Palermo, 7th November 2014

GENERAL MODEL FOR LONGSHORE TRANSPORTLONGSHORE TRANSPORT

by G.R. Tomasicchio, Felice D’Alessandro and Elena Musci

University of Salento, Lecce, Italy

IntroductionIntroduction

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;

� sedimentation rates in

navigation channels

they all require accurate predictions of the LT

material;

� beach nourishment

projects;

CERC FORMULA

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).

[1]

(Dean 1987; USACE 2001).

Originally proposed for sandy beaches

K = 0.77

The shingle beachesThe shingle beaches

Basic classification of sediments (after Wentworth, 1922)

Natural shingle beaches are not rare

Nourishing projects use more and more shingle material

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 maximum

run-up

infiltration

back-wash

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 atweakens 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 Commonly adopted formulae for LT

estimation at shingle beaches

CERC FORMULA

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 coarse-

( )( )a

gKPKQ

s

b

−−=⋅=

116LT

ρρ

γρ[1]

The study conducted by van Wellen et al. (2000) confirmed the reduction in K for coarse-

grained 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:

( )bnbpbsDmTHQ θ2sin27.2 6.025.050

75.05.12,LT,m

−= [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.

( )bnbpbs 50,LT,m

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:

( ) ( )

−= −

hD

H

D

H

TgD

Q dsds

s

LT

π

θθθ

2tanh

sin3.8

coscos1210.7

90

2/1,

90

2/1,4

290

[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.

L

hDDTgD sπ2

tanh9090290

CHADWICK (1989)

Chadwick (1989) recasted the Delft experimental data in terms of conditions at the

breaking position to give:

( ) ( ) θsin3.80013.0 290LT −= WWTgDQ s

90

, cos

D

HW

bs θ= [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:

bn

bsbspn

D

HHTgDQ θ

θθ sin11

coscos0012.0

5050LT

−= [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:

It is noticed that in Eq. [6] the diameter or grain size is not present in accordance with the

CERC formula.

bscHQ θπ 2sin0012.0LT = [6]

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 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 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 breakwaterstones 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 stabilityDifferent 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. Anwaves. 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

1∆DH <

4-1∆DH =

6-3∆DH =

63∆DH −=

Classification of types of structures

for different Ns values

20-6∆DH =

500-20∆DH =

500∆DH >

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.

A longshore transport model for any coastal body

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:

where:

( )**,50

sin1000

sbkod

n

dn Nf

N

D

lS =θ= [units/wave]

where:

( ) 5/20

5/1

,

0,

50

** cosθ

∆=

−

km

m

nk

ks

s

s

DC

HN

( )502

**

tanh

3.14.1n

sd D

kh

Nl

−=

LT dataLT 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 coarse-

grained 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)occur in nature (Brampton and Motyka 1987)

�A large basin is needed to undertake research into LT under oblique waves

Model verificationModel verification

FIELD DATA

LABORATORY DATALABORATORY DATA

1,E+04

1,E+05

1,E+06

1,E+07

1,E+08

1,E+09

1,E+10

1,E+11

1,E+12

1,E+13

1,E+14N

,c /

sin θ

k,b

Van Hijum & Pilarczyk (1982)

Shoreham, UK (1989)

Hurst Castle Spit, UK (1991)

Burcharth & Frigaard (1987,1988)Berm

Shingle

beaches

NS** = 6

NS** = 9

NS** = 23

1,E-04

1,E-03

1,E-02

1,E-01

1,E+00

1,E+01

1,E+02

1,E+03

1,E+04

1 10 100 1000 10000 100000

SN

,c

NS**

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)

Sandy

beaches

Berm

breakwaters

1,E+04

1,E+06

1,E+08

1,E+10

1,E+12

1,E+14

N ,c

/ si

n θ

k,b

Van Hijum & Pilarczyk (1982)

Shoreham, UK (1989)

Hurst Castle Spit, UK (1991)

1,E-04

1,E-02

1,E+00

1,E+02

1,E-04 1,E-02 1,E+00 1,E+02 1,E+04 1,E+06 1,E+08 1,E+10 1,E+12

SN

,c

SN ,o / sin θk,b

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-05

1,E-04

1,E-03

1,E-02

1,E-01Q

LT

,c(m

3/s

)GLT - Shoreham, UK (1989)

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)

QLT,c/QLT,o = 0.25QLT,c/QLT,o = 2

QLT,c/QLT,o = 4

1,E-08

1,E-07

1,E-06

1,E-08 1,E-07 1,E-06 1,E-05 1,E-04 1,E-03 1,E-02 1,E-01

Q

QLT,o (m3/s)

c

QLT,c/QLT,o = 0.5

GLT MODEL

MIL-HOMENS ET AL. (2013)

CALIBRATION

VERIFICATION

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)� 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.

ConclusionsConclusions

� 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

roberto.tomasicchio@unisalento.it