: Significant height of the dominant swell,
H sdom
αi: direction of the swell n° I compared to the
transverse profile, α dom : direction of the dominant
swell compared to the transverse profile.
Results obtained
Hydrodynamic
equations
α = 0.91
γ = 0.69
fc = 1
k r = 0.58
k r = 0.030
Formulas of
transport
Limit of the
dynamic zone and
the zone of
Transport
n= 0.4
epsb = 0.14
epss = 0.024
xrb = 373
xrb =391
Y (m)
Y (m)
X (km)
Fig 1: evolution of the shoreline in the northern part of the Mamaia beach
X (km)
Fig 2: evolution of the shoreline in the southern part of the Mamaia beach
We observe an agreement between the shoreline
observed in the morphological chart and shoreline
simulated by the model.
In order to respect the assumptions of
UNIBEST, the shore of the Mamaia is subdivided
in two sub-sectors the following figures show the
result obtained.
The result of simulation is presented in the
figures. It shows the evolution of the coast of
Mamaia on the horizon 2010 starting from its
position in 2006. Mamaia beach shows accretion in
its northen part and erosion in the southern one.
The northern sub-sector: shoreline beginning
from the Midia port and width of approximately 40
meters (the foreshore slop is 1/6, and backshore
profile is 1/46) tends towards a stable position, and
it has been registered an accumulation of
approximately some 10 meters only in a small area.
The coast has a general tendency to fattening
(1m/an on average)
The southern sub-sector: in this sub-sector,
many bars restaurants are built on the backshore
and a beach of only 24 m wide is opened to beach
users, out of the total beach width of 54 m. the
overall beach slope is 1/37. The shoreline is
retreated up to 38 m, between 1978 and 1999 . the
coast has a general tendency to erosion (-2m/an on
average) this is primarily on the one hand, with the
energy brought by the swell six detached
breakwaters built at the distance of some 400 m
from the shore, though they have subsided greatly,
are exercising a certain accretionary function as
evidenced by slight advance of the shoreline behind
them `compared with the area without the
breakwaters. The shoreline change is typical of
low-crested detached breakwaters located at a large
distance from the shore.
3.
Intervention requirements
Coastal protection and flood defence
techniques can be described in relation to the
development of what are termed “hard and soft”
engineering techniques. The hard engineering
techniques involve the construction of solid
structures designed to fix the position of the
coastline, while soft techniques focus on the
dynamic nature of the coastline and seek to
work with the natural processes, accepting that its
position will change over time.
The protection measures began with the
construction of the groin and the artificial
143
nourishment, which prevented the collapse under
wave action of the covered swimming pool “Parc”,
in the southern extremity of the Mamaia beach.
Also, artificial nourishment with sand transferred
from Siutghiol Lake was realised. An aerial view of
this zone, before and after the achievement of the
protection works.
Fig.3. The southern zone of the Mamaia beach,
before and after the achievement of the
protection works (gryone)
In the second phase of the protection
measures, the entire southern zone of Mamaia
beach was considered. The construction of
protection works began in 1988, the adopted
solution being as shown in figure 2 .Each
breakwaters are 250 m length, having the crest level
at +2.5 m. The weight of armour unit (individual
artificial block) in primary
cover layer is 20 tons. About 500,000 m3 of sand
were transferred (by dredging and hydrotransport)
from Siutghiol Lake to the Mamaia beach. The
effect of protection works was an increment of the
beach area with approximately 64,000 m2 (7.8 m3
of sand for 1 m2 of beach area). At last, the
transferred sand was redistributed by the action of
waves and marine currents, but now the beach area
in southern zone of Mamaia is equivalent to the
year 1962 beach area.
Breakwaters and groynes will only affect the wave
climate and sediment transport in the immediate
area.
They do not create solutions for adjacent
coastal areas where the sediment transport
capacities are unchanged. On the contrary, they
may cause a spectacular increase in sediment
transport on the lee-side of the construction causing
new coastal erosion. In fact the problem has been
moved from one area to other.
Applying various techniques, which can be
hard or soft, or a combination of both, provide the
means of dealing with the problems. The solutions
vary according to the local situation, but ultimately
the aim is to identify the best option or options,
which secure the coastline both in the interests of
the environment and of people, in the most efficient
and cost effective way. The overall objective is to
provide policy-makers and managers with
information on the available options to aid the
decision-making process in order to identify the
coastal defence or other management technique
most appropriate for each problem area.
Other solutions are proposed: reinforcement
of 6 detached breakwaters with the rehabilitation of
beach by the artificial nourishment of sand is
accompanied, on occasion, by auxiliary works of
permanent nature, such as submerged groins (200
m).
Beach nourishment at Mamaia was applied to
recharge the eroded beach with a appropriate sand
material Basic guidelines include the principle that
as much as possible, the material used for
replenishment must correspond in form and size to
the local beach material. Unfortunately the sand
material used was too fine in the case of Mamaia
beach. The nourishment resulted in local turbidity
and water retention problems.
Utilization of the sand bar: the basis of this
shore protection methodis to use large sand-filled
bags and sheets of textile to form an artificial sand
bar. A low sand dun/ bar was constructed parallel to
and in front of the main sand wall. This sand bar
was covered with a textill sheet, the adges of which
were pinned down with sand bags. In general this
protection method was found to be successful.
4.
Conclusion
Field observations and measurement on
Romanian coastline have showen a strong
degradation evolution due to the beach erosion, in
the paper, the Mamaia shoreline is analysed.
The study of the coast of Mamaia of the
required its division in areas of the study in order to
respect the basic hypothesis for the UNIBEST
model. The modelling of the coast line evolution in
the Mamaia showed that there are two sub-sectors,
accretion in its northern part and erosion in the
southern one.
Some protective solutions have been
recommended in this work. They consist either on
the reinforcement of 6 detached breakwaters by the
artificial nourishment, accompanied by auxiliary
works such as submerged groins
5.
References
[1] Bonnefille R., Cours d’hydraulique
Maritime. 1992, 3° édition - Ed. MASSON.
[2] Chertic, E. et al., Studiul dinamic al
caracteristicilor meteorologice pentru furtuniledin
bazinul vestic al Marii Negre in scopul determinarii
campului vantului. Posibilitati demodelare si
prognoza, Studii de Hidraulica, XXXIII.1992,
Minist. Mediului, ICIM, Bucuresti, pp.77-103.
[3] Coman, C.and I. Postolach., Protection
Measures for Romanian Schore, proceedings of the
international conference on Coastal Zone
Management and Coastal Engineering. 1997 Varna
Bulgaria. Pp. 104-109
[4] Dean R., Equilibrium beach profiles.
Characteristics and applications. 1991, Journal of
Coastal Research, vol. 7, n° 1 – ASCE.
[5] Delft Hydraulics., 1992 , Manual of UNIBEST.
[6] Gootjes, G,. Dunes as a source of sediment
for Delft3D-MOR. MSc. 2000, thesis, Delft
University of Technology.
[7] Van Rijn, Handbook of sediment transport
by current and waves. 1990, Delft Hydraulics, 2ème
édition.
Explanatory Aspects of the Research Concerning the National Land Reclamation Digital
Data Fund (FNDDIF)
Irina STATEa
Tudor Viorel BLIDARUb
Dr. ing., CPII, Project Director, S.C. ISPIF-SA Bucharest
b
Dr. ing., CPII, Project Vice-Director, ISPIF Branch Iassy
a
Rezumat: Îmbunătăţirile Funciare, ce au drept scop principal creşterea cantitativă şi calitativă a producţiilor
agricole cu păstrarea, protecţia şi ameliorarea calităţii mediului, necesită o permanentă actualizare a informaţiilor
de specialitate utilizate în procesele de evaluare, gestiune şi protecţia resurselor implicate (naturale, umane,
tehnice şi economice). Beneficiarii potenţiali ai sistemului informatic dezvoltat în cadrul proiectului de
crecetare-dezvoltare* sunt instituţii şi regii autonome cu competenţe în domeniul amenajării şi gestionării
teritoriului şi a resurselor naturale, cercetarea universitară de profil, societăţi şi firme de profil, producătorii
agricoli, unităţi de producţie agricolă, publicul larg.
*) „Proiectarea şi implementarea fondului naţional de date digitale al îmbunătăţirilor funciare(FNDDIF).
Studiu de fundamentare şi proiect pilot pentru zona judeţului Iaşi”, contract CEEX 76/2006
Abstract: Land Reclamation having as its main purpose an increase in the quantity and quality of the
agricultural production, as well as the conservation, protection and the improvement of the quality of the
environment, requires a permanent process of updating the specific information used in processes of assessment,
management and (natural, human, technological and economic) resource conservation. The potential
beneficiaries of the IT system developed as part of the research-development project* are institutions and
autonomous companies specializing in the development and management of the land and its natural resources,
university research in the field, specific companies, small and large agricultural producers, general public.
*) „Project and Implementation of the National Land Reclamation Digital Data Fund (FNDDIF). Explanatory
Study and Pilot Project for the Iasi County Area”, contract CEEX 76/2006
Keywords: Land reclamation, GIS
1. Introduction
In Romania, Land Reclamation issues
have represented a concern ever since the 17th
century and have registered an ample and rapid
progress in the 1970’s and 80’s. Significant areas
of land were earmarked for intensive agricultural
crops and irrigation as part of projects addressing
soil hydro reclamation of over 3.25 million
hectares; soil erosion, which threatens
approximately 7 million hectares in Romania, has
been stopped effectively on a surface of more than
2.2 million hectares. Of great significance are also
certain undertaken drainage projects. There have
been important water management projects aiming
at limiting the impact of natural disasters and
ISSN 1584 - 5990
encouraging the use of water from hydro-energetic
systems.
Considering all of the above, as well as the large
percentage of rural inhabitants and farm workers –
over 45% - the arguments in favor of approaching the
issues related to natural resource management and
sustainable agricultural development via an IT system
are convincing. Land reclamation works concerning
and having an impact on the environment can take
advantage of the use of IT in all stages of the specific
decision drafting process – study, analysis, evaluating
and testing various planning and/or project options,
execution, operating, maintenance and management.
146 Explanatory Aspects of … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 145-150 (2007)
2. Objectives
The main objective is to achieve an IT
system based on GIS technology able to assist in
making decisions concerning Land and
Environment Reclamation.
We anticipate a series of research activities
– developing scientific and practical bases for
models, technologies, procedures, and support
applications meant to help define and achieve the
software system based on GIS together with the use
of remote sensing data as a database for specific
works in the area – land studies, planning and
operating land reclamation projects, impact studies.
The specific objectives refer to the
following aspects:
- Research-development and technological
transfer activities with the purpose of achieving
land reclamation and environmental
engineering with the help of an IT system,
together with specific studies aiming at works
of land reclamation, their management and the
state of the environmental systems involved;
- To integrate in the software system and use
various networks, technologies, procedures and
models meant to help elaborate analyses,
solutions, and decisions concerning the
problems related to land reclamation and
environmental engineering;
- Creating the opportunity to disseminate the
good practices by adequately popularizing
them.
Measurable
objectives
–
performance
indicators to be achieved as a consequence of
implementing the suggested system throughout the
mentioned territory – associated with the above
mentioned objectives are:
•
Improving the land reclamation management
performance parameters;
•
Improving natural resource conservation,
protection and regeneration as well as
diminishing the environmental risk factors;
•
Increasing the quality and effectiveness of
technical and economic decisions specific to
the field of land reclamation and
environmental engineering;
•
•
Achieving a timely and effective promotion
campaign for the IT product that addresses the
specialists in the area, the relevant public
authority bodies and the general public;
Promoting the top technologies in the field and
the development of new social facilities and
services for the common citizen.
3. The theoretic framework of the project
Concepts like sustainable development and
integrated resource management must be supported by
an adequate IT basis which allows for real parameter
evaluations and effective assistance in making specific
decisions by analyzing options and offering the best
solutions.
The main relevant directions for sustainable
development are:
•
The use of sustainable development indices;
•
Promoting international use of sustainable
development indices;
•
Improving the process of gathering and using
data;
•
Improving the data evaluation and analysis
methods;
•
Establishing an adequate IT framework;
•
Strengthening traditional informing methods;
•
Producing adequate information to assist in the
decision-making process;
•
Creating documentation to accompany the
information;
•
Establishing standards and methods to use the
information;
•
Implementing and developing electronic data
networks;
•
Using commercial information sources.
In order to set a theoretic framework for the
project in accordance with the sustainable development
objectives, a number of internationally implemented
and used models were examined.
The PSR Model
The PSR model (pressure – state – response) used, for
instance, to evaluate indicators of soil quality,
associates the pressure on the environment as a
consequence of human activities with changes in the
state
of
the
environment.
I. State and T. V. Blidaru / Ovidius University Annals Series: Civil Engineering 9, 145-150 (2007)
147
Driving Forces and Pressure. 10 areas of concern were
selected: air pollution, climate change, loss of
biodiversity, marine environments and coastal areas,
ozone layer depletion, resource depletion, toxic
substance disposal, urban waste problems, water
pollution, and water resources.
The PSIR Model
It represents an intermediate approach
(between PSR - DPSIR) which emphasizes and
connects four of the five aspects mentioned earlier.
Fig. 1. Pressure – State – Response Model
The advantage of this model consists of the
fact that it can be used for activities on areas as large
as a hydrographic basin, for instance. The disadvantage
of this model consists of the fact that its components
and objectives are not easily identifiable for the scale
at which the project is implemented.
The PSIR model emphasizes four aspects of
the problems that have an impact on the territory
and/or the environment:
- The pressure variable feature describes the
causes that generate a problem, be it an
existing problem or the result of a new project
or investment.
- The state variable feature usually describes a
measurable physical characteristic which
occurs as a result of an existing pressure.
- The impact variable feature monitors the long
term consequences of the pressure
The response variable feature is represented by
strategies, actions or investments aiming at solving the
problem.
LEGEND:
Presiune – pressure, Stare – state, Raspuns – response,
Informatii – information
Activitati umane – human activities: energy, transportation,
industry, agriculture, others
Starea mediului si a resurselor naturale – state of the
environment and natural resources: water, air, soil, natural
resources
Agenti economici si de mediu – environmental and economic
agents: administration, domestic households,
economic
institutions, international environment
Raspuns social – social response: decisions, actions
The DPSIR Model
The Driving force – Pressure – State – Impact –
Response: DPSIR model, created by Anthony
Friend in the 1970’s represents an improvement
over the Pressure – State – response (PSR) model
and was widely adopted by science circles and most
member states of the European Community, as well
as European Agencies like Eurostat, (European
Environment Agency: EEA), etc. The main focus of
this model was placed on the aspects of Response,
RESPONSE
PRESSURE
Water
protection
indicators
STATE
Water use
indicators
Water requirement
indicators
Irrigation water use
indicators
Water emission
indicators
Resource availability indicators
Water quality indicators
Water
requirement
satisfaction
indicators
IMPACT
Population risk indicators
Water effect indicators
Fig. 2 PSIR model, emphasizing the types of indicators associated with water resources
Specialized analyses have emphasized the fact
that a sufficiently general model which would
totally satisfy all requirements is the DPSIR &
Composite Indicators model (Driving force +
Pressure + State/Impact + Resource) & Composite
indicators, suggested by several European
researchers because it seems to be the most
sustainable European model. This model, not used
at this time in our country, will have to go through
a period of adaptation to the specific circumstances
of Romania, given our country’s accession to the
European Community.
The basic principle of this model is the
inclusion of all factors able to ensure total
sustainability (indicators and parameters relevant
for sustainable development) – as seen in Figure 3.
This is essentially a tri-dimensional matrix model,
based on four columns: Environment, Institutional,
Social, Economic, and four lines: State, Impact,
Pressure, and Driving Force, which will generate a
model Response. The Composite Indicators to be
used are those of the Eurosat.
Integrating remote sensing data
The development of Geographical
Information Systems that could operate at different
levels (regional, intermediary and local) is focused
at present on the issue of correlating the GIS
system’s high potential with the available data
volume.
Remote sensing may prove to be a useful
tool assuming that the data is selected according to
its quality and the status of the trustworthy and up
to date information.
Integrating the remote sensing data into
the GIS involves a number of studies and specific
stages concerning the information processing as
well as the use of specific IT techniques like data
fusion, for instance.
Together with the interdisciplinary
character of the environmental research in all its
static and dynamic aspects, the present challenges
of the IT field justify the integration of the remote
sensing into spatial databases.
4. Work method and first results
In cooperation with our project partners,
during the first stage, we carried out a number of
activities concerning:
- Resource management analyses in order to
organize the data and define the categories of
interest for the issues concerning the
implementation of a land reclamation digital
data fund;
- Ways to delineate and specify the features of
this land reclamation digital data fund so that
it meets the basic requirements of the database
that represents the theme of the project;
- Preliminary studies, researches and analyses
related to the implementation of a land
reclamation digital data fund for Iasi County;
- Criterion-based analysis to decide upon the
sample areas, representative areas and
environmental issues;
- Early collection and processing of the existing
data from specialized units and sites.
In order to build a graphic database and to
assess further information needs, the process of
primary data centralizing and processing consisting
of transposing onto a digital format the data
collected on paper has begun.
Once the model has been decided upon by
the IF team, the task of the IT team was to identify
the best software solution to support this model, for
example, the solution of an integrated system made
up of several specialized software applications
conveniently interfaced for a multi/bi/lateral data
transfer. The integration can take place only around
a main database. The personal database model will
include the universal composite indicators for all
the integrated applications, but also all the inherent
constraints.
The operating method requires the use of a
software application, based on the data stocked in
the personal database or even of composite
indicators obtained from the BDIF (database).
As a consequence of these activities, the
following results were achieved:
- An assimilation of the model necessitating
an understanding of the main software
requirements, limitations and major risks
that could occur during implementation;
I. State and T. V. Blidaru / Ovidius University Annals Series: Civil Engineering 9, 145-150 (2007)
-
-
The set up of a general model for the
software structure which could support the
proposed model;
An assessment of the international software
product offers (commercial or for
research/development purpose) compatible
with the requirements of the software system
model;
A quick assessment of all software
applications which seem to offer functions
required by the model;
An in-depth assessment of all applications
that passed the quick assessment phase;
An evaluation of the basic hardware and
software requirements;
A period of adjusting to the chosen models;
149
-
Internationally, there are numerous software
applications able to address one model
project aspect or another;
In our country, there are several partially
completed attempts to build software
applications addressing the issues identified
in the model but which cannot ensure the
support for further development;
There is not one single software application
available on the market that could
completely fulfill all the requirements of the
model;
Out of a list of several hundred assessed software
packages, only 15 were chosen as potential choices.
They will undergo detailed testing by our project
specialist team who will eventually decide upon
those
to
be
used
for
the
project.
Fig. 3. The DPSIR & Composite Indicators Model
LEGEND:
Prioritatile EU – EU priorities
Strategii si politici nationale – national strategies and politics
Viabilitate totala – total sustainability
Institutional: decision making, social response, economic
response, environmental response
Environment – air, soil and abiotic, water, biotic
Economic – wealth, trade, help, innovation
Social – health, well-being, attitude, knowledge
Stare/impact – State/Impact
Presiune – Pressure
Forta Motoare – Driving force
Eurostat indices
5. Conclusions. Further activities
There have been a series of activities involving
existing data fund documenting, analysis,
centralizing and basic processing, as well as data
collecting from specialized organizations and sites.
Studies aiming at defining the characteristics of the
land reclamation digital data fund, as well as
preliminary
studies
aiming
at
software
implementing and use of remote sensing have taken
place.
According to the adopted work plan, the subsequent
phases of the project stipulate research and
development activities in sample areas of Iasi
County aiming at land and environment
reclamation, as well as finalizing the IT system –
pilot project.
6. Acknowledgments
We wish to thank hereby our collaborators and
project partners: The Hydro-technical Faculty of the
‘Gh. Asachi’ Technical University Iasi, Project
Director Conf. Dr. Ing. Dan Prepeliţă; the Faculty of
Geography of the ‘Al. I. Cuza’ University, Iasi,
Project Director Lecturer Dr. Ciprian Mărgărint;
S.C. Matrix S.R.L. Iaşi – Project Director Prof. Dr.
Ing. Gheorghe Ungureanu.
7. Bibliography
[1] Barko J. W., Johnson B.L., Theiling Ch. H
(editors). - Environmental science panel report:
Implementing adaptive management. Upper
Mississippi River System. Navigation and
Ecosystem Sustainability Program NESP ENV
Report 2, 2006
[2] Biali Gabriela, Popovici N. – GIS Techniques
In Monitoring Degradation By Erosion „Gh.
Asachi” Publishing House, Iasi, 2003
[3] Blidaru T.V., Prepeliţă D., Neagu I. –
Possible Uses of the GIS in the computerized
management
of
irrigations,
International
Symposium „Geographical Information Systems”,
ed.XII, Univ. „Al.I.Cuza” Iaşi, 16-17 October 2004.
[4] Blidaru V., Wehry A., Pricop Gh. – Irrigation
and drainage works. INTERPRINT Publishing
House, Bucuresti, 1997
[5] Bonazountas M., Smirlis Y., Despina
Kallidromiton – Assessing Sustainability of EU
Regions: The case of the `EPSILON` tool. EU
RTD-IST Project – EC Contract No IST – 2001 –
32389
[6] Borduselu C. – Contributions to the
Processes
of
Conception,
Planning
and
Implementation of the
Geographical Information System with the Help of
Tele-detection and Photogramming in the Field of
Land Reclamation Referat 2 al tezei de
doctorat,Institutul de Constructii Bucuresti, 1989
[7] Gobin A., Jones R., Kirkby M, Campling P.,
Govers G., Kosmas C., Gentile A.R. - Indicators
for pan-European assessment and monitoring of
soil erosion by water. Environmental Science &
Policy 7 (2004)
[8] Meadows Donella – Indicators and
information systems for sustainable development. A
report to the Balaton Group The Sustainability
Institute, 1998
[9] Pietersen K. – Multiple criteria decision
analysis (MCDA): A tool to support sustainable
Management of groundwater resources in South
Africa. Water SA Vol 32. No 2 April 2006
(www.wrc.org.za) ISSN 1816-7950
[10] Scientific Software Group. Environmental
and Water Resources Software Catalog, 2005
[11] State Irina, Blidaru V., Blidaru T. V. –
Hydrotechnical works for Rural Development
through Land Recovery, Protection and Complex
Planning. Optimized solutions including Examples
of Romanian and International Techniques.
Performantica Publishing House, Iasi, 2006, ISBN
973-730-171-4
[12]*** Revised European Charter for the
Protection and Sustainable Management of Soil.
Adopted by the Committee of Ministers of the
Council of Europe, Strasbourg, 17 Jul. 2003
Hydraulic Checking of a Sewerage Collector
Gabriel TATU
Technical University of Civil Engineering Bucharest, B-dul Lacul Tei nr.122-124, sector 2
__________________________________________________________________________________________
Rezumat: Articolul prezintă instrumentele teoretice şi o procedură pentru verificarea funcţionarii din punct de
vedere hidraulic a colectoarelor de canalizare existente. Ca exemplu se prezintă un studiu de caz.
Abstract: The paper presents the theoretical tools and a proposed procedure for checking the existing sewerage
collectors from a hydraulic point of view. A case study is also presented as an example.
Keywords: Hydraulic systems, free surface motion, sewerage collectors.
__________________________________________________________________________________________
1. Basic data
2. Theoretical tools
The main basic data, used within the
hydraulic calculations are presented bellow (on this
occasion, the main notations are also presented):
- the longitudinal profile, defined as the
bottom level variation along the space; the bottom
levels in the manholes have been considered;
- the type (the shape) of the cross section is
defined by the ITIP indicator, having the following
signification: ITIP=1 means circular shape; ITIP=2
means ovoid shape; ITIP=3 means a bell’s shape;
ITIP=4 means rectangular shape;
- the dimensions of the cross section are
defined by the height D and the width B; implicitly,
for the circular shape B=D, for the ovoid shape
D=1.5*B and for the bell’s shape B=1.5*D; for the
rectangular shape B and D are given explicitly;
- the roughness of the collector is given using
the roughness coefficient n and the head losses
have been calculated using the Manning-Pavlovski
formulas; for the case study, a value of n=0.016 has
been used;
- the „injecting points”, i.e. the ramification
points where other smaller collectors are reaching
the actual one are numbered from upstream to
downstream and the used indicator is IRAM.
Two types of hydraulic calculation have been
performed, namely:
a. using the uniform movement hypothesis;
b. using the non-uniform movement hypothesis.
ISSN 1584 - 5990
In both cases, the calculations have been made on
„calculation sectors”, having constant cross sections
and slopes. Generally, these „sectors” are the same as
those between the manholes but when the length
between the manholes was too big, for a better
accuracy in the non-uniform movement hypothesis,
they have been devised into several smaller ones,
respecting a maximum admitted length (in the case
study, this maximum admitted length was 60 m).
a. The uniform movement hypothesis is an unreal
one but generally used for practical (common)
designing calculations; it considers that, on each
sector, the velocity and the water depth are constant
(and, consequently, suddenly changing from a sector to
another, not considering the inter-connections with the
adjacent sectors). This hypothesis allows making an
evaluation of the maximum flowing capacity of the
considered sector and this indicator was noted with
QPLIN. It was calculated using the uniform movement
formulas bellow, for the maximum admitted filling
degree:
152
Hydraulic checking of … / Ovidius University Annals Series: Civil Engineering 9, 151-154 (2007)
- Q = K i where Q is the flow rate, K is
the flow rate modulus and i is the bottom slope;
1
-
K = AC R → R =
A
1
→ C = R6
P
n
where A and P are the area and the wetted
perimeter of the cross section, depending on the
water depth h (or the filling degree GRU=h/D) and
of the cross section shape (ITIP=1/2/3/4).
b. The non-uniform movement hypothesis is the
real one since it considers the inter-connections
between the flow on a given sector with the flows
on the adjacent ones (upstream and downstream),
depending on the flow regime (slow or rapid) and
generating either a gradual varied movement or, on
the contrary, a rapid varied one (the hydraulic jump
occurrence).
For the gradual varied movement, using the
finite difference method, the corresponding
differential equation has been solved, namely:
dh i − J
=
ds 1 − Fr
For the hydraulic jump, the relation between
the conjugated depths (the entering depth h’ and the
exiting one h”) has been considered: S(h’)=S(h”).
In the formulas before, the notations have the
following signification and calculating formulas:
-
J=
2
2
2
Q
Q
V
= 2 2 = 2
2
K
AC R C R
is
the
hydraulic slope;
- Fr =
αQ 2 Bs
g A3
is the Froude number; Bs is
the width of the channel at the free surface of the
water;
- S ( h) = hG A +
αQ 2 1
g
A
is the hydraulic
jump function; hG represents the depths of the mass
center for the flowing section A.
This differential equation has been "re-written"
using the finite differentials and the principle of the
"commanding depths" has been followed for
calculating the depth at one end of a given sector,
knowing the depth at the opposite one. Step by step,
the depths in all the "calculation points" (separating the
"calculating sectors"), i.e. all along the collector, have
been obtained.
In these conditions, the continuity law could also
be fulfilled and constant flow rates have been
considered between two successive injecting points
(like in the real situation).
The calculation of the maximum flowing capacity
has been made by successive trials, raising the flow
rates but not allowing the collector to be put under
pressure on any section. It is interesting to notice that
apparently on some sectors the flowing capacity could
be raised but this is not really true because it would
cause the pressurizing of the adjacent sectors (usually
the upstream ones).
In the figures showing the results of the
calculations, the maximum flowing capacity has been
noted by Q and (as shown before) it has constant
values between two injecting points. The
corresponding velocities have been noted by V and
they have variable values even for constant flow rates
because they depend also of the depth h (or the filling
degree GRU=h /D) and of the cross section shape
which are variable along the collector.
In the same figures, the indicator PRES also
appears and it represents the pressure in the collector in
the points where it is put under pressure; that is why
this indicator appears only in a few isolated cases (as a
rule, the collector is not under pressure).
The units for the different parameters appearing in
the figures are the following:
- D, meters (m);
- GRU, non-dimensional (-);
- ITIP, has no units;
- PRES, meters of water column (m.w.c.);
- Q , QPLIN, cubic meters per second (m3/s);
- V, meters per second (m/s).
The results of the calculations performed for a case
study are presented, in a graphical shape, in the
annexes.
153
G. Tatu / Ovidius University Annals Series: Civil Engineering 9, 151-154 (2007)
3. Comments and conclusions based on the
results of the case study
Annexes
Collector 1
3.5
3
D
2.5
IRAM
2
1.5
1
0.5
463
430
397
364
331
298
265
232
199
166
133
67
100
1
0
34
a. A first conclusion, having a general
character, i.e. referring to any collector, is that the
model of the uniform movement is not suitable in
spite of the fact that it is commonly used when
dimensioning the sewerage networks. As seen from
the comparison between Q (non-uniform) and
QPLIN (uniform), the differences are considerable.
4
Collector 1 - Injecting points
0.6
IRAM
465
436
407
378
349
320
291
262
233
204
175
146
117
88
59
30
1
0
Collector 1
5
4
ITIP
3
IRAM
2
1
449
417
385
353
321
289
257
225
193
161
129
97
65
33
1
0
Collector 1
30
25
20
Q
15
IRAM
10
5
456
421
386
351
316
281
246
211
176
141
106
71
36
0
1
b. For a specific case, the calculations allow
to draw several conclusions regarding the given
collector. For the case study given here as an
example, there are the next remarks:
- the collector has not the normal, telescopic
shape, with cross section areas which should
continuously grow along the space (see the
parameters D and ITIP);
- the available charge of the hydraulic system
(the difference of the ground levels between the
upstream and the downstream ends of the
collector), which is rather considerable, is not used
efficiently: there are sectors with very great slopes
and very great velocities, with the risk of erosion
and, on the other part, there are sectors with very
small slopes and very small velocities, with the risk
of sedimentation (see the parameter V and the
longitudinal profile or the figure showing the flow
appearance);
- as a result of the above remarks but also of
the inter-connections between the flows in the real
non-uniform movement, the "evolution" of the flow
capacity along the collector does not correspond to
the "telescopic", continuously growing, "evolution"
of the flow rates that should be transported along
the collector: as seen (parameter Q), the flow
capacity does not grow continuously along the
space.
Collector 1
140
120
100
Q
80
QPLIN
60
IRAM
40
20
4. References
463
430
397
364
331
298
265
232
199
166
133
100
67
34
1
0
Collector 1
12
10
GRU
8
V
PRES
6
IRAM
4
2
449
417
385
353
321
289
257
225
193
161
129
97
65
33
0
1
Tatu, G. – Hydraulique II, Cours et Applications,
U.T.C.B., Departement de Genie Civil, 1998
(French language).
Tatu, G. – Hydraulique I, Cours et Applications,
Editura Orizonturi Universitare Timisoara, 2005
(French language).
154
Hydraulic checking of … / Ovidius University Annals Series: Civil Engineering 9, 151-154 (2007)
Bottom level - meters
Collector 1 - Longitudinal Profile
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78
76
74
72
70
68
66
64
62
60
58
56
54
52
0
2000
4000
6000
8000
10000
12000
14000
Space - meters
16000
18000
20000
22000
24000
The Increase of Strong Rainfall Concentrated
on Small Areas as an Effect of Climatic Changes
Marius TELIŞCĂ a
Catrinel-Raluca GIURMA-HANDLEY a
Petru CERCEL a
a
__________________________________________________________________________________________
Rezumat: Primele semne ale schimbărilor climatice sunt cele mai vizibile. Observaţiile meteorologice sunt cele
mai indicate pentru a compara valorile parametrilor actuali cu valorile înregistrate în timpul monitorizării
meteorologice a mediului înconjurător. Datele obţinute prin studierea inelelor copacilor, nucleul ghetii superficiale
şi prin alte metode de analiză indirectă a climei, sugerează că la ora actuala temperatura globală a solului are nivelul
cel mai ridicat din ultimii 600 de ani. Se estimează că aceste tendinţe vor continua, exceptând mici variatii
sezoniere, în special în Europa de Sud. Meteorologii apreciază că gheaţa de la Polul Nord va fi topită aproape
complet în timpul verii. Până la sfârşitul secolului temperatura globală va creşte cu 4° Celsius, ceea ce va determina
o creştere a nivelului oceanului cu până la 30 de centimetrii[7]. În Europa verile vor fi caniculare şi secetoase, dar
va avea loc o creştere a umidităţii în sezonul rece. O altă consecinţă a încălzirii globale va fi creşterea cantităţii de
precipitaţii şi evident a pericolului de producere a inundaţiilor.[8].
Abstract: The first signs of the climatic changes are the most visible. The meteorological observations are the
closest to compare the values of the actual parameters with the values recorded along the meteorological
monitoring of the environment. The dates obtained by studying the rings of the trees, the core of the superficial ice
and other methods of indirect analysis of the climate suggest that in these times the global temperatures at the soil
level are higher then in any other stage from the last 600 years. These tendencies are expected to continue,
excepting the small seasonal variations, especially in Southern Europe. The meteorologists estimate that the ice on
the North Pole will melt almost completely during the summer season. By the end of the century the global
temperature will increase by 4° Celsius and that will cause an increase on the ocean level up to 30 centimeters [7].
In Europe, the summers will be dryer and warmer, but it will be an increase of the humidity on the cold season.
Another consequence of the global warming will be the increase of the precipitation quantity and obvious, of the
flooding. [8]
Keywords: climatic changes, global temperature, global warming, precipitation.
__________________________________________________________________________________________
1. Climatic extremes and climatic changes events
at global level and on Romania territory
At planetary level exists a complex of specific
phenomena named ENSO (the acronym from “El
Niño Southern Oscilation”) with great influence
over the global climate. Despite the fact it is
happening in southern hemisphere, the scale of
ENSO affects the entire planetary climatic system.
El Niño is a relatively recent meteorological
phenomenon, associated with the unusual warming
of the waters in the central and eastern area of the
Pacific Ocean.
ISSN 1584 - 5990
El Niño appears without a pattern, but tends to
reappear on periods between 3 and 7 years. Its
“Counterparty” is named La Niña and is characterized by
an accentuate cooling of the waters in those areas. This
complex of phenomena has an extremely big influence
over the cyclonic activity. [6].
The effects of the climatic changes were noticed
also in Romania particularly in the last years. Also the
passing from the cold season to the warm one it’s not
gradual, but sudden with important temperature
variations, and in the passed year were registered many
meteorological phenomena.
In the year 2000, the average temperature on our
country was with 1,8 C higher than the normal
156 The increase of … / Ovidius University Annals Series: Civil Engineering Volume 1, Number 9, 155-160 (2007)
temperature( 8,3°C). Unlike the multiyear average
values, the medium temperatures of the year 2000,
presented positive deviations seized between 1-2°C,
in the largest part of the territory. The highest
temperatures of this year passed 40°C in the south
of the country and were registered in the days of 45 of July and 21-22 of August. The annual highest
temperature was 43,5°C registered at Giurgiu on
the 5th oh July.
The lowest temperatures were registered in
the days 26-27of January, the values of these ones
were under -25°C in the mountain area.
The minimum temperatures have recorded in
the days of 25+26 of January, the values being
under +25°C in the mountain area, on small
territories in north-west and south-west of the
country, and in the depressions of the Easter
Transylvania have drop below -30°C.
The yearly precipitation quantity on the level
of the entire country have been lower with 33,4%
than the normal average multiyear. Excepting the
months of January, March and September, with
exceeding precipitation regime, the rest of the
months have been deficit.
As an example: in October, the average
precipitation quantities have been of 3,2 mm (the
climatologically normal is 38,0 mm). In Oltenia,
western Muntenia and Carpatii de Curbura the
precipitation did not appear.
2. The effects of the climatic changes over the
circulatory water regime
By modifying the thermal regime of the
atmosphere due to the climatic changes, results
implicitly the changes on the water circulatory
regime. In the areas that became warmer due to this
changes is obvious that will increase the
evapotranspiration at surface level. The water
evaporation intensify with the increase of the
warming, that because the natural vapors pressure
increase proportionally with the increase of the
temperature. [5]
The prolonged droughts affects not as much
the quality of the resources but especially there
quality, the water becoming then a strategically
resource for those area. Due to the meteorological
dates analyzed over a period of 40 years, 19612000, has became obvious that the most vulnerable
areas for the extreme agricultural drought phenomena
in Romania are the southern and south-eastern areas,
especially in southern Oltenia, Muntenia and Moldova,
Baragan and Dobrogea.
Certain that all the evaporated water from a
certain area will be transported as vapors and where
are favorable conditions for condensing will return to
the ground as very strong rainfalls.
The size of the precipitation drops
(200…5000μm) depends on the length of the road
through the clouds and the atmospheric turbulence.
The biggest drops emerge from Cumulus and
Cumulonimbus clouds, where are intense ascendant
currents that appears from ascendant convection. [4].
The severe floods are the most common type of
natural disaster in Europe. The climatic changes,
including the intensification of abundant rains, cause
rivers to flood in certain areas, especially in the center,
north and north-eastern Europe. The most frequent
disastrous phenomena encountered lately in the case of
floods caused by precipitations in the case of
precipitations concentrated on small areas, phenomena
that causes strong and fast flood.
3. Case study – precipitations in Prahova County in
the year 2005
We considered a representative case for the
impact of strong rainfalls concentrated on small
hydrographic basins. On the Territory of Prahova
County, the multiyear average precipitations drop from
1200 l/m2 in the highest area of the Bucegi Mountains
to less than 600 l/m2 in the plain area, as shown in
Figure 1.
The territorial repartition of the precipitations in
the year 2005 (Figure 2) was between 1600-1200 l/m2
on mountain and hilly areas to the lineament Floresti Lipanesti - Apostolache and 1200-800 l/m2 in the plain
area, on the south of this lineament and the southern
border of the county.
The monthly repartition of the precipitations in
the year 2005 compared to the multiyear average in
situated in three categories:
Normal (January, March, April, November,
December);
Higher than normal (February, May, June, July,
August, September)
Below normal (October)
M. Telişcă et. al. / Ovidius University Annals Series: Civil Engineering 9, 155-160 (2007)
The month of September – considered one of
the months in the year with the lowest precipitation,
has its multiyear average values (Figure 3) between
less then 40l/m2 and more than 80 l/m2. The
quantities recoded in this period (Figure 4) were in
157
over 85% of the surface of the county surface between
180-230 l/m2. In the area of the Doftana and Teleajen
interfluves recorded a value of 240-250 l/m2.
Punctually were recorded values even higher than 300
l/m2 (Teisani 319,7 l/m2).
Figure 1 Average multiyear precipitations
4.1. The situation of precipitations in Prahova
County in the period May - September 2005
By analyzing the maps results that in 50% of
the months of 2005, the precipitations in Prahova
County were higher than the multiyear average of
which 5 months were consecutive (May September).
Comparing the precipitations from May
September with the yearly quantities recorded in
2005 we can see that in this period were between
60,2% and 75,6% of the total yearly precipitations.
Figure 2 Average precipitations in 2005
1
2
3
4
5
6
7
8
9
10
12
13
Station
Baltita
Baba Ana
Corlatesti
Gura Vitioarei
Moara Domneasca
Poiana Campina
Tesila
Varbilau
Cocorastii Mislii
Provita de Sus
Teisani
Paltinu dam
Total V-IX
741,5
694,2
697,9
880,9
633,0
832,2
1114,6
1059,9
895,1
902,9
1032,4
837,2
TOTAL I-XII
1014,0
917,7
970,0
1205,8
874,6
1141,3
1538,4
1441,1
1206,0
1242,9
1376,9
1151,3
%
73,1
75,6
71,9
73,0
72,3
72,9
72,4
73,5
74,2
72,0
75,0
72,7
M. Telişcă et. al. / Ovidius University Annals Series: Civil Engineering 9, 155-160 (2007)
4.2 Effects of the very strong rainfalls
These precipitations had as effects:
¾Making strong effluence on slopes, especially on
hilly and mountain areas.
159
¾Causing strong floods with unusual debits on rivers
with small surface basins affecting works on these
rivers and also over localities and agricultural terrains
(rivers Alunis, Varbilau, Slanic, Provita, Bughea,
Mislea, Drajna, Stamnic, Batraneanca)
Figure 5 The flood in 19 - 28 September 2005 on the main rivers of the Prahova County
¾Through propagation, the floods on these small
rivers caused on the big rivers of the County
(Cricovul Dulce, Prahova, Teleajen, Cricovul Sarat)
to record very high flows (flows with the assurance
of 1-2%) that overflow the flooding level causing
damages on important localities from the County
as: Moara Domneasca, Gherghita, Draganesti,
Buda-Palanca, Finari, Bratesti.
¾In plain areas:
-Rehabilitation and maintenance of the
irrigation drainage channels
¾On river beds:
-Promoting flood defensive works.
-Keeping the correct gauge by un-colmation
and bed profiling
-Maintaining the river beds clean.
4.3 Proposed measures to reduce the damages
caused by strong rainfalls
5. Conclusions
Reducing the risk on flooding can be realized
Prognosis methods over the global climatic evolution
by climatic scenarios
¾In mountain and hilly areas:
-Foresting the cleared areas
-Managing the valley’s with torrentially
character by building dams for slowing the torrents
-Maintaining the culverts on the side of the
roads [2].
The climatic changes scenarios were generated
on the National Plan for Climatic Changes using the
results of the general circulation models GISS, GFDL,
UK89, CCCM. The results consist in the average
monthly multiyear temperature and precipitations,
calculated with the actual concentration of CO2
(1xCO2) and with the presumption on instant doubling
by:
of that value (2xCO2) – experiment of equilibrium
and gradual increase of CO2 – transitory
experiment. [3].
The climatic scenarios build on the mentioned
dates express the fact that doubling the
concentration of CO2 in atmosphere will conduct
the same climatic signal meaning an increase of the
air temperature, varying between 2,4 and 7,40C,
depending on the model. The lowest increase are
anticipated by CCCM, between 2,8-4,90 C
depending on the month, and the biggest increase
by UK89, between 3,2-7,40 C, especially on
summer months.
Referring on the precipitations, the climatic
signal is different from a model to another.
The UK89 effect anticipates a decrease for all
the moths of the year, especially during summer (up
to 50%), and that is consistent with the biggest
temperature increase simulated by the model in this
season.
The GISS model indicates, generally, an
increase of the precipitation in all the months, the
maximum increase being in October (40%). The
Canadian and GFD3 models anticipate an increase
of precipitations in the cold months and a decrease
in the warm ones.
6. Bibliography
[1] Giurma I., Crăciun I., Giurma R. (2001),
Hidrologie şi Hidrogeologie. Aplicaţii, Ed. Gh. Asachi,
Iaşi
[2] Giurma I., 2003 – Viituri şi măsuri de apărare, Ed.
Gh. Asachi, Iaşi;
[3] A. Mirin, M. Wickett, P. Duffy, D. Rotman, 2005 Climate
Modeling
using
High-Performance
Computing, U.S. Department of Energy by the
University of California Lawrence Livermore National
Laboratory
[4] Sun, B., P.Ya. Groisman, R.S. Bradley, and F.T.
Keimig, 2000: Temporal changes in the observed
relationship between cloud cover and surface air
temperature. J. Climate, 13, 4341-4357.
[5] Ştefanache D., Giurma R. (2004) – Monitorizarea
Parametrilor Meteorologici şi Hidrologici, Ed. „Gh.
Asachi” Iaşi
[6] Trenberth, K.E., 1998: El Nino and global
warming, J. Marine Education, 15, 12-18
[7] ***, Impacts of Europe’s changing climate, Raport
of European Environmental Agency, Nr 2/2004, AEM,
Copenhaga
[8] www.ipcc.ch
Energetic improvement of joinery embrasures
a
Virgil-Barbu UNGUREANU a
__________________________________________________________________________________________
Rezumat: Lucrarea prezintă unele probleme care apar în cele mai multe cazuri la reabilitarea termică a faţadelor
blocurilor realizate din panouri prefabricate din beton armat. Golurile pentru ferestre şi uşi sunt realizate cu un
umăr exterior („cu urechi”) pentru uşurarea montajului şi fixarea mai rigidă a tocului. Se realizează o analiză a
transferului de căldură în regim staţionar pentru diferite variante de soluţii de montare a stratului de izolaţie termică, rezultând unele recomandări pentru evitarea apariţiei condensului pe suprafeţele adiacente golului ferestrei.
Abstract: The work presents some problems that shall be appear in energetic rehabilitation operations for front
walls made by reinforced concrete slab. The embrasures for windows and doors are realised with an external
shoulder for an easy montage and a rigid attachment of the window frame. It is realised a steady state heat
transfer analysis for different variants of solutions for thermal insulation layer montage, resulting some
recommendations for sweat appearance avoidance on internal surfaces adjacent of the windows embrasures.
Keywords: Heat transfer, thermal insulation, heat transfer analysis.
__________________________________________________________________________________________
1. Introduction
Energetic auditing of existent buildings is an
activity for identify technical solutions in order to an
energetic vindicate of buildings and its installations
based on real characteristics of the system building installations for thermal energy utilisation as well as
technical solutions optimisation by its energetic
efficiency analysis.
The main goal of building energetic improvement is to decrease the heat consumption for
space and water heating, in order to assure the
comfort and micro clime. For this goal, the technical
solution is to insulate outside walls. But there are
various places where the insulation is not efficiently
or it cannot be realised. Thus, there are some
locations where the inside wall surface temperature
is lower than the wet point temperature. Only the
bidirectional heat transfer analysis can offer a good
solution in order to build an efficient insulation.
The work presents some problems that shall be
appear in the cases of front walls made by reinforced
concrete slab. The embrasures for windows and
doors are realised with an external shoulder for an
easy montage and a rigid attachment of the window
frame. It is realised a steady state heat transfer
ISSN 1584 - 5990
analysis for different variants of solutions for
thermal insulation layer montage.
2. Heat transfer model
The temperature on the internal surface of a
construction element without heat bridges (or in the
current thermal field of construction elements with
heat bridges) can be determined [1] with the
relation:
t −t
t si == ti − i e [°C]
αi ⋅ R
(1)
in which ti is the internal temperature, α i - inside
convection coefficient, R - thermal resistance in the
current thermal field, Te - outside temperature.
In the heat bridge zones temperatures on
internal surfaces of external walls t si can be
determined by an automatic calculus of the
temperatures field.
In order to obtain correct results it is needed to
consider some minimum dimensions, for establish
the geometric model for the plain temperatures field.
162
Energetic improvement … / Ovidius University Annals Series: Civil Engineering 9, 161-168 (2007)
So, distances measured from the outside contour of
the joinery to interior is minimum twice wall
thickness. For outside joinery there are admitted
some approximations:
• the window frame and sash can be stylised in
the shape of one or more rectangles;
• the assembly of glass panels and air layers
between its can be considered that a single layer
having the thickness equal with the distance between
external glass panels respectively the stylised width
of the window frame and sash.
The geometric model situated between
horizontal and vertical planes of section is divided
with auxiliary planes composing a calculus network
for the temperature field calculus. Usually, distances
between auxiliary planes will have a gradually
increasing to sectional planes; in the plane field
theses distances cannot exceed 25 mm.
For external joinery the glass panels and air
layers can be substituted by a materiel having
equivalent heat conductivity:
λg =
dg
1
Ug
⎡ W ⎤
⎢m⋅K ⎥ ,
⎣
⎦
(2)
in which U g is the thermal heat transfer coefficient
of the glass panels and air layer assembly. In this
problem it is considered a twice glass panel having
dimensions 4 - 15 - 4 mm, argon, emissivity
0.1 < e < 0.2 with U g = 1.5 W (m 2 K) ; d g distance between external faces of the external glass
panels: d g = 23 mm .
It results:
λ g = U g ⋅ d g = 0.0345 W (mK) .(3)
There are considered the following surface
thermal convection coefficients:
• inside surfaces: α i = 8 W (m 2 K) ;
• outside surfaces: α e = 24 W (m 2 K) .
For window frame and sash made from plastics
(PVC) and metallic reinforces with two chambers:
U f = 2.2 W (m 2 K) [1]. It is considered in this
study a security value: U f = 3.0 W (m 2 K) and
results an equivalent heat conductivity coefficient:
λ f = U f ⋅ d f = 0.186 W (m 2 K) .
(4)
For concrete it is considered:
λ c = 1.75 W (m ⋅ K)
(5)
and for gypsum:
λ gy = 0.41 W (m 2 K) .
(6)
The sash frame is fixed with polyurethane
foam having a heat conduction coefficient:
λ p = 0.04 W (m 2 K) .
(7)
For the thermal insulation, realised by plates of
polystyrene it is considered the same heat
conduction coefficient.
3. Analysis results
It is used the demonstrative program ELCUT
that permits to compose a calculus network having a
total number of 500 elements. The program is
available to define a model composed by 5 or 6
blocks having various properties: concrete, window,
gypsum, glass and insulation.
It is proposed to study the temperature
variation on the internal wall surface in various
cases of thermal insulation of the external wall.
The first model takes account of some shoulders build even the putting phase, in the reinforced
concrete panel with a view to facilitate the montage
and fixation of the joinery in embrasure.
Figure 1 presents the temperature distribution
for an outside temperature t e = −21 °C correspondent to the four climatic zone and an inside temperature of t i = 20 °C . However, the concrete
panel includes a thermal insulation made from
polystyrene, but on the contour and joinery gap the
reinforced concrete is massive.
V.B. Ungureanu / Ovidius University Annals Series: Civil Engineering 9, 161-168 (2007)
Fig. 1. Temperature distribution in the wall without thermal insulation
Fig. 2. Temperature distribution in the wall with 5 cm of thermal insulation
163
164
ti = 20 °C
ϕi = 60% .
Figure 2 and 3 presents the temperature
distribution in the same conditions but it is added
50mm, respectively 100mm of polystyrene
([2]…[5].
On shoulders is not applied the thermal
insulation.
The internal dew-point temperature can be
obtained function of the internal temperature
and
normalised
air
First, it must to obtain the saturated vapour
partial pressure function of the internal temperature:
pvi, s = 2340 Pa .
20
18
16
12
s
t [oC]
14
10
External concrete corner
Internal, window gap corner
Internal, current field
8
6
-25
-20
-15
-10
-5
0
5
10
t [oC]
e
Fig. 4. Temperature variation on the wall surface without thermal insulation
20
18
16
12
0 mm
50 mm
100 mm
si
t [oC]
14
10
8
6
-25
-20
-15
humidity:
-10
-5
0
5
10
t [oC]
e
Fig. 5. Temperature variation on the internal wall surface with and without thermal insulation
(8)
Than it results the vapour partial pressure:
pvi = ϕi ⋅ pvi, s = 1404 Pa .
(9)
and afterwards the dew/point temperature:
θ r = 15 °C .
(10)
Figure 4 presents the temperature variation on
the wall surface: external concrete corner, internal
window embrasure corner and internal current field
for various external temperatures without thermal
insulation.
165
Figure 5 presents the temperature variation on
the internal wall surface with and without thermal
insulation.
From figures 1, 4 and 5 it results a surface
temperature in current field lower than the dewpoint temperature. Thus, for lower external
temperatures it arises condense on the inner surface
of the external walls and the thermal improvement
is required.
From figures 2, 3 and 5 it results internal
surface temperatures in current field higher than the
dew-point temperature in the case of thermal
insulation.
Fig. 6. Temperature distribution in the wall with 5 cm of thermal insulation and insulated shoulders
Fig. 7. Temperature distribution in the wall with 10 cm of thermal insulation and insulated shoulder
166
The minimum value of the temperature on the
inner surface of the external walls is reached on the
interconnecting line between the joinery and gypsum
wall covering from embrasure. From figures 2 and 3
result that the minimum temperature values of
internal surfaces is lower than the dew-point
temperature.
It must to cover the shoulder with thermal
insulation. Figures 6 and 7 show the temperature
field for the wall covering with 50 mm and 100 mm
(like cases from figures 2 and 3), but shoulders are
coated with polystyrene prepared in a triangular
unconventional section shape. This shape needs a
labour increasing.
From these figures it results the same
minimum temperature value reached in the previous
models, without thermal insulation on shoulders
presented in figures 2 and 3.
without concrete shoulder
without concrete shoulder
Many flats have a partial thermal improvement
in order to increase the joinery tightness by PVC
joinery utilisation. For this reason the above models
take into account that improvement.
From the above study it results that it needs to
remove shoulders. Figures 8 and 9 shows the
temperature field for the current field covering with
50 mm and 100 mm (like cases from figures 2, 3 and
5, 6) but the joinery embrasure is covered around
with 5 cm of polystyrene.
It can observe an improvement by a clear
homogeneous temperature field on the entirely
internal surface of the wall.
Figure 10 shows the temperature variation on
the wall surface in current field with or without
shoulders Also, it is represented the dew-point
temperature. There is a comfortable difference from
the dew-point temperature but the shoulder
replacement with polystyrene increase the internal
wall surface temperature in the current field.
Also, it can conclude that the polystyrene
thickness increasing with 50 mm from 50 mm to 100
mm determine a modest wall surface temperature
increasing (with about 1 K ), but in the case of
shoulder removal this difference is greater.
Figure 11 shows the minimum temperature
variation on the wall surface with or without
shoulders. Also, it is represented the dew-point
temperature.
For an external temperature less than − 10 °C ,
any cases of embrasures with shoulder (covered or
uncovered with polystyrene) lead to wetting of the
wall internal surface. It needs to increase the internal
air temperature of the room.
Both cases when the shoulder is removed and
replaced with polystyrene, the minimum wall
temperature is greater with minimum 1 K than the
dew-point temperature. This difference is greater
2 K for an insulation thickness of 100 mm.
19
18
si
t [oC]
17
16
5 cm shouldered
10 cm shouldered
5 cm without shoulder
10 cm without shoulder
15
14
θ
r
13
12
-25
-20
-15
167
-10
t
e
-5
o
[ C]
0
5
10
Fig. 10. Temperature variation on the wall surface (current field) with or without shoulders
168
50 mm shouldered
100 mm shouldered
50 mm without shoulder
100 mm without shoulder
θ
18
r
t
si,min
[oC]
16
14
12
10
-25
-20
-15
-10
-5
0
5
10
t [oC]
e
Fig. 11. Minimum temperature variation on the wall surface with or without shoulders
4. Conclusions
It is proposed to study the temperature
variation on the concrete wall surface and joinery
embrasure in various cases of thermal insulation of
the external wall.
The first model takes account of some
shoulders build even the putting phase, in the
reinforced concrete panel with a view to facilitate
the montage and fixation of the joinery. It results a
surface temperature in current field lower than the
dew-point temperature and needs to utilise a
thermal insulation realised by 50 mm or 100 mm
thickness of polystyrene (the second model).
The minimum value of the temperature on the
inner surface of the external walls is reached on the
interconnecting line between the joinery and
gypsum wall covering from embrasure. However,
for lower external temperatures it arises condense
on the inner surface of the external walls and
another thermal improvement is required.
Another 3rd model is needed in that the
shoulders are covered with polystyrene in a
triangular unconventional section shape. It results
any improvement of the heat transfer.
Thus, it results from this study the
recommendation to remove shoulders and to cover
around the joinery embrasure with 5 cm of
polystyrene.
Any cases when the shoulder is removed and
replaced with polystyrene, the minimum wall
temperature is greater with 1...2 K than the dew-point
temperature.
5. References
[1] C 107/3 Normativ privind calculul termotehnic al
elementelor de construcţie ale clădirilor.
[2] C 107/4 Ghid pentru calculul performanţelor
termotehnice ale clădirilor de locuit.
[3] GP 058/2000 Ghid privind optimizarea nivelului de
protecţie termică la clădirile de locuit.
[4] NP 048 Normativ pentru expertizarea termică şi
energetică a clădirilor existente şi instalaţiilor de
încălzire şi preparare a apei calde de consum aferente
acestora.
[5] Normativ pentru realizarea auditului energetic al
clădirilor existente şi instalaţiilor de încălzire şi
preparare a apei calde de consum aferente acestora.
Analysis of heat exchangers obtained by division or multiplying of units
Virgil-Barbu UNGUREANU a*
Neculae ŞERBĂNOIU a
Maria MUREŞAN a
a
“Transilvania” University , Eroilor Boulevard, 29, Braşov, 500036, Romania
__________________________________________________________________________________________
Rezumat: Obţinerea unor schimbătoare de căldură eficiente se poate face utilizând module care şi-au dovedit
performanţele în exploatare şi legarea acestora în serie, paralel sau mixt. Astfel, se pot realiza atât schimbătoare
de căldură mai mari prin multiplicarea numărului de module, sau mai mici, prin divizarea unui modul. În practică
se întâlnesc numeroase exemple ca: baterii cu aripioare, schimbătoare de căldură cu plăci, schimbătoare de căldură cu tuburi termice, radiatoare pentru autovehicule. Alegerea variantei, de regulă, nu este susţinută printr-un studiu teoretic. Lucrarea propune o metodă pentru determinarea performanţelor energetice şi exergetice ale ansamblurilor de schimbătoare de căldură obţinute prin multiplicare şi divizare. Se determină astfel fluxurile de căldură, temperaturile agenţilor termici la ieşire şi eficienţa dând posibilitatea alegerii variantei corespunzătoare.
Abstract: In order to obtain heat exchangers with high efficiency we can use units that prove its working
performances and series, parallel or mix coupling of them. By using that method we can realise bigger heat
exchangers by multiplying the number of units, or smaller heat exchangers by dividing an unit. In practical
activities we have numerous of these heat exchanger types: fin type batteries, flat plate heat exchangers, heat
pipe heat exchangers, radiators for automotive etc. As a rule, the choice of the optimal variant isn’t sustained by
a theoretical study. The paper proposes a method to calculate the energetic and exergetic performances of heat
exchanger assemblies obtained by multiplying and dividing. Thus there are obtained heat flow rates output
temperatures of heat carriers and thermal efficiency in order to choice the optimal variant.
Keywords: Heat exchanger, heat exchanger unit, heat exchanger efficiency.
__________________________________________________________________________________________
1. Introduction
In order to obtain heat exchangers with high
efficiency we can use units that prove its working
performances and series, parallel or mix coupling of
them. By using that method we can realise bigger
heat exchangers by multiplying the number of units,
or smaller heat exchangers by dividing an unit. In
practical activities we have numerous of these heat
exchanger types.
Finned heat exchanger batteries are composed
by a copper or stainless steel pipe bundle connected
one with another by bends and grouped in rows.
Pipes are provided with aluminium or copper fins
often continuous (fig. 1). Through their interior
circulates water, a cold carrier or a refrigerant and
through fins a gas, usually air. Number of pipe rows
can vary from a single in the case of air conditioning
batteries to some tens.
ISSN 1584 - 5990
Last years fin shape is improved from plane to
corrugated and further perforated, obtaining a heat
convection coefficient increasing with about 90%.
To improve the heat transfer inner of pipes, these
can be provided with internal grooves.
Fig. 1. Heat exchanger batteries with plane
fins: 1 - liquid; 2 - gas; 3 - air; 4 - fins; 5 - pipes
170 Analysis of heat exchangers.… / Ovidius University Annals Series: Civil Engineering 9, 169-176 (2007)
Fluids had cross flow in finned heat exchanger
batteries.
It is a heat exchanger having parallel-flow for
water into pipes from a row and rows are series
coupled. Air parallel circulates through pipes of a
row and series through rows.
In the case of heat exchanger apparatus having
a little number of rows, for the mean temperature
difference calculus is necessary to introduce an
supplementary correction that take into account by
fluid that circulates inner pipes ranged in many
rows.
Flat plate heat exchangers are much littler and
light than those conventionally and are outstanding
by easy assembling and maintenance. Are compact,
has a flexible design, saving of costs and five times
efficiently than those conventionally. For any
industry where there are necessitate a flat plate heat
exchanger are available in many shapes: with gasket
semi welded, welded, electrically. Plates are made
by stainless steel, titanium or graphite.
There are various technologies among that
some of its recently developed for flat type heat
exchangers.
It can distinguish two categories of such
apparatus: heat exchangers with primary surface and
heat exchanger with secondary surface.
Heat exchangers with primary surface can be
realised that heat exchanger with plates and sealing
element (gasket) this being the most known type of
apparatus, with welded or soldered plates.
In the case of apparatus with secondary
surface, between plates is inserted a metallic filling
that represents an additional heat transfer surface.
The construction and operating principle of a
plate and gasket heat exchanger is presented in
figures 2 and 3.
Heat exchange surface is composed by some
metallic plates provided with gaskets and clamping
one to another aided by rods.
There are made some channels one fluid
wetting a plate surface and the other fluid, the other
plate surface (fig. 3).
Plates are realised by stamping generally from
stainless steel or titanium but there are plates from
other metals enough ductile that is Hastelloy,
Incoloy, Monel or copper-nickel alloy.
The plate thickness is about 0,6...0,8 mm and
exceptionally exceeds 1mm. The plate profile is very
important because it must to assure a turbulence
improving to increase heat convection coefficient
but also a uniform distribution of fluids on the entire
plate surface and supporting points on metal to
assure the mechanic rigidity of the apparatus.
Present day there are over 60 various geometries of
plates, patented by productive firms.
Fig. 2. Construction of the plate and
gasket heat exchanger
Fig. 3. Operating principle of the plate
and gasket heat exchanger
Soldered or welded heat exchangers, last years
developed, permits a heat transfer surface utilisation
at bigger pressure and temperature levels than the
above presented heat exchangers, because of the
sealing elements absence. In this type of apparatus it
can be reached pressure of about 40..50 bar and
temperatures 450...500 oC.
The principle schema of a heat pipe heat
exchanger is presented in figure 4.
V.B. Ungureanu et al. / Ovidius University Annals Series: Civil Engineering 9, 169-176 (2007) 171
From various shapes of these heat exchangers
Each heat pipe is considered that an assembly
existent on market, figure 6 presents heat exchanger
of two coupled heat exchangers (an evaporator and a
type „bayonet” and with jet impact realised by
condenser) in that vapour phase has approximately,
silicon carbide.
the same temperature. It is considered also, that heat
pipes of the same row (on the same perpendicular to
the flow direction) have the same temperature,
considering for the calculus of a row a single heat
pipe with heat transfer surface.
Fig. 5. Heat recovery heat exchanger
with steel smooth pipes: 1 – waste gas ; 2 –
cold air ; 3 – warm air
Fig. 4. The principle schema of the heat
pipe heat exchanger: 1 – heat pipes ; 2 – strainer
plate ; 3 – primary heat carrier ; 4 – secondary
heat carrier ; 5 - heat transfer
To calculate heat pipe heat exchangers can be
used methods based on the decomposition of the
heat exchanger in elementary units heat exchangers.
Figure 5 presents a heat recovery heat
exchanger provided with four pass of the air and
mounted on the vertical waste gas duct of a heattreatment furnace. Air circulates inner pipes, the heat
exchanger operating by the parallel – cross-flow
regarding waste gas.
Heat recovery heat exchangers with smooth
pipes have the heat exchange surface composed by
bundle of rectilinear pipes. This type of heat
recovery heat exchangers are used especially for
furnaces having the waste gas temperature until
600oC.
Ceramics heat exchangers are generally used in
high operating temperature, for example those of
metallurgic, cement or glass industry. There are used
for heat recovery heat exchangers or regenerators.
Fig. 6. Ceramics heat exchangers: a type bayonet; b - with jet impact; 1- metallic
distributor; 2 - ceramics pipes; 3 - perforated
screen; 4 - ceramics heat exchange surface;
A – air; G - gas
Figure 7 presents an element of cooling
radiator for the LDE locomotive and the modality of
elements coupling in a battery. Water and air parallel
circulates in the battery. On a locomotive there are
emplaced two parallel coupled batteries.
Heating radiator for DACIA car is a compact
heat exchanger assembly composed by the mixed
coupling of the units (fig. 8).
Fig. 8. Heating radiator for DACIA car
Fig. 7. Cooling radiator for the LDE
locomotive
As a rule, the choice of the optimal variant
isn’t sustained by a theoretical study. The paper
proposes a method to calculate the energetic and
exergetic performances of heat exchanger
assemblies obtained by multiplying and dividing.
Thus, there are obtained heat flow rates, output
temperatures of heat carriers and thermal efficiency
in order to choice the optimal variant.
T '12 = γ ⋅ (T11 − T '11 ) + T '11 ,
notations being:
1 − exp
α = η⋅ m ⋅cp
2. Basic model
For a cross-flow heat exchanger (fig. 9) there
are known relations for the heat flow rate transferred
and both fluids output temperatures:
(ϕ − 1)kS
ηmc p
(ϕ − 1)kS
1 − ϕ exp
ηmc p
(1 − ϕ)exp (ϕ − 1)kS
β=
ηmc p
(ϕ − 1)kS
1 − exp
ηmc p
⎡
(ϕ − 1)kS ⎤
ϕ⎢1 − exp
⎥
ηmc p ⎦⎥
⎢
⎣
γ=
(ϕ − 1)kS
1 − ϕ ⋅ exp
ηmc p
Fig. 9. Flow scheme for a single unit
Q1 = α ⋅ (T11 − T '11 ) ;(1)
T12 = β ⋅ (T11 − T '11 ) + T '11 ;
(3)
(2)
where: m, m’ are mass flow rates of hot respectively
cold fluid; T11, T12 input and respectively output
temperatures of the hot fluid; T’11,T’12 -input and
respectively output temperatures of the cold fluid; η
- retaining coefficient for the heat; k - overall heat
transfer coefficient; S - surface area of heat
transfer; Q - heat flow rate. It is noted with ϕ the
expression:
ϕ=η
mc p
m' c ' p
,
(7)
c p and c' p being specific heat at constant pressure
of both fluids.
The thermal efficiency of the heat exchanger is
defined by the ratio between the real heat flow rate
Q1 and the maximum possible heat flow rate,
Q1max correspondent to an apparatus with an
infinite heat transfer surface:
ε=
m1c p1 ⋅ (T11 − T12 )
Q1
=
=
Q1 max m1c p1 ⋅ (T11 − T '11 )
m2 c p 2 ⋅ (T12 − T11 )
T −T
= 12 11
m2 c p 2 ⋅ (T11 − T '11 ) T11 − T '11
.
(8)
Fig. 10. Series-parallel coupling variant
obtained by multiplying
3. Series-parallel coupling variant obtained by
multiplying
In this case there are obtained relations:
By generalisation:
Q2 sp = β ⋅ Q1 ;
(9)
Qnsp = β n −1 ⋅ Q ;
(15)
T22 sp = β 2 ⋅ (T11 − T '11 ) + T '11 ;
(10)
Tn 2 sp = βn ⋅ (T11 − T '11 ) + T '11 ;
(16)
T '22 sp = β ⋅ γ (T11 − T '11 ) + T '11 ,
(11)
T 'n 2 sp = β n −1 ⋅ γ ⋅ (T11 − T '11 ) + T '11 .
(17)
rd
and for the 3 unit:
Output temperature of fluids is:
2
Q3sp = β ⋅ Q ;
(12)
T32 sp = β3 ⋅ (T11 − T '11 ) + T '11 ;
(13)
T '32 sp = β ⋅ γ ⋅ (T11 − T '11 ) + T '11 .
(14)
n
T 'm =
∑ mi ⋅ c pi ⋅ T 'i 2
i =1
m ⋅cp
,
(18)
where: T 'm is the average temperature, mi - mass
flow rate, m1 = m2 , m - overall mass flow rate:
m = n ⋅ m2 , c pi = c p - specific heat, T 'i 2 secondary heat carrier temperature at the output
from heat exchanger „i”.
It results:
T 'm sp =
1 n
⋅ T 'i 2 =
n i =1
∑
n
γ 1−β
(T11 − T '11 )
T '11 + ⋅
n 1− β
,
(19)
If the heat exchanger is divided in two equals
units it has the following parameters:
S 2 - heat transfer surface area;
•
•
•
m1 2 - mass flow rate of the primary fluid;
m2 2 - mass flow rate of the secondary.
Mass flow rates of both fluids are established
from the condition that velocities remain unchanged
thus the overall heat exchanger coefficient k
remains unchanged.
For the first heat exchanger (considered in the
hot fluid circulation direction) it can write relations:
Q1( 2) = α1 (T11 − T '11 ) ;
(21)
T12( 2) = β1 (T11 − T '11 ) + T '11 ;
(22)
( 2)
T '12
= γ1 ⋅ (T11 − T '11 ) + T '11 .
(23)
and the heat flow rate:
1 − βn
Qsp = Q1 ⋅
.
1− β
(20)
3. Series-parallel coupling variant obtained by
dividing
The variant obtained by division is presented
in figure 11. The heat exchanger, considered a basic
unit, can be divided in many smaller heat exchangers
by utilisation of separation walls so the obtained
units has been series coupled by primary fluid
circulation and parallel coupled by secondary fluid
circulation. The figure represents a cross section
through a cooling radiator perpendicular on the
water pipes and its dividing scheme in n heat
exchangers. Proceeding analogous with the
multiplying variant it can obtain the following
results.
Considering relations (4), (5), (6) and (7) and
taking account the parameters of this heat
exchanger, ϕ being unchanged, it results:
α1 =
α1( 2) =
α
; β1 = β ; γ1 = γ ;
2
(24)
1
( 2)
= T '12 . (25)
α1 ; T12( 2) = T12 ; T '12
2
Analogously for the 2nd heat exchanger and
taking into account by:
α 2 = α1 ; β 2 = β1 ; γ 2 = γ1 .
(26)
There are obtained relations:
Q2( 2) = α 2 (T12 − T '11 ) =
=
Fig. 11. Schema of unit division
; (27)
1
1
αβ(T11 − T '11 ) = β ⋅ Q1
2
2
( 2)
T22
= β(T12 − T '11 ) + T '11 =
= β 2 (T11 − T '11 ) + T '11
;
(28)
• for the 3rd heat exchanger it results:
T '(222) = γ (T12 − T '11 ) + T '11 =
.
(29)
= βγ (T11 − T '11 ) + T '11
1
Q3(3) = α 3 (T22 − T '11 ) = ⋅ β 2 ⋅ Q1 ;
3
The heat flow rate of both heat exchanger units
is:
Q
( 2)
= Q1( 2)
+ Q2( 2)
1
= (1 + β ) ⋅ Q1 .
2
(3)
T32
= β ⋅ (T22 − T '11 ) + T '11 =
(30)
= β3 ⋅ (T11 − T '11 ) + T '11
In the case of dividing in three identical heat
exchangers it results:
•
S 3 - heat transfer surface area;
•
•
1
= α1 (T11 − T '11 ) = ⋅ Q1 ;
3
(31)
= β ⋅ (T11 − T '11 ) + T '11 ;
(32)
( 3)
T '12
= γ ⋅ (T11 − T '11 ) + T '11 ;
(33)
Q1(3)
T12(3)
; (38)
(3)
T '32
= γ ⋅ (T22 − T '11 ) + T '11 =
= β 2 ⋅ γ ⋅ (T11 − T '11 ) + T '11
m1 3 - primary fluid mass flow rate;
m2 3 - secondary fluid mass flow rate.
In this conditions both fluids velocities remain
the same thus, the overall heat transfer coefficient
k is the same. Following the same algorithm it can
write:
• for the 1st heat exchanger, because:
α1 = α 3 ; β1 = β ; γ1 = γ and the same
ϕ , relations becomes:
(37)
. (39)
It results the overall heat flow rate:
Q (3) = Q1(3) + Q2(3) + Q3(3) =
(
)
1
1 + β + β2 ⋅ Q1 . (40)
3
By generalising, for the n th heat exchanger it
results:
Qn( n ) =
1 n −1
⋅ β ⋅ Q1 ;
n
(41)
Tn(2n ) = β n ⋅ (T11 − T '11 ) + T '11 ;
(42)
T '(nn2) = β n −1 ⋅ γ ⋅ (T11 − T '11 ) + T '11 ,
(43)
and the heat flow rate of the assembly is:
•
nd
for the 2 heat exchanger, by keeping the
above conditions it results:
Q2(3)
( 3)
T22
1
= α 2 (T12 − T '11 ) = ⋅ β ⋅ Q1 ;
3
= β ⋅ (T12 − T '11 ) + T '11 =
= β ⋅ (T11 − T '11 ) + T '11
2
T '(223) = γ ⋅ (T12 − T '11 ) + T '11 =
= β ⋅ γ ⋅ (T11 − T '11 ) + T '11
;
Q ( n ) = Q1( n ) + Q2( n ) + ... + Qn( n ) =
=
(34)
(
)
, (44)
1
1 + β + β 2 + ...β n −1 ⋅ Q1
n
or:
;
(35)
(36)
Q (n) =
1 1 − βn
⋅
⋅ Q1 .
n 1− β
(45)
The thermal efficiency of the assembly composed by
n heat exchangers according to relation (8) is:
ε=
T '(mn2) −T '11
,
T11 − T '11
(46)
in which T '(mn2) represents the secondary fluid output
4. Conclusions
temperature, so the temperature of the mixed fluid
composed by the n fluids that exit from the n heat
exchanger units:
The above presented method permits to easy obtain
the output temperatures of fluids and the thermal
efficiency for a suited heat exchanger which can be
obtained by dividing or multiplying a unit having
known characteristics (for example experimentally
obtained). The heat exchanger is appropriate
according to thermal performances and/or
dimensions.
n
T '(mn2) =
∑ mi ⋅ c pi ⋅ T 'i(2n)
i =1
,
m ⋅ c p2
(47)
m2
is the mass flow rate of the
n
secondary fluid through the heat exchanger i , m2 in which mi =
mass flow rate of the secondary fluid that pass
through the assembly , T 'i(2n ) - temperature of the
secondary fluid at output from the heat exchanger i
and c pi = c p 2 . It results:
n
T '(mn2) =
=
∑ mi 2 ⋅ T 'i(2n)
i =1
(
m2
=
)
1
(n)
⋅ T '12
+T '(22n ) +... + T '(nn2) +
n
+
.(48)
γ 1 − βn
(T11 − T '11 ) + T '11
⋅
n 1− β
The thermal efficiency is:
ε=
γ 1 − βn
.
⋅
n 1− β
(49)
5. References
* [email protected]
[1] Badea A. , Necula H., Stan M., Ionescu L., Blaga
P. şi Dane G. Echipamente şi instalaţii termice.
Editura Tehnică, Bucureşti, 2003.
[2] Vidil R., Marvillet Ch ş.a. Les echangeurs a
plaque: description et elements de dimensionnement.
Imp. Coquand, grenoble, 1990.
[3] Bontemps A., Garrique A. Ş.a. Technologie des
echangeurs thermique. Techniques de l’ingineur.
Paris, 1998.
[4] Muersan M., Serbanoiu N., Sora G.
Veraligeminerte Glichungen zur Ermittlung aus
Warmeflusses und der Flussigkeitstemperatur beim
Austritt aus modulaufgebauten Kuhlern, B.W.K.
VDI Verlag, nr. 3, 1995, p. 97-99.
[5] Şerbănoiu N., Mureşan M., Ungureanu V.B.
Metodă de obţinere a unor schimbătoare de căldură
mai mici prin divizarea în module a unuia mai mare.
Conferinţa Naţională de Termotehnică, ediţia a XVa. Editura Universităţii din Pitesti, 26-28 mai 2005,
Craiova.
[6] Fetcu D., Ungureanu V.B. Tuburi termice.
Editura Lux Libris, Braşov, 1999.

analele - “Ovidius” University Annals of Constanta

Transcription

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