952

ALONGSHORE EXTENSION OF BEACH EROSION
AROUND A LARGE-SCALE STRUCTURE
TAIKI SAKASHITA1, SHINJI SATO1 and YOSHIMITSU TAJIMA1
1.

Department of Civil Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyoku, Tokyo, 113-8656, JAPAN. sakashita@coastal.t.u-tokyo.ac.jp, sato@civil.t.utokyo.ac.jp, yoshitaji@coastal.t.u-tokyo.ac.jp

Abstract:

Extensive beach erosion is observed around a large-scale structure
constructed on the coast. However, the extent of the impact of coastal topographic
change seems to be larger than that predicted in the past studies. In this study, theinfluence of large-scale structure on coastal erosion was investigated throughlaboratory experiments and numerical simulation. Significant extension of coastal
erosion area around a large-scale structure was observed in laboratory experiments
when offshore currents were superimposed and waves with alternately changing
incident angles were introduced. The development of circulation currents behind thestructure and the arrest of sand in the sheltered zone were considered to be theessential mechanisms for the erosion.

Introduction
Change of the movement of littoral sand drift due to a large-scale structure is one
typical cause of beach erosion. It is empirically known that such coastal erosion ismainly developed in the area where the angle between the shoreline direction andthe direction to the tip of the structure is smaller than 45 degrees (e.g. Sato et al,1974). Extensive beach erosion like this pattern has been observed around largescale structures constructed on the coast. However, many recent examples showthat the erosion extends further than this ’45-degree-zone’. In addition to this, sincebeach erosion is complexly related with many various factors such as decrease insand supply in a watershed scale, it is very important to understand the extent of
impact of large-scale structures on coastal topography change. In this study, theinfluence of large-scale structure on coastal erosion was investigated throughlaboratory experiments and numerical analysis with focuses on various factors suchas variability of incident wave angles and large-scale coastal currents.
Laboratory Experiments in a Basin
Experimental Conditions and Methods
Laboratory experiments were conducted in an 11m-long and 6.5m-wide wave
basin. Ground plan and cross section of the basin are shown in figure 1 The bed

953

slope of the basin is 1/20 in the nearshore zone and 1/10 on the offshore side.
Water depth is determined as 22.5cm in order that the shoreline should be 1.1m
from the onshore edge of the basin. Gray zone in Fig.1 is observed area. In thisexperiment, X-axis denotes the alongshore direction, and Y-axis is in the crossshore direction, and θ is the angle of wave direction defined in the anti-clockwise
direction. Quartz sand with median diameter of 0.3mm was filled on the bottomof the basin to make a 4cm-thick movable bed. A breakwater was installed at 4m
from left side edge of the basin. The breakwater consists of two metal panels,
each length is 1m and one is situated normal to the shoreline and the other issituated obliquely with 45 degrees. Water circulation system was also arranged
on both sides of the basin to generate steady coastal longshore currents withvelocity as high as 10cm/s. Table 1 summarizes conditions for threeexperimental cases in which regular obliquely incident waves were generated
for 10 hours with or without steady alongshore currents. In Case A, incident
wave angle was fixed at +20 degree. Case B added artificially generated
longshore currents to Case A. In Case C, the incident wave angle was alternatelychanged between +20 and -20 degree at every hour. For all cases, wave height in
the offshore uniform depth region is 0.04m and the wave period is 1.0 second.
Besides measurements of wave and current fields, measurements of bottom
topography at every 3 hours were conducted by a digital camera installed above
the basin.
Wave generator

θYcamera

0
-400

4m

w
ak

Median diameter=0.3mm

e
br

Pumps

Observation area

Initial shoreline
1.1m

X

plan

1m

3m
1/20

4m
er
at

1/1
0

Boxes

4cm
sectionFig. 1. Wave basin layout

In Case B, steady longshore currents were artificially generated in the basin. To
genetate uniform current from left to right in Fig. 1, three pumps were installednear the right boundary of the basin. Water taken from these pumps wereconveyed to left side through houses and poured in the basin through diffusers.
The diffuser is made of acrylic boxes which have many small holes near thebottom, whose diameter are 1 cm. By the operation of this circulation system,
10cm/s currents were observed in the basin.

954
Table 1. Experiments condition
Wave Height and Period
Case A(Wave Only)
Case B(Wave and Current)

H=4cm
T=1s

Case C(Alternate Wave)

Wave Direction

Current

20 degreeNo

20 degreeYes±20 degree

No* In Case C, initial wave angle was 20 degree and changed between +20 and -20 degree at every hour.

In every run of experiments, shoreline position, topography change andnearshore current field were measured. Shoreline was measured every hour by
manual observation at an interval of 50 cm. Topography was measured every 3
hours by using image analyzing technique. Multiple pictures were taken while
the water was gradually drained and filled back in the basin. Image-rectification
techniques were then applied to extract the actual coordinates of the shoreline atdifferent water level. Then contour lines of 0cm, -2cm, -4cm, -6cm and -8cm
were detected and analyzed. The accuracy of this image analysis technique wasfound to be smaller than 5 cm. Blue colored dye was injected behind thebreakwater while generating waves and nearshore current field was observed byanalyzing the sequential images that recorded the movement of the ink. Figure 2
shows an example of measurement of nearshore current field. In this photograph,the blue ink area was enhanced to be visualized easily as white color. It showsthat circulation current and longshore current to the right was clearly visualized
behind the breakwater.
t=0(s)

t=30(s)Fig. 2. An example of measurement of nearshore current (Case A, white area means inked area)

Results of Shoreline and Topography Changes
Results of shoreline and topography changes of each case will be discussed in
the following. In this paper, we focus on the topography after 10 hours. Figure 3
shows the comparison of shoreline change of each case after 10 hours, and955

figure 4 shows contour lines at interval of 2cm of each case after 10 hours.
Dotted lines in figure 4 mean initial contour lines at an interval 2 cm depth.
250
230
230
210

C:73

Y (cm)

190
190

A:
50

170

150
150

°

B:6
2

°

°
Case B

130

InitialShoreline

110
110
90
70
70

Case C

Case A

0
0

50

100
100

200

150

200

250

X (cm)

300
300

350

400
400

450

Fig. 3. Shoreline changes after 10 hours
Case A (Wave Only)

270
270

-8cm

Y (cm)

230
230

-6cm

190
190

°

-4cm

45

150
150

-2cm

110
110

0cm
70
70

00

100
100

200
200

X (cm)

300
300

400
400

Case B (Wave and External Current)

270
270

-8cm

230
230

Y (cm)

-6cm
190
190

-4cm
150
150

-2cm
110
110

0cm

70
70

00

100
100

200
200

X (cm)

300
300

400
400

Case C (Alternating Wave)

270
270

-8cm

Y (cm)

230
230
190
190

-6cm

150
150

-4cm
-2cm

110
110

0cm

70
70

00

100
100

200
200

X (cm)

300
300

400
400

Fig. 4. Topography change for each case after 10 hours

956

From the results of shoreline change illustrated in figure 3, the angle of erosion
area was 40 degree in Case A, 23 degree in Case B and 17 degree in Case C.
Therefore the erosion area was extended in the order of A<B<C. It means thatboth of additional longshore currents and alternately change in incident wave
angles have an influence on the extension of the erosion area. Moreover, theextension of erosion area was 20% in Case B and more than 100% in Case C
compared with Case A.
Figure 4 illustrates significant differences in the erosion area as well as the shapeof contour lines. The comparison between Case A and Case B shows that theaccumulation, which is shown as the offshore ward movement of contour lines,
in the sheltered area (shown in colored area in figure 3) can be observed in bothcases, but Case B has more accumulated sands on the right hand side of the tip ofthe breakwater (around X=100cm) than Case A. Therefore Case B entraps moresands in the sheltered area than Case A. Moreover, in Case A, the area in which
contour lines move to offshore side is X=200~220cm, on the other hand in Case
B, the area is X=300cm which is farther away from the breakwater than Case A.
It means that additional longshore currents could cause this difference because
currents enhanced the circulation behind the breakwater. This strengthened
circulation currents in Case B were also observed by the measurement ofnearshore currents using blue ink.
The comparison between Case A and Case C shows that accumulation of sand in
the sheltered area is observed in both cases, but the advancement of contour
lines is larger in Case C than in Case A. This is considered that littoral sand drift
to the breakwater side was generated when the incident wave angle was θ=-20
degree, and the sands were transported into the sheltered area and deposited
there, but these sands were arrested in the sheltered area even if the wave angle
changed to θ=20 degree. In addition to this, the offshoreward movement ofcontour lines were not observed in Case C because the circulation currents
behind the breakwater were not generated when the incident wave angle was θ=20 degree. Consequently it is considered that topography change is strongly
related with nearshore current fields around the breakwater, and this will be
investigated in next section by using numerical analysis.
The comparions of topographies described in the above clearly indicates that
additional longshore currents have significant influence on alongshore extensionof the erosion area from the comparison with Case A and Case B, and further
extension of the erosion zone was also observed in Case C due to the sedimentarrestment in the sheltered area of the breakwater.

957

Comparison of Volume of Sand Accumulated in Sheltered Area
The amount of sands accumulated in the sheltered area was calculated from therebuilt topography data by interpolating contour lines and the difference in thevolume between the initial topography and the topography after 10 hours wascomputed. Figure 5 shows the comparisons of the amount of sand in sheltered area.
6000

4000

Changes in the amountof sands (cm3)

4000

Sedimentation

2000

0

B

C

0

-2000

A

-4000
-4000

-6000

-8000
-8000

Erosion-10000-12000-12000Fig. 5. Changes in the amount of sands in sheltered area between initial moment and after 10 hours.

Figure 5 shows that severe erosion is observed in Case A while accumulation isdeveloped in Case B and Case C. Both of additional external currents andalternate change of incident wave angle could be effective to accelerate
entrapment of sands in the sheltered area. The sands entrapped in the shelteredarea were originated from the area of X>0 and the change of circulation currents
behind the breakwater might increase the volume of littoral sand drift to left
hand side. Detailed investigation for this will be tried in next section ofnumerical analysis.
Numerical Analysis by Shoreline Change Model
In order to confirm the physical mechanisms observed in laboratory experiments,
numerical analysis of beach deformation around a structure was made based on
the shoreline change model concept.
Firstly, the wave field was calculated by the time-dependent mild slope equation(Watanabe and Maruyama 1986) which could consider nearshore wave
deformation including diffraction, refraction and breaking. Nearshore currents inevery mesh point were then computed based on the radiation stress fieldcalculated from the wave field. Figure 6 shows wave height and nearshore
current field of three cases used in the experiments. It is confirmed that thecirculation currents are enhanced in Case B in the area sheltered by thebreakwater. It is also illustrated that the longshore currents due to waves with 20 degrees are decelerated in the sheltered area. It is therefore suggested that the958change in nearshore currents plays an essential role in the entrapment of
sediments.
Lastly, the sediment transport rate was calculated based on these wave andcurrents field. The shoreline changes were calculated from longshore transport
rates estimated either by Ozasa and Brampton model (1980) or by local sedimenttransport model (Shimizu et al., 1994). The former model calculates shorelinechange by sediment transport rate modeled by the longshore distributions ofwave heights and directions at breaking points. On the other hand the lattermodel calculates local sediment transport rates from bottom shear stress andnearshore currents.

Y(cm)

280

Case A (Wave Only) θ=-20°

240

0.04

200

0.03

160

0.02

120

0.01

80

Y(cm)

280

0

100

200
X(cm)

300

400

Case B (Wave and Current) θ=-20°

0
(m)
0.05

240

0.04

200

0.03

160

0.02

120

0.01

80

280

Y(cm)

0.05

0

100

200
X(cm)

Case C (Alternate Wave) θ=-20°

300

400

0
(m)
0.05

240

0.04

200

0.03

160

0.02

120

0.01

80

0

0

100
0.30(m/s)

200
X(cm)

300

400

Fig. 6. Computed wave height and current fields.

波高(m)

959

Computation by Ozasa and Brampton model
The shoreline change in 10 hours was computed by Ozasa Brampton (1980)
model. This model is very practical and widely applicable to compute theshoreline change around structures by considering wave diffraction andgeneration of nearshore currents. The longshore sand transport rate is calculatedby the following equation: Eq.1.

K2
∂HB 

I = ( Ecg ) B  K 1 sin α B cos α B −cos α B
tan β
∂y 


(1)

where K1, and K2 are dimensionless coefficients, tanβ is the bottom slope, αB isthe wave angle at the breaking point, HB is wave height at breaking points and I
is the longshore sand transport rate expressed in underwater weight as shown in
Eq.2.
I = ( ρ s − ρ ) g (1 − λv )Q(2)

where ρs is the density of sand (=2.65(g/cm3)), ρ is the density of water(=1.0(g/cm3)), and λv is the porosity of sand (= 0.4). For the value of K1, 0.77 isoften used, but this value is based on the field data and could be changed forexperimental data. In this study, the value of 0.077 was used considering
matching with experimental data. The coefficient K2 means the relative strength
between circulation currents and alongshore currents which is determined at K2=K1/1.5.
Computed shoreline after 10 hours by using the Ozasa Brampton model is shownin figure 7. This result is based on the wave fields generated from initial
topography and on the assumption that they do not change even if the
topography changed. However, the relative changes of breaker angle due to theshoreline changes were considered in this calculation.
It is confirmed in figure 7 that the accretion in the sheltered area is significant inCase C compared with those of Case A and B. At the same time, severe erosion
is observed in the area farther than the location of X=80cm in Case C.

960

1.90
190
1.70

Y (cm)

1.50
150

Case A, B

1.30

Initial shoreline

1.10
110

Case C

0.90

70

0.70
0.50

00

5

10
100

15

20
200
X (cm)

25

30
300

35

400

Fig. 7. Computed shorelines after 10hours with Ozasa and Brampton model (θ=20 deg.)

1.90
190
1.70

θ=10°
θ=±10°Y (cm)

1.50
150
1.30

Initial shoreline

110

1.10
0.90

70

0.70
0.50

00

5

10
100

15

20
200
X (cm)

25

30
300

35

400

Fig. 8. Computed shorelines after 10hours with Ozasa and Brampton model (θ=10 deg.)

Additional case of the incident wave angle was 10 degree was also calculated inthis model as shown in figure 8. From these results, erosion area was a little bitof enlarged compared with the wave angle was 20 degree. This is because theshoreline direction got mild to be perpendicular with the wave angle and thewave heights at breaking point were high due to less refraction. In case ofalternate change in wave angle, erosion area was also enlarged farther just likethe case of the incident wave angle was 20 degree.
Consequently, application of Ozasa and Brampton’s model showed that in caseof alternate change in incident wave angle erosion area was significantly
extended compared with the case of constant wave angle, although the longshore
component of energy flux of incident waves was zero on the average. However,as this model cannot consider the influence of additional currents (Case B), local
sediment transport model was introduced in the next section in order to simulate
the effects of additional longshore currents on the topograhy change.

961

Computation by local sediment transport model
In the 3D-SHORE model introduced by Shimizu et al.(1994), local sedimenttransport rate qc due to currents was computed by the following equation (eq.3)
by considering the steady states of nearshore currents field.
2

2

(3)

qc = Ac (u* − u*c )uc / gwhere u* is the maximum bottom friction velocity, u*c is the critical friction velocity
corresponding for general movement of sand particles(u*c2= c sgD), ψc is theShields number, g is the gravitational acceleration, D is grain diameter, uc is current
velocity, Ac is a dimensionless coefficient. The coefficient Ac was estimated fromthe following equation (eq.4) using sediment transport coefficient Bw.

ψ{

AC = 10 Bw w f 0.5 f w / (1 − λv ) s sgD}(4)where wf is the settling velocity of sand particles, fw is the friction coefficient, λv
is the porosity, s is the specific gravity of sand particle in water.
After calculating local sand transport rates in the longshore direction, total
longshore sand transport rate across the surf zone was calculated by integratingthem in surf zone. In this calculation, the offshore boundary of the surf zone wasdetermined at Y=190cm on the basis of the observation of wave fields. In the
sheltered area, the offshore boundary was limited by the position of the
breakwater. The calculations of topography and shoreline changes were based on
the assumption that the cross-shore profile of beach topography would change inparallel form as was assumed in the conventional shoreline model. Topography
was renewed on the assumption of the parallel movement of contour lines at 3
and 6 hours in order to consider the change of nearshore currents and waves withbeach deformation. Figure 9 shows the results of computed shoreline at 10 hours.

180

Case AY (cm)

Case B
140

Case C
Initial Shoreline

100
60
0

100

200
X (cm)

300

400

Fig. 9. Computed shorelines after 10hours with local sediment transport model

962

It is shown in figure 9 that the area of the severest erosion in Case B is located at
X=140(cm) which is farther from the structure than that in Case A, that is
X=100(cm). Therefore, it is considered that additional alongshore currents
resulted in larger erosion by strengthening the circulation currents behind thebreakwater as illustrated in figure 6.
From the results of distribution of littoral sand drift as illustrated in figure 10, it
is also confirmed that the boundary location where moving direction of littoralsand drift changed was farther from the structure in Case B than that in Case A.
This resulted in larger erosion in Case B than in Case A.
2

Littoral sand drift
10-6(cm2/s)

1.0e-005
7.5e-006

15.0e-006

Case A

2.5e-006(Wave Only)×0

Case B(Wave and Currents)

0.0e+000-2.5e-006-1-5.0e-006

00

50

100
100

150

200
200
X (cm)

250

300
300

350

400

Fig. 10. Computed distribution of littoral sand drift

The shoreline advancement in the sheltered area is the largest in Case C,
indicating largest amount of sand entrapment in Case C. Also the position of theseverest erosion in Case C is located at X=250(cm), very far from the breakwater.
It is therefore confirmed in numerical analysis that the alternate change inincident wave angle substantially increases the entrapment of sand behind alarge-scale structure and enhances the beach erosion in the nearby coast.
Comparison of the amount of entrapped sand based on the local sedimenttransport model
The balance of amount of the sands captured in the sheltered area in 10 hours
was quantitatively calculated from the topographies in the shoreline modelcomputed with the local sediment transport model. Figure 9 illustrates the results
together with experimental data.
Figure 11 demonstrates that the model simulates the loss of sand in Case A andthe gain in Case C. The loss of sand in Case A is because the erosion at the
downdrift end of the sheltered area is larger than the accretion in the vicinity ofthe breakwater. The gain of sand in Case C is considered to be due to thearrestment of sand by alternating waves.

963

However in Case B, the model failed to predict the gain of sand. The reason ofthis mismatch is considered to be due to the inadequacy of the assumption ofparallel movement of contour lines introduced in the shoreline model. This canbe confirmed in the results of experimental topography change (see figure 4).
There is a clear difference in the bed slopes between Case A and Case B, that is,
the slope of Case A is steeper than that of Case B around the sheltered area.

Changes in the amountof sands (cm3)

8000
6000
4000
2000
0
-2000
-4000

Experiment

A
B

C

実験Numerical Model
数値計算(local sediment transport model)

-6000
-8000

-10000-12000Fig. 11. Changes in the amount of captured sands after 10 hours

Therefore, it is considered that the cross shore profile change was significant inCase B, possibly due to the sand movement enhanced by the dominatedcirculation currents behind the breakwater. Since such three-dimensional sandmovement was ignored in the numerical model, the amount of sand entrapped in
the sheltered area is underestimated especially in Case B. The simulation by
three-dimensional beach deformation models is remained as a future task.
Conclusions
In order to understand the mechanism of extensive erosion around large-scale
coastal structures, laboratory experiments were conducted for various conditions
simulating additional longshore currents and alternate change in incident wave
angle. Numerical analysis based on shoreline change model was also conducted.
The applicability of the numerical model was verified with the experimental
results. Main conclusions are summarized as follows.
(1) The influence of the additional longshore currents and the variability inincident wave angle on the extension of beach erosion around large-scale
structures was investigaetd by laboratory experiments and numerical analysis.

964(2) In case of the presence of additional longshore currents, erosion area wasextended by 20%. This was considered to be due to the changes in nearshore
current field behind the breakwater.
(3) In case of the alternate change of incident wave angle, the erosion area wasextended two times farther than the case with constant wave angle although thetotal longshore components of energy flux of incident waves were zero. This isbecause more sands were entrapped in the sheltered area than the case of
constant incident wave angle.
(4) In case of the additional longshore currents or the alternately changing
incident wave angle, topography changes can be computed well based on the
shoreline change model by applying proper sediment transport model for eachcase. The extension of erosion area was simulated in both cases.
(5) A model was proposed to estimate the influence of a large-scale structure on
the coast in which additional longshore currents or the seasonal variability ofincident wave angle exists were introduced.
References
Sato, S., Tanaka, N., and Sasaki, K., (1974). “Coastal topography changes withthe construction of Kashima Port,” Proc. Coastal Engineering Conf., JSCE,
21: 147-153. (in Japanese)
Tanaka, N. (1977). “Study on typical topography changes around harbors” Proc.
Coastal Engineering Conf., JSCE, 24: 190-194. (in Japanese)
Watanabe, A., Maruyama, K. (1986). “Numerical modeling of wave field under
combined refraction, diffraction and breaking” Coastal Engineering inJapan, JSCE, Vol. 29: 19-39.
Ozasa, H., and A.H. Brampton, 1980. “Mathematical modeling of beaches backed
by seawalls” Coastal Engineering, Vol. 4, 47-64.
Shimizu, T., Tsuru, M. and Watanabe, A., (1994). “Field verification of anumerical model of beach topography change due to nearshore currents,
undertow and waves” Proc. 24th Int. Conf. on Coastal Engineering: 26102624.
Horikawa, K. ed., 1988. “Nearshore Dynamics and Coastal Processes”
University of Tokyo Press., 522p.