SIMULATION OF SEISMIC BEHAVIOUR OF GRAVITY QUAY WALL USING A GENERALIZED PLASTICITY MODEL

Transcription

1 4 th Intenational Confeence on Eathquake Geotechnical Engineeing June 25-28, 2007 Pape No SIMULATION OF SEISMIC BEHAVIOUR OF GRAVITY QUAY WALL USING A GENERALIZED PLASTICITY MODEL Mahdi ALYAMI 1, S. M. WILKINSON 2, M. ROUAINIA 3 and Fei CAI 4 ABSTRACT Well-documented case histoies of damage duing eathquake to pot stuctues made of gavity etaining quay walls duing the peiod ( ) show that the damage is often associated with significant defomation of liquefiable soil deposits. Gavity quay walls failues such as these have stimulated much pogess in the development of a defomation-based design method fo watefont stuctues, such as the effective-stess analysis method. This method has been applied in this pape based on an elasto-plasiticity constitutive model developed by Pasto et al. (1990) with some mino modifications which is incopoated into a new FEM code called (UWLC). The simulations of the poposed model ae compaed with the published monotonic and cyclic tests fo diffeent types of sand unde diffeent initial densities, confining pessues and diffeent Cyclic Stess Ratios (CSR). Futhe, the FEM code is evaluated by e-analysing the typical Pot Island PC-1 caisson type quay wall which was damaged by the 1995 Hyogoken-Nanbu eathquake. The esults ae compaed with obseved esults which wee obtained fom the Ministy of Tanspot, Japan (1997) which includes seawad displacement, tilting and settlement which ae known as typical failue modes of quay walls due to eathquake. Aftewads, seveal quay walls systems in diffeent conditions have been analysed in ode to identify the effect of each facto on the esidual defomation of gavity quay walls. Keywods: quay wall, liquefaction, eathquake, habou, effective stess, constitutive model INTRODUCTION Gavity quay walls ae the most common type of constuction fo docks because of thei duability, ease of constuction and capacity to each deep seabed levels. The design of gavity quay walls equies sufficient capacity fo thee design citeia; sliding, ovetuning and allowable beaing stess unde the base of the wall. Although the design of gavity quay walls is easonably well undestood fo static loads, analysis unde seismic loads is still in being developed. Duing stong gound shaking, the poe wate pessue of cohesionless satuated soils builds up. This incease in pessue not only causes the lateal foces on the wall to incease (which may make the wall fail), but also educes the effective stess of the soil which may esult in liquefaction. The occuence of the liquefaction in back fill was the main eason fo the damage fom eathquakes to gavity quay walls in 1964 at Nigata Pot (Hayashi, et al., 1966), also in 1993 at Kushio-oki and in 1994 at Hokkaido Toho-oki (Sasajima, et al., 2003). In addition, liquefaction caused majo damage to pot facilities in Kobe, Japan, in the 1995 Hyogo-ken Nanbu eathquake. Moeove, obsevations of 24 maine stuctues in the eathquake in 1999 at Kocaeli, Tukey showed the backfill of quay walls also 1 School of Civil Engineeing and Geosciences, Univesity of Newcastle, Mahdi.Alyami@ncl.ac.uk 2 School of Civil Engineeing and Geosciences, Univesity of Newcastle, S.M.Wilkinson@ncl.ac.uk 3 School of Civil Engineeing and Geosciences, Univesity of Newcastle, M. Rouainia@ncl.ac.uk 4 Depatment of Civil Engineeing, Gunma Univesity, cai@ce.gunma-u.ac.jp

2 liquefied and the quay walls wee displaced seawad (Sume, et al., 2002). The same obsevations wee epoted in 1999 duing the Chi Chi eathquake in Taiwan, (Chen & Hwang, 1999). The seismic coefficient method containing Mononobe-Okabe s fomula is usually used in the stuctual design of gavity type quay walls to esist eathquake damage but this design method does not take account of the liquefaction of backfill gound and foundations (Sasajima, et al., 2003). Gavity quay walls failues such as these have stimulated much pogess in the development of a defomation-based design method fo watefont stuctues. Much significant expeimental and theoetical eseach wok has been done on the subject (Dakoulas & Gazetas, 2005; Iai, 1998; Iai, et al., 1998; Iai & Sugano, 2000; Ichii, et al., 2000; Inagaki, et al., 1996; Inoue, et al., 2003; Nozu, et al., 2004; Sugano, et al., 1996) Many advanced constitutive models ae being developed and much defomation effective stess analysis has been caied out which has analyzed and studied the ecoded cases histoy of the behaviou of gavity quay walls founded in liquefiable soils. In this study, an elasto-plastisity constitutive model developed by Pasto, et al. (1990) that can simulate the monotonic and cyclic behaviou of cohesionless satuated soils has been slightly modified and used to investigate liquefiable soils with a wide ange of confining pessues and elative densities. The modified constitutive model has also been incopoated in the FEM code UWLC (Foum 8, Co., 2006). In ode to assess the pedictive capability of the poposed model, numeical esults have been compaed with published expeimental esults fo monotonic and cyclic tests using diffeent types of sand unde diffeent initial densities, confining pessues and diffeent Cyclic Stess Ratios (CSR). In ode to identify the effect of each facto on the esidual defomation of gavity quay walls, seveal quay wall systems in diffeent conditions have been investigated. The eseach focused on the analysis of a typical Pot Island PC1 caisson type quay wall which was damaged by the 1995 Hyogoken-Nanbu eathquake. The esults ae compaed with obseved esults which wee obtained fom the Ministy of Tanspot, Japan (1997) which include seawad displacement, tilting and settlement which ae known as typical failue modes of quay walls due to eathquake. DESCRIPTION OF THE CONSTITUVE MODEL AND METHOD OF ANALYSIS Matin, et al., (1975) poposed a model fo excess poe wate pessue build up based on the incemental volumetic stain in dained condition between the shea wok and the excess poe wate pessue. Zienkiewicz, et al., (1985) poposed a simple model fo tansient soil loading in eathquake analysis, efeed to as Mak I, which gives a easonable pediction of poe pessue changes occuing duing cyclic loading. Pasto, et al., (1985) extended the bounding suface and genealized plasticity of model Mak I to epoduce the behaviou of sands unde both static and tansient loading and they efe to it as Mak II, in 1986, Pasto and Zienkiwicz descibed the P-Z Mak III model and modelled the behaviou of sand in a hieachical manne and wee able to captue impotant featues of soil behaviou unde cyclic loading, such as the pogessive decease in the stiffness of soil with inceasing poe pessue, accumulation of defomation, stess-dilatancy and hysteetic loops. Finally, Pasto, et al. (1990) outline the theoy of genealized plasticity in which yield and plastic potential suface need not be explicitly defined, and show how a vey effective geneal model descibing the behaviou of sands unde monotonic o tansient loading can be developed. This model is cuently one of the simplest and yet one of the most effective ones descibing the full ange of behavious such as the cyclic behaviou of soil. In the pesent study the constitutive model fo sand which was developed by Pasto et al. (1990) was adopted, afte some mino modifications. Model evaluation To test the validity of the poposed model, simulations ae compaed with the published monotonic and cyclic test of diffeent types of sand unde diffeent confining pessue and initial elative densities. The expeimental tests ae those of Casto, (1969) and Toyota, et al., (2004).The model equies a total of 15 paametes which ae shown in Table 1. Figue 1 shows a compaison between

3 expeimental and pedicted esults of the effective stess paths with diffeent elative densities D =27%, D =44% and D =64% fo undained tiaxial test of Banding sand (Casto, 1969). Figue 2(a) compaes the stess path duing undained cyclic tiaxial test in Toyoua sand (Toyota, et al., 2004) testing a sample with elative density D =38%, Figue 2(b) compaes the Deviato stess veses Axial stain fo the same sample. Figue 3(a) compaes the stess path duing undained cyclic tiaxial test in PI Masado sand (Moist placement) (Toyota, et al., 2004) testing a sample with elative density e=0.58. Oveall, the model seems capable of descibing soil behavious unde monotonic and cyclic loading in undained and dained conditions fo a wide ange of elative densities. Fom the figues it can be seen that the model gives excellent ageement with monotonic test esults and while diffeences between the cyclic esults do exist, the model captues the essential ange of stess and stain behaviou. Fom these esults, it is concluded that this soil model applied in the commecially available finite element code, UWLC, can be employed to assess liquefaction behaviou. a) b) Figue 1. Simulation of expeimental data fom Casto, (1969) unde monotonic undained loading: a) stess path and b) stess stain elationship a) b) a) b) Figue 2. Simulations of expeimental data fom Toyota, et al., (2004) of Toyoa sand (Moist placement), cyclic tiaxial test: a) stess path and b) stess stain elationship

4 a) b) a) b) Figue 3. Simulation of expeimental data fom Toyota, et al., (2004) of PI Masado sand (Moist placement), cyclic tiaxial test: a) stess path and b) stess stain elationship Test M f M g C α f α g K ev0 G es0 mv ms β 0 β 1 0 H U 0 H γ γ U p 0 Casto (27%) Casto (44%) Casto (64%) Toyota (Toyoa) Toyota (PI Masado) Table 1. Mateial paametes used in simulation of figues 1 3 Case histoy Kobe Pot is located in an aea 6km long and 12km wide, thee ae two man-made islands, Pot Island and Rokko Island. The soils used fo landfill wee excavated fom the Rokko Mountains to the noth west of Kobe city, this soil is called PI Masado (Ikuo, et al., 1996; Inagaki, et al., 1996; Sugano, et al., 1996). Figue 4 shows Pot Island which is divided into two phases, the fist, efeed to as phase 1, was constucted on the nothen half of Pot Island between 1966 and 1981, the est is efeed to as phase 2; landfilling in the southen half of Pot Island was almost complete when the Hyogoken- Nanbu eathquake hit Kobe City in Januay 1995 (Toyota, et al., 1996). Kobe Pot had significant gound subsidence as a esult of liquefaction duing the eathquake; the extent of liquefaction was intense on Pot Island and ove 250 caissons type quay walls wee damaged thee with a epai cost exceeding US$11 billion (Ishihaa, 1997). Those walls wee constucted on loose satuated decomposed ganite which had been used to eplace the alluvial clay laye in ode to attain the equied beaing capacity fo the foundations. The typical types of damage obseved afte the eathquake wee: seawad displacement, appoximately 5m maximum and appoximately 3m aveage; the walls also settled appoximately 1 to 2m and tilted appoximately 4 degees (Ichii, 2004). Caisson

5 type quay walls in Kobe Pot including Pot Island and Rokko Island wee designed using the pseudostatic method, with limit equilibium mechanics based on the Mononobe-Okabe method developed by Okabe, (1924) and Mononobe & Matsuo, (1929) using hoizontal seismic coefficients anging fom 0.1 to 0.15 (Inagaki, et al., 1996). Figue 4. Plan of Kobe Pot, showing the location of the ecoding station, quay walls and sites fo geotechnical investigation afte Inagaki, et al, (1996) This study focuses on the analysis of typical Pot Island caisson quay wall failue duing the 1995 Hyogoken-Nanbu eathquake; the quay used as a case study is called PC1, constucted in phase one it is shown in Figue 5. The fiction angle used in the design was 30 degees except beneath the wall whee a fiction angle of 40 degees was used, the facto safety was 1.2. The hoizontal seismic coefficient was 0.1 and the vetical seismic coefficient was zeo (Towhata, et al., 1996). This wall displaced towad sea appoximately 2.75m, settled appoximately 1.36m and tilted appoximately 3 degees on aveage as shown in Figue 6 as obtained by Ministy of Tanspot, Japan (1997) Figue 5. Coss section of a quay wall PC1 at Pot Island afte Inagaki, et al., (1996) The elative density of the backfill soil was obtained by the Standad Penetation Test (SPT) conducted by (Inagaki, et al., 1996) and was equal to D = %. Case study and effective stess analysis method The seismic pefomance of a typical Pot Island caisson quay wall PC1 has been modelled using a dynamic nonlinea effective stess analysis method in ode to evaluate the effectiveness of vaious soil impovement stategies. The compute pogam UWLC was used fo this study. The UWLC code is a fully coupled numeical code, which can undetake initial stess analysis, one-dimensional and two dimensional dynamic finite element analyses based on total and effective stess. Figue 6. Coss section of the caisson quay wall PC1 in Pot Island with obseved esidual defomation afte Kobe 1995 eathquake, Ministy of Tanspot, Japan, (1997)

6 The finite element mesh shown in figue 7 was used fo the analysis unde plane stain conditions. A total of 1989 nodes and 644 elements wee used. Five mateials divided into nine zones wee used in the analysis. The mateials and thei popeties ae listed in Table 2. The backfill and foundation layes ae modelled by using the PZ-sand modified constitutive model descibed ealie; the paametes used in the calculation wee obtained fom the unique seies of cyclic tiaxial tests conducted pio to the eathquake by Nigase et al., (1995) and pesented by Ishihaa et al., (1996). In thei wok, undistubed fozen samples of Massado soils excavated fom the nothen section of Pot Island wee tested with thee elative densities. Since the SPT-N value tests pesented by Injaki et al. (1996) showed the aveage density fo eclaimed Pot Island sand was 41%, as discussed above, the esults of the sample with D =37% pefomed by Nigase et al., (1995) ae used in this study. The esults of the cycling loading tests in tem of the cycles equied to geneate cyclic development of 5% double-amplitude axial stain ae computed and compaed with the tiaxial tests on samples fom Pot Island conducted by Nigase et al., (1995) ae shown in Figue 8 and the paametes ae shown in Table 3. Table 2. Mateial popeties fo model afte Iai, et al., (1998) and Dakoulas and Gazetas, (2005) Mateials Density (ton/m 3 ) Fiction angle( o ) Pemeability (m/s) Land fill *10-5 backfill and foundation *10-5 Caisson wall 2.1 Alluvial clay *10-8 Rubble in backfill and foundation *10-4 Figue 7. Geomety (in natual scale) and mateial zones of the Pot Island PC1 quay wall; 1 is satuated backfill soil, 2&3 ae submeged backfill and foundation soil, 4&5 ae backfill and foundation ubble, 6&7ae alluvial clay, 8 is the caisson wall and 9 is the inteface Figue 8. Cyclic stess atio (CSR) fom tiaxial tests on samples fom Pot Island conducted by Nigase et al., (1995) (Ishehaa et al., 1996): Compaison with pedictions using modified PZ-sand model, D =37% and fo dense sand D 75%

7 Mateial paamete Table 3. Model paametes fo elative density M f M g C α f α g K ev0 Ges0 D =37% and fo dense sand m v ms β 0 β 1 0 D 75% H γ H U 0 γ U p 0 Loose Dense Pactically, whethe low wate level o high wate level is consideed as a wost case fo designing quay walls is not of significance as the active eath pessue on the wall is consideed to be the failue foce. In the low wate level case the active pessue is less than in high wate level the eason being the eduction in the density of backfill soil, on the othe hand, the stability weight of the caisson wall will also be educed fo same eason, equally, the density of soil and the density of caisson will incease in the high wate level case. Theefoe, fo pactical engineeing it is known that it is vital to design the caisson wall fo both cases and then the wost case is taken. In this model the low wate level is consideed in the calculation as ecommended by Elshanobi et al., (2004), because it poduces the wost case concening stess at ock base level. As a esult, the backfill laye is divided into layes, the top laye is satuated soil with unit weight γ sat. measued unde the wate level with submeged unit weight sub. =1.8 ton/m 3 and 4m thickness, the submeged soil is γ =0.8 ton/m 3. The wall is modelled as an elastic model having inteface slip elements which ae equied between the quay wall model and soil to allow slippage and sepaation at the base and the back of the caisson with the fiction angle at caisson bottom of 30 degees and fiction angle at the caisson back of 15 degees. The clay zones ae modelled using the Hadian-Dnevish model (HD). The seismic excitation input file in both hoizontal (E-W) and vetical (U-D) diections espectively wee ecoded by a seismomete installed at a depth of 32m in the nothen aea of the Pot Island site vey close to PC1, adopted by the development Division, Kobe city, in Octobe,1991 epoted by Iwasaki & Tai (1996). The peak acceleation value ecoded eached 540gal (cm/sec 2 ) and 200gal (cm/sec 2 ) as shown in Figue 9. The digital data wee collected fom Ishii, (2006). a) b) Figue 9. Recoded motions at Kobe Pot duing the 1995 Hyogoken-Nanbu eathquake a) Hoizontal (E- W) component, b) Vetical (U-D) component RESULT AND DISCUSSION Befoe the dynamic esponse analysis and to take the effect of gavity into account, a static analysis was pefomed to simulate the initial stess distibutions. Figue 10 and Figue 11, below, shows the computed stess esults fo effective esidual defomation including seawad displacement, settlement and tilting fo Case 1 which coesponds to a typical quay wall section of PC1 in Pot Island whee the backfill, landfill and foundation ae liquefiable soils. The figue shows the state 30 seconds afte the end of the eathquake. The computed displacement at point A on the seawad side cone of the quay wall was 3.3m (2.75 m measued), the wall settled vetically by about 0.59m (1.36 m measued) and tilted into the foundation by 4.5 degees (3 degees measued),. The majo facto which may have educed the vetical displacement could be the absence of the effect of shaking paallel the face of quay wall. Howeve the computed esidual defomation esults fo Case 1 wee consistent with field obsevations shown in Figue 6. Computed acceleations at uppe sea side cone of the caisson fo a quay wall ae shown in Figue 12. Computed distibutions of excess poe wate pessue atio fo quay

8 wall ae shown in Figue 13. It can be seen fom Figue 13 that maximum poe pessues wee geneated in the backfill athe than undeneath the wall. Figue 10. Case 1 computed defomation at the end of eathquake ( t = 30sec ) of Pot Island caisson quay wall PC1 a) b) Figue 11. Case 1 computed displacements fo quay wall afte (30 sec); a) Hoizontal and b) Vetical a) Acceleation (m/sec2) Time (sec) b) Acceleation (m/sec2) Time (sec) Figue 12. Computed acceleations at uppe sea side cone of the caisson at (point A) fo case 1: a) Hoizontal and b) Vetical Figue 13. Case 1 computed distibutions of excess poe wate pessue atio fo quay wall afte (30 sec) In ode to investigate the effect of gound impovement techniques on the liquefaction behaviou of the wall, Case 2 was analyzed using PZ paametes of dense sand, fo both the backfill and foundation layes. The esults ae shown in Figue 14. Figue 14 demonstates that the soil impovement leads to a eduction of the maximum displacement to 0.91m, fom the 3.3m of case 1. The settlement at point A is educed fom 0.59 to 0.25m. Figue 14. Case 2 computed defomation at the end of eathquake ( t = 30sec ) of Pot Island caisson quay wall PC1 whee the backfill and foundation ae non-liquefiable

9 In Case 3 the effect of the size of the gavity quay wall is investigated. The equivalent egional hoizontal seismic coefficient (K h ) fo Kobe egion of 0.15 accoding to the Eathquake Resistance Designed Codes in Japan epoted by Ichii, (2003), and is pesented in ode to investigate the effectiveness of using the egional seismic coefficient in the design. It should be noted that PC1 was designed based on the simplified method which was developed by Okabe, (1924) and Mononobe & Matsuo, (1929) with K h = 0.1, K v = 0 and the safety facto = 1.2 (Inagaki, et al., 1996). Fist, PC1 was designed with K h = 0.1 by using the simplified method assuming the live load equal to 2 ton/m 2. The esults show the equied width fo the quay wall to be stable in case of K h = 0.1 was 10 m. Next the same pocedue was used to evaluate the suitable quay wall width in case of K h = The new wall dimensions wee width 11.5 m and height 16.5 m. The computed esidual defomation esults fo Case 3 ae shown in Figue 15. In this case the hoizontal displacements have educed by appoximately 5% and settlement has slightly inceased by appoximately 10% when compaed with Case 1 (this is pobably due to the inceased mass of the wall). Compaing the esults of Case 2 and Case 3 to Case 1, it is clea that the impoved backfill soil of caisson has a moe ponounced effect on the pefomance of seismic esistance quay walls than inceasing the wall width. Figue 15. Case 3 computed defomation at the end of eathquake ( t = 30sec ) of edesigned Pot Island caisson quay wall PC1 with K h = 0.15 whee the backfill and foundation ae liquefied In Case 4 the design used in Case 3 with non-liquefiable soil was applied, in ode to evaluate the pefomance of an idealized seismic design of gavity quay walls. The idealized design was achieved by using the egional seismic coefficient and with assumption that the backfill, landfill and foundation soils wee impoved enough to avoid the geneation of poe wate pessue duing the eathquake. The esults fom Case 4 ae shown in Figue 16. A summay of the majo esults of the analysis is given in table 4. The displacements in both diections the hoizontal and vetical fo each case ae shown in Figue 17. Finally the esults of Case 1, Case 2 and the obseved defomations ae summaized in Figue 18 by dawing the outline of the quay wall. This Figue clealy demonstates that 1) the calculated and measued wall movement ae simila and 2) that a soil impovement stategies of inceasing the density of the soil, esults in geatly educed oveall movement of the wall. Figue 16. Case 4 computed defomation at the end of eathquake ( t = 30sec ) of edesigned Pot Island caisson quay wall PC1 with Kh=0.15 whee the backfill and foundation ae non- liquefiable

10 a) b) Figue 17. Computed displacement time histoy at the uppe seawad cone of caisson (point A) fo all cases: a) hoizontal diection and b) vetical diection Case Table 4. Summay of computed esults of paamete study fo quay wall PC1 Wall Diminutions (m) Hoizontal seismic coefficient Displacements (m) Rotation (degee) Backfill and foundation conditions Width Height (Kh) Hoizontal Vetical Case Loose Case Dense Case Loose Case Dense a) b) Vetical displacement (m) Case 1 Case 2 Oiginal caisson Obsevation esults Vetical displacement (m) Case 3 Case 4 Oiginal caisson Obsevation esults Hoizontal displacement (m) Hoizontal displacement (m) Figue 18. Compaison between computed defomation with oiginal caisson and obsevation defomation: a) case 1 and 2 and b) case 3 and 4 CONCLUSIONS A Two-dimensional effective stess method of analysis based on an elasto-plastic constitutive model of Pasto (1990) with slightly modifications has been used fo the analysis Pot Island quay-wall PC1. The model was fist validated by simulating published monotonic and cyclic test esults. The esults of the monotonic testing showed excellent ageement between the physical and numeical expeiments. Fo the cyclic tests, the simulations wee able to captue the geneal behaviou exhibited in the physical expeiments (i.e. stess and stain histoies of the numeical simulations showed compaable shapes to the physical expeiments). A model of Pot Island quay walls was then developed using a finite element package UWLC and the influence of the density of the soil and wall dimensions on the liquefaction behaviou of the soil was investigated. Both vetical and hoizontal acceleations wee applied to the model and the esults compaed to the obseved field measuements. The pefomance of the quay wall is summaized as follows:

11 1) Computed oveall displacement and otations of the wall wee simila to those obseved in the field. 2) Impoving the backfill soil of caisson educes the vetical settlement at the toe of the wall by ove 200% while the hoizontal displacement is educed by ove 350%. 3) Inceasing the width of the wall also educed the hoizontal displacement of the wall (although not as much as inceasing the wall width), while the vetical settlement inceased slightly. Finally, Effective stess analysis is poweful tool can descibe the seismic esponse of pot stuctues including liquefaction failue modes. AKNOWLEDGEMNT The authos gatefully acknowledge the technical suppot of FORUM 8 fo the softwae used in this wok. The fist autho wishes to thank M. Hiokazu NAKAMURA fo the fuitful discussions thoughout the eseach. REFRENCES CASTRO, G. Liquefaction of sands. Ph.D. Havad Univesity, Cambidge, Massachusetts, 1969 CHEN, C. & HWANG, G Peliminay Analysis fo Quay wall Movement in Taichung Habou Duing The Septembe 21, 1999,Chi-Chi Eathquake. Eathquake Engineeing and Engineeing Seismology, 2, 43-54, 1969 CUBRINOVSKI, M. & ISHIHARA, K. Coelation between penetation esistance and elative density of sandy soil. In: 15th Intenational confeence on soil mechanics and geotechnical engineeing, Istanbul, Tukey. pp , 2001 DAKOULAS, P. & GAZETAS, G. Seismic effective-stess analysis of cassion quay walls: Application to Kobe. Soils and Foundations, 45, , 2005 ELSHARNOBY, B., ELKAMHAWY, H., ELNAGGAR,, E.& ALYAMI, M. Enhancing load capacity pefomance of Habo bethes. In: The 20th Intenational Pot Confeence, Alexandia, Egypt. pp.session 4, 1-11, 2004 FORUM8 CO., LTD. Dynamic effective stess analysis fo gound (UWLC), Instuction manual fo ve , HAYASHI, S., KUBO, K. & NAKASE, A Damage to habou stuctues by the Nigata eathquake. Soils and Foundations, 6, , 2005 IAI, S. Seismic analysis and pefomance of etaining stuctues. In: Poceedings of the 1998 Confeence on Geotechnical Eathquake Engineeing and Soil Dynamics III. Pat 2 (of 2), Aug , ASCE, Reston, VA, USA, Seattle, WA, USA. 2, pp , 1998 IAI, S. & SUGANO, T. shaking table testing on seismic pefomance of gavity quay walls. In: 12 WCEE,2000 IAI, S., ICHII, K., LIU, H. & MORITA, T. Effective stess analysis of pot stuctues. Special issue of soils and foundations, , 1998 ICHII, K. Application of isk density analysis fo seismic design: A gavity-type quay wall case. In: Fouth Intenational Confeence on Compute Simulation in Risk Analysis and Hazad Mitigation, RISK ANALYSIS IV, Sep , WIT Pess, Southampton, SO40 7AA, United Kingdom, Rhodes, Geece. 9, pp.41-50, 2004 ICHII, K.. Pesonal contact, 2006 ICHII, K., IAI, S. & MORITA, T. Pefomance of the quay wall with high seismic esistance. Jounal of Computing in Civil Engineeing,2000 IKUO, T., GHALANDARZADEH, A., SUNDARRAJ, K. & VARGAS-MONGE, W Dynamic failues of subsoils obseved in watefont aeas. Special Issue of Soils and Foundations, 1, INAGAKI, H., IAI, S., SUGANO, T., YAMAZAKI, H. & INATOMI, T. Pefomance of cassion type quay walls at Kope Pot. Special issue of soils and foundations, , 1996

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