Journal of JSCE, Vol. 2, 116-135, 2014

THE DYNAMIC BEHAVIOR OF A STEEL PIPE SHEET PILE FOUNDATION IN A LIQUEFIED LAYER DURING AN EARTHQUAKE

Nguyen Thanh TRUNG1, Osamu KIYOMIYA2 and Makoto YOSHIDA3

1Member of JSCE, Doctoral Student, Dept. of Civil & Env. Eng., Waseda University (Okubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan) E-mail: [email protected] 2Member of JSCE, Professor, Dept. of Civil & Env. Eng., Waseda University (Okubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan) E-mail: [email protected] 3Member of JSCE, Penta-Ocean Construction Co. Ltd. (Nasushiobara, Shikuchou 1534-1 Tochigi 329-2746, Japan) E-mail: [email protected]

Various forms of damage to the bridge foundation structure in the revetment along riverbanks and sea coasts caused by liquefaction had been observed during past earthquakes. Several studies on liquefaction using physical model tests and numerical analysis have been conducted in recent years. However, few studies have investigated the seismic behavior of the foundation in a revetment with a slope. In strong earthquakes, the sloped ground is expected to be unstable, and lateral spreading of the ground may occur simultaneously with the loss of soil strength in the liquefaction layer. Moreover, in the seismic design specification (JRA-2002) of the bridge, the liquefaction verification of the foundation is stipulated for a flat ground but not for a sloped ground. Therefore, the effect of the lateral pressure of the liquefaction layer on the foundation in the revetment must be investigated further. This study aims to investigate the dynamic behavior of a steel pipe sheet pile (SPSP) foundation of a cable-stayed bridge and its effect on the per- formance of the superstructure in the revetment with a slope. A 1-G shaking table test with a scale of 1:60 was conducted on a flat model and a slope model of 15°. In addition, 2-D numerical modeling was applied in an effective stress analysis method that was used on a multi-spring model and cocktail glass model. The differences in the dynamic responses between the two models clearly illustrate the significant effect of the ground slope on the seismic behavior of the SPSP foundation and superstructure.

Key Words: SPSP foundation, liquefaction, shaking table test, effective stress analysis

1. INTRODUCTION insights regarding the basic mechanisms of soil-pile interaction in liquefied soil and their effect on the Various forms of damage to the pile and caisson performance of a superstructure during liquefaction foundation structures had been observed in areas of have been understood from field observations, liquefaction in past earthquakes1), 2). Some of these shaking model tests, and numerical analysis. How- were pile failures near the bottom of the liquefied ever, most of these studies were conducted on flat layer, whereas others were pile failures near the pile ground or ground with a mild slope line for a pile head. These failures were likely caused by the liq- foundation structure. Ramin et al.6) conducted a large uefaction that occurred due to a decrease in the soil shaking table test on the pile foundation near a grav- strength and lateral movement of the liquefied layer. ity-type quay with flat ground. Haeri et al.7) and Moreover, significant damage was observed at both Ramin et al.8) investigated the response of a group of the pile body and pile head in the sites located near or piles to liquefaction-induced lateral spreading by on the revetment with a sloped surface ground along large-scale shake testing using a sloped ground with riverbanks or sea coasts3), 4), 5). This damage was an angle of 5°. In addition, Tokida et al.9) conducted likely caused by the unstable ground during lique- tests on various sloped ground models at 5° angle and faction. In recent years, many important lessons and varying slope lengths. Miyajima et al.10) performed a

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Tower of Cable Stayed Bridge Steel Pipe Sheet Pile Foundation

11000 (SPSP Foundation)

unit: mm

52000 SPSP foundation

A A 95500

36456

5500 (A-A)

D1500xt25 43500

12670 n=165 piles

29469 12060

15000 36456 Fig.1 Tower of Cable-stayed Bridge. shaking table test and determined that the pile re- the liquefied ground and bridge foundation during sponse depends on the sloping surface of the ground, vibration. The eigen value analysis technique was ranging from 2° to 6°. Tokimatsu et al.11), 12) studied used to investigate the dynamic characteristics of the seismic behavior of soil-pile-superstructure sys- models. Furthermore, the ESA technique was used to tem during soil liquefaction and liquefaction-induced consider the liquefaction of loose sand for both ground displacement by shaking table test. There- drained condition and undrained condition. fore, the researches simulated the dynamic behavior of pile foundation on the flat ground or with mild slope from 2° to 6°. However, the SPSP foundation, 2. SHAKING TABLE TEST a type of caisson foundation, works not only as a support structure but also as a retaining wall in the This study was conducted using the 1-G shaking revetment, that may not have been discussed before. table facility of the Penta-Ocean Construction Cor- Consequently, in this study, the behavior of SPSP poration in Japan. The shaking table test was de- foundation with a slope of 15° will be investigated. signed for both the sloped and flat models to inves- Moreover, in the current bridge seismic design tigate the difference in the dynamic response be- specification by JRA et al.13), the verification of the tween the models under liquefaction conditions, as liquefaction of the foundation structure is stipulated described in the following sections. for flat ground. The verification of liquefac- tion-induced lateral spreading is conducted for a (1) Prototype foundation that is less than 100 m from the water- The tower and superstructure of a cable-stayed front. The foundation in the revetment with a slope, bridge supported by the SPSP foundation on the whether affected by liquefaction-induced lateral ground was modeled in the shaking table test. The spreading or not, is not clearly mentioned, thus fur- outline of the tower is shown in Fig.1. The founda- ther investigations and studies are required. tion has 165 steel pipe piles with dimensions of In this study, a 1-G shaking table test with a 36.456 m length and 29.469 m width. Each steel pipe 1:60-scale model was designed for two test models of pile has a diameter of 150 cm and a thickness of 2.5 SPSP foundation to determine the behavior of the cm. bridge foundation during vibration. The first model To simplify the structure for constructing the was on a flat ground surface (denoted by the flat physical model, the superstructure-tower system of model), and the second model was on a 15°-sloped the prototype was modeled as a single degree of ground (denoted by the slope model). Additionally, a freedom system. The mass of the system includes the 2-D numerical finite element method using the ef- mass of the superstructure and tower at the top of the fective stress analysis (ESA) and eigen value analysis column. The natural frequency of the system (fL) was techniques was conducted to simulate the behavior of calculated as suggested by Yoneda14) as follows:

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Photo 1 1-G shaking table test on the flat model.

Table 1 Scaling factors of shaking model test. 100 %)

( 90 Yamagata sand

λ = prototype 80 (No. 6) Parameter Scale /model 70 Length λ 60 60 Density 1 1 50 Time λ0.75 21.56 40 Stress λ 60 30 Pore water pressure λ 60 20 Displacement λ1.5 464.76 bypercentweight Pass 10 Acceleration 1 1 0 Strain λ0.5 7.75 0.001 0.01 0.1 1 10 Water permeability Grain size (mm) λ0.75 21.56 coefficient Bending stiffness λ4.5 100,387,728 Fig. 2 Grain size distribution of Yamagata sand.

i height and a cross section in a tubular shape of 2.27 3EI /(h)3 cm diameter and 0.19 cm thickness. The foundation 1  f  0 (1) is a caisson made of acrylic materials with a dimen- L 2 m e sion of 49 cm width, 60.8 cm length, and 83.4 cm height. The cap at the top of the foundation is an where fL is natural frequency; me is the mass of the acrylic plate that is 60.8 cm long, 49 cm wide, and superstructure; h is the height from the bottom of the 9.8 cm thick. The footing of the pier is constructed of pier to the position of the lowest cable; α is the factor steel with dimensions of 26.6 cm length, 46.6 cm that depends on the ratio of stiffness between the width, and 18.5 cm thickness. tower and girder; and I is the area moment of inertia The ground in the models consists of a 48.8 cm of the tower. liquefiable sand layer with a relative density of 50% using Yamagata sand No. 6 (D50 = 0.3 mm) overlying (2) Test model and material properties a 74.3 cm non-liquefiable layer with a relative den- All material properties of the physical model and sity of 90%. The soil layers of the model ground were ground were scaled using a similitude law suggested constructed using the sand drop method. The sand by Iai15). Table 1 summarizes the scaling factors was gradually dropped into the vessel up to the water applied in this shaking model test. level step. However, the relative density of the Photo 1 shows a set-up of the flat model on the non-liquefiable layer was controlled by the amount shaking table. The test model includes the pier, su- of tamping and the measured weight of the sand perstructure, and foundation in the sand ground. The layer. The thickness of the sand layer for each natural frequency of the pier-superstructure system tamping period was 10 cm. of the model was determined by the dynamic char- The rubble layer consists of Grade 6 crushed stone acteristics of the single-degree-of-freedom system of with a particle size of 13-20 mm. The grain size dis- the prototype using a scale of 1:60. The pier in the tribution of the Yamagata sand used for the ground is model consists of four steel columns that are rigidly provided in Fig.2. The slope of the ground in the case fixed together by a steel plate at the top with a mass of the slope model was 15° in the longitudinal direc- of 60 kg. Each column has dimensions of 1.1 m tion.

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250 AH4 DH2 68 Laser Displacement transducer Steel plate Accelerometer B250 x L450 x t68 Pore water pressure gauge Strain gauge（component 1） (Superstructure) Tubular column (STK400) Strain gauge（component 3） 200 Unit (mm) 1100 φ27.2mm, t1.9mm Target

552 700 615 266 615 700 552 DV1 DV2 55 213 AH7 AH12 DH1 (Footing) AH17 Rubble layer AH20 W.L 185 55 AH6 AH11 50AH3 50 AH16 AH19 244 W2 W4 98 (Acrylic cap) 148 W6 W8 AH10 AH15 488 210 Liquefied layer 244 1500 AH5 AH9 AH14 AH18 932 SPSP 834 287 foundation 372 W1 W3 W5 W7 AH8 237 AH13 743 AH2 50 Non-liquefied layer 372 170 490 AH1 4000 Unit (mm)

250 T1-2 T1-4 T1-6 T1-c T1-11 T1-13 T1-15 446 Steel Pipe Pile Foundation (SPSP) 750 266 T2-6 T2-11 500 250 Rubble layer 200 T3-1 T3-2 T3-3 T3-4 T3-5 T3-6 T3-7 T3-10 T3-11 T3-12 T3-13 T3-14 T3-15 T3-16 608400 450466 1500 T3-8 T3-9 300 300 300 300 300 173 150 150 173 300 300 300 300 300 500 44 44 T4-6 T4-11 750 490 1755 446 T5-2 T5-4 T5-6 T5-c T5-11 T5-13 T5-15 250

4000 Fig.3 General view of the flat model and transducers arrangement.

250 AH4 DH2 68 Laser Displacement transducer Steel plate Accelerometer B250 x L450 x t68 Pore water pressure gauge (Superstructure) Strain gauge（component 1） Tubular column (STK400) Strain gauge（component 3） 200 Unit (mm) 1100 φ27.2mm, t1.9mm Target 1252 1205 1544 552 700 615 266 94 230 292 700 552 DV1 DV2 55 213 269 DH1 (Footing) AH14 Rubble layer AH17 W.L 185 55 50AH3 50 AH13 AH16 235 244 98 (Acrylic cap) 148 W6 W8 AH6 AH9 AH12 488 253 W2 W04 210 Liquefied layer 244 1500 AH5 AH8 AH11 AH15 932 SPSP 287 834 372 997 foundation W5 W7 W1 AH7 W03 237 AH10 743 AH2 50 Non-liquefied layer 372 170 490 AH1 4000 Unit (mm)

250 T1-2 T1-4 T1-6 T1-c T1-11 T1-13 T1-15 446 Steel Pipe Pile Foundation (SPSP) 750 266 T2-6 T2-11 Non-liquefied layer 500 250 Rubble layer 200 T3-1 T3-2 T3-3 T3-4 T3-5 T3-6 T3-7 T3-10 T3-11 T3-12 T3-13 T3-14 T3-15 T3-16 608 400 450466 1500 T3-8 T3-9 300 300 300 300 215 200 200 94 230 300 300 300 300 300 500 44 52 T4-6 T4-11 750 490 1755 446 T5-2 T5-4 T5-6 T5-c T5-11 T5-13 T5-15 250

4000 Fig.4 General view of the slope model and transducers arrangement.

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60 The initial shear modulus (G0) of the sand layer was calculated using the following equation: (Gal) 30 0 -30 2 (2) Time(s) G0  vs  -60

Acceleration 6.5 7 7.5 8 8.5 9 9.5 10 where G0 is the initial shear modulus, ρ is the mass Fig.5 Acceleration wave input of 50 Gal at the base. density of sand, and s is the shear wave velocity of the soil layer. The pulse method was used to determine the shear 3. NUMERICAL ANALYSIS velocity of the sand.

An impulsive sin wave (amplitude: 100 Gal, pe- The 2-D finite element method model was adopted riod: 0.0176 s) was inputted at the bottom of the to simulate the behavior of foundation and shaking table by the electrohydraulic vibration ma- soil-structure interaction. First, the eigen value chine. The acceleration responses at two locations, analysis was used to determine the dynamic charac- one at the top of the soil layer and another at the teristics of the two models before liquefaction in this bottom of the layer, were recorded in time-history analysis. Eigen value analysis was conducted by the waves to capture the difference in the peak time TDAP III program (developed by Taisei Corpora- between the two locations. Then, the shear wave tion, Tokyo, Japan). Second, the ESA technique was velocity (s) was calculated by the following equa- used both by the multi-spring and cocktail glass tion: models suggested by Iai16). The FLIP program (de- veloped by Port and Airport Research, Institute, H v  (3) Yokosuka, Japan) was used in this analysis. s T (1) Calculation model where s is the shear wave velocity, H is the height The boundary at the bottom of the model was fixed of the soil layer or distance between the two loca- in the vertical and horizontal directions, and the lat- tions, and T is the difference in the peak time be- eral boundary at the two sides was fixed in the hor- tween the two locations. izontal direction. The walls of the SPSP foundation, and the acrylic plate at the top of the pier were mod- (3) Instrument and deployment eled as elastic beam elements. The steel footing plate, The instruments and their placements are shown in acrylic cap of the piles, and partition walls for lon- Figs.3 and 4, respectively. The accelerometers and gitudinal bridge axis were modeled as plane strain pore water pressure transducers were arranged in the elements. The soil was modeled as plane strain ele- near- and far-field areas of the ground at various ments. Along the soil-wall interface, the walls and depths of the liquefaction and non-liquefaction lay- adjacent soil elements were connected by a few ers. The accelerometers were attached at the top and springs in the vertical and horizontal directions. The bottom of the pier. Two horizontal laser displace- horizontal springs were modeled as cut-off tension ment transducers were installed at the top and bottom springs. The thickness of the plane strain element of the pier, and two vertical displacement transducers was the same as the width of the test vessel. By were installed at the bottom of the pier. The strain modeling the pile in the 2-D calculation model, non- gauges were installed on opposite sides of the foun- linear spring elements between the pile and ground dation at different depths. The small, circular targets are usually adopted to consider soil movement were embedded in the ground surface to record their among piles: the 3-D effect. By modeling the steel movements before and after shaking. pipe sheet pile foundation, side wall friction is con- sidered by the spring element. This spring property is (4) Base excitation the same as that of the vertical spring at the front The models were shaken with a base harmonic wall. acceleration at a constant frequency of 10 Hz. The duration time was 2 s. The amplitude increased in- (2) Effective stress analysis (ESA) crementally from 50 to 300 Gal, and one of the input In the ESA, the nonlinear dynamic analysis was stages is shown in Fig.5. conducted by the time-history direct integration The frequency and wave numbers of input ground method. The boundary condition of pore water in motion was selected in the consideration of the ESA using the cocktail glass model was considered subduction zone earthquakes (level 2 earthquake in the undrained conditions (no seepage) at side walls motion) and the similarity law. and bottom wall of the test vessel. The numerical

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Fig.6 Numerical slope model in Effective Stress Analysis (ESA).

Simulation Experiment

) 10 2 5 0 -5

Shear stress (kN/m Shear -10 -1 -0.5 0 0.5 1 Shear strain (%)

Fig.7 Joint property of interface element between soil and the Fig.8 Stress-strain curves from liquefaction parameters. foundation.

Estimation of PWP during time history analysis Migration analysis

Pn+1 Pn+1 Pn

Pn Pn-1

n (step) n+1 n-1 n-1 n (step) n+1 Pore water pressure( an undrained condition) Pore water pressure( a drained condition)

Fig.9 Multi-spring model in effective stress analysis. Fig.10 Cocktail glass model in effective stress analysis. model in the analysis is shown in Fig.6. The influence of stress (or strain) history on cyclic Fig.7 shows the property of the joint element deformation-strength characteristics of soil in the between soil and foundation on two sides (front and liquefaction layer is shown in Fig.8. The figure back side of the foundation) and at the bottom of shows the relationship between stress and strain of foundation. The effect of side friction of the founda- liquefaction layer in both the indoor three-axial vi- tion is not considered because this friction force is bration test and ESA. small during liquefaction of the ambient loose sand. The soil was modeled as plane strain elements

121

Table 2 List of soil parameters. Liquefaction Non-liquefaction Rubble Symbol Parameter layer layer layer Wet unit weight ρ (t/m3) 1.96 2.05 1.37

Initial shear modulus Gma (kPa) 3,866 21,788 2,993 Parameters for Initial bulk modulus Kma( kPa ) 10,083 56,819 7,805 deformation Standard confining pressure σma'(kPa) 2.27 6.85 0.28 characteristics Poisson’s ratio ν 0.33 0.33 0.33

Internal friction angle f (degree) 36.55 42.80 41.60 Hysteretic damping ratio hmax 0.24 0.24 0.24

Phase transformation angle p(degree) 28 - - Overall cumulative dilatancy w1 8.2 - - Initial phase of cumulative dila- - Parameters for p 0.45 - tancy 1 Muti-Spring Final phase of cumulative dila- - model p 1.07 - tancy 2

Threshold limit for dilatancy c1 4.48 - - Ultimate limit of dilatancy S1 0.005 - - Reduction factor of bulk modulus - r 0.5 - for liquefaction analysis K Power index of bulk modulus for - l 2 - liquefaction analysis K Parameter controlling dilative and - r 0.5 - contractive components d Parameter controlling contractive - rc 2 - Parameters for component d Cocktail glass Parameter controlling initial phase - q 1 - model of contractive component 1 Parameter controlling final phase - q 1 - of contractive component 2 cm Limit of contractive component  d 0.5 - - Small positive number to avoid - S 0.005 - zero confining pressure 1 Parameter controlling elastic range - c 4.48 - for contractive component 1 using two liquefaction models of the loose sand. development and dissipation as follows: The first model is called a multi-spring model and is shown in Fig.9. The multi-spring model is a c d  d   d   d (4) strain-space multiple-mechanism model. This model considers the effect of the rotation of the principal where  is the volumetric strain;  is the contrac- stress axes on the cyclic behavior of the sand. The tive component; and  is the dilative component. effect results in the rise of pore water pressure under Ozutsumi18) presented the migration of water ob- the undrained conditions. As shown in this figure, tained by the multi-dimension equation of consoli- pore water pressure increases by calculation steps. dation by Biot: The second model is a cocktail glass model improved from a strain-space multiple-mechanism model in the 17)  i,i   h  drained condition suggested by Iai et al. , as shown   (5) k( )hi i   Sr  C    0 in Fig.10. Migration analysis was carried out at every  t   t  calculation steps and pore water pressure decreased. There are two main assumptions in this model. where ( ) is the coefficient of permeability;  is First, the volumetric strain is decomposed in a dila- the pressure head;  Sr  is the relative water tive component and contractive component, as de- C   n     termined in Eq.(4). The dilative component affects content; n is porosity; S is the degree of saturation; h the dissipation of pore water pressure in the steady r is hydraulic gradient; is displacement. k is state and the horizontal displacement response. The determined by the sand size and the void ratio in the second is a relationship between relative velocity and test vessel. coefficient of permeability determined in Eq.(6). The coefficient of permeability (k) suggested by This assumption influences the rate of pore water Chapuis and Aubertin 19) for sand used in the cocktail

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(a) Flat model (b) Slope model

Fig.11 Fundamental frequencies of the flat and slope models in initial state.

Flat Model-Multi-spring model Slope Model-Multi-spring model Flat Model-Experiment Slope Model-Experiment Flat Model-Cocktail glass model Slope Model-Cocktail glass model 1.0 1.0

W4

W4

0.5 0.5 EPWP EPWP ratio EPWP EPWP ratio 0.0 0.0 1.0 1.0

W8 W8

0.5 0.5 EPWP EPWP ratio

EPWP EPWP ratio Time(s) Time(s 0.0 0.0 ) 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 Fig.12 Time history of EPWP ratio at W4 and W8 in the flat Fig.13 Time history of EPWP ratio at W4 and W8 in the slope model under 300 Gal. model under 300 Gal. glass model as follows: Table 3 Result of the eigen value analysis.

3 g e (6) Flat model Slope model k  C 2 2   S D (1 e) Mode Mode Mode w w R Frequency Frequency No damping damping (Hz) (Hz) (%) (%) where k is the coefficient of permeability; C is a 1 5.97 3.21 5.86 3.21 constant; μw is the dynamic viscosity of water; ρw is 2 16.84 9.63 16.56 9.56 the density of water; DR is the specific weight of sand; S is the specific surface; and e is the void ratio. The liquefaction parameters of the soil layers for 4. RESULTS AND COMPARISONS the multi-spring and cocktail glass models were de- termined using the shear modulus and relative den- (1) Eigen value result sity of the sand, among other parameters, which are Table 3 summarizes the fundamental frequencies summarized in Table 2. The hydrodynamic pressure and mode damping of both models when liquefaction acting along the slope surface of the revetment was does not occur. Their modal mode of the first natural considered using fluid elements. The numerical in- frequency is presented in Fig.11. This table illus- tegration was performed using the Wilson- method trates that both the first and second frequencies in the with  = 1.4. A Rayleigh damping method with pa- slope model were lower than those in the flat model. rameters  = 0 and  = 0.002 was used to ensure the However, the difference between the frequencies in numerical stability of the analysis. In the analysis, the the two models was quite small. The mode damping self-weight analysis step was conducted first to cal- of the slope model was almost identical to that of the culate the initial stress and strain of the model before flat model. Therefore, there was a slight difference in the calculation of the dynamic analysis. the dynamic characteristics of the two models in the initial state when liquefaction did not occur.

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Fig.14 EPWP ratio distribution in the flat model under 300 Gal Fig.15 EPWP ratio distribution in the slope model under 300 Gal in the ESA multi-spring. in the ESA multi-spring.

W4-Experiment W8-Experiment W4-Experiment W8-Experiment W4-Multi spring W8-Multi spring W4-Multi spring W8-Multi spring W4-Cocktail glass W8-Cocktail glass W4-Cocktail glass W8-Cocktail glass 1 1

0.8 0.8

0.6 0.6

EPWP EPWP ratio 0.4 EPWP EPWP ratio 0.4 0.2 0.2 0 0 50 75 100 150 200 300 50 75 100 150 200 300 Input ground motion (Gal) Input ground motion (Gal)

EPWP ratio in the slope model from 50 to 300 Gal. Fig.16 EPWP ratio in the flat model from 50 to 300 Gal. Fig.17

W4-Multi-spring W4-Cocktail glass a) Excess pore water pressure of the surface layer W8-Multi spring W8-Cocktail glass W4-Experimnet W8-Experiment The time histories of the EPWP at points W4 in the 1 near field and W8 in the far field of the experiment

0.9 and ESA under the 300 Gal input ground motion are 0.8 shown in Figs.12 and 13 for the flat and slope mod- 0.7 els, respectively. The EPWP ratio did not exceed 0.8

flat model and perfect liquefaction did not occur at 300 Gal. The 0.6 results of the EPWP among the experiment, mul-

of the 0.5 ti-spring model, and cocktail glass model are fairly 0.4 different from each other. The liquefaction start time 0.3 was almost identical for both methods, whereas the 0.2 EPWP dissipation, maximum EPWP ratio, and vi- EPWP EPWP ratio 0.1 bration components differed considerably. The EPWP ratio gradually decreased after the vibration 0 0 0.2 0.4 0.6 0.8 1 stopped in the experiment; this phenomenon can be EPWP ratio of the slope model explained using the cocktail glass model. The EPWP ratio was almost the same between the experiment Fig.18 Comparison of EPWP ratio at W4 and W8 between the and the cocktail model after 12 s. However, the flat and the slope models. generation and dissipation of EPWP in the model (2) Comparison of the ground motion between the occurs very quickly during vibration time of 2 s. The effective stress analysis and the experiment cocktail glass model displayed a vibration compo- A comparison was conducted between the ex- nent of the EPWP. We assumed that the quick dis- periment and the ESA using the multi-spring model sipation of EPWP was due to the large value of co- (ESA-multi-spring) and the cocktail glass model efficient of permeability of the test sand and low (ESA cocktail glass). value of water viscosity. These items are limitations

124

Flat-Multi-Spring model Slope-Multi spring model Flat-Experiment Slope-Experiment

Flat-Cocktail glass model Slope-Cocktail glass model 600 600

AH8 (Gal)

(Gal)

400 300 AH7 200 0 0 -200 -300 -400 Acceleration Acceleration -600 -600

600 600 AH10 AH9 300 (Gal) (Gal)

300 0 0 -300 -300 -600 Acceleration -600 Acceleration -900

600 600

AH19 AH16 300 300 (Gal)

(Gal) 0 0 -300 -300 -600 Time(s) Time(s)

-600 Acceleration -900

Acceleration 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

Fig.19 Time history of acceleration at AH8, AH10 and AH19 in Fig.20 Time history of acceleration at AH7, AH9 and AH16 the flat model under 300 Gal. in the slope model under 300 Gal.

AH13 (AH16)-Spring W16(W19)-Cocktail ratio increased due to the increase in input ground AH13(AH16)-Cocktail AH16(AH19)-Spring motion in the multi-spring model. In the vibration, AH13 (AH16)-Experiment AH16(AH19)-Experiment test, the EPWP ratio increased to 0.7 even though the

input ground motion was 100 Gal. The EPWP ratio at 800 W4 given by the calculation was approximately 0.2. The sand of liquefied layer in the vessel may have been looser than expected at this point. 600 Fig.18 compares the EPWP at W4 and W8 be- flat model (Gal) model flat tween the slope and flat models obtained by the ex- 400 periment and ESA from 50 to 300 Gal. There are six red points in Fig.18, and their values gradually in- crease. The EPWP ratio of the slope model at W4 200 was 1.11.25 times higher than that of the flat model in both the experiment and ESA. At W8 the EPWP Acceleration of the of Acceleration 0 ratios of ESA using both the multi-spring and cock- 0 100 200 300 400 500 600 700 800 900 tail models were nearly identical between the two Acceleration of the slope model (Gal) models, but in the experiment, the ratios of the flat Fig.21 Comparison of acceleration at AH13, 16 in the flat model model were larger than those of the slope model. and AH16, 19 in the slope model. b) Acceleration of the surface layer Fig.19 presents the time histories of the horizontal of the 1-G vibration model test. We also assumed that accelerations at points AH8, AH10, and AH19 in the the vibration component was due to unstable calcu- flat model. In the non-liquefaction layer, the accel- lation of double integrations of the constitutive eration at AH8 of ESA corresponded well with that equation. of the experiment, and the acceleration did not ex- The EPWP ratio distribution of the ground under hibit any amplitude variations during the shaking 300 Gal in the ESA multi-spring is shown in Figs.14 period. Meanwhile, the acceleration at the near-field and 15 for the flat and the slope models, respectively. AH10 and far-field AH19 of the liquefaction layer The EPWP ratio reached approximately 1.0 at the varied significantly starting at 7.5 s, and this ampli- surface liquefied layer in both models after ap- tude gradually decreased between 7.5 and 10 s, as proximately 4 s. However, the EPWP was not uni- shown in Fig.19. form at the surface layer in the multi-spring model. The horizontal accelerations at points AH7, AH9, The EPWP ratios from the 50-300 Gal input and AH16 in the slope model are shown in Fig.20. ground motions are shown in Figs.16 and 17 for the These points are at the same position, corresponding flat and the slope models, respectively. The EPWP

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Scale factor of displacement 4:1

Target before shaking Target after shaking

Unit scale: 0 40 mm

Scale factor of displacement 4:1

Target before shaking Target after shaking

Unit scale: 0 40 mm

Fig.22 Measured displacement distribution of the ground surface movement in the slope model under 300 Gal.

Scale factor of displacement 4:1

Target before shaking Target after shaking

Unit scale: 0 40 mm

Scale factor of displacement 4:1

Target before shaking Target after shaking

Unit scale: 0 40 mm

Fig.23 Measured displacement distribution of the ground surface movement in the flat model under 300 Gal. to points AH8, AH10, and AH19 in the flat model. AH19 in the flat model. The difference in the accel- Similar to the acceleration behavior in the flat model, eration in the near field between AH13 in the slope the acceleration amplitude in the liquefaction layer at model and AH16 in the flat model was minimal in the points AH9 and AH16 decreased and did not appear 50-150 Gal cases in both the experiment and ESA. in the non-liquefaction layer at AH7. However, the acceleration ratio steadily approached However, Fig.20 illustrates that the amplitude of 2:1 in the 150-300 Gal cases. The acceleration at AH the acceleration toward the water at AH9 and AH16 13 in the flat model became approximately 1.5 times became larger compared to that of the acceleration that of the slope model in the experiment under 300 toward the land in the vibration test. The instability Gal. In the far field, the acceleration at AH19 in the of the slope ground generated the high acceleration in flat model was less than that at AH16 in the slope the direction of the water. However, the calculation model, approximately 1.5 times in both the experi- did not provide the same result as the test. Fig.21 ment and ESA. The ESA using multi-spring and presents a comparison of the horizontal accelerations cocktail glass models had the same trend in the ac- at AH13, AH16 in the slope model and at AH16, celeration development in the experiment.

126

40 T3-6 T3-6 15 T3-11 T3-11 30 T1-c 10 T5-c T1-c 20 Footing 5 T5-c 10 0 0 -5 -10 -10 Displacement (mm) Displacement Displacement (mm) Displacement 50 75 100 150 200 300 50 75 100 150 200 300 Input ground motion (Gal) Input ground motion (Gal)

Fig. 24 Measured residual displacement at T1-c, T3-6, Fig. 25 Measured residual displacement at T1-c, T3-6, T3-11, T3-11, T5-c and the footing in the slope model T5-c and the footing in the flat model from 50 to 300 from 50 to 300 Gal. Gal.

6.5 7.5 8.5 9.5 2 these cases. The foundation clearly retained the Time (s) 0 movement of soil on the back side and pushed the -2 soil forward on the front side. -4 Fig.23 presents the distribution of the measured -6 residual horizontal displacement under the 300 Gal -8 T3-12-Slope-Multi-spring case in the flat model. The figure illustrates that the T3-12-Slope-Cocktail -10 T3-12-Flat-Multi-spring displacement distribution on the back side of the

-12(mm) Verticaldisplacement T3-12-Flat-Cocktail foundation from T1-6 to T5-6 was nearly uniform. T3-12-Flat-Experiment However, the displacements of points from T2-11 to T3-12-Slope-Experiment T4-11 on the front of the foundation were larger than Fig.26 Vertical displacement on ground in the slope and flat those of T1-11 and T5-11 in the free field. Moreover, models under 300 Gal. the displacement on the right side was larger than that on the left side. The foundation vibration created a c) Displacement of the surface ground disturbed adjacent sand layer. Fig.22 displays the distribution of the measured Fig.25 presents the horizontal residual displace- residual horizontal displacement at the maximum ment values of points near the foundation in the input ground motion of 300 Gal in the slope model. 50-300 Gal cases for the flat model. The figure il- The figure illustrates that the movement of the slope lustrates that from 50 to 150 Gal, there was a slight ground was in the direction from T3-11 toward the difference in the displacement among points, in- land to T3-6 toward the water when liquefaction cluding points T3-6, T3-11, T1-c, and T5-c of the occurred. The displacement distribution from T1-6 to front, back, and two sides of the foundation, respec- T5-6 in front of the foundation was nearly uniform. tively. The movement of the ground was from T3-6 However, the displacement at T3-6 in front of the to T3-11 to the right side of the foundation. The foundation was slightly smaller than that of the other movement was in the opposite direction from 150 to points. The displacement of the points near the 300 Gal. foundation was less than that in the free field from Fig.26 presents the vertical displacement of the T1-11 to T5-11 behind the foundation. The residual free field near the foundation at T3-12. The dis- displacements at the front and back of the foundation placement of the multi-spring model was approxi- were smaller than those of other points. A lateral mately four times less than that of the cocktail glass relative soil movement around the foundation oc- models. The ESA using the cocktail glass model curred due to sand liquefaction in the slope model. corresponded more closely with the results of the The foundation that was inserted into the experiment than did the ESA using the multi-spring non-liquefaction layer blocked the horizontal dis- model with regard to the vertical displacement. placement of the points in the free field. d) Acceleration of the superstructure The measured horizontal displacement value of Fig.27 presents the time histories of the horizontal the points near the foundation is shown in Fig.24. acceleration of the superstructure and pile cap of the The figure illustrates that in the 50-100 Gal cases, flat model under the 300 Gal input ground motion in there was a slight difference in the displacement both the experiment and the ESA. between points, including points T3-6, T3-11, T1-c, For the superstructure, the acceleration at AH4 of and T5-c near the front, back, and two sides of the the experiment was nearly identical to that of the foundation, respectively. However, the difference ESA in the multi-spring and was larger than that of became significantly larger in the 150-300 Gal cases. the cocktail model by approximately 1.5 times. The The displacement of the footing was the smallest in acceleration of the experiment was larger for the pile

127 Slope-Multi spring model Flat-Multi spring model Slope-Experiment Flat-Experiment Slope-Cocktail glass model Flat-Cocktail glass model

1,000 1,000 AH3 (Gal)

(Gal) 500 AH3 500 0 0 -500 -500 Acceleration -1,000 Acceleration -1,000 1,000

1,000 AH4 500 AH4 (Gal)

500 (Gal) 0 0 -500 -500 Time (s) Time(s) -1,000 -1,000 Acceleration Acceleration 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

Fig.27 Time history of horizontal acceleration response of Fig.28 Time history of horizontal acceleration response of superstructure and pile cap in the flat model under superstructure and pile cap in the slope model under 300 Gal. 300 Gal.

700 AH3-Experiment 700 AH3-Experiment AH4-Experiment 600 600 AH4-Experiment

AH3-Multi-spring AH3-Multi spring 500 AH4-Multi-spring 500 AH4-Multi spring AH3-Cocktail glass 400 400 AH3-Cocktail glass AH4-Cocktail glass AH4-Cocktail glass 300 300 200 200 100 100 Acceleration (Gal) Acceleration Acceleration (Gal) Acceleration 0 0 50 75 100 150 200 300 50 75 100 150 200 300 Input ground motion (Gal) Input ground motion (Gal)

Fig.29 Maximum horizontal acceleration of the super- Fig.30 Maximum horizontal acceleration of the superstruc- structure AH4 and pile cap AH3 in the flat model ture at AH4 and pile cap at AH3 in slope model from from 50 to 300 Gal. 50 to 300 Gal.

AH4-Experiment 300 Gal input ground motion in the slope model. The 800 AH3-Experimnet AH3-Multi spring accelerations of the superstructure and pile cap of the 700 AH4-Multi spring experiment were larger than those of the ESA from AH3-Cocktail glass 600 AH4-Cocktail glass 9% to 21%. Fig.30 illustrates that the accelerations of the superstructure and pile cap display a similar trend 500 in both the experiment and the ESA. The difference flat model (Gal) model flat 400 in the maximum acceleration amplitude between the multi-spring and cocktail models was quite little. 300 Fig.31 presents a comparison of the maximum 200 horizontal accelerations of the superstructure and 100 pile cap in the experiment and ESA under the 50-300

Acceleration of the of Acceleration Gal input ground motion in both models. The accel- 0 erations are nearly identical between the flat and 0 100 200 300 400 500 600 700 800 slope models. The difference in acceleration was Acceleration of the slope model (Gal) minimal in the 50-100 Gal cases but a little larger in Fig.31 Comparison of acceleration at AH3 and AH4 between the 100-300 Gal cases. the flat and slope models. e) Displacement of the superstructure Fig.32 presents the time histories of the horizontal cap at AH3, with a difference between the values of and vertical displacements of the pile cap and super- 9%-12%. Additionally, Fig.29 illustrates that the structure in the flat model in both the experiment and acceleration development of AH4 and AH3 from 50 the ESA. The displacements at DH1 and DH2 in the to 300 Gal in the vibration test was in good agree- experiment were larger than those in the ESA. The ment with that of the ESA. displacements in the ESA cocktail glass model were Fig.28 presents the time histories of the horizontal considerably smaller than the displacements in other acceleration of the superstructure and pile cap for the cases.

128

Flat-Multi-spring model Slope-Multi-spring model Flat-Experiment Slope-Experiment Flat-Cocktail glass model Slope-Cocktail glass model 2.0 2.5

1.0 DH1 DH1

(mm) 0 0.0 -1.0 -2.5 Disp. -2.0 Disp. (mm) -3.0 -5 6.0

3.0 DH2

DH2 1.0 2.0 -1.0 -2.0

Disp. (mm) -3.0 -6.0 Disp. (mm) -5.0 -10.0 0.3 0.3

0.2 DV1 DV1 0.1 0.1 0.0 -0.1 -0.1 Disp. (mm) -0.2 Disp. (mm) -0.3 -0.3 0.30 0.2 DV2 DV2

0.15 0.0

0.00 -0.2 -0.4 Disp. (mm)

-0.15

Disp. (mm) -0.6 Time (s) Time (s) -0.30 -0.8 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

Fig.32 Horizontal and vertical displacement response of super- Fig.33 Horizontal and vertical response of superstructure and pile structure and pile cap in the flat model under 300 Gal. cap in the slope model under 300 Gal.

8 DH1-Experiment DH2-Experiment 1.4 DH1-Experiment DH1-Multi-spring DH2-Multi-spring 1.2 DH2-Experiment Allowable disp.-JRA DH1-Cocktail glass DH1-Multi-spring 6 1 DH2-Cocktail glass DH2-Multi-spring 0.8 DH1-Cocktail glass 4 0.6 DH2-Cocktail glass 0.4 2 0.2 Displacement (mm) Displacement 0 0

50 75 100 150 200 300 (mm) displacementResidual 50 75 100 150 200 300 Input ground motion (Gal) Input ground motion (Gal)

Fig.34 Maximum horizontal displacement of the superstructure Fig.35 Residual horizontal displacement of the superstructure DH2 and pile cap DH1 in the flat model from 50 to 300 DH2 and pile cap DH1 in the flat model from 50 to 300 Gal. Gal.

8 DH1-Experiment DH2-Experiment 7 DH1-Experiment 7 DH1-Multi spring DH2-Multi spring 6 DH2-Experiment Allowable disp.-JRA DH1-Cocktail glass 6 DH2-Cocktail glass 5 DH1-Multi spring 5 DH2-Multi spring 4 DH1-Cocktail glass 4 3 DH2-Cocktail glass 3

isplacement (mm) isplacement 2 d

2 1 1 Displacement (mm) Displacement 0 0 50 75 100 150 200 300 50 75 100 150 200 300 Residual Input ground motion (Gal) Input ground motion (Gal) Fig.36 Maximum horizontal displacement of the superstructure Fig.37 Residual horizontal displacement of the superstructure DH2 and pile cap DH1 in slope model from 50 to 300 DH2 and pile cap DH1 in the slope model from 50 to 300 Gal. Gal.

129

7 DH2-Experiment DV1-Experiment DH1-Experimnet DV1-Multi spring

6 DH1-Multi spring 0.3 DV2-Experiment DH2-Multi spring DV2-Multi spring 5 DH1-Cocktail glass DV1-Cocktail glass DH2-Cocktail glass DV2-Cocktail glass 4 0.2 flat model (mm) model flat 3 of the 2 0.1

1 Vertical displacement (mm) Verticaldisplacement 0 0

Displacement 50 75 100 150 200 300 0 1 2 3 4 5 6 7 Displacement of the slope model (mm) Input ground motion (Gal)

Fig.38 Comparison of maximum horizontal displacement at Fig.39 Maximum vertical displacement of the pile cap at DV1 DH1 and DH2 between the flat and slope models. and DV2 in the flat model from 50 to 300 Gal.

A residual displacement was observed in the ex- 300 Gal in the slope model are shown in Figs.36 and periment. However, a small residual displacement 37, respectively. Compared with the allowable dis- was calculated by the ESA. The vertical displace- placement of the pile cap, the maximum displace- ment at DV1 and DV2 in the 300 Gal case in the ment at the pile cap was approximately 0.7 times less experiment was approximately 1.5 times less than than that in the experiment, 0.4 times less than that in that in the ESA multi-spring and the displacements in the ESA multi-spring, and 0.15 times for ESA the ESA cocktail glass were smallest. The maximum cocktail-glass. The maximum horizontal displace- and residual displacements during shaking from 50 to ment at the pile cap satisfied the allowable design 300 Gal are shown in Figs.34 and 35, respectively. value. Moreover, from 50 to 150 Gal there was a There was a remarkable agreement between the ex- good agreement in the maximum and residual dis- periment and ESA multi-spring for the maximum and placement between the experiment and ESA mul- residual displacement between 50 to 150 Gals; ti-spring; however, in the 300 Gal case, the dis- however, the displacements in the ESA multi-spring placements in both the ESA multi-spring and cocktail were considerably less than those in the experiment glass was much less than that in the experiment. for the 150-300 Gal cases. Based on JRA-2002, the Fig.38 illustrates that when the range of the allowable displacement of 4.9 mm for the top of the maximum displacement is 0-1 cm in the 50-100 Gal foundation was calculated by multiplying the width cases, the difference in the displacement of the su- of the foundation by 1%. Thus, when liquefaction perstructure and pile cap between the flat and the occurred, the maximum horizontal displacements of slope models was minimal, and their ratio was ap- the pile cap under the 300 Gal input ground motion proximately 1:1. The range of the displacement in- was approximately 0.35 times less than the allowable creased for the 100-300 Gal cases, and the difference displacement for the experiment, and 0.2 times less progressively increased; the displacement ratio ap- than that for the ESA multi-spring. Moreover, the proached 1:2, indicating that the displacement of the maximum displacements in the ESA cocktail glass slope model became approximately twice that of the were approximately 2 times less than those in the flat model in this experiment. The ESA had the same experiment. The residual displacements were very trend with the vibration test. However, the differ- small and not significant during shaking. ences in displacement between the two models were Fig.33 presents the time histories of the horizontal smaller. Fig.39 presents the maximum vertical dis- and vertical displacements at the pile cap and super- placements in the flat model during shaking under structure in the slope model under 300 Gal. The re- the 50-300 Gal input ground motion. There was a sidual displacement calculated in the ESA and the remarkable agreement between the experiment and difference in the maximum displacement between ESA multi-spring. Moreover, there was a slight dif- the ESA and experiment were rather large. The dis- ference in the displacement value between DV1 and placement of DV1 exhibited a downward trend and DV2 in both the experiment and ESA multi-spring. that of DV2 exhibited an upward trend. This result of The settlement of the foundation in the flat model vertical displacement indicates that the foundation was almost even. The displacements in the ESA rotated and inclined toward the left. The maximum cocktail glass were much smaller than those of other and residual displacements during shaking from 50 to cases.

130

0.8 DV1-Experiment 0.3 Slope-Experiment DV1-Multi spring Flat-Experiment

0.6 DV2-Experiment Slope-Mutil spring DV2-Multi spring Flat-Mutil spring

(%) 0.2 DV1-Cocktail glass Slope-Cocktail glass 0.4 DV2-Cocktail glass Flat-Cocktail glass 0.1 0.2 Inclination 0 0 Vertical displacement (mm) Verticaldisplacement 50 75 100 150 200 300 50 75 100 150 200 300 Input ground motion (Gal) Input ground motion (Gal) Fig.40 Maximum vertical displacement of the pile cap at Fig.41 Comparison of the inclination of foundation between DV1 and DV2 in the slope model from 50 to 300 Gal. the flat and slope models from 50 to 300 Gal.

3 8 DH2 Unit: mm DH2 Unit: mm 2 6 1 Flat model Slope model DH1 0 300 Gal 4 300 Gal -3 -2 -1 0 1 200 Gal 200 Gal -1 100 Gal 2 100 Gal -2 0 DH1 -3 -2 0 2 4

-4 -2 Fig.42 Relation of displacement time history between DH2 Fig.43 Relation of displacement time history between DH2 and DH1 in the flat model of experiment. and DH1 in the slope model of experiment.

800 AH3 Slope model tion model occurred in the slope. The inclination of (Gal) the foundation was determined by the following 600 300 Gal 200 Gal equation: 400 100 gal DV2  DV1 200 DH1   100 (7) (mm) L 0 -1 0 1 2 3 4 -200 where α is the inclination of the foundation (%); DV1 -400 and DV2 are the residual values of vertical dis- placements at the top of the footing (mm); and L is -600 the distance between DV1 and DV2 (266 mm). Figs 39 and 40 show almost constant displace- Fig.44 Relation between acceleration at AH3 and displacement ments from 50 to 150 Gal. This is because in the at DH1 time histories in the slope model of experiment. lower input ground motion, the inclination of foun- dation was small, thus the maximum vertical dis- Fig.40 presents the maximum vertical displace- placement increased a little. However, in the higher ments in the slope model during shaking under the input motion, the inclination became larger, and the 50-300 Gal input ground motion. There was a slight residual displacement component increased more difference in the displacement value between DV1 significantly. The difference in maximum vertical and DV2 from the 50 to 200 Gal input ground motion displacement was also more significant. in both the experiment and ESA multi-spring. Fig.41 presents the inclination of the foundation in However, the difference between the values became the experiment and ESA under the 50-300 Gal input larger, and the displacement at DV2 was approxi- ground motion in both models. In both the experi- mately three times larger than that at DV1 for both ment and ESA multi-spring, the difference in the the experiment and ESA multi-spring in the 300 Gal inclination between the two models was minimal for case. The displacements in the ESA cocktail glass the 50-150 Gal cases. However, in the 300 Gal case, were also much smaller than other cases. Based on the inclination in the slope model was approximately Eq.(7), the inclination in this case was 0.23% in the 0.2 and 0.05 times less than the allowable inclination experiment. The inclined settlement of the founda- (1%) for the experiment and ESA multi-spring, re-

131

Bending strain of a flat model (μ) Bending strain of a slope model (μ) 0 10 20 30 0 10 20 30 40 0 50 Gal 0 50 Gal 75 Gal 75 Gal

S4 200 S4 100 Gal 200 100 Gal 150 Gal S3 150 Gal (mm) S3 400 200 Gal (mm) 400 200 Gal 300 Gal 300 Gal 600 600 S2

Depth S2 Depth 800 S1 800 S1 1000 1000 Axial strain of a flat model (μ) Axial strain of a slope model (μ) 0 5 10 15 0 5 10 15 0 50 Gal 0 50 Gal S4 75 Gal S4 75 Gal

200 100 Gal 200 100 Gal 150 Gal S3 S3 150 Gal (mm)

(mm) 200 Gal 400 400 300 Gal 200 Gal 300 Gal 600 S2 600 S2 Depth Depth 800 800 S1 S1 1000 1000 Fig.45 Bending and axial strain in experiment in the flat model. Fig.46 Bending and axial strain in experiment in the slope model.

Bending strain of a flat model (μ) Bending strain of a slope model (μ) 0 10 20 30 0 10 20 30 40 0 50 Gal 0 50 Gal S4 75 Gal S4 75 Gal

200 100 Gal 200 100 Gal 150 Gal S3 150 Gal (mm) (mm) 400 S3 400 200 Gal 200 Gal 300 Gal 600 600 S2 300 Gal Depth Depth S2 800 800 S1 S1 1000 1000 Axial strain of a flat model (μ) Axial strain of a slope model (μ) 0 5 10 15 20 0 5 10 15 20 0 50 Gal 0 50 Gal 75 Gal S4 75 Gal S4

200 100 Gal 200 100 Gal 150 Gal S3 150 Gal S3

(mm) 400 200 Gal 400 (mm)

200 Gal 300 Gal 300 Gal 600 S2 600 Depth S2 Depth 800 800 S1 S1 1000 1000

Fig.47 Bending and axial strain in ESA in the flat model. Fig.48 Bending and axial strain in ESA in the slope model. spectively. While, in the flat model, the inclination layer was liquefied more significantly and frequency was approximately 0.11 times less than the allowable of the layer also reduced significantly; the hysteresis value for the experiment and 0.03 times less for the loop extended widely to the area where the super- ESA multi-spring. The inclinations in ESA cocktail structure and pile cap almost moved in the same glass were very small in both models. horizontal direction during liquefaction. Their dif- The comparison of horizontal displacement time ference became smaller. These were in agreement histories between DH1 and DH2 in the flat and slope with the results by Tokimatsu et al.11). In this vibra- models in the vibration test are shown in Figs.42 and tion test, higher second and third vibrational modes 43. It shows that in the case of 100 Gal, most of dis- were dominant in 100 Gal and the first vibrational placements at DH1 were much less than and out of mode was dominant during liquefaction phase with those at DH2. However, when the input Fig.44 shows the relationship between accelera- ground motion increased to 200 and 300 Gal, the soil tion at AH3 and displacement at DH1 in the slope

132 model. Amplitude of the acceleration wave form did not decrease even after liquefaction. The shape of the Axial-Multi spring loop was almost constant during vibration. Bending-Cocktail glass 30 Bending-Experiment f) Behavior of the foundation Axial-Experiment The maximum bending and axial strain distribu- Axial-Cocktail glass tion in the experiment along the foundation in both Bending-Multi spring the flat and slope models from 50 to 300 Gal are 20 flat model flat model shown in Figs.45 and 46, respectively. The bending strains dominated the axial strain when the input of a acceleration amplitude was less than 100 Gal. The strain distribution of the axial and bending strains was 10 uniform along the foundation depth. When liquefac- tion occurred, the strain increased at the bottom of Maximum Maximum the foundation rather than at the upper location. The strains of the ESA multi-spring are shown in Figs.47 and 48. Generally, Figs.45, 46, 47, and 48 0 0 10 20 30 illustrate that the bending strains in both the exper- Maximum strain of a slope model iment and ESA multi-spring reached a maximum value near the bottom of the pile foundation at S2 in Fig.49 Comparison of maximum strain along the front and both models. back sides between the flat and slope models.

Fig.50 Maximum shear strain distribution in the flat model Fig.51 Maximum shear strain distribution in the slope under 300 Gal. model under 300 Gal. Superstructure Superstructure UNIT SCALE: Displacement: 0 8 mm Resistance: 0 12 kPa/m

Liquefaction layer  

Non-liquefaction layer q1 q1 Note: - q1, q2: Lateral resistance( per q2 unit depth) q2 - q3 : Vertical resistance ( per unit depth) q3 q3 -  Rotation angle of foundation 300 Gal 100 Gal

Fig.52 The ground reaction stress distribution of the SPSP foundation in the slope model.

133

Fig.49 presents a comparison of the maximum The reaction stress of the bottom was nearly zero bending strain and axial strain of the pile foundation on the back side of the foundation, except for the area between the two models from 50 to 300 Gal in both at the rear of the bottom due to the rotation of the the experiment and the ESA. foundation and cut off tension in the 300 Gal case. The maximum bending strain of the flat model in The foundation resisted the movement due to the the experiment was almost larger than that of the unliquefied sand. slope model in the 50-150 Gal cases. However, when the liquefaction process was complete, the strain of the slope model became 1.5 times larger than that of 5. CONCLUSIONS the flat model in the 300 Gal case. For the ESA using both multi-spring and cocktail models from 50 to 200 A vibration test and numerical analysis on a steel Gal, the difference in the bending strain between the pipe sheet pile foundation were conducted on both two models was minimal, and in the case of 300 Gal, slope and flat models to investigate their dynamic the strain of the slope model was approximately 1.3 behavior on the SPSP foundation. The following times larger than that of the flat model. The result of conclusions can be drawn based on the results: the experiment also illustrates that the maximum 1) The horizontal response movement of the SPSP axial strain in the slope model was approximately 1.5 foundation increased due to the increase in the input times larger than that of the flat model. However, the acceleration in the flat and slope models in the vi- axial strain difference in the ESA between the two bration test. The lateral movement on the foundation models was small. became large when liquefaction occurred, and re- Moreover, ESA multi-spring had the same trend as sidual displacement at the top of foundation was that of the experiment; however, the strain in the observed for both models. The residual displacement slope model was slightly larger than that in the flat in the slope model was considerably larger than that model. in the flat model. g) Strain of the ground and reaction stress 2) In the slope model, the foundation moved down Fig.50 presents the maximum shear strain distri- the slope and inclined in the shaking table test. The bution of the surface layer using the ESA mul- movement of the slope at the foundation that was ti-spring. Large strain values were calculated in the inserted into the non-liquefaction layer was smaller area around the foundation in both the liquefaction than that of the free field. and non-liquefaction layers. The strains were also 3) The bending and axial strains along the foun- quite large in the far field. Moreover, the maximum dation axial were nearly uniform before the lique- strains in the 0.008-0.01 range in the liquefaction faction of sand occurred. When liquefaction oc- layer distribution are presented by the black dashed curred, the strains in the non-liquefaction layer be- line shown in Fig.50; the distribution had a sym- came larger compared to the strains in the liquefied metric pattern. layer. The reaction stress of the slope model was Fig.51 presents the maximum shear strains in the small in the liquefied layer. The reaction force at the area around the foundation and on the down- and front wall was small in the liquefied layer for the up-slope areas. The maximum strain distribution in slope model. However, the reaction at the back wall the 0.04-0.07 range in the liquefaction layer is pre- was large enough to move the foundation to the front sented by the black dashed line in Fig.51; however, direction. The foundation resisted the movement due the distribution had an asymmetric pattern. The strain to the non-liquefaction layer. of the soil elements on the front of the foundation 4) The effective stress analysis (ESA) has almost was larger than that on the back of the foundation. the same trend as the dynamic responses in the ex- Fig.52 presents the distribution of the reaction periment. The difference in dynamic response of the stresses along the foundation obtained by the ESA foundation, superstructure, and ground between the multi-spring in the slope model. The reaction stress flat and the slope models is minimal in the became small in the liquefied layer but large in the low-amplitude input ground motion, indicating that unliquefied layer after liquefaction in both the flat the effect of the ground slope is not significant. In and the slope models. cases of higher amplitude when liquefaction is ob- For the slope model, the reaction stress was small served, the effect of the ground slope becomes more at both the front wall and the back wall. Inversely, the significant, with the following trends: the slope reaction stress at the back wall was large even though causes an increase in the maximum and residual the sand was liquefied for the slope model. This re- displacements of the pile cap and superstructure and action stress at the back wall pushed the foundation a decrease in the horizontal acceleration. Further- to move forward and rotated around the tip of the more, the slope causes an increase in the inclination foundation. of the foundation and the maximum value of the

134 bending and axial strain in the foundation pile. 7) Haeri, S. M., Kavand, A., Rahmani, I. and Torabi, H.: Re- Therefore, the lateral movement of liquefaction layer sponse of a group of piles to liquefaction-induced lateral spreading by large scale shaking testing, Journal of Soil due to the slope may partially affect the foundation Dynamic and Earthquake Engineering, Vol. 38, pp.25-45, during liquefaction. 2012. 5) The ESA using the multi-spring model can ex- 8) Ramin , M., Sesove, V. and Towhata, I.: Shaking model test on behavior of group piles undergoing lateral follow of plain the behavior of the foundation with regard to th maximum displacements, EPWP ratios, and bending liquefied subsoil, Proc. 14 World Conference on Earth- quake Engineering, Beijing, China, pp.12-17, 2008. strains during liquefaction. However, the calculated 9) Tokida, K., Matsumota, H. and Iwasaki, H.: Experimental values of the residual displacement, etc. did not dis- study on drag acting on piles in ground flowing by soil play a good agreement with the values observed in liquefaction, Proc. 4th US-Japan Workshop on Earthquake the vibration test. Resistant Design of Lifeline Facilities and Countermeas- 6) The cocktail glass model that considers the di- ures for Soil Liquefaction, NCEER report 92- 0019, SUNY, Buffalo, pp.511-523, 1992. lative component of the sand and seepage of water 10) Miyajima, M., Kitaura, M. and Ando, K.: Experiments on can be used to estimate the dissipation of the pore liquefaction-induced large ground deformation, Proceed- water pressure and vertical displacement. However, ings of the third Japan-U.S. workshop on earthquake re- the response displacement using the cocktail glass sistant design of lifeline facilities and countermeasures for soil liquefaction, Technical report NCEER, New York: model is smaller than that using the multi-spring SUNY, Vol. 1, pp. 269-278, 1991. model. The cocktail model could explain the dissi- 11) Tokimatsu, K., Suzuki, H. and Sato, M.: Influence of iner- pation of the pore water pressure in the vibration test; tial and Kinematic components on pile response during however, the calculation result had the vibration earthquakes, Proc. 11th International Conference on Soil component and was not stable. Methods for deter- Dynamics and Earthquake Engineering, pp.768-775, 2004. 12) Suzuki, H. and Tokimatsu, K.: Loading combinations for mining the parameters in the ESA using both the inertial and kinematic components in dynamic multi-spring model and the cocktail glass model to soil-pile-structure interaction during soil liquefaction, Proc. correlate the test results should be examined in future US-Japan Seminar on Seismic Disaster Mitigation in Urban studies. Area by Geotechnical Engineering, 2002. 13) JRA: Specifications for highway bridges, Japan Road As- sociation, Preliminary English Version, prepared by Public REFERENCES Works Research Institute (PWRI) and Civil Engineering 1) Miles, J. W. : On the generation of surface waves by shear Research Laboratory (CRL), Japan, November 2002. flows, J. 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