Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanNUMERICAL ANALYSIS OF DAMAGE OF RIVER
EMBANKMENT ON SOFT SOIL DEPOSIT DUE TO
EARTHQUAKES WITH LONG DURATION TIME
Fusao OKA1, Peter SongyenTSAI2 , Sayuri KIMOTO3 and Ryosuke KATO4
1Professor, Department of Civil and Earth Resources Engineering, Kyoto University,Kyoto, Japan, oka.fusao.2s@kyoto-u.ac.jp
2
Graduate student of Kyoto University,
petersongyeu.tsai@kw8.ecs.kyoto-u.ac.jp
3Associate professor, Department of Civil and Earth Resources Engineering,
Kyoto University, Kyoto, Japan,
kimoto.sayuri.6u@kyoto-u.ac.jp
4Engineer, Nikken Civil Ltd., Osaka, Japanryousuke.katou@nikken.co.jp

ABSTRACT: we have analyzed model river embankments on the clayey foundation
with different ground water tables using a dynamic liquefaction analysis method.
From the analysis results, we have found that the effects of the water saturated region
in the bank and the duration time of earthquake motion on the deformation
behavior of river embankments are important. The results are consistent with theinvestigation results of the feature of the deformation and failure of the embankments
due to the 2011 off the Pacific coast Tohoku Earthquake.
Key Words: River embankment,, Soft soil deposit, Liquefaction, Clayey soil, Great East
Japan earthquake
INTRODUCTION
The 2011 off the Pacific coast Tohoku Earthquake damaged many soil made infrastructures
such as river dikes, road embankment, railway foundations and coastal dikes. The river dikes and its
related structures have been damaged at 2115 sites over the Tohoku and Kanto areas. In the presentpaper, the main patterns of the damaged river embankments are presented based on the in-situ researchby the authors, MLIT and JICE. The main causes of the damage are, 1) Liquefaction of foundation
ground, 2) Liquefaction of the soil in the river embankments with water saturated region above the925

ground level 3)Duration time of the earthquake is long since the fault zone was very large and themagnitude is 9.0. In the second part of the paper, we have analyzed model river embankments on theclayey foundation with different ground water tables using a dynamic liquefaction analysis method.
From the analysis results, we have found that the effects of the water saturated region in the bank andthe duration time of earthquake motion on the deformation behavior of river embankments areimportant. The results are consistent with the investigation results of the feature of the deformationand failure of the embankments due to the 2011 off the Pacific coast Tohoku Earthquake.
Pattern of the deformation and failure of river embankments

River embankments have been damaged due to the earthquake in both Tohoku and Kanto
districts. The usual reason for the damage of the river embankments is a liquefaction of thefoundation sandy ground which was observed at the failure of the left embankment of
Yodogawa during the 1995 Hyogoken-Nanbu Earthquake. By the detailed study of the heavily
damaged river embankments, we have found that the embankments on the soft clay deposit
have been extensively collapsed due to the liquefaction. Typical patterns of soil profile areillustrated in Figure 1. Taking account of the investigation of the soil profile and the watertable in the damaged embankments, the reason of the damage is a liquefaction of thewater-saturated region bounded by the soft clay layers with smaller permeability. The effectof the water-saturated region is pointed out by MLIT. This region extends to the lower part ofthe embankments which have been settled below water table. The water table in theembankments which is higher than ground surface is formed by the rain fall and the capillaryetc. In the following section we will show numerically analyzed results of the behavior of riverembankments with the closed saturated region.

NUMERICAL ANALYSIS
Numerical method
It is well known that the one of the reason for the failure of the river embankment is earthquake loads.
In this section, we have numerically analyzed the deformation behavior of river embankments during
earthquakes using a soil-water coupled finite element analysis method. The two-dimensional
water-soil analysis method has been developed based on the two-phase porous theory. In the numericalsimulation of the dynamic behavior of ground, we used a liquefaction analysis program“LIQCA2D011” which has been developed by Oka et al.(Oka et al., 2005,2011).

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Fig. 1 Patterns of soil profile
The LIQCA2D11 adopted a u-p formulation with the finite element method and the finite difference
method in the infinitesimal strain field. The equation of motion is discretized by FEM and thecontinuity equation is discretized by the finite difference method (e.g., Oka et al., 2004). As for thetime discretization in the time domain, Newmark’s  method is used. In addition, Rayleigh’s
damping is used in the analysis which is proportional to the initial stiffness matrix and the massmatrix.
For the constitutive model for soils, we have used a cyclic elasto-plastic model considering both thestrain-induced degradation for sandy soils(Oka et al., 1999) and an elasto-viscoplastic model forclayey soils which has been developed recently(Kimoto, Sahbodagh, Mirjalili, and Oka 2012) basedon the previous model(Oka et al., 2004) shown in Appendix. We have analyzed model riverembankments with different soil profiles and water tables. In addition, we have studied the effect ofsaturated region in the embankment considering the duration of earthquakes. In the numerical analysis
the u-p formulation was adopted. For the discretization of the equations of the motion (or equilibriumof the mixture) FEM (Finite Element Method) was used, while for discretization of the continuity927

equations of the pore fluids (water and gas) FDM (Finite Difference Method) was used. The time
discretization is based on Newmark's  method, with  and  set at 0.3025 and 0.6, respectively. Thetime increment in the calculation was set to be small enough to guarantee the accuracy of the results
without having large computational time (i.e. 0.01 seconds).
3.2 Finite element mesh and boundary conditions
Figure 2 shows the model of the river embankment and the finite element mesh used in the analysis.
The soil parameters are listed in Table 1 in which sandy soil is a liquefiable loose sand and for clay theparameters of soft clay at Torishima of the levee of the Yodo river (Mirialili, 2011) are used.
Table 2 indicates simulation cases with different soil profiles and earthquake motions. In
the simulations we used different soil profiles with the clayey subsoil because the groundprofiles of the many damaged embankments in Miyagi prefecture includes clayey soillayer about 10m thick.

Fig.2 Finite element mesh and boundary conditions
Figure 3 shows the different soil profiles that taking account of the discussion inprevious section; Type 2 illustrates the a levee embankment where the bottom of theembankment is below the ground water level. Type 3 shows the case in which theembankment is settled and ground water level is in the embankment. Type 3 corresponds
to the typical case of severely damaged embankment due to the 2011 off the Pacific coast
Tohoku Earthquake such as Shimokakanome-jyouryuu site of Naruse river. Type 4corresponds to the case of the damaged embankment at Sekijyuku of Edo river (Kantoregional development bureau of MLIT, 2011. Figure 4 shows the input earthquakemotions; Input 1 is an earthquake record obtained during the 1995 Kobe earthquake at a
depth of 33m of Higashi Kobe ohashi. Input 2 is the earthquake record at a depth of 80m
obtained at Tajiri ; MYGH06, KiK-net, 2011 (National Research Institute For Earth928

Science and Disaster Prevention, 2011). The features of these waves are that the duration
time of Input 2 is very long more than 2 min, which is longer than Input 1 but themaximum acceleration of Input 1 is larger than that of Input 2.

Fig.3 Soil profile and water table
In Figure 5, the vertical displacement-time profiles of the top of the embankment (Node 1978) andthe horizontal displacement-time profiles of the toe of the embankment (Node 3178) are illustrated for
all cases. The settlement of the top of the ground is maximum for Case 2-B. For the cases 2-A and2-B, the maximum settlement of the top of the embankment and the maximum horizontal
displacement of the toe of the embankments are obtained for Case2-B. For Case 2-A, the settlement ofthe top of the embankment is small and less than others.

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Input 1:Higashi-Kobe Ohashi,
1995 Hyogoken Nanbu
Earthquake (PWRI,1995)

Input 2:MYGH06(at a depth of 80m)
-NS(Tajiri,KIK-net,
2011 of the Pacificcoast Tohoku Earthquake)

Fig.4 Input earthquake motions
Figure 6 shows the displacement distribution at the end of earthquake motions. For Case 1-A, thelarger portion around the right toe of the embankments moves and it is seen that the displacement
discontinuity can be seen below the ground level and in the clay layer, while in Case 1-B, the larger
displacement is seen just around the toe of the embankment above the clay layer. Figure 6 indicates thedistributions of displacement of Cases 2-A and 2-B. The largest displacement is seen in the central partof the embankment and below the top of the embankment for Case 2-B. Figure 7 shows thedistribution of accumulated deviatoric plastic strain for Cases 1-A, 1-B and 2-A, 2-B. The accumulated
deviatoric plastic strain is defined as:1/ 2 p   (deijp deijp ) ; deijp : Increment of deviatoric plastic tensor. For Case 1-A, we can see that thelocalized large strain beneath the river embankment, which is larger than the other cases, i.e., larger
strain develops in the clay layers. In Figure 7 , we can see the larger plastic strain develops for Case2-B in the saturated sand portion in the embankment as well as upper part of the embankment. The
shear strain localized above the saturated region in the embankment and this trend is consistent withthe observed

failure pattern. Figure 8 shows the distribution of ESDR for Cases 2-A~2-B. ;ESDR (Effective stress decreasing ratio:

 m' 0   m'ESDR ) m' 0.

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Table 1 Material parameters

Parameter
3Density 𝜌 (t/m )Water permeability k (m/s)
Initial void ratio e0Compression index λSwelling index 𝜅Normalized initial shear modulus 𝐺0 /𝜎𝑚′ 0(kPa)Stress ratio at Maximum Compression∗𝑀𝑚
Stress ratio at failure 𝑀𝑓∗
Quasi-overconsolidation ratio 𝑂𝐶𝑅 ∗ (=′𝜎𝑚𝑎𝑖/ 𝜎𝑚′ 0 )Hardening parameter
𝐵0∗ , 𝐵1∗ , 𝐶𝑓′′Structure parameter𝜎𝑚𝑎𝑓/ 𝜎𝑚𝑎𝑖,βControl parameter of anisotropy 𝐶𝑑Parameter of Dilatancy 𝐷0∗ , n
Reference Value of Plastic Strain 𝛾𝑟𝑃∗
Reference Value of Elastic Strain 𝛾𝑟𝐸∗
Viscoplastic parameter 𝑚′
Viscoplastic parameter (1/s) 𝐶1
Viscoplastic parameter (1/s) 𝐶2Hardening parameter𝐴∗2 , 𝐵2∗
Strain-dependent modulus parameter
𝛼 ,𝑟

Sand
1.8 / 2.0
2.20× 10−50.8
0.02500.0003Clay
1.7
5.77× 10−101.25
0.34100.0190

761

75.2

0.909

1.24

1.229

1.24

1.0

1.0

2000, 40, 00.5, 50
2000
1.0, 4.00.005
0.003-100, 40, 100.3, 3.6
24.68
1.00× 10−5
3.83× 10−6
5.9, 1.8-

10 , 0.4

Table 2 Analysis Cases

Input1

Input2

Type1

Case1-A

Case2-A

Type3

Case1-B

Case2-B

For Case 2-B, we can see the liquefaction of the water saturated region in the embankment.
From the above discussions, it is worth noting that the water saturated region leads to the larger
settlement of river embankment and the larger deformation/failure. This deformation behavior isconsistent with the damaged embankments such as the embankments of Eai river931

in the Miyagi prefecture due the 2011 off the Pacific Tohoku Earthquake. From the numerical resultsof Case 1-A and Case 2-A, we can say that the earthquake wave form affects the deformation
characteristics of the river embankment-subsoil layer system. Of course the amplitude of theearthquake is an important factor for the damage.

Node-1978

Case1-A 0.0
Case1-B

-0.5

-0.5

-1.0

-1.0

Vertical displacement (m)node-1978

00.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
-3.5
-4.0

5

101520Time(sec)

2530

0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
-3.5
-4.0Case2-A
Case2-B
02550

Horizontal displacement (m)node-3178

0.0

Horizontal displacement (m)node-3178

Vertical displacement (m)node-1978

Node-3178

1.5

1.5

1.0

1.0

0.5

0.5

0.0
-0.5

0

3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

5

1015
20Time(sec)Case2-A
Case2-B

0-0.5
3025

3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

25 50 75 100 125 150 175 200Time(sec)

75 100 125 150 175 200Time(sec)

Fig.5 Vertical and horizontal displacement-time profiles of top and the toe of the bank932

0.0

Case1-A
Case1-B

Case1-A

Case1-B

CONCLUSIONS

Case2-A

Case2-B933

Fig.6 Displacement distribution

Case2-A
Max 0.22

Case2-B
Max 8.99

Fig.7 Distribution of accumulated plastic deviatoric strain

Case2-A

Case2-B

Fig.8 Distribution of effective stress decreasing ratio934

From the investigation work of the damaged river embankments and the numerical simulation ofriver embankments with various subsoil profiles, we have obtained the following main conclusions:
By the detailed study of the heavily damaged river embankments, it has been found that theembankments on the soft clay deposit have been extensively collapsed due to the liquefaction. The
feature of the damage is a liquefaction of the saturated region in the embankments downwardly
bounded by the soft clay layers. From the numerical results, it has been found that the water saturated
region in the embankments leads to the larger settlement of river embankment and the larger
deformation/failure. This deformation behavior is consistent with the pattern of the damaged
embankments due the 2011 off the Pacific Tohoku Earthquake. In addition, the earthquake wave formsuch as duration time affects the deformation characteristics of the river embankment-sub soil layer.
Of course the amplitude of the earthquake is an important factor for the damage.
ACKNOWLEDGMENTS
The authors wish to express their sincere thanks for the advice and the materials given by Tohoku andKanto regional development bureaus of MLIT and JICE. In addition, the authors want to give their
thanks to the emeritus professor Y.Sasaki of Hiroshima University for his kind advice.

REFERENCES
Investigation committee of the 1978 Miyagiken-oki Earthquake at Tohoku Branch of JSCE(1078) ,”General report on the 1978 Miyagiken-oki Earthquake”.
Kanto regional development bureau of MLIT (2011), “Material-1 and Reference materialsof the 3rd Exploratory Committee of MLIT on the earthquake resistant measure of riverembankments,2011.9.4”,http://www.ktr.mlit.go.jp/river/bousai/river_bousai00000090.html
Kimoto, S. and F. Oka,F.(2005),”An elasto-viscoplastic model for clay considering
destructuralization and consolidation analysis of unstable behavior”, Soils andFoundations,Vol. 45, No.2, 29-42.
Kimoto,S., Sahbodagh,K.B., Mirjalili,M. and Oka,F.(2012), “A cyclic elasto-viscoplastic
constitutive model for clay considering the nonlinear kinematic hardening rules and thestructural degradation”, Int., J. Numerical and Analytical Methods in Geomechanics, 2012,
submitted.
Mirajalili,M.(2010)”Numerical analysis of a large-scale levee on soft soil deposits using two-phasefinite deformation theory”, PhD Thesis, Kyoto University.

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Oka, F. , T. Kodaka, Y.-S. Kim,Y.-S.(2004), “A cyclic viscoelastic-viscoplastic constitutive model for clayand liquefaction analysis of multi-layered ground”, Int. J. Numerical and Analytical Methods inGeomechanics, Vol.28, 2, 131-179.
LIQCA research and development group (representative: F.Oka Kyoto University).(2005),

User’s manual for LIQCA2D04(2005 released print).
LIQCA research and development group (representative: F.Oka Kyoto University).(2011),

User’s manual for LIQCA2D11, 2011(in Japanese).

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