Scholarly article on topic 'Damage patterns of river embankments due to the 2011 off the Pacific Coast of Tohoku Earthquake and a numerical modeling of the deformation of river embankments with a clayey subsoil layer'

Damage patterns of river embankments due to the 2011 off the Pacific Coast of Tohoku Earthquake and a numerical modeling of the deformation of river embankments with a clayey subsoil layer Academic research paper on "Earth and related environmental sciences"

CC BY-NC-ND
0
0
Share paper
Academic journal
Soils and Foundations
Keywords
{"The 2011 off the Pacific Coast of Tohoku Earthquake" / "River embankment" / "Coupled liquefaction analysis" / Elasto-plasticity / Elasto-viscoplasticity/D7/E8/E13}

Abstract of research paper on Earth and related environmental sciences, author of scientific article — F. Oka, P. Tsai, S. Kimoto, R. Kato

Abstract Due to the 2011 off the Pacific Coast of Tohoku Earthquake, which had a magnitude of 9.0, many soil-made infrastructures, such as river dikes, road embankments, railway foundations and coastal dikes, were damaged. The river dikes and their related structures were damaged at 2115 sites throughout the Tohoku and Kanto areas, including Iwate, Miyagi, Fukushima, Ibaraki and Saitama Prefectures, as well as the Tokyo Metropolitan District. In the first part of the present paper, the main patterns of the damaged river embankments are presented and reviewed based on the in situ research by the authors, MLIT (Ministry of Land, Infrastructure, Transport and Tourism) and JICE (Japan Institute of Construction Engineering). The main causes of the damage were (1) liquefaction of the foundation ground, (2) liquefaction of the soil in the river embankments due to the water-saturated region above the ground level, and (3) the long duration of the earthquake, the enormity of fault zone and the magnitude of the quake. In the second part of the paper, we analyze model river embankments on a foundation ground with various soil profiles, including a clayey soil layer and various ground water tables, using a dynamic liquefaction analysis method. From the analysis results, we find the effects of the soil profiles and the duration time of the earthquake motion on the deformation behavior of the river embankments. The results are consistent with those of the investigation of the features of the deformation and the failure of the embankments due to the 2011 off the Pacific Coast of Tohoku Earthquake.

Academic research paper on topic "Damage patterns of river embankments due to the 2011 off the Pacific Coast of Tohoku Earthquake and a numerical modeling of the deformation of river embankments with a clayey subsoil layer"

The Japanese Geotechnical Society

Soils and Foundations

www.sciencedirect.com journal homepage: www.elsevier.com/locate/sandf

SOILS AND

FOUNDATIONS

Damage patterns of river embankments due to the 2011 off the Pacific Coast of Tohoku Earthquake and a numerical modeling of the deformation of river embankments with a clayey subsoil layer

F. Okaan, P. Tsaia, S. Kimotoa, R. Katob

aDepartment of Civil & Earth Resources Engineering, Kyoto University, Japan Nikken Sekkei Civil Engineering Ltd., Osaka, Japan

Received 3 February 2012; received in revised form 25 July 2012; accepted 1 September 2012 Available online 11 December 2012

Abstract

Due to the 2011 off the Pacific Coast of Tohoku Earthquake, which had a magnitude of 9.0, many soil-made infrastructures, such as river dikes, road embankments, railway foundations and coastal dikes, were damaged. The river dikes and their related structures were damaged at 2115 sites throughout the Tohoku and Kanto areas, including Iwate, Miyagi, Fukushima, Ibaraki and Saitama Prefectures, as well as the Tokyo Metropolitan District. In the first part of the present paper, the main patterns of the damaged river embankments are presented and reviewed based on the in situ research by the authors, MLIT (Ministry of Land, Infrastructure, Transport and Tourism) and JICE (Japan Institute of Construction Engineering). The main causes of the damage were (1) liquefaction of the foundation ground, (2) liquefaction of the soil in the river embankments due to the water-saturated region above the ground level, and (3) the long duration of the earthquake, the enormity of fault zone and the magnitude of the quake. In the second part of the paper, we analyze model river embankments on a foundation ground with various soil profiles, including a clayey soil layer and various ground water tables, using a dynamic liquefaction analysis method. From the analysis results, we find the effects of the soil profiles and the duration time of the earthquake motion on the deformation behavior of the river embankments. The results are consistent with those of the investigation of the features of the deformation and the failure of the embankments due to the 2011 off the Pacific Coast of Tohoku Earthquake.

© 2012 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.

Keywords: The 2011 off the Pacific Coast of Tohoku Earthquake; River embankment; Coupled liquefaction analysis; Elasto-plasticity; Elasto-viscoplasticity/D7/E8/E13

1. Introduction

The 2011 off the Pacific Coast of Tohoku Earthquake damaged many soil-made infrastructures, such as river

dikes, road embankments, railway foundations and coastal dikes. Due to the very high strength of this earthquake, which had a magnitude of 9.0, many soil-made infrastructures, such as river dikes, road embankments, railway foundations and coastal dikes, were damaged. The river dikes and their related structures were damaged at 2115 sites over the Tohoku and Kanto areas, including Iwate, Miyagi, Fukushima, Ibaraki and Saitama Prefectures, as well as the Tokyo Metropolitan District. In the first part of the present paper, the main patterns of the damaged river embankments are presented and reviewed based on in situ

nCorresponding author. E-mail address: oka.fusao.2s@kyoto-u.ac.jp (F. Oka). Peer review under responsibility of The Japanese Geotechnical Society.

0038-0806 © 2012 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sandf.2012.11.010

research carried out by the authors, MLIT (Ministry of Land, Infrastructure, Transport and Tourism) and JICE (Japan Institute of Construction Engineering (JICE), 2011).

The damage was due tone or a combination of the following: liquefaction of the foundation ground, liquefaction of the soil in the river embankments since the water-saturated region was above ground level, and the long duration of this huge earthquake, over such a huge area. The damage and failure of the coastal dikes due to overflow and erosion from the tsunami is not within the scope of the present study. In the second part of the paper, we analyze model river embankments on a foundation ground with various soil profiles, including a clayey soil layer and various ground water tables, using a dynamic liquefaction analysis method. From the analysis results, we find the effects of the soil profiles and the duration time of the earthquake motion on the deformation behavior of the river embankments. The results are consistent with those of the investigation of the features of the deformation and the failure of the embankments due to the 2011 off the Pacific Coast of Tohoku Earthquake.

2. Damage to river embankments and river structures

River embankments were damaged due to the earthquake in both the Tohoku and Kanto districts.

A summary of the damage to river embankments and river structures due to the 2011 off the Pacific Coast of Tohoku Earthquake follows:

1. The number of damaged river embankments and river structures is 1195 under the jurisdiction of the Tohoku Regional Development Bureau of MLIT. A total of 773 river embankments were damaged, with 29 of them in urgent need of restoration. The rivers are the Mabuchi River (Aomori Prefecture), the Kitakami River (Iwate and Miyagi Prefectures), the Eai River, the Naruse River, the Yoshida River, the Natori River and the Abukuma River (Miyagi Prefecture).

2. River embankments were damaged at 611 sites along the 146 rivers under the jurisdiction of Miyagi Prefecture, including the Hasama River, the Nanakita River and the Sunaoshi River, and river structures were damaged at 25 sites along 21 rivers.

Fig. 1. Distributions of the heavily damaged river embankments and the earthquake motion observation stations (National Research Institute for Earth Science and Disaster Prevention, MLIT), webmapc of MLIT is used in this figure.

3. River embankments and river structures were damaged at 210 sites in Fukushima Prefecture.

4. Under the jurisdiction of the Kanto Regional Development Bureau of MLIT, river embankments and related river structures were damaged at 939 sites, with 55 heavily damaged embankments, 149 medium-level damaged embankments and 735 minimal-level damaged embankments.

5. In Ibaraki Prefecture, embankments were damaged at 106 sites under the jurisdiction of Ibaraki Prefecture, while river embankments under the control of the Kanto Regional Development Bureau of MLIT were damaged at 343 sites along the embankments of the Tone River, Kasumigaura Lake, the Kuji River, the Naka River, the Hinuma River, a 2.7 m settlement of a tributary of the Naka River and the Shin Tone River in Inajiki City.

6. In Chiba Prefecture, the right embankments of the Tone River were heavily damaged and the left embankments of the Edo River were damaged.

7. In Saitama Prefecture, the right embankment of the Edo River was damaged in Satte City, while about 50

embankments of the Nakagawa River were damaged. 8. In Tokyo, sand boils occurred on the river bed of the Arakawa River.

In the Tohoku District (Aomori, Iwate, Miyagi and Fukushima Prefectures), many river embankments were damaged due to the earthquake. River basins in the Tohoku District include the Mabuchi River Basin, the Kitakami River Basin, the Naruse River Basin, the Natori River Basin and the Abukuma River Basin. In the Tohoku District, embankments were damaged at 1179 sites. From the report by JICE (2011), the patterns of the damage consisted of failures and/or washouts (25 sites), cracks (565 sites), lateral flows (90 sites), settlements (117 sites), damage to revetments (196 sites), sluice gates, etc. (81) and others (105).

Fig. 1 shows the main damaged sites in the northern part of Miyagi Prefecture and the measured accelerations at several points on the ground surface; K-net (Furukawa: NS = 444, EW = 571 gal), Kitami: NS = 372, EW = 294 gal), KiK-net (Tajiri: NS = 247, EW = 263 gal), etc.

Settlement

Settlement of Crown

Settlement of the top of the shoulder and the crown

Division of the bank due to cracks

Boiled

Lateral expansion of the sand toe of the bank and the lateral

movement of the

Fig. 2. Typical damage and failure patterns of river embankments.

The damage can be largely attributed to the liquefaction of the foundation ground, the liquefaction of the water-saturated soil in the river embankments above the ground level or overflow and erosion due to the tsunami (Oka et al.,

Type A

Type B

Type C

Type D

Fig. 3. Patterns of soil profiles.

Photo 1. Left embankment at Fuchishiri-jyoryu of the Eai River (27.6 km) (courtesy of Kitakamigawa-Karyu River Office Tohoku Regional Bureau of MLIT, 2011).

2012). As for the liquefaction of the water-saturated soil in the river embankments above ground level, it is possible that the damage was caused by the subsidence of the river embankments to levels below the water table due to the consolidation of the soft clay foundation, and the high level of water in the river embankments due to the hydraulic conditions. According to the Tohoku Regional Development Bureau of MLIT (2011), failures accompanied by the observation of sand boils and a high level of water were reported for the following river dikes: the right embankment of the downstream of the Abukuma River in the Edano District, the left embankment of the downstream of the Abukuma River in the Noda District, the left embankment of the Eai River in the Uetani District (14.0 km-14.6 km), the right embankment of the Eai River in the Nakajima Otsu District (14.0 km + 43m-14.6km + 43), the right embankment of the Eai River in the Fukunuma District (26.6-26.8 km), and the left embankment of the upstream of the Eai River in the Fuchishiri District (27.6 km), among others. The embankments of the Eai River, the Naruse River and the Yoshida River are underlain by soft soil deposits with a thickness of about 10 m. The soft soil deposits consist of clay, fine sand and silt, e.g., the soft soil deposit of the dike of the Yoshida River at Yamazaki consists of soft clay, including silt and sand (General Report on the 1978 Miyagi-Oki Earthquake, Investigation Committee of the 1978 Miyagiken-oki Earthquake at Tohoku Branch of JSCE, 1980). The soft clay deposits affect the earthquake-resistant characteristics through consolidation, amplification and deformability. The typical failure and deformation patterns of the river embankments are illustrated in Fig. 2.

Type D-1 shows the settlement of the crest of the bank with a heave around the toe of the bank.

This type of damage was observed at many river embankments; sometimes with a small crack observed along the slope.

Type D-2 includes longitudinal cracks and a lateral expansion of the slope of the bank near the toe as well as the settlement of the crest. This type of damage occurred at the embankments of Kokai River (3.8 km), along the bank of Watatanuma of Naruse River (20.1-20.3 km), and along the bank of the Yoshida River (15.4 km), etc.

In type D-3, settlement of the top of the shoulder and crest occurred, as well as lateral expansion and subsequent cracking. This type of D-3 damage was seen along the left bank of Noda of Abukuma River (28.6-30.0 km), and at Nishisekiyado along the right bank of the Edo River (57.5 km), etc.

Type D-4 is the most severe damage in which the bank is divided into number of blocks with boiled sand and large lateral movement of the banks. This very severe damage

Fig. 4. Damaged embankment of the Eai River (27.6 km) Tohoku regional development bureau of MLIT.

was observed at Fuchishiri-jyoryu (27.5-27.8 km) and at Fukunuma (26.6-26.8 km) along the Eai River. The banks of the Naruse River were damaged at Shimonakanome (30.0-30.5 km), and at Edano (30.6-31.4 km) along the Abukuma River, etc.

In Fig. 3, the typical patterns of soil profiles where severe damage was observed due to the 2011 off the pacific coast of the Tohoku earthquake are shown. In Section 3, the relationship between pattern of the soil profile and the observed damage will be explained.

2.1. The Eai River embankment

underlain by soft deposits which consist of, from the top, a 2-m clayey sandy layer (Acs) and soft clay layers (Ac1 and Ac2) with a thin sandy layer (As1) (Ac1(1.5m) + As1(0.5 m) + Ac2(10 m)) having a thickness of 12 m; the N value of the Acs layer is about 5-11. Beneath the clay layer, there is a sandy layer (As2) with a thickness of 4.5 m, and the N value varies with depth from 10 to 40. The undrained strength of Ac1 and Ac2 is 16 kN/m2. For Acs, D50 is around 0.0850.25 mm and D10 is 0.005-0.009 mm; Ip < = 15. The D50 of embankment Bs0 is 0.22 m and the Fc is about 25%. As2 is underlain by a rather stiff sandy layer with clay, Ds1, and the N value is more than 10.

The most severely damaged or failed embankment is the one on the left embankment of the Eai River (27.2-27.8 km) in the Fuchishiri District of Osaki City, Miyagi Prefecture, as shown in Photo 1. A length of 400 m of the dike of the left levee was damaged. As depicted in Fig. 4, several large cracks developed at the crest, and the crest was deformed in a wavy pattern. The river embankment was cracked and settled. The maximum settlement of the crest was 0.83 m, the failed embankment moved laterally toward the river side in a block style, with a maximum lateral movement of 9.37 m. The observed number of blocks was 11. The lower part of the embankment is composed of loose sandy soil with an N value of less than 10. This failure pattern is similar to the pattern D-4 in Fig. 2. The embankment at 27.6 km was

Photo 2. Cracks and sand boils near the land side of the river embankment of the Eai River (27 km).

Photo 3. Sand veins due to liquefaction in the left embankment observed at Shimonakanome-jyoryu of the Naruse River (30.0-30.5 km).

Photo 4. Cracks at the top of the right embankment at Kimazuka of the Naruse River (around 11 km).

(m) 25 —I

20 —

15 —

10 —

Land side

Estimated water table

River side

Fig. 5. Soil profile of the embankment of the Eai River before the earthquake Tohoku regional development bureau of MLIT.

Sand boils were observed in the cracks at the slope and the toe of the river side embankments. The ground water has been supplied from the land side of the embankments; hence, the ground water level in the embankments has always been observed. Judging from the observation of the sand boils, the soil profiles and the ground water levels, the occurrence of the liquefaction of the sandy soil of the embankment and the Acs layer has been considered. At the crest of the left embankment of the Eai River, at 27.2-27.4 km, we observed three long cracks along the axis of the embankment and a settlement of several 10 cm; slope failure occurred on the rear side. In the rice field around the embankment (27.33 km), we have seen sand boils from the cracks, 5-10 m in length, shown in Photo 2.

2.2. Naruse River

The river dikes of the Naruse River were heavily damaged and failed at eight sites, namely, the left embankment (29.7-30.1 km) in the Shimonakanome-jyouryuu District, the right embankment (29.7-30.1 km) in the Shimoibano District, the left embankment (29.0-29.1 km) in the Shimogawara District, the left embankment (20.120.3 km) in the Wadanuma District, the right embankment (11.9-12.0 km) in the Komazuka District, the left embankment (11.3-11.5 km) in the Sunayama District and the right embankment (0-0.4 km) in the Nobiru District. The number of middle-level damaged sites is 121.

2.2.1. Shimonakanome-jyouryuu District

The left embankment of the Naruse River dike in the Shimonakanome-jyouryuu District (30.0-30.537 km) was heavily damaged and failed, as shown in Fig. 5. The dike moved 13.3 m to the land side and the maximum settlement of the crest was about 5.5 m, while 13 cracks were observed on the river side of the dike. The failure mode has been classified as a type D-3 in Fig. 2 by the Tohoku Regional development Bureau of MLIT (2011). Boiled sand was observed in the longitudinal cracks and the toe of the slope on the land side. The water level was in the dike on the 4th April, 2011; the water level was 6 m below the original crest. This suggests that there was water in the dikes above the water table of the surrounding ground. The MLIT Committee referred to the region with water in the dike as the saturated region with water since the ground just beneath the dike is a clayey

ground. The high water level in the embankment is believed to be due to rainfall and the surrounding environment. The main reason for the failure is the liquefaction of the dike material, i.e., silty sand and sandy silt with N values less than 5 due to earthquakes. Soil profiles of the dike and the foundation ground are presented in Fig. 5.

The subsoil ground consists of alternate layers of sand and clay. The bottom of the dike is under the water table, and from the top of the subsoil layer (Ac1:4m), there is a sandy layer (As1:1-2m), a clay layer (Ac2:3m), a sandy layer (As2:2m), a clay layer (Ac3:6m) and a rather stiff sandy layer with an N value of 30. The excavation of the dike was carried out to investigate the damage after the earthquake. The cross section of the dike shows that sand veins were observed from the bottom to the upward-land side direction and/or the upward-land side direction in the cracks shown in Photo 3.

2.2.2. Kimazuka District

The right embankment of the Naruse River in Kimazuka, Kashimadai of Osaki City was damaged. This site is located between Kamamaki and Hutagoya. The soil profile is as follows: the dike is underlain by, from the top, a soft clay deposit of 1-2 m (N value < 5) at a depth of 1-2 m, a thin sandy layer, a soft clay deposit with a thickness of 1-2 m and a sandy layer with a thickness of 3-4 m.

As shown in Photo 4, large cracks, 80 cm in width and 50 cm in depth, developed at the crest; the settlement at the center of the crest is about 30 cm. The back and front two slopes were moved laterally. We observed many cracks near the toe of the embankment on the land side. The failure pattern is similar to the pattern D-2 in Fig. 2 adopted by Tohoku Regional development Bureau of MLIT (2011).

[■.■.■.■.■.■.■.-.■.■ .day. ■.■.■.-.■.-.■.■.■.■..■.■.

i \WWV 10m ^w^wwv^v^wv Peaty soil awwwwwwwwwwto ...................................... ........................................

Fig. 7. Soil profile at Yamazaki of the Yoshida River after JICE (2011).

Fig. 6. Soil profile of the embankment at Shimonakanome-jyoryu of the Naruse River (30.0-30.537 km) after Tohoku regional development bureau of MLIT.

On the river side, concrete blocks were broken due to lateral displacement, and the upper block penetrated into the ground at several points under the toe of the lower blocks. On the land side, sand boils were observed around the channel along the river embankments. The embankments near this site (12.9km + 60m-13.1km + 94 m), which had been damaged by the 2003 Miyagiken-hokubu Earthquake, were not damaged because the subsoil had been improved after the 2003 earthquake.

2.3. Yoshida River

The dikes of the Yoshida River were damaged as highly damaged dikes at two sites, middle-level damaged ones at 17 sites and low-level damaged ones at 150 sites. The highly damaged embankments of the upstream of the Yoshida River are located in the reclamation land of the old Sinai-numa Pond. The heavily damaged dikes of the Yoshida River are at the left embankment of the Oobazamakamishida-jyouryu District (15.2-15.5 km) and at the left embankment of the Oobazamakamishida-karyu District (14.6-14.8 km). Fig. 6 shows a typical ground

profile beneath the dike of the Yoshida River (around 16 km). It is worth noting that the subsoil includes rather thick clayey soil.

2.4. Kitakami River

The dikes of the Kitakami River were damaged by the earthquake and the tsunami. Middle-level damage was observed at two sites in the upstream region and at 30 sites in the downstream region. A high level of damage was observed at two sites around the mouth of the river due to the tsunami, namely, at the right embankment at Kama-tani (3.8-4.6 km) and at the left embankment at Tsuki-hama (0.8-2.8 km). From the observation of the Geospatial Information Authority of Japan, the tsunami ran up more than 12 km to the maximum 50 km from the mouth of the Kitakami River. The left bank in the Tsukihama district (0.8-2.8 km from the river mouth) and the right bank in the Kamaya district (3.8-4.6 km from the river mouth) were heavily damaged due to the tsunami. The tsunami flowed over the river levee, damaged the embankments and the land was inundated.

;hitone R

Heavily

damaged

embankments

Fig. 8. Distribution of the heavily damaged river embankments in the Kanto District, webmapc of MLIT is used in this figure.

H.W.L.

Fig. 9. Soil profile and damaged shape of the embankment at Nishisekyado of the Edo River (57.5 km +100 m-57.5 km + 300 m), after JICE (2011).

Fig. 10. Finite element mesh and boundary conditions.

Table 1

Material parameters.

Parameter Sand Clay

Density r (t/m3) 1.8/2.0 1.7

Water permeability k (m/s) 2.20 x 10~5 5.77 x 10 "10

Initial void ratio e0 0.8 1.25

Compression index l 0.0250 0.3410

Swelling index k 0.0003 0.0190

Normalized initial shear modulus G0/sm0 761 75.2

Stress ratio at maximum compression Mm 0.909 1.24

Stress ratio at failure M* 1.229 1.24

Quasi-overconsolidation ratio OCR*^ = nmai/sm0j 1.0 1.0

Hardening parameter B*, B*, Cf 2000, 40, 0 100, 40, 10

Structure parameter Smaf /smai , ß 0.5, 50 0.3, 3.6

Control parameter of anisotropy Cd 2000 -

Parameter of dilatancy D*, n 1.0, 4.0 -

Reference value of plastic strain gp* 0.005 -

Reference value of elastic strain gf* 0.003 -

Viscoplastic parameter m! - 24.68

Viscoplastic parameter C1 (1/s) - 1.00 x 10 "5

Viscoplastic parameter C2 (1/s) - 3.83 x 10"6

Hardening parameter A*, B* - 5.9, 1.8

Strain-dependent modulus parameter a, r - 10, 0.4

Number of cycles

Fig. 11. Cyclic shear strength curves.

2.5. Abukuma River

The river dikes of the Abukuma River were heavily damaged and failed at three sites: the right embankment

Table 2

Simulation cases for various wave and soil profiles.

Input 1 Input 2

Type 1 Case 1-1 Case 2-1

Type 2 Case 1-2 Case 2-2

Type 3 Case 1-3 Case 2-3

Type 4 Case 1-4 Case 2-4

(30.6 km + 34 m-31.4 km + 160 m) in the Edano District, the left embankment (28.6 km + 368 m-29.0 km + 94 m) in the Noda District and the right embankment (22.4 km +174 m-22.6 km + 59 m) in the Sakatsuda District.

2.5.1. Edano section

This section has been investigated in detail by Tohoku Regional development Bureau of MLIT (2011). The embankment is composed of sandy soil, and clayey soil was underlain beneath the embankment. The fine fraction content and the D50 of the soil in the embankment are less than 35% and less than 10 mm, respectively.

The embankment moved severely in the form of several blocks to the land side, but almost no deformation occurred on the river side. This is due to the old embankment made of clayey soil on the river side of the embankment. The soil blocks run up on the waterway on the land side, and the settlement is 2.9 m. Boiled sand was observed at the toe of the embankment on the

Type 1

Type 2

Type 3

Type 4

land side and in the cracks of the embankment. It is worth noting that a water table is observed in the embankments. The expected reason for the failure of the embankment is that the sandy soil in the embankment was liquefied due to the earthquake motion.

2.6. Kanto District

According to the report of the Kanto Regional Development Bureau of MLIT (2011), many river embankments were damaged due to the earthquake in the Kanto District (Ibaraki, Chiba and Saitama Prefectures as well as the Tokyo Metropolitan Area), which are shown in Fig. 7. The river basins in the Kanto District include the Kuji River Basin, the Naka River Basin, the Tone River Basin and the Arakawa River Basin. In the Kanto District, river embankments were damaged at 920 sites. The patterns of the damage are failures and/or washouts (0 sites), cracks (385 sites),

Fig. 12. Soil profiles and water table.

Period (sec)

Fig. 14. Acceleration response spectrum.

Input 1

Higashi?Kobe Ohashi, 1995 Hyogoken Nanbu Earthquake (Public Works Research Institute ,1995)

Time (sec)

Input 2

MYGH06 (at a depth of 80m) -NS (Tajiri, KIK-net, 2011 Off the Pacific Coast of Tohoku Earthquake)

^ 150-

3 100-

c o 50-

<B -50-

u cj -100-

< -150-

Inp ut 2 |

max:155gal min:-138gal

80 120 Time (sec)

Fig. 13. Input earthquake motions.

lateral flows (43 sites), settlements (153 sites), damage to revetments (174 sites), sluice gates, etc. (80) and others.

2.6.1. Tone River

The river embankments of the Tone River were heavily damaged at 11 sites of both the downstream (around 18 km in Kamisu City and around 27 km and 40 km in Katori City)

and the upstream (around 50 km in Shinzaki Town, 66 km in Kouchi Town and 70 km in Tone Town). The typical patterns of the damage are the slides of the top and the shoulder of the embankment and the settlements on the river side. In addition, the river embankments (around 35.0 km and 31.8 km) of the Kokai River, a tributary of the Tone River, were heavily damaged at 5 sites. The embankments are made of clayey soil and their slopes collapsed.

10 15 20 25 Time (sec)

10 15 20 25 Time (sec)

0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -4.0

—•- Case2-1

Case2-2 Case2-3 Case2-4

0 25 50 75 100 125 150 175 200 Time (sec)

75 100 125 150 175 200

Time (sec)

Fig. 15. Vertical and horizontal displacement-time profiles at the top and the toe of the bank.

„ 4 -2 3 -E 2 -

"S -1 -© -2 -0 3

10 15 20 Time (sec)

4 -3 2 1 0 -1 -2 -3 -4 -5

|Case1-3|

Time (sec)

10 15 20 Time (sec)

Case1-4

1 l/v V v w

I— .......;......... ........;........ ........;.......

..... - ax- 1978 iJ—.-1-.-

Time (sec)

ax- 1978

ax- 1978

Table 3

Compressions and settlements.

|Node-1978|

a |Node-1954|

Unit: m dy-Node 1978 dx-Node 3178 Da Db Dc D(b + c)

Case 1-1 1.098 1.213 0.570 (9.5%) 0.132 (13.2%) 0.396 (2.8%) 0.528 (3.5%)

Case 1-2 0.902 0.921 0.409 (6.8%) 0.092 (9.2%) 0.401 (2.9%) 0.493 (3.3%)

Case 1-3 0.813 0.928 0.370 (6.2%) 0.071 (7.1%) 0.372 (2.7%) 0.443 (3.0%)

Case 1-4 0.851 1.083 0.378 (6.3%) 0.104 (10.4%) 0.369 (2.6%) 0.473 (3.2%)

Case 2-1 0.186 0.106 0.094 (1.6%) 0.015 (1.5%) 0.077 (0.6%) 0.092 (0.6%)

Case 2-2 2.342 1.683 1.348 (22.5%) 0.946 (94.6%) 0.048 (0.3%) 0.994 (6.6%)

Case 2-3 3.862 3.561 2.770 (46.1%) 1.057 (105.7%) 0.035 (0.3%) 1.092 (7.3%)

Case 2-4 1.543 2.122 0.859 (14.3%) 0.030 (0.2%) 0.684 (4.6%)

dy, vertical displacement; dx, horizontal displacement.

100 Time (sec)

0 20 40 60 80 100 120 140 160 180 200 Time (sec)

100 Time (sec)

100 Time (sec)

2.6.2. Edo River

The embankments of the Edo River were damaged by the earthquake, as shown in Fig. 8. The right embankment of the Edo River (57.5 km + 100m-57.5km + 300 m) at Nishisekiyado in Satte City was heavily damaged by the liquefaction of the sandy ground just beneath the levee, except for the toe of the right embankment below which a clay layer exists (Fig. 9). The ground water level was in the sandy layer. Boiled sand, due to liquefaction, was observed in the deep cracks in the right embankment around the toe. The damaged levee moved to the land side and settled. The maximum settlement is 1.1 m. This site is located at the old river (Fig. 8).

3. Discussions on the patterns of the deformation and the failures of the river embankments

The usual reason for the damage of river embankments is the liquefaction of the foundation sandy ground which was observed at the failure of the left embankment of the Yodogawa River during the 1995 Hyogoken-Nanbu Earthquake. As for the damaged river embankments, we have found that many were embankments on clayey ground, as shown in Figs. 3 and 5. Through a detailed study of the heavily damaged river embankments, we have found that a large number of embankments on soft clay deposits collapsed due to liquefaction.

0.00 0.21 0.43 0.64 0.86 1.07

Fig. 18. Distribution of displacement vectors (cases 1-1 to 1-4).

Typical patterns of the soil profiles are illustrated in Fig. 3. The four patters have been observed at the foundation of the damaged levee due to the 2011 off the pacific coast of the Tohoku earthquake.

1. Type A

In the soil profile Type A, embankment is on the sandy layer where the water table is below ground level. This type is seen such as the case of Kakai River.

2. Type B

In Type B, the subsoil layer of the embankment is composed of clayey soil and the water table is in the bank, i.e., the water saturated region appears. This type includes damaged levees at Edano and Sakashita of Abukuma River, at Shimononakanome-jyoryu of Naruse River and at Hinuma of Naka River, etc.

3. Type C

The soil profile Type C in which the sandy layer exits below the bank bounded by the clay layer with high water table in the banks. In this type, a water saturated region appeared in the bank, as it did in Type B. This type has been observed at Nishisekiyado of Edo River and Fuchishiri-jyoryu of Eai River, among others. The most severe damage was observed in this type of soil profile due to the 2011 Off the Pacific Coast of Tohoku Earthquake. 4. Type D

In Type D, the sandy layer is sandwiched in the clayey layer beneath the embankment.

This type corresponds to the soil profile of banks at Yamazaki of Yoshida River and at Fukunuma of Eai River, for example.

After taking the investigation of the soil profiles and the water tables of the damaged embankments into account, it was determined that the most damage was caused by the

Case2-1 №\\\

Case2-3

O.OO 0.40 0.80 1.20 1.60 2,00

Fig. 19. Distribution of displacement vectors (cases 2-1 to 2-4).

liquefaction of the water-saturated region bounded by the soft clay layers with smaller levels of permeability. The effect of the water-saturated region in the levee on the behavior during earthquakes has been pointed out by Sasaki et al. (1994)and Kaneko et al. (1995). The same effect of the water saturated region in the bank has been reported by Tohoku Regional development Bureau of MLIT (2011). This region extends to the lower part of the embankments which have settled below the water table. The water table in the embankments, which is higher than the ground surface, is formed by the rainfall and the capillaries, etc. In the following section, we will numerically analyze the behavior of the river embankments with the various saturated region.

4. Numerical analysis

4.1. Introduction

It is well known that one of the reasons for the failure of river embankments is earthquake loads. In this section, we have numerically analyzed the deformation behavior of river embankments during an earthquake 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 numerical simulation of the dynamic behavior of the ground, we used a liquefaction analysis program, ''LIQCA2-D11''(LIQCA Research and Development Group, 2011), which was developed by Oka et al.(2004). LIQCA2D11

adopts 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 the continuity equation is discretized by the finite difference method. As for the time discretization in the time domain, Newmark's b method is used. In addition, Rayleigh's damping is used in the analysis, which is proportional to the initial stiffness matrix and the mass matrix.

In the constitutive model for soils, we used a cyclic elasto-plastic model capable of indicating both the strain-induced degradation for sandy soils (Oka et al., 1999) and an elasto-viscoplastic model for clayey soils, which has been developed recently (Kimoto et al., 2012) based on the previous model shown in Appendix A (Oka and Yashima, 1995; Oka et al., 2004). We analyzed a model river embankment with different soil profiles and water tables. In addition, we studied the effect of a saturated region in the embankment with the duration of earthquakes as the main focus.

In the numerical analysis, a u-p formulation was adopted. For the discretization of the equations of motion (or the equilibrium of the mixture), FEM (Finite Element Method) was used, while for the discretization of the continuity equations of the pore fluids (water and gas), FDM (Finite Difference Method) was used. Although the embankment is in general in unsaturated state, we assumed that the river bank outside the water-saturated region was dry in the present study because there was no data for the unsaturated soil. In the dynamic analysis, it is possible to

Case1-1

Time=30.00

Max: 1.92

Case1-2

Time=30.00

Max: 1.85

Case1-3

T i rae=30.00

Max: 1.89

Case1-4

T i rae=30.00

Max: 1.32

0.00 0.20 0.40 0.60 0.80 1.00

Fig. 20. Accumulated plastic deviatoric strain.

take the unsaturated soil into account (i.e., Oka et al., 2011). The time discretization is based on Newmark's b method, with b and g set at 0.3025 and 0.6, respectively. The time increment in the calculation was set to be small enough to guarantee the accuracy of the results without requiring a large amount of computational time (i.e., 0.01 s). In order to obtain a more accurate estimation of the large deformation and/or flow indicated in Figs. 4 and 5, we would need a more elaborated version of the analysis method based on the finite deformation theory and/or particle method, such as MPM (Material point method, e.g. Higo et al., 2010), but in the present study we used a method based on the infinitesimal strain theory.

4.2. Finite element mesh and boundary conditions

Fig. 10 shows the model of the river embankment and the finite element mesh used in the analysis. The soil parameters are listed in Table 1. The material parameters of the sandy soil were determined based on the parameters

of the loose sand at the Akita port damaged due to liquefaction reported by Iai and Kameoka (1993), and the parameters of the soft clay at Torishima at the levee of the Yodo River (Mirjalili, 2011) were used for the clay. The liquefaction strength curve shown in Fig. 11 indicates that the parameters for sand are typically for the liquefiable sand. The cyclic strength of clay, shown in Fig. 11, is larger than that for loose sand.

Table 2 indicates the simulation cases with different soil profiles and earthquake motions. In the simulations, we used different soil profiles with the clayey subsoil because the ground profiles of the many damaged embankments in Miyagi Prefecture include a clayey soil layer of about 10 m in thickness, as shown in Section 2.

Fig. 12 shows the different soil profiles presented in the discussion in Section 2. Type 2 illustrates the levee embankment where the bottom of the embankment is below the ground water level, while Type 3 shows the case in which the embankment is settled and the ground water level is in the embankment. Type 3 corresponds to the

Case1-1

Time:20.000

Case1-2

Case1-3

Case1-4 Time:20.000

0.00 0.20 0.40 0.60 0.80 1.00

Fig. 21. Distribution of effective stress decreasing ratios (cases 1-1 to 1-4).

typical case of a severely damaged embankment due to the 2011 off the Pacific Coast of Tohoku Earthquake, such as the Shimonakanome-jyouryuu District of the Naruse River. Type 4 corresponds to the case of the damaged embankment at Sekiyado of the Edo River. Fig. 13 shows the input earthquake motions. Input 1 is the recorded earthquake record obtained during the 1995 Kobe Earthquake at a depth of 33 m of the Higashi-Kobe Ohashi Bridge. Input 2 is the earthquake record of MYGH06 at a depth of 80 m, obtained at Tajiri of KiK-net, 2011. It is worth noting that the record is very similar to the record at Yamazaki by JICE (2011). The response spectrums of these motions are illustrated in Fig. 14. 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 the maximum acceleration of Input 1 is larger than that of Input 2.

In Fig. 15, the vertical displacement-time profiles of the top of the embankment (Node 1978) and the 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 1 and minimum for Case 4. Fig. 16 indicates that the acceleration motions of the top of the embankments are similar for the four cases. Table 3 lists the displacements and the compressions of the embankment and the ground for all of the cases. The largest compression of the embankment (Case 1-1), Da (the change of height of the river embankment above the ground level), is shown in Table 3. It is

consistent with the largest lateral displacement at the toe of the embankment.

For Cases 2-1 to 2-4, the maximum settlement of the top of the embankment and the maximum horizontal displacement of the toe of the embankment are obtained for Case 23. For Case 2-1, the settlement of the top of the embankment is small and less than the others. For Cases 2-2 and 2-3, the liquefiable layers are fully compressed, as indicated in Table 3. In addition, the degree of amplification of the acceleration is the smallest for Case 2-4, as shown in Fig. 17.

Figs. 18 and 19 show the displacement distribution at the end of the earthquake motions. In Fig. 18, the larger portion around the right toe of the embankment moves, and displacement discontinuity was seen below the ground level and in the clay layer, while in Case 1-4, the larger displacement is seen just around the toe of the embankment above the clay layer. Fig. 19 shows the distributions of displacement in Cases 2-1 to 2-4. The largest displacement is seen in the central part of the embankment and below the top of the embankment for Case 2-3. On the other hand, for Case 2-4, the largest displacement develops just around the toe of the embankment and the displacements below the top of the embankment are relatively small.

Fig. 20 shows the distribution of accumulated deviatoric plastic strain for Cases 1-1 to 1-4.

The accumulated deviatoric plastic strain is defined as f =/(de^dep1/2. For Case 1-1, we can see the localized large strain beneath the river embankment, which is larger

Case2-1

Time=200.0

Max 0.22

Case2-2

Time=200.i)

0.03 0.10

Max 3.73

Case2-3

Time=200.0

Max 8.99

0.00 0.20 0.40 0.60 0.30 1.00

Case2-4

T¡re=200.0

Max 3.68

0.00 0.20 0.40 0.60 0.80 1.00

Fig. 22. Distribution of accumulated plastic deviatoric strain. ( Case 2.1-2.4).

than the other cases, i.e., a larger level of strain develops in the clay layers. Fig. 21 indicates the corresponding distribution of ESDR (effective stress decreasing ratio, ESDR = (ffm0-ffm)/sm0). In Fig. 22, a larger level of plastic strain develops for Case 2-3 in the saturated sand portion of the embankment as well as in the upper part of the embankment. The shear strain localized above the saturated region in the embankment; this trend is consistent with a failure pattern B in Fig. 2. Figs. 23 and 24 show the distribution of the ESDR and the distribution of the pore water pressure for Cases 2-1 to 2-4. For Case 2-3, we can see the liquefaction of the water-saturated region in the embankment.

From the above discussions, it is worth noting that where the region is water-saturated, a larger settlement of the river embankment occurs, and the deformation/failure is larger. This deformation behavior is consistent with damaged embankments, such as the embankments of the Eai River in Miyagi Prefecture, brought about by the 2011 off the Pacific Coast of Tohoku Earthquake. From the

numerical results of Cases 1-1 and 2-1, we can say that the earthquake wave form affects the deformation characteristics of the river embankment-subsoil layer system. It should also be added that the amplitude of the earthquake is also an important factor in the damage.

5. Conclusions

From the investigative work of the damaged river

embankments and the numerical simulation of river

embankments with various subsoil profiles, we have obtained the following main conclusions:

1. Due to the very strong 2011 off the Pacific Coast of Tohoku Earthquake, which had a magnitude of 9.0, many river embankments were damaged. The river embankments and their related structures were damaged at 2115 sites over the Tohoku and Kanto areas, including Iwate, Miyagi, Fukushima, Ibaraki and Saitama Prefectures, as well as the Tokyo Metropolitan District.

Case2-1 Time:120.000

Case2-2 Time:120.000

Case2-3 Time:120.000

Case2-4 Time:Î20.000

0.00 0.20 0.40 0.60 0.S0 1.00

Fig. 23. Distribution of effective stress decreasing ratios (cases 2-1 to 2-4).

2. Through a detailed study of the heavily damaged river embankments, it has been found that the embankments on soft clay deposits extensively collapsed due to liquefaction. The main feature of the damage was the liquefaction of the saturated region in the embankments downwardly bounded by soft clay layers.

3. From the numerical results, it has been found that the water-saturated region in the embankments leads to the larger settlement of the 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 Coast of Tohoku Earthquake. In addition, the earthquake wave form,

such as the duration time, affects the deformation characteristics of the river embankment-sub soil layer. The amplitude of the earthquake is also an important factor in the damage.

Acknowledgments

The authors wish to express their sincere thanks for the advice and the materials given by the Tohoku and Kanto Regional Development Bureaus of MLIT, Emeritus Prof. Y. Sasaki of Hiroshima University and JICE.

Case2-1

0 00 7.82 15.6-4 23.46 31.26 39.10

Appendix A. Cyclic elasto-viscoplastic model based on nonlinear kinematical hardening rule (Kimoto et al., 2012)

Oka and Yashima (1995) proposed a cyclic elasto-viscoplastic model by adopting the nonlinear kinematical hardening rule by Armstrong and Frederick (1966). Kimoto and Oka (2005) proposed an elasto-viscoplastic model considering structural degradation for the behavior of clay under monotonic loading conditions. Kimoto et al. (2012) developed a cyclic elasto-viscoplastic model considering the effect of the structural degradation of clay. Taking into account structural degradation and microstructural changes, a cyclic elasto-viscoplastic model has been developed based on the nonlinear kinematic-hardening rules for changes in both the stress ratio and the mean effective stress. In addition, the kinematic hardening rule for changes in viscoplastic volumetric strain is generalized to predict the behavior during the cyclic loading process (Shahbodagh, 2011).

A.1. Static yield function

The static yield function is obtained by considering the nonlinear kinematic hardening rule for changes in the stress ratio, the mean effective stress, and the viscoplastic volumetric strain, as

fy = zn + M •( +

n n n n

ZnZn -w,

in-m -y*ml

in which amk is the unit value of the mean effective stress,

y^] is the scalar kinematic hardening parameter and a^k denotes the static hardening parameter. w* is the so-called back stress parameter, which has the same dimensions as stress ratio z*.

Incorporating strain softening into the structural degradation, the hardening rule for a my can be expressed as

s'(s) =

Smaf + (S'mai-s'maf) eXP(-bz) ,(s)

A.2. Viscoplastic potential function

In the same manner as for the static yield function, viscoplastic potential function fp is given by

fp=zn+m n ins

in-m -y'i

Dilatancy coefficient M is defined separately for the normally consolidated region (NC) and the

(A. 5)

overconsolidated region (OC) as

* _ J M* NC region

(a*m/0mc)M*m OCregion

where amc is the mean effective stress at the intersection of the overconsolidation boundary surface and the am axis, which is defined by

Smc = SmbeXP

In addition, s' denotes the mean effective stress at the intersection of the surface, which has the same shape as fb and is given by

Sm = SmeXP

(A. 7)

A.3. Kinematic hardening rules

The evolution equation for nonlinear kinematic hardening parameter w* is given by

dw* — B* ^A*deVy ~w*jdyvp^ (A.8)

where A* and B* are material parameters, dej is the viscoplastic: deviatoric strain increment tensor and dgvp — . /de'Vj de'Vj is the viscoplastic shear strain increment. A* is related to the stress ratio at failure, namely, A* — Mf, and B*is proposed to be dependent on the viscoplastic shear strain as

B* — (Bmax-Bf)exp(-Cf gjnf) + B* (A.9)

in which B* is the lower boundary of B*, Cf is the parameter controlling the amount of reduction and yvp is the accumulated value of viscoplastic shear strain between two sequential stress reversal points in the previous cycle. Bmax is the maximum value of parameter B , which is defined following the proposed method by Oka et al. (1999) as

Before reaching failure line

. vpn : vpn 1 ' g(n)max = g(n)r

After reaching failure line

(A. 10)

where B* is the initial value of B*, gVp*nax is the maximum value of yvp in past cycles and g^* is the viscoplastic reference strain.

In order to improve the predicted results under cyclic loading conditions, a scalar nonlinear kinematic hardening parameter y*m1 is introduced as

dym1 — B*(A^deV^-ymi|deV^|) (A.11)

where A* and B* are material parameters and dsjf is the increment in the viscoplastic volumetric strain tensor. The

values for A* and B* are determined by a data-adjusting method from the laboratory test data.

The degradation of the elastic shear modulus from the beginning of loading can be expressed by its dependency on accumulated viscoplastic shear strain gvp as

(1 + a(yvp)r)V sm

(A. 12)

where r and a are the strain-dependent parameters, which can be determined from the laboratory test results. In this study, based on the experimental results, r—0.4 was chosen.

A.4. Viscoplastic flow rule

Based on the overstress type of viscoplastic theory first adopted by Perzyna (1963), the viscoplastic strain rate

tensor e? is defined as

ej — Cijkl<0(fy)> f

, ) f F(fy) : fy > 0

<f > — { 0 : f > 0

Cijkl — ad j dkl + b ( dik djl + da j)

(A. 13)

(A. 14)

(A. 15)

where <> are Macaulay's brackets, 0fy) is the ratesensitive material function and Cjki is a fourth order isotropic tensor. a and b in Eq. (A.15) are material constants. Material function 0 (fy) is determined as

®(fy) = SmexP

ln Sr ~fmX

(A. 16)

in which m' is the viscoplastic parameter. Finally, by combining Eqs. (A.13), (A.15) and (A.16), viscoplastic deviatoric strain rate eV and viscoplastic volumetric strain rate £y can be expressed as

ej = Qexp m'[ Z* + M *

ln Smk

ln -m -y*m1

(A. 17)

ekk = C2exp

Z* + M *( ln -mt +

ln-m-fm!

* -ml-mk) -y*m\ Zlnj Ztn,-^

-ml-mk) -y*m1 I

(A. 18)

where C1 = 2b and C2 = 3a + 2b are the viscoplastic parameters for the deviatoric and the volumetric strain components, respectively.

References

Armstrong, P.J., Frederick, C.O., 1966. A Mathematical Representation of the Multiaxial Baushinger Effect, C.E.G.B., Report RD/B/N 731.

Higo, Y., Oka, F., Kimoto, S., Morinaka, Y., Goto, Y., Chen, Z., 2010. An coupled MPM-FDM analysis method for multi-phase elasto-plastic soils. Soils and Foundations 50 (4), 515-632.

Iai, S., Kameoka, T., 1993. Finite element analysis of earthquake induced damage to anchored sheet pile quay walls. Soils and Foundations 33 (1), 71-91.

Investigation Committee of the 1978 Miyagiken-oki Earthquake at Tohoku Branch of JSCE, 1980. General Report on the 1978 Miyagiken-oki Earthquake.

Japan Institute of Construction Engineering (JICE), 2011. Third Urgent Exploratory Committee for the Earthquake Resistant Measure of River Embankments, August 27, 2011, Material-1 <http://www.jice. or.jp/sonota/t1/201106210.html >.

Kaneko, M., Sasaki, Y., Nishikawa, J., Nagase, M., Mamiya, K., 1995. River dike failure in Japan by earthquakes in 1993. In: S. Prakash (Ed.), Proceedings of the 3rd International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, vol. 1, St. Louis, Missouri, pp. 495-498.

Kanto Regional Development Bureau of MLIT, 2011. Material-1 and Reference Materials of the 3rd Exploratory Committee of MLIT on the Earthquake Resistant Measure of River Embankments <http://www. ktr.mlit.go.jp/river/bousai/river_bousai00000090.html > (2011.9.4).

Kimoto, S., Oka, F., 2005. An elasto-viscoplastic model for clay considering destructuralization and consolidation analysis of unstable behavior. Soils and Foundations 45 (2), 29-42.

Kimoto, S., Sahbodagh, K.B., Mirjalili, M., Oka, F., 2012. A cyclic elasto-viscoplastic constitutive model for clay considering the nonlinear kinematic hardening rules and the structural degradation, International Journal of Geomechanics, ASCE, submitted for publication.

LIQCA Research and Development Group (Representative: F. Oka, Kyoto University), 2011. User's Manual for LIQCA2D11 (in Japanese).

Mirjalili, M., 2011. Numerical Analysis of a Large-Scale Levee on Soft Soil Deposits Using Two-Phase Finite Deformation Theory, Ph.D. thesis, Kyoto University.

Oka, F., Yashima, A., 1995. A cyclic elasto-viscoplastic model for cohesive soil. In: Proceedings of the XI European Conference on Soil Mechanics and Foundation Engineering, Copenhagen, vol. 6, The Danish Geotechnical Society, pp. 6.145-6.150.

Oka, F., Yashima, A., Tateishi, A., Taguchi, Y., Yamashita, S., 1999. A cyclic elasto-plastic constitutive model for sand considering a plastic-strain dependence of the shear modulus. Geotechnique 49 (5), 661-680 October.

Oka, F., Kimoto, S., Kato, R., 2011. Seepage-deformation coupled numerical analysis of Unsaturated river embankment using an elasto-plastic model. In: First International Conference on Geotech-nique, Construction Materials and Environment, Mie, Japan, November21-23, 2011, CD-ROM, ISBN: 978-4-9905958-0-7 C3051.

Oka, F., Yoshida, N., Kai, S., Tobita, T., Higo, Y., Torii, N., Kagamihara, S., Nakanishi, N., Kimoto, S., Yamakawa, Y., Touse, Y., Uzuoka, R., Kyoya, T., 2012. Reconnaissance report of geotechnical damage due to the 2011 off the Pacific Coast of Tohoku Earthquake - 4 Northern Area of Miyagi Prefecture. Journal of the Geological Society 7 (1), 37-55.

Oka, F., Kodaka, T., Kim, Y.-S., 2004. A cyclic viscoelastic-viscoplastic constitutive model for clay and liquefaction analysis of multi-layered ground. International Journal of Numerical and Analytical Methods in Geomechanics 28 (2), 131-179.

Sasaki,Y., Oshiki,H., Nishikawa,J.(1994):Embankment failure caused by the Kushiro-Oki earthquake of January 15, 1993. In: Performance of Ground and Soil Structures During Earthquakes, 13th ICSMFE, JGS, pp. 61-68.

Shahbodagh, K.B., 2011. Large Deformation Dynamic Analysis Method for Partially Saturated Elasto-Viscoplastic soils, Ph.D. thesis, Kyoto University.

Tohoku Regional Development Bureau of MLIT, 2011, Material-3, Interim Report by the 3rd Investigative Commission for the Restoration of the River Dikes of Kitakami river, etc. July 29, 2011, pp. 18-19 (in Japanese).