Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

3-D Behaviour of Coastal Dyke Installed by Double Sheet-piles with Partition
Wall
Kakuta FUJIWARA
Assistant Manager, Construction Products Development Division, Nippon Steel & Sumitomo Metal Corporation, Tokyo,
Japan
Email: fujiwara.8fa.kakuta@jp.nssmc.com

Shinji TAENAKA
Senior Researcher, Steel Structures Research Laboratories, Nippon Steel & Sumitomo Metal Corporation, Chiba, Japan

Kousuke TAKAHAMA
Student, Faculty of Engineering, Gifu University, Gifu, Japan

Atsushi YASHIMA
Professor, Faculty of Engineering, Gifu University, Gifu, Japan

ABSTRACTIn the near future, there is fear that coastal dykes will sink by liquefaction due to a large earthquake such as Nankai
Trough Earthquake. To overcome the potential damage, the application of double sheet-piles with partition walls tocoastal dyke has been proposed. The partition wall is installed perpendicular to the double sheet-piles with a certain
interval. Authors confirmed that this structure should be effective in reducing the settlement of coastal dyke onliquefied ground through the model tests. To propose a design method for the double sheet-piles with partition walls
countermeasure, the authors carried out 2-D numerical analyses (code:LIQCA2D15) based on the model tests. As aresult, good reproducibility of dyke behaviour such as settlement, sheet-pile deformation and excess pore waterpressure could be confirmed. However, the applicability of numerical analyses was only discussed in 2-D framework.
Therefore, in this study, authors discussed the 3-D behaviour of this structure using 3-D numerical analyses(code:LIQCA3D15). It was found that the wider the interval of partition walls becomes, the larger the bending
deformation of sheet piles as well as the settlement of coastal dyke itself become.
Key words: Coastal dyke, Earthquake, Liquefaction, Sheet-pile, Reinforcement

1. Introduction
Several coastal dykes collapsed due to shaking andSheet-piletsunami caused during the 2011 off the Pacific coast of
Tohoku Earthquake(Oka

et.al.

2012). A Large

subduction-zone earthquake such as Nankai TroughTie-rod

Earthquake is also concerned to occur in the near future(Cabinet Office 2015). As a countermeasure against alargeearthquake

andtsunami,installing

doublesheet-piles into a dyke has been proposed. For theenhancement of the effectiveness this countermeasure,the double sheet-piles with partition walls have been
investigated, as shown in Fig. 1 (Fujiwara 2017).

Partition wall(a) Construction situation(b) Sheet-piles structure

Fig. 1 Schematic of the reinforced coastal dyke

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Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

The partition walls are sheet-pile walls that areextension of dyke direction (equal to approximately 9m

installed perpendicular to the double sheet-piles. The

in an actual structure). More detailed experimental

effectiveness of this countermeasure against earthquake

conditions can be found in the literature (Fujiwara et.al.

has been studied through model tests and numerical2017). The wave recorded at Kamaishi during the 2011

analyses. The authors confirmed that dyke settlement due

off the Pacific coast of Tohoku Earthquake was adjusted

to ground liquefaction should be reduced remarkably. In

as the input earthquake motion for shaking model tests,

addition, since sheet-piles keep their height, sheet-piles

considering the similarity rule. In this study, input

even without partition walls prevent tsunami fromearthquake motion was modified by extending theoverflowing (Furuichi. et.al. 2015). However, the design

observed time duration three times to emphasize themethod of this countermeasure has been proposed only ineffect of countermeasures (Fig. 2).

a 2-D framework (Fujiwara et.al. 2017). As the double
sheet-piles with partition walls have a 3-D structure, the2.2. Test results

behavior of coastal dykes with countermeasure should be

Deformed configuration of Case-C after shaking is

confirmed in a 3-D framework. For an example of Kochi

shown in Fig. 2. While the foundation ground deformed

coastal dyke, partition walls are generally spaced

due to liquefaction, the settlement of double sheet-piles

approximately every 9 m conventionally. In this study,

themselves and the ground inside sheet-piles are reduced

the authors carried out 3-D numerical analyses as a basic

significantly. The settlements at two points along thestudy to propose a design method. First, shaking model

extending direction of the dyke are shown in Fig. 2 (C),tests were conducted to verify the validity of theand these both values were approximately 10mm.

numerical models.

Therefore, the behavior of dyke settlement was almost
constant along extending direction. The time history of

2. Overview of model tests

the settlement at the top of the dyke in Cases-A~C is2.1. Test procedures
The shaking table model tests were carried out

shown in Fig. 3. The residual settlement in Case-C was
10% and 24% compared to Case-A and B respectively.

under a gravity field. The model ground consisted of adyke, liquefiable and unliquefiable layers. The height ofthe model dyke was 300 mm. That condition isapproximately 1/25 geometrical scale to the actual
structure. As shown in Table 1, three cases: Case-A(without

countermeasure),

Case-B(withdoublesheet-piles), and Case-C (with double sheet-piles andpartition wall), were examined. The ground andsheet-pile conditions are shown in Table 1. The model
sheet-pile and partition wall were steel plates withthickness of 3.2 mm and 2.3 mm, respectively based on
the similarity rule (Iai. 1988). The tops of double
sheet-piles were connected with tie-rods. The side of thepartition wall was welded to double sheet-piles. The
partition walls were installed at a gap of 340 mm for the
Table 1.

Fig. 2

Soil conditions and countermeasures- 258 -

Test results

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

However, the extension direction of the dyke is 170mm
which is half of the model test container due to thesymmetric nature along the extension direction of thedyke. The displacements of the bottom boundary are fixedin all directions. The horizontal displacement of sideboundaries is also fixed.
The dyke and liquefiable layer are modeled by aFig. 3cyclic elasto-plastic model, and the unliquefiable layer is

Input motion and settlement

modeled by the Ramberg-Osgood model (Ramberg et.al.
The very satisfactory settlement reduction effect was1943).

confirmed by the double sheet-piles with a partition wall.

elastic-plastic model are summarized in Table 2. The

The

materialparameters

for

the

cyclicparameters for the liquefiable layer were determined by
3. Numerical analysis

considering the results of undrained cyclic triaxial

3.1. Outline of the Numerical Code, LIQCA
We will discuss the reproducibility of numericalcompression tests.

analyses in this chapter. In this study, we use a

Fig. 5. Since the double sheet-piles did not yield for thethree-dimensional program, LIQCA3D15 (LIQCARI.

model tests, double sheet-piles are modeled by a solid2015). The governing equations for coupling problems

elastic material. A joint element in which the slipping andbetween the soil skeleton and pore water pressure wereseparation are taken into account is not used between theformulated based on the two-phase mixture theory (Biot.

ground and sheet-pile in this model. The tie-rod and1962) and u-p (displacement of solid-phase and pore

partition wall are not modeled by the element itself but

water pressure) formulation was adopted in 3-D analysis.

modeled by the displacement constraint condition of

The finite element method (FEM) was employed fornodes. The interval of tie-rod in the extension direction of

spatial discretization of the equation of motion, whereas

the dyke is 113 mm. The nodes on both side ends ofthe finite difference method (FDM) (Oka et.al. 1994) was

tie-rod are put on the nodes of the sheet-piles in the same

employed for spatial discretization of pore water pressure

position and they are given equal displacement boundary

in the continuity equation. In this simulation, a cyclic

conditions in the vertical and horizontal directions.

The stress strain relation, effective

stress path and liquefaction resistance curve are shown aselastic-plastic model (Oka et.al. 1999) was applied to thecoastal dyke with liquefiable layer.
170mm

Table 2.

tie-rod

Material parameters for liquefiable layer

Initial void ratio

𝒆

0.813

Compression index

𝝀

0.015

Swelling index

𝜿

0.002

𝑮𝟎 ⁄𝝈𝒎𝟎1000

Phase transformation stress ratio

𝑴∗

0.909

Failure stress ratio

𝑴∗

𝒇

1.122

Reference strain parameter

𝜸𝑷

0.01

Reference strain parameter

𝜸𝑬

0.02

Hardening parameter

𝑩𝟎

7000

Hardening parameter

𝑩𝟏

50

Hardening parameter

𝑪𝒇0

Dilatancy parameter

𝑫𝟎

3

Dilatancy parameter𝒏3

Anisotropy parameter

𝑪𝒅

2000

Initial shear modulus ratio
300mm (height)←partition wallz(height of dyke)y(extension direction)x(width direction)
Fig. 4320mm(liquefiable layer)
200mm(unliquefiable layer)

Numerical model (Case-C)

3.2. Conditions for numerical model
The size of the numerical model (i.e. width of theground, thickness of layers, etc) is basically equal to theconditions of the model tests, as shown in Fig. 4.

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𝒎

50
40
30
20
10
0
-10
-20
-30
-40
-50

Experiment

-20

-10

Deviator stress (kN/m 2)

Deviator stress (kN/m2)

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

0

10

50
40
30
20
10
0
-10
-20
-30
-40
-50

corresponds to the 3.0% damping factor to the first natural

Experimentperiod of 0.3 seconds of the level ground portion.
3.3. Verification of reproducibility
For Case-A ~ C, the dyke deformation together withexcess pore water pressure ratio distribution (t=80sec.) are
0 10 20 30 40 50 60 70 80 90 100

20

Axial strain (%)

shown in Fig. 6. As soil conditions were uniform across

Mean effective stress (kN/m2)

Deviator stress (kN/m2)

Deviator stress (kN/m2)

the test model, the deformations of dyke and ground
50
40
30
20
10
0
-10
-20
-30
-40
-50

Simulation

-20

-10

0

10

50
40
30
20
10
0
-10
-20
-30
-40
-50

caused by liquefaction were symmetrical, as shown by

Simulation

the model tests.
Model test

0 10 20 30 40 50 60 70 80 90 100

20

Mean effective stress (kN/m2 )Axial strain (%)

analysis (Set-A)

analysis (Set-B)

experiment

Analysis

Stress ratio

0.25

Simulation

0.2

200mm

0.15

P2

0.1

P1

Elemental test

0.05(a) Case-A

0
1

10

100
Number of cycles

Fig. 51000

Model test

Elemental tests

As far as the movement of the partition wall isconcerned, the equal-displacement conditions in all
directions are set for all nodes located on the partition wall.

Analysis

Therefore, shear and bending deformations are notallowed for the partition wall.

200mm

P2

Boundary conditions are as follows:

P1A) The bottom of the ground is fixed in the horizontal andvertical direction.

(b) Case-B

B) The side boundary of model is fixed in the horizontal

Model test

direction.
C) The water level is adjusted to the surface of theliquefiable layer.
D) The drainage boundary is set on the surface of theliquefiable layer.

AnalysisE) The bottoms of sheet-piles are given free condition
200mm

same as experimental ones.

P2

The input wave is shown as Fig. 3. The incremental

P1

time interval is 0.002 seconds, the coefficient β of theNewmark method is set at 0.3025, and γ is set at 0.6. For(c) Case-C

Rayleigh damping, a proportional type to the initial

Fig. 6

stiffness is used. The coefficient is set at 0.003 which

deformed mesh

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Excess pore water pressure ratio distribution inProceedings of the First International Conference on Press-in Engineering 2018, Kochi

Case-A (experiment)

Case-A (analysis)

Case-B (experiment)

Case-B (analysis)model tests in which the horizontal ground was liquefied

Case-C (experiment)

Case-C (analysis)

virtical displacement (mm)The result of Case-A reproduced the behavior of theand the ground beneath the dyke flowed laterally, causing
the dyke to settle while spreading horizontally.
For Case-B and C, although the dyke settled anddeformed due to liquefaction, sheet-piles and partition
walls did not settle because the bottom end of sheet-pile is

0
-20
-40
-60

-80
-100
0

installed into the unliquefiable layer. It is thought that the

40

60

80

time (sec)sheet-piles can protect the landside area from tsunami
caused by earthquakes.

20

Fig. 7The settlement of dyke

surrounded by sheet-piles was reduced because theTime histories of vertical displacement
P1(analysis)

P2(analysis)P1(experiment)

P2(experiment)

8
E.P.W.P (kN/m2)

sheet-piles restricted deformation. Especially for Case-C,
the enhancement of the performance of partition walls
for reducing the settlement of dykes was confirmed.
For Case-A ~ C, the time histories of the vertical

Initial effective stress (P1)

6
Initial effective stress (P2)420displacement at the top of dyke are shown in Fig. 7.

0

Numerical analyses can reproduce quantitatively for

20

Case-A and B. In contrast, the predicted settlement in

40
Time (sec.)(a)because settlement due to slipping and separating is not80

Case-AP1(analysis)P1(experiment)

Case-C is thought to be smaller than test results. This is60

P2(analysis)P2(experiment)

8

E.P.W.P (kN/m2)

reproduced without joint element.
For Case-A ~ C, the time histories of the excess porewater pressure at points P1 (beneath the dyke, Fig. 6) andP2 (horizontal ground, Fig. 6) are shown in Fig. 8.

6
4
2

0

Although the ground at P2 liquefied, the excess water0

pore pressure at P1 did not reach the initial effective

20

stress. It is found that numerical analyses reproduced

40
Time (sec.)(b)pressure at P1 did not correspond well, it should be
E.P.W.P (kN/m2)

8

improved in the future work.
For Case-B and C, the sheet-pile deformation at
t=80sec. are shown in Fig. 9. For Case-B, sheet-piles
bended toward outside supported by top (tie-rods) and80

Case-BP1(analysis)P1(experiment)such behaviors qualitatively. As the excess pore water60

P2(analysis)P2(experiment)

6
4
2
0

bottom (unliquefiable layer) in both analyses and model

0

20

40
Time (sec.)

tests. The horizontal displacement of the bottom ofsheet-piles are little in analyses. This is thought that the(c)Ramberg-Osgood model applied for unliquefiable layer

60

80

Case-C

Fig. 8 Time histories of settlement at top of dyke

estimated soil harder than that in model tests. No dilatancy
is considered in the Ramberg-Osgood model, this model is

In both the analysis and experiment, sheet-piles exhibited

applicable to dense sand and clays in which little excess

little deformation.

pore water pressure builds up. Though the unliquefiable

From the abovementioned results, although the proposed

layer made of dense sand (Dr=90%), the model applied

numerical model needs some improvements, it almost

for unliquefiable layer should be reconsidered. For

can simulate deformation and settlement of dyke

Case-C, the results at the intermediate location ofquantitatively. We decided to use this numerical model toneighboring partition walls (y=170mm) are also plotted.

investigate the behavior of the double sheet-piles with a- 261 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

0partition walls is, the more vertical settlement at top of100

dyke surrounded by sheet-piles and partition walls willbe.

depth (mm)200

The interval of partition walls was varied under the300

condition in which all other numerical conditions were the400same as those employed in the previous chapter. Theintervals employed for parametric studies are 170, 226,500

280, 510, 680, 1360, 3400 and 6800mm.
600

The relationship between the settlement of the top ofanalysisdyke at t=80sec. and the interval of partition wall is shown

700

experimentin Fig. 10. It is found that the larger the interval of800-15 -10

-5

0

5

10

15

partition wall becomes, the more settlement of top of dyke

horizontal displacement (mm)(a)

will be.
The horizontal deformations of the sheet-piles at

Case-Bdifferent distance from the partition wall are shown in Fig.

0depth (mm)

11 for cases of the interval of partition wall with 170mm
100

and 6800mm. The value of “y” in Fig. 4 represents the

200

distance from the partition wall. It is understood that thehorizontal deformation becomes larger if the interval of a300

partition wall becomes larger by comparing the results
y: extension direction axis

400

shown in Fig. 11. It is found that a large verticalshown as Fig.4 (mm)

500
600
700

displacement of dyke is caused by a large horizontal

analysis(y=0)

deformation of aanalysis(y=170)

deformation of a sheet-pile just beneath the top of dyke atsheet-pile. A small horizontal

y=3400mm is due to the existence of tie-rod.

experiment

The time histories of excess pore water pressures at

800-15 -10 -5

0

5

10

15

points P1 (beneath the dyke, Fig. 6) and P2 (horizontal

horizontal displaement (mm)Case-C

interval of partition wall with 170mm, 340mm andHorizontal displacement of sheet-piles

6800mm, respectively. There is no difference of excess(b)
Fig. 9ground, Fig. 6) are shown in Fig. 12 for cases of the

堤体天端の鉛直変位(mm)Settlement (mm)pore water pressure generation for all cases at point P2. In
contrast, at P1, while the excess pore water pressure

隔壁の設置間隔(mm)Intervalof partition wall (mm)
0

1000

2000

3000

4000

5000

6000

generations for all cases almost coincide each other before

7000

0

t=15sec. The dissipation of the excess pore water pressure
for narrower interval case is faster than that for wider-10

internal case after t=15sec. The time histories of the
maximum opening of a sheet-pile at the intermediate-20

location of neighboring partition walls are plotted in Fig.
-30

13. There is no difference in the increase in the opening of
the sheet-pile for all cases before t=15sec. In contrast, theFig. 10 Settlement of levee vs. interval of partition wall

opening of the sheet-pile for a wider interval case is morepartition wall structure.

than that for narrower case after t=15sec. The large
opening of the sheet-pile induces the expansion of the soil
surrounded by sheet-piles. The fast dissipation of excess

3.4. Influence of the interval of partition walls
In Case-C, it is expected that the larger the interval ofpore water pressure is partly due to the expansion of soil

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Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

0
Depth (mm)
堤体天端までの距離(mm)

100
200
300

y: extension direction axis

400

shown as Fig.4 (mm)

500
600

y=0

700

y=43

800

y=85
-10

-5

0

5

Fig. 1310水平変位(mm)Horizontal
displacement (mm)surrounded by sheet-piles. This typical three dimensional(a) interval of 170mm

堤体天端までの距離(mm)Depth (mm)Time histories of the maximum opening of sheet-piles

deformation characteristic can only be explained by 3-D00

analysis. As the slippage between the partition wall and

100
100

soil was not allowed, the settlements for the cases with
the interval of 170, 226 and 280 were underestimated.

200
200

maximum
300
300

opening

400
400
500
500

sheet-piles with a partition wall as coastal dyke

600
600

reinforcement method. The following conclusions werey=0
y=1700y=3400

700
700
800
800
-10

Fig. 11

4. Conclusions
Authors investigated the effectiveness of double

obtained by carrying out model tests and 3-D numericalanalyses (code: LIQCA3D15).

-5
0
5
10
Horizontal displacement (mm)
水平変位(mm)(b) interval of 6800mm
Horizontal deformation of sheet-piles

1)

Althoughthenumerical

model

needs

some

improvements, it almost can simulate deformation andsettlement of dyke quantitatively. Authors decided to use
this numerical model to investigate the behavior of the
double sheet-piles with a partition wall structure.

excecc pore water pressure(kN/m2)8

interval 170mm(P1)62) Through the parametric study focusing on the intervalinterval 340mm(P1)of partition walls, authors confirmed with an increase ininterval 6800mm(p1)4

the interval of the partition walls,
2・the settlement of coastal dyke increased

0
0

20

40

60

80

・the excess pore water pressure of the ground enclosed(a) P18

excecc pore water pressure(kN/m2)・ the bending deformation of the double sheet-piles
increasedtime (sec)by double sheet-piles and partition walls decreased

6interval of 170, 340, 6800mm (P2)

3) For the improvement of the reproducibility of the(Almost same line)

numerical model, joint elements in which the slipping and4

separation are taken into account should be used between
2

the ground and sheet-pile in the future study.

0
0

20

40

60

80

time (sec)(b) P2
Fig. 12References
Biot, M. 1962. Mechanics of deformation and acoustic
propagation in porous media, Journal of Applied

Time histries of excess pore water pressure

Physics, 33 (4).

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Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

Cabinet Office., Government of Japan. 2015. Disastermanagement in Japan, p. 15.
Fujiwara, K. 2017. Reinforcement method for coastal
dyke

using

doublesheet-pileagainstlarge

earthquake, Doctoral dissertation. (in Japanese)
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Sawada, K., Hara, T., Ogawa, T. and Takeda, K.
2017. Study on coastal dyke reinforcement using
double sheet-piles with partition walls, International
Journal of Offshore and Polar Engineering, pp.
310-317.
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