Dynaflow Lecture: Buried Piping

Transcription

Contents
Introduction to Buried Piping
!  Introduction to Buried Piping
!  Soil Properties & Classification
!  Some Principles of Soil Mechanics
!  Rigid Pipe - Soil Interaction
!  Flexible Pipe - Soil Interaction
Dynaflow Lecture: Buried Piping
Rotterdam, 8 March 2012
Copyright 2011 @ Dynaflow Research Group
Why burying a pipe?
Why burying a pipe?
Advantages of burying a pipe
Disadvantages of burying a pipe
!  Piping has to be designed for soil and surface loads,
which makes the stress and flexibility of the piping
more complex.
!  Reduces plant congestion and avoids existing above
ground obstructions.
!  Allows for shorters route (fewer bends).
!  Careful trenching and backfill is required to avoid
excessive soil settlement.
!  Soil can be used as uniform supporting, no above
ground supports and constructions are needed.
!  There are some ‘uncertain’ parameters involved in
the design of buried piping.
!  Protection from ambient temperature changes.
!  Identification and repair of failures is more
problematic (quality control is very important for
buried systems).
!  Protection from wind loads.
!  Long stretches of buried pipe act as a virtual anchor
and the need for large axial restraints or expansion
loops is eliminated.
2
!  Corrosion challenges, coathing/cathodic protection
might be required.
3
4
Soil-Pipe Interaction
Underground Failure Mechanism
It is useful to have a basic understanding of the fundamental principles
Examples of typical failures in buried piping
!  Soil is an earthen material consiting of loose solid particles with water in between. When burying
a pipe, soil is effectively used as a construction material.
!  Buried steel pipe failures are most often corrosion
related – a good coating is the first line of defence.
!  Soil is not a distinctly defined material with constant properties. Soil has a variety of
appearances with widely varying properties.
!  If soil and surface loads are excessive the pipe crosssection can buckle or crack.
!  The mechanical behavior of soil (soil mechanics) on its own is a very specialized field of study.
!  The moving portion of a pipe will generally be resisted
by the soil, creating significant bending stresses at
changes of direction, e.g. elbows and tees.
!  Buried pipelines are for their strength and stability behaviour dependent on the support and
resistance of the surrounding soil.
!  Deformation of the pipeline can also deform the soil. Additionally, external influences may cause
the soil to deform as well, causing additonal loads on the pipe.
!  All in all, there is a complex and continuous interaction between a buried pipe and the soil and
therefore soil-pipe interaction should be considered in any buried pipe design.
5
!  Upheaval buckling due to a high water table or
buckling due large thermal expansion.
!  Fiberglass (FRP/GRP) pipes are more flexible than
steel pipes and therefore very senstive for abrupt
changes in soil settlements.
High bending stresses in elbows and tee’s
Steam line failure in New York City
7
6
8
Steam line failure in New York City
Pipe upheaval due to high water table
9
Relevant Design Codes
Various “bad” design solutions
Codes and manuals that touch on the subject of buried piping
10
Buried pipelines are not extensively covered by the ASME B31 codes. Some of the B31 codes have
additional requirements for buried pipes such as:
!  ASME B31.4 (Liquid Petroleum Transportation Piping)
!  ASME B31.8 (Gas Transportation Piping)
!  ASME B31.1 (Power piping)
Often codes refer to “competent engineering judgement”. However, the following codes and
standards address the issue of buried pipe lines in detail:
! 
! 
! 
! 
NEN3650
AWWA M11 and M23 (American Water Works Association)
ASCE (American Socitiey of Engineers)
German ATV-DVWK
Apart from these codes there are well-known publications about this matter by:
!  L.C. Peng, Stress Analysis Methods for Underground Pipelines
( Peng’s papers are also added to the course material)
!  G. Kruisman, Influence of the Soil in Avanced Buried Pipeline Flexibiltiy Analysis
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12
Contents
Soil Classification According to Grain Size
Soil properties & classification
Soils can be classified according to the size of the grains
!  Most basic classification of soil is based grain-size.
!  Soils with large grains are called “gravel” and soils
with small grains “sand”.
300 mm
63 mm
!  Internationally it is defined that sand contains grains
larger than 0.063mm and smaller than 2mm.
2 mm
!  Gravel contains grains with sizes between 2mm and
63mm.
!  Grains smaller than 0.063mm are called “silt”.
0.063 mm
!  Grains smaller than 0.002mm are called “clay”.
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0.002 14
mm
Soil Classification Diagram
Porosity, Void Fraction & Water Saturation Parameter
The grain-distribution diagram contains the distribution of the various grain sizes
Fundamental soil composition parameters
!  “Porosity of Soil” (n): void volume between the grains
devided by the total soil volume:
!  A steep curve indicates that the soil grains are
similar of size (uniform soil).
!  A flat curve means that the soil consits of various
grain sizes.
well graded
bad graded
Most soils have porosity numbers between 0.30-0.45.
When porosity is small soil is “closely packed”, when
large soil is “losely packed”.
!  For grains larger than 0.05mm the distribution
diagram may be determined by means of
seaves.
!  A similar parameter to describe the porosity of the soil is
“Void Fraction” (e):
!  The uniformity coefficient is defined by the
following ratio:
D
CU = 60
D10
e=
Vvoid
Vgrain
n = 0.2595
!  Water Saturation Parameter (S) is the water volume
devided by the void volume:
!  Values of Cu < 2 indicate that the soil is bad or
discontineously “graded”.
S=
n = 0.5236
V
n = void
Vsoil
15
Vwater
Vvoid
16
Classification According to Soil Density
The Relative Soil Density
Dry, wet, grain and total soil density
The relative soil density is a measure how well soil may be compacted
!  Dry soils have a dry density (ρdry) and wet soils have a wet
density (ρwet) .
ρdry
!  The relative density (RD) is an indicator of the
“compaction ability” of the soil and depends on
the void fraction:
ρwet
!  The dry density should not be confused with the density of
the grains (ρgrain) itself.
RD =
!  To illustrate this sand for instance has a grain density
typically around: ρgrain=2650 kg/m3. The dry density of sand
as a bulk itself is typically ρgrain=2000 kg/m3.
!  Soils with values of (RD) < 0.5 can easily be
compacted.
!  Based on earlier defined parameters the total density (ρ) of
the soil can be expressed as:
!  Tests may be used to determine the relative density
of the in-situ soil. Example os such test is the
“Proctor Test”.
ρ = S ⋅ n ⋅ ρ wet ⋅ g + (1 − n) ⋅ ρ grain ⋅ g
ρ dry,max ⋅ (ρ − ρ dry,min )
emax − e
=
emax − emin ρ ⋅ (ρ dry,max − ρ dry,min )
17
Other Soil Parameters & Properties
International Soil Classification Table
Chemical composition and soil cohesion
Examples of international soil classifications
!  Chemical composition of the soil (content of minirals; organic
particles, ect). Sands and gravels consit for instance out of
quartz, felspar, mica spots. Clays contain next to above
mentioned minirals also so called clay minirals (kaoliniet,
montmorilloniet, illiet).
!  Classification attempts have been made to derive a
“global” soil classification table.
!  Cohesion is another property of the soil. Cohesion indicates
that loads may be transferred by for instance roughness or
attraction forces between grains in the soil. Examples are:
!  More extended classification tables give also
measures for: the compaction properties of the soil
and other useful guidelines.
1.  Electrostatic forces in stiff clays,
2.  Root cohesion (which may be caused by vegetation).
3.  Negative capillary pressure
!  Classifications tables are found in ASTM D2487,
NEN3650, DIN18196.
18
!  A well known (international) classification system is
shown in the table on the top right; for which a two
letter designation is given to the soil.
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20
Contents
Macroscopic Stresses on Soil Elements
Some basics of soil mechanics
Soils can only be loaded by compression
!  On soil stresses can work similar to other materials.
!  Soils however can only accomodate “compression”
stresses not tensile stresses.
!  For wet soils it is true that a large part of stresses are
accomodated by the water content in the soil.
!  The water content inside the soil cannot accomodate
shear stresses; however the soil itself can.
!  Typical (macroscopic) stress tensors working on an
arbitatry soil element are shown on the right.
21
Microscopic Soil Stress Distribution
Example of Vertical Stress in a Soil Layer
Loads in a wetted soil are transferred by the water and contact between grains
Application of Terzaghi’s formula
!  When a soil element is subjected to a uniform
normal stress (σ) as shown in the figure on the
right stresses can be accommodate by two
effects:
!  According to Terzaghi the effective grain stress in a
soil can be found as the difference between total
stress and water pressure.
σ
σ
!  The total weight of the soil below the “freatic
surface” is: ρwet*Hwet. In which ρwet is the volume
weight of the wet soil and Hwet is depth of the wet soil
layer.
1.  water pressure
2.  soil contact force
!  The nett stress is:
σ "= σ − p
!  The total weight of the soil above the freatic surface
is: ρdry*Hdry. In which ρdry is the volume weight of the
dry soil and Hdry is depth of the dry soil layer.
σ
σ
!  p is the fluid pressure in between the voids
!  σ" is called the “effective (grain) stress”
!  Formulas were first derived by “Terzaghi”
p
p
Hdry
Hwet
!  The effective grain stress then becomes:
p
Fcontact = σ”*A
σ " = σ − p = g ⋅ ( ρ dry ⋅ H dry + ρ wet ⋅ H wet ) − g ⋅ ρ water ⋅ H wet
p
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24
Shear Stress in Soils
The Horizontal Stress in a Soil at Rest
The ability to resist shear stresses depends on the friction and cohesion
The horizontal stress in a soil is directly related to the vertical stress
!  When cohesionless soils are poured to the ground
from above it will spread due to gravity. Because of
friction the area of spread is limited creating an angle of
repose (φ) at the balanced state.
!  At rest the vertical soil load induces also a horizontal load due to contraction effect.
!  The ratio σ’’h/σ’’v is a constant known as coefficient of neutral earth pressure at rest (K0).
!  Values for K0 are typical between 0.5 and 1.
!  From this experiment the friction force that resists the
shear loads may be calculated and the internal friction
coefficient (µ) of the soil may be determined:
!  Sometimes Jaky’s correlation is used:
K 0 = 1 − sin(ϕ )
σ h'' = K 0 ⋅ σ v''
f =resistance
µ ⋅ n = µ ⋅(s)
w ⋅of
cos
ϕ→
tanplane
ϕ
!  The friction
any
soilµin=any
is
then expressed as:
σ’’v
σ’’h
!  The angle (φ) is also
theϕ soil
s =called
n ⋅ tan(
) + cangle of internal
friction.
25
The Max Horizontal Soil Stress Nnar a Retaining Wall
Contents
Rankine determined the relation between max horizontal and vertical soil stress
Some basics of soil mechanics
26
!  When a burried object start to move the horizontal soil pressure changes.
!  Based on Rankin’s Theory (1857) the maximum increase and decrease in horizontal soil
pressure on each side of the object may be calculated.
!  The active coefficient of soil pressure is:
!  The passive coefficient of soil pressure is:
''
h
''
h
σ − Δσ = K A ⋅ σ
2
K A = tan ( 45 −
ϕ
)
2
ϕ
2
)
''
h
''
v
''
h
σ + Δσ = K p ⋅ σ
σ’’v
σ’’h-∆σ’’h
K P = tan 2 ( 45 +
σ’’h+∆σ’’h
''
v
σ’’v
27
28
Modeling Soil – Pipe Interaction
Modeling Soil – Pipe Reaction in a Pipe Mechanical Model
Soil stiffness & ultimate soil load are key parameters for a proper soil model
Soil reaction is often represented by spring type elements in a mechanical model
!  A buried pipeline is continuously supported and restrained by the soil.
!  It is custom practise to approximate soil-pipe interaction by means of spring elements; which are
applied along a mechanical model of the piping system.
!  When the pipe line moves inside the soil the soil exerts a reaction force counteracting the
movement of the pipe.
!  These spring elements are placed along the “wire” model to simulate the distributed reaction of
the soil.
!  The soil itself has a certain stiffness which describes the relation between applied load and
displacement as in a regular material.
!  The spings carry both information regarding the stiffness of the soil and the ultimate load it may
accomodate.
!  Another important property is the ultimate load which it can accomodate before it fails/
collpases .
!  Knowing both soil properties are crusial when one is aiming to estimate soil pipe interaction
and resulting pipe stresses.
!  Rigid buried pipe theory addresses longitudinal pipe deformations only.
29
Representation of Maximum Soil Loads
Upward Soil Resistance Depending on Soil Prism
Three different soil loads may be developed
Marston’s load theory may be used for vertical soil resistance
!  Generally pipe experiences 3 types of soil loads:
1.  Vertical Soil Load (Upward & Downward)
2.  Horizontal Soil Load
3.  Axial Soil Load (Friction)
!  When the pipe is in rest and does not move the
loads extered on the pipe are in balance and are
normally called: “neutral soil loads”
!  When on the pipe another external load is exerted
neutral soil loads modify to balance the external
loads: we then talk about: “active and passive
soil loads”
!  Vertical soil resistance can be described by the
application of the “soil prism theory” also know as
“Marston’s load theory”
Vertical Upward
!  This theory states that the soil resistance is determined
by (a) the weight of a soil prism above the pipe and
(b) the shear forces exerted on either sides of the
prism.
Horizontal
!  The shear conditions depend on the installation layout
of the pipe and soil; but in this case negative shear will
be assumed.
Vertical Downward
!  Next to the soil prism the weight of the pipe needs to
be taken into consideration as well.
friction
30
31
32
Derivation of Upward Soil Resistance
Upward Soil Resistance for Deep Buried Pipes
Shear effects are found by integration of the loads on both sides of the prism
Marston theory does not apply for deep buried pipes
!  Shear stresses can be found by intergrating the friction
along both side surfces of the prism.
!  Marston’s method assumes that the “friction
planes” run from the outer edges of the pipes
towards grade level.
!  Let’s assume cohesionless soil (c=0, e.g. sand); ϕ is the
friction angle of the soil.
!  For deep buries pipes (H > 5*D /10*D) this is not
true anymore.
!  The upward soil resistance q [kg/m] is:
!  The failure mechanism for deep buried pipes can
be determined according to deep burried
foundations; which is beyond the scope of this
course.
2
q = ( S + WS ) = tan(ϕ ) ⋅ K A ρH + ρDH
!  The weight of the prism is:
WS = ρ ⋅ D ⋅ H
!  The shear along the prism is calculated using Rankine’s
theory:
S = 2 ⋅ N ⋅ µ = K A ⋅ ρH 2 ⋅ tan(ϕ )
N
!  These failure planes do not strech until the grade
surface.
N
1
N = K A ⋅ ρH 2
2
σ v'' = ρH
33
Downward Vertical Soil Resistance
Lateral Soil Resistance
Downward soil resistance requires the definition of the soil bearing capacity
Lateral soil resistance restrains the pipe to move laterally
34
!  When a structure is buried it experiences lateral
(horizontal) soil loads at rest.
!  When the pipe moves downwards the soil
resistance can be determined from the “vertical
bearing capacity”.
!  There are numerous theories to describe the
relation between the lateral load and the soil
reaction.
!  Detailed geotechinical evaluation is required to
determine the vertical bearing capacity.
!  We will discuss Rankine’s Method developed
for retaining walls.
!  For a general idea the downward resistance can
be roughly estimated to be as twice the horizontal
resistance.
!  When the structure moves horizontally when
buried the equilibrium loads change.
!  The vertical bearing capacity is the vertical load
required to break the soil underneath the pipe
over the full width of the pipe.
!  Also for buried non-pipe structures lateral soil
pressure is of great relevance.
!  The failure mode is illustrated in the figure on the
right.
35
36
Soil in Equilibrium without Lateral Movement
Passive & Active Lateral Soil Resistance
In equilibrium there is a balanced lateral load called the neutral lateral load
When the pipe moves laterally the neutral soil load is altered in an active and passive
load
!  When a pipe is buried it also experiences a horizontal
soil load at rest.
!  The horizontal equilibrium loads (qneutral) at rest are
called the “neutral horizontal loads”.
!  Netto no horizontal force works on the pipe.
A-A
A-A
!  To move the pipe horizontally inside the soil a load (Q)
is required.
!  In front of the pipe the neutral load increases to resist
this movement; “passive soil resistance”.
qneutral
qneutral
!  At the back side of the pipe the neutral soil load
decreases: “active soil resistance”.
!  Lateral loads can be represented by 2 symmetric
“wedges” shearing along planes A-A.
A-A
B-B
Q
qactive
!  In most cases the active soil load (qactive≈0) can be
ignored; since a void is created direclty next to the pipe
and no load is transfered to the pipe.
qpassive
Q = q passive − qactive
!  Lateral stresses can be represented by 2 asymmetric
“wedges” shearing along planes A-A & B-B.
37
38
Lateral Loads and “Wedge Effect”
Maximum Passive & Active Lateral Soil Resistance
Example of an experiment
Mohr-Coulomb theory may be used to calculate the passive and active loads
!  To calculate the maximum active and passive horizontal loads the equilibrium of
the forces along the shear planes of the wedge may be determined.
!  Theory assumes that the soil fails at a friction surface planes Ѳ.
S = shear force (friction)
N= normal force
Ws= prism weight load
Ѳ = slip plane
qactive
39
Q
qpassive
40
Determining the maximum lateral soil load
Lateral Soil Resistance For Deep Buried Pipe
Maximum soil load is found by differentiation
Rankine’s model is not valid for deep buried pipes
(A) Load Equilibrium:
: F →: 0 = q
Σ
passive − S cos θ − N sin θ
!  The wedge model is valid only when the depth of the cover is less than the diameter of the
pipe.
ΣF ↑: 0 = WS + S sin θ − N cosθ
WS =
qpassive
θ
!  When it is applied to larger cover depths it over estimates the lateral resistance.
1
γ (H + D )2 tan(Θ)
2
(B) Solving for qpassive:
1
2
q passive = γ (H + D ) cot θ * tan(Θ − ϕ )
2
!  Special theory is required to define the ultimate load for this cases, which beyond the scope
of the training.
Expressed as Rankine’s Coefficient Kp:
K P = tan 2 (45 +
ϕ
2
!  For deeper buried piping the failure mode is tunneling and pipe punching.
!  For this case the soil resistance is typically much smaller than according to the wedge
theory.
(C) Determining Maximum qpassive
1
ϕ
2
q passive = γ (H + D ) tan 2 (45 + )
2
2
1
2
q passive = γ (H + D ) K p
2
!  However for a cover depth equal to 3 times the diameter of the pipe the overestimate is
only 10%.
)
41
42
Axial Soil Resistance
An Equation for Axial Soil Resistance
Axial soil resistance is caused by the effects of friction
Axial soil resistance is proportional to the weight of the soil cover and pipe
!  Axial loads are generated by the shear resistance
developed over the pipe outer surface.
!  In the case of an idealized model the axial
resistance (f) can be determined by the following
expression:
!  Shear resistance comprises two parts:
1. 
2. 
f = µ (2WS + W p )
cohesive forces
friction forces
!  The active soil force is defined as:
!  A typical soil pressure distribution on a pipe is
shown in the figure on the right.
WS ≈ ρDH
!  A more practical approach is to idealize the
methodology and determine the axial friction based
on the vertical loads as shown in the figure on the
right.
!  The resulting axial resistance force is than:
Typical friction values of µ:
f = µ (2 ρDH + W p )
!  (µ) is called the friction coefficient (not to be
confused with the soil friction coefficient).
43
44
Pipe/Soil Stiffness Definition
The Axial Pipe/Soil Stiffness
Pipe/Soil stiffness defines the interaction stiffness between soil and pipe
The definition of the axial pipe stiffness is similar
!  Stiffness describes the amount of soil displacement
that is required to reach ultimate soil load.
!  Axial friction can also modelled as a bi-linear curve as
is shown on the right.
!  As can be seen from the stress-strain curve the
behavior is generally non-linear.
!  The movement before full fracture is reached, is
considered to me small or instantenous in most
mechanical representations of axial friction.
!  Soil stiffness values may be determined from soil
investigation.
!  In pratise the non-linear behavior is approximated by a
so-called bi- or tri-linear curve as can be seen from
the graph on the right.
!  The strain at which maximum (ultimate load) is reached
is also called the “yield displacement”. Some sources
report that this value is about 1.5 – 2% of the pipe
bottom depth.
!  After reachring full axial load the load remains
unchanged.
!  The relation between load and displacement in the
linear part is desribed by:
q
Kq =
de
kf =
45
f
de
Contents
Flexible Pipe – Soil Interaction
Flexible pipe – soil interaction
Ring deformation is especially relevant for flexible pipes
!  Flexible Pipes can also experience significant
circumferential deformation effects due to soil load.
!  Exessive circumferential deformation of the pipe may
lead to collapse/fracture of the pipe.
46
!  Determining the amount of ring ovalisation is therefore
a key factor in the design of a flexible pipe.
47
48
Pipe Ring Deformation and Stresses
Some Notes on the Iowa Formula
Ring deformation is especially relevant for flexible pipes
The Iowa formula includes 2 stiffness effects
!  M. Sprangler (student of Marston) observed that Marston
Theory for vertical loads on buried pipes was not
adequate for flexible pipes.
!  If one studies the Iowa equation one can note that
the ring deflection is resisted by 2 effects:
1.  Pipe ring stiffness
2.  Stiffness of the surrounding soil
!  Flexibile pipes provide little inherent stiffness in
comparison to rigid pipes, but still perform remarkably
well when buried.
(B) Soil lateral
stiffness
!  The bedding constant (K) accounts for the the
supporting “bed” underneath the pipe.
∆X
!  The ability of flexible pipes to support vertical loads is
dervied from:
1.  The redistribution of loads around the pipe
2.  It generates passive pressures at the sides of the pipe
when it moves outward against the earth
!  Typical values for different bedding angles are
shown in the table on the right.
!  Since soil consolidates at the sides of the pipe
over time the factor (DL) is used to account for the
additional ring deflection.
!  His derived formula is called “Sprangler’s” or “Iowa“
formula which relates ring deflection (∆X) to the vertical
soil loads.
(A) Pipe ring stiffness
49
Contents
50
Dynaflow Buried Piping Training
End
!  Two days buried lines with CAESAR II
training course.
!  17 - 18 September 2012.
!  You can register using our webpage.
www.dynaflow.com
!  End
51
52
Questions ?
53

Dynaflow Lecture: Buried Piping

Transcription

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