S - AIOM

Palermo, 7th November 2014
GENERAL MODEL FOR
LONGSHORE TRANSPORT
by G.R. Tomasicchio, Felice D’Alessandro and Elena Musci
University of Salento, Lecce, Italy
Introduction
The knowledge of the LT in the surf zone are central in coastal
engineering studies; practical engineering applications, such as:
design of dinamically
stable reshaping/berm
breakwaters;
dispersion of beach-fill
and placed dredged
material;
beach nourishment
projects;
sedimentation rates in
navigation channels
they all require accurate predictions of the LT
CERC FORMULA
[1]
There is no direct inclusion of the influence of the grain size in the formula, other than
via the coefficient K, which has been found to be quite variable even at sandy beaches
(Dean 1987; USACE 2001).
Originally proposed for sandy beaches
K = 0.77
The shingle beaches
Natural shingle beaches are not rare
Nourishing projects use more and more shingle material
Basic classification of sediments (after Wentworth, 1922)
A shingle beach is composed of gravel or cobbles: the sorting ranges
from 2 to 250 mm diameter
In the UK, one third of the coastline is protected by shingle beaches, but they are
widespread also in Canada, Japan, Argentina, South of Italy, New Zeland, Philippines,
Bahrain and they occur along considerable stretches of the Pacific coast of the USA.
Valuga Beach, Batanes, Philippines
South East towards Creag a' Chaise, UK
Seaham Harbour, UK
Sangineto, Tyrrhenian coast, south of Italy
Marina di Ragusa, Sicily, south of Italy
Bari, Puglia, south of Italy
For the case of shingle beaches, LT is determined by the bed load and not by
a combination of bed load and suspended load as in the case of a sandy beach
steep slope
1:8
LT at gravel beaches is influenced by a steeper beach slope, typically 1:8,
which encourages waves to form rapidly plunging or surging breakers close
to the shoreline; thus, most of the energy dissipation is restricted to a narrow
region that includes the swash zone (van Wellen et al. 2000)
run-up
back-wash
infiltration
run-up maximum
A well sorted coarse sediments mound also exhibits a larger porosity compared
to the sand; this allows infiltration of water during the swash run-up, which
weakens the backwash and can be identified with the formation of the berm at
the run-up maximum
These phenomena lead to a different mode of energy dissipation compared to sandy
beaches, which may partially invalidate the most popular formulae (e.g. USACE 1984;
Kamphuis 1991) for LT estimates.
For this reason, a research activity on LT at shingle beaches has been performed in the
past to deal with the erosion problems along these types of beaches. Only a few formulae
(e.g. van Hijum and Pilarczyk 1982; Chadwick 1989; van der Meer 1990) have been
proposed specifically for LT at shingle beaches and most of them have been calibrated
for a very limited data sets.
Commonly adopted formulae for LT
estimation at shingle beaches
CERC FORMULA
ρK g γ b
Q LT = K ⋅ P =
16(ρ s − ρ )(1 − a )
[1]
There is no direct inclusion of the influence of the grain size in the formula, other than
via the coefficient K, which has been found to be quite variable even at sandy beaches
(Dean 1987; USACE 2001).
The study conducted by van Wellen et al. (2000) confirmed the reduction in K for coarsegrained sediment and indicated that the value of K when in the presence of gravel
beaches is around 30% of the value of K from a sandy beach, although other values of K
from field experiments of coarse-grained beaches have been much lower; for instance,
Nicholls and Wright (1991) found K to be between 1% and 15% of that for sand, whereas
Chadwick's (1989) trap data suggested a K value 7% of that for sand. This adds further
inaccuracy about the LT estimation at gravel/cobbles beaches when using the CERC
equation which remains site specific.
KAMPHUIS (1991)
The effects of the wave period and beach slope, which both influence wave breaking, and
the grain size neglected in the CERC formula, have been considered by Kamphuis
(1991), resulting in a more refined equation. The formula which Kamphuis (1991) found
to be applicable to both field and laboratory data at sandy beaches is:
0.25
QLT,m = 2.27 H s2,b Tp1.5 mb0.75 Dn−50
sin 0.6 (2θ b )
[2]
Kamphuis also investigated whether the formula was applicable to gravel beaches by
comparing its predictions with the experimental results of Van Hijum and Pilarczyk
(1982). He found that it over-predicts these results by a factor of 2 to 5, concluding that
this was to be expected, since gravel beaches absorb substantial wave energy by
percolation.
VAN HIJUM AND PILARCZYK (1982)
Van Hijum and Pilarczyk (1982) proposed the following formula specifically valid at
gravel beaches; Eq. [3] has been obtained from the laboratory experiments conducted by
van Hijum (1976) and van Hijum and Pilarczyk (1982) at Delft Hydraulics:
QLT
2
gD90
Ts
= 7.1210
−4

H s ,d (cosθ )1 /2  H s ,d (cosθ )1 /2
sin θ
− 8.3

D90
D90

 tanh 2πh 
 L 
[3]
According to van Wellen et al. (2000), this formula introduces unwanted complications
by using wave parameters measured at an offshore location and at the toe of the
structure.
CHADWICK (1989)
Chadwick (1989) recasted the Delft experimental data in terms of conditions at the
breaking position to give:
2
Q LT = 0.0013(gD90
Ts )W (W − 8.3) sin θ
W =
H s ,b cos θ
D90
[4]
VAN DER MEER (1990)
Van der Meer (1990) also re-analysed the van Hijum and Pilarczyk (1982) formula in
order to make it more practical:
 H s cos θ b


Q LT = 0.0012 gDn50Tp H s cos θ b
− 11  sin θ b
 Dn50



[5]
VAN DER MEER AND VELDMAN (1992)
Van der Meer and Veldman (1992) specified that Eq. [5] should only be applied within
the limit Ns=12–27, i.e. fairly large gravel in prototype. Eq. [6] shows a dependency on
the grain diameter. For small grain sizes (gravel/sandy beaches) Eq. [5] reduces to:
Q LT = 0.0012πH s c sin 2θ b
[6]
It is noticed that in Eq. [6] the diameter or grain size is not present in accordance with the
CERC formula.
FORMULA
WEAKNESS
CERC
Site specific (via the coefficient K, which has
been found to be quite variable even at sandy
beaches)
KAMPHUIS (1991)
Over-prediction by a factor of 2 to 5
VAN HIJUM AND PILARCZYK (1982)
According to van Wellen et al. (2000), this
formula introduces unwanted complications by
using wave parameters measured at an offshore
location and at the toe of the structure
VAN DER MEER AND VELDMAN (1992) Only to be applied within the limit Ns=12–27
------------MOST RECENT PAPERS------------
also called Kamphuis modified
LT ≈ (d50)-α
α = 0.25 (sandy beaches, Kamphuis 1991)
α = 0.6 ÷ 0.7 (shingle beaches, Mil-Homens et al. 2013)
Does not consider the wave period influence
Development of a general model
for LT at coastal bodies
Sandy beach, a natural coastal structure
28
Beach made of cobbles, a natural coastal structure
29
Reshaping berm breakwater
stones 6-8 tons
Genova – Duca di Galliera
breakwater
Rehabilitated with a bb design
Definition 1:
Typically a coastal strucure is intended as a body which reduces and
absorbs the wave energy. In this sense, both a rubble mound breakwater
and a beach are bodies made of not cohesive units functioning as a
coastal structure
---------§§§--------Definition 2:
Different coastal strucures can be identified by means of the stability
number (van der Meer, 1988):
Ns = Hs/∆Dn50
Hs = significant wave height
∆ = relative mass density = (ρs – ρ)/ρ
Dn50 = nominal diameter of the units composing the structure
The stability of a coastal body is based on the concept of “dynamic
stability” (van der Meer, 1988, 1992).
Definition 3:
Dynamically stable: units are displaced by the wave action until a profile
is reached where the transport capacity along the profile is riduced to a
minimum for a given wave condition. Material around the still water
level is continuously moving during each run-up and run-down of the
waves. An
influence from the rock shape on the reshaping process has been
investigated by several authors (e.g. Frigaard et al., 1996).
Dynamic stability can roughly be classified by Ns>4
Classification of types of structures for different Ns values
Classification of types of structures
for different Ns values
H ∆D < 1
H ∆D = 1 - 4
H ∆D = 3 - 6
H ∆D = 3 − 6
H ∆D = 6 - 20
H ∆D = 20 - 500
H ∆D > 500
A longshore transport model for any coastal body
Tomasicchio et al. (2013) proposed a general model to determine the total LT at coastal
bodies accounting for a large number of mobility conditions of the units composing the
mound: from stones to sands.
The new model considers an energy flux approach combined with an empirical/statistical
relationship between the wave induced forcing and the number of moving units.
Assuming that a number Nod of particles removed from a Dn50 wide strip moves under the
action of 1000 waves, then the number of units passing a given control section in one
wave is:
Sn =
ld N od
sin θ k ,b = f N s* *
Dn 50 1000
( )
where:
ld =
N s* *
1.4 N s* * − 1.3
2
tanh (kh )
Dn 50
 sm , 0 
Hk


=
C k ∆Dn 50  sm , k 
−1 / 5
(cosθ0 )2 / 5
[units/wave]
LT data
Field Experiments
Particular lack of information for grain sizes coarser than 0.6 mm and beach slopes
steeper than 0.06 (1/15) (Schoonees and Theron 1993) are found.
The principal reasons for the lack of data are due to the lack of robust instrumentation to
measure the hydrodynamics and inability to measure sediment whilst it is in transport.
Sediment transport data from shingle beaches has traditionally relied on one of three
methods: tracers, traps or profile/shoreline changes.
Only two field experiments on coarse-grained beaches satisfied Schoonees and Theron
(1993) criteria, which essentially required measurements of wave conditions (height,
period, angle), transport rate, beach gradient and grain size; the two experiments were by
Nicholls and Wright (1991) and Chadwick (1989).
Since Schoonees and Theron’s review in 1993, several other field data experiments have
been conducted although again, in some cases, insufficient information has been included
to make them useful for further evaluation (e.g. Workman et al. 1994, Bray et al. 1996,
Van Wellen et al. 1997, 1998).
Laboratory Experiments
Impossibility of representing the hydraulic characteristics of the individual coarsegrained particles and bulk properties of the sediment
Kamphuis’ (1991) experiments: the particle size and associated beach slope can be
adequately scaled but the scale effects of hydraulic conductivity have not yet been
quantified, which introduces an unknown scale effect when predicting prototype transport
rates from laboratory models for coarse-grained sediment. The result is that LT observed
in a laboratory model using scaled sediment is often very different from that which would
occur in nature (Brampton and Motyka 1987)
A large basin is needed to undertake research into LT under oblique waves
Model verification
FIELD DATA
LABORATORY DATA
SN,c / sin θk,b
1,E+14
NS** = 23
1,E+13
1,E+12
1,E+11
NS** = 9
1,E+10
1,E+09
NS** = 6
1,E+08
Shingle
1,E+07
beaches
1,E+06
1,E+05
1,E+04
Berm
1,E+03
breakwaters
Sandy
1,E+02
beaches
1,E+01
1,E+00
1,E-01
1,E-02
1,E-03
1,E-04
1
10
100
NS**
Van Hijum & Pilarczyk (1982)
Shoreham, UK (1989)
Hurst Castle Spit, UK (1991)
Burcharth & Frigaard (1987,1988)
Duck 85 - Kraus (1989)
Van der Meer & Veldman (1992)
Schoonees & Theron (1993)
DHI (1995)
Wang et al. (1998)
Sandyduck - Miller (1999)
LSTF - Smith et al. (2003)
1000
10000
100000
1,E+14
1,E+12
1,E+10
SN ,c / sin θk,b
1,E+08
1,E+06
Van Hijum & Pilarczyk (1982)
Shoreham, UK (1989)
Hurst Castle Spit, UK (1991)
Burcharth & Frigaard (1987,1988)
Duck 85 - Kraus (1989)
Van der Meer & Veldman (1992)
Schoonees & Theron (1993)
DHI (1995)
Wang et al. (1998)
Sandyduck - Miller (1999)
LSTF - Smith et al. (2003)
1,E+04
1,E+02
1,E+00
1,E-02
1,E-04
1,E-04
1,E-02
1,E+00
1,E+02
1,E+04
1,E+06
SN ,o / sin θk,b
1,E+08
1,E+10
1,E+12
1,E-01
1,E-02
1,E-04
1,E-05
=4
QLT,c/QLT,o = 0.25
QLT,c/QLT,o = 2
1,E-06
1,E-07
c
QLT,c (m3/s)
1,E-03
GLT - Shoreham, UK (1989)
QLT,c/QLT,o
GLT - Hurst Castle Spit, UK (1991)
GLT - Van Hijum & Pilarczyk (1982)
Mil-Homens et al. (2013) - Shoreham, UK (1989)
Mil-Homens et al. (2013) - Hurst Castle Spit, UK (1991)
Mil-Homens et al. (2013) - Van Hijum & Pilarczyk (1982)
Van Rijn (2014) - Shoreham, UK (1989)
Van Rijn (2014) - Hurst Castle Spit, UK (1991)
Van Rijn (2014) - Van Hijum & Pilarczyk (1982)
1,E-08
1,E-08
1,E-07
1,E-06
QLT,c/QLT,o = 0.5
1,E-05
1,E-04
QLT,o (m3/s)
1,E-03
1,E-02
1,E-01
GLT MODEL
CALIBRATION
VERIFICATION
MIL-HOMENS ET AL. (2013)
VAN RIJN (2014)
GLT MODEL FURTHER VERIFICATION: A CASE STUDY
Dn50 = 0.02 m
(van Wellen et al. 2000 CENG)
Observed LT =15,000 m3/annum (van Wellen et al. 2000 CENG)
The estimated net LT by GLT model is about 14,500 m3/annum.
The Mil-Homens et al. (2013) formula predicts a net shingle transport
of 8,500 m3/annum.
Van Rijn (2014) varied the input parameters yielding a net LT of
shingle in the range of 7,000 to 16,000 m3/annum.
Conclusions
The present paper applies and verifies a general model to determine the total LT at
shingle beaches. The model aims to represent an engineering single tool allowing to
predict the LT rate at any given coastal mound.
As in the case of well popular formulae (e.g. CERC formula), the new model does
not distinguish between bed load and suspended transport.
The verification of the LT model has been favorably conducted for a number of
experimental and field data sets.
Dependant on the wave period.
No need of information on the bottom slope.
Reliable, robust.
THANKS FOR YOUR ATTENTION
Torre Quetta, Bari
[email protected]