1

4th International Conference on Earthquake Engineering Taipei, Taiwan

October 12-13, 2006

Paper No. 031

STUDY AND ANALYSIS ON SHAKING TABLE TESTS OF DYNAMIC INTERACTION OF SOIL-STRUCTURE CONSIDERING SOIL

LIQUEFACTION

Peizhen LiTP

1PT, Xilin Lu TP

2PT and Yueqing Chen TP

3PT

ABSTRACT

Shaking table model tests and analysis on soil-structure interaction system with liquefaction soil are described in this paper. A flexible container is fabricated to minimize the box effect. Pile foundation is used in the test. A 12-story cast-in-place R.C. frame model are used as superstructure, and Shanghai soft soil is employed as model soil. In the tests, macro-phenomena of soil liquefaction and structure failure due to natural earthquake are reproduced well, such as sand boil, water to be emitted, foundation and structure sink. The failure status of scale model agrees with the actual failure phenomena of prototype. Some important findings from the present tests and calculation are as follows. Based on these tests, the issues of the development of excess pore water pressure in soft soil under simulated earthquake excitations are investigated. Excess pore water pressure in soil increases with the increasing of excitations. And variation of excess pore water pressure is related to the situation of measuring point, soil characteristics, the spectral characteristics of seismic excitation, and so on. The effective stress method of considering the soil as equivalent linear material in divided time intervals is introduced. And the method is realized in ANSYS program by using the ANSYS Parameter Design Language. Furthermore, the method of equivalent linearity is improved to the method of calculating nonlinearity step by step. Nonlinear model and computer simulation method of high-rise building considering liquefiable soil-structure interaction is established through comparison between shaking table test and theoretic analysis. The rule drawn from the calculation is agreed with those from the tests, though there have some difference between the calculation and tests in quantity. Key words: shaking table test; interaction; high-rise building; liquefaction; earthquake resistance

INTRODUCTION Dynamic test and analysis on soil-structure interaction (SSI) in ground of liquefaction soil is one highlight of soil-structure interaction study, also is recognized difficulty. Abroad scholars have got a lot of valuable conclusions on shaking table scale model test of soil-structure dynamic interaction in ground of liquefaction soil (Hatsukazu et al. 2000, Funahara et al. 2000, Yasuda et al. 2000, Takahiro et al. 2004). And domestic scholars have begun to study on this theme (Chen et al. 1995, Ling et al. 2006). With the development of model similitude theory and structural seismic testing technology,

TP

1PT Associate Professor, State Key Lab. for Disaster Reduction in Civil Eng., Tongji Univ., Shanghai, China.

TP

2PT Professor, State Key Lab. for Disaster Reduction in Civil Eng., Tongji Univ., Shanghai, China.

Email: lxlst@mail.tongji.edu.cn TP

3PT Professor, Wuhan Urban Construction Investment & Development Group Co. Ltd, Wuhan, China.

2

shaking table model test has played more and more important role on the research of SSI. However, this kind of test is rather difficult due to its complexity. This paper presents shaking table scale model tests of soil-structure interaction in ground of liquefaction soil and its comparative calculation. In the tests, macro-phenomena of soil liquefaction and structure failure due to natural earthquake are reproduced well, such as sand boil, water to be emitted, foundation and structure sink. The failure status of scale model agree with the actual failure phenomena of prototype. The effective stress method of considering the soil as equivalent linear material in divided time intervals is introduced. And the method is realized in ANSYS program by using the Ansys Parameter Design Language. Nonlinear model and computer simulation method of high-rise building considering liquefiable soil-structure interaction is established through comparison between shaking table test and theoretic analysis. The rule drawn from the calculation is agreed with those from the tests, though there have some difference between the calculation and tests in quantity.

SHAKING TABLE TESTS AND RESULTS Similitude Design of Models To study the seismic characteristics and response of the dynamic SSI system, the similitude design of test models is based on the following principles (Sabnis et al.1983, Lu et al. 1999). (1) The same similitude relation is applied to soil, foundation and superstructure. (2) Distortion of gravity is permitted. The method of adding additional weight is not adopted in present study in that it is almost impossible to be realized in soil and pile foundations. (3) Parameters of dynamic loads are controlled to meet the performance requirements of shaking table. (4) Requirements of construction and capacity of equipment must be accessible in laboratory. Consequently, non-gravity model with similitude rules controlled materials is adopted in present test. Similitude formulas and similitude factors of all physical quantities are induced from Bockingham π theorem. A 12-story cast-in-place frame is used as prototype superstructure, and Shanghai soft soil is selected as prototype soil. Thus, the prototype system can be regarded as a typical small high-rise building system of Shanghai. The scales of models are 1/10. The similitude factor of mass density is 1, and the similitude factors of elasticity modulus for both soil and structure are 1/4. Simulation of Soil Boundary Condition In the shaking table model test, the model soil should be held in a box of reasonable size. Due to wave reflection on the boundary and variation of vibration mode of the system, an error called ‘boundary effects’ will affect the test results. In order to reduce the boundary effect, a flexible container and proper constructional details are designed in the model test, and the ratio between the ground plane diameter D and the structural plane size d is taken as 5 by controlling the size of the structural plane. The cylindrical container is 3000 mm in diameter and its lateral rubber membrane is 5mm in thickness. Reinforcement loops of 4 mm in diameter spaced at 60 mm are used to strengthen the outside of the container in the tangential direction. Fig.1 shows the flexible container used in present test. Design and Fabrication of the Models Having taken the test purpose, test condition, model material, and construction technique into account, three layers of Shanghai soft soil are used for the soil model. The top layer consisted of silty clay, the

Fig.1 Sketch of flexible container used in present test

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middle layer is sandy silt and the bottom layer is medium sand. For the foundation of the superstructure, a 3×3 group-pile foundation is used. The superstructure is a 12-story reinforced concrete frame structure with a single bay and a single span. Foundation and soil are designed according to the similitude relation. The scaling factors is 1/10. The layout and reinforcement details of the models are shown in Fig.2.

The superstructure and foundation is made of micro-concrete and fine steel bar. Shanghai soft soil is used as model soil. Properties of all materials are measured by material tests before the shaking table test. Fig.3 is typical dd GG γ~0 and dD γ~ curves of Shanghai soft soil in this test, where

dd DGG γ,,, 0 is dynamic shear modulus, initial dynamic shear modulus, damping ratio and shear strain. Nonlinear properties of soil can be seen clearly in the figure. Arrangement of Measuring Points Accelerometers and strain gauges are used to measure the dynamic response of the superstructure, the foundation and the soil. Pore pressure gauges are embedded in soil to measure the change of pore pressure. Pressure gauges are used to measure the contact pressure between piles and the surrounding soil. The arrangement of measuring points of the test is shown in Fig.4. Test Loading Schedules Ground shaking is simulated as unidirectional (X direction of the shaking table), as well as bi-directional (X and Z directions of the shaking table) motions. The records selected for the study include a) the 1940 El Centro earthquake; b) a synthetically generated record (SHW2) that matches the Shanghai design spectrum; and one of the records from the 1995 Kobe earthquake (N-S and vertical direction from oceanic observatory station). Acceleration peak value, which is determined according to the corresponding epicentral intensity in the seismic code of China, and time interval, are adjusted to

H

h4h3

h2h1

2 21

1

33

振动方向

4 4

B6F1

F2

B6

B7

U1－1

B9

B8

G1

G2

U2－2

B4

E

E

B3

U4－4

L1

B10

B11

L1

U3－3

参数 1/10模型 H 1600 h1 3600 h2 100 h3 1200 h4 300 E 45 F1 30 F2 60 G1 50 G2 60 L1 600 B3 Φ2.11 B4 Φ0.9@15 B6 Φ2.11 B7 Φ0.9@20 B8 Φ2.11 B9 Φ0.9@15 B10 Φ0.9@15 B11 Φ0.9@15

Fig.2 Model layout and reinforcement detail

Fig.3 Typical dd GG γ~0 and dD γ~

curves of Shanghai soft soil

0.0

0.2

0.4

0.6

0.8

1.0

G-γd

γd

Gd /

G0 sandy silt

silty clay medium sand

1E-6 1E-5 1E-4 1E-3 0.01

D-γd

0

5

10

15

20

25

D(%

)

4

accord with the similitude relation.Seven levels of excitation are used in this study. From level 1 to level 6 the peak acceleration is, respectively, 0.093g, 0.266g, 0.399g, 0.532g, 0.665g, 0.798g and 0.931g. The time interval of the test is 0.00388s (Lu et al. 2002). Summary of Test Results The container and model fixed on the shaking table is shown in Fig.5. The summary of some important findings from SSI system tests is presented as follows. It should be noted that only parts of test evidences are described here due to the limitation of paper length. (1) The macro-phenomena of soil liquefaction and structure failure due to natural earthquake are reproduced well, such as sand boil (see Fig.6), water to be emitted, foundation and structure sink. The failure status of scale model agree with the actual failure phenomena of prototype. The settlement of the structure occurs during excitation. The incline of structure is little for SSI system with pile foundation. The degree of settlement and incline has close relation with characteristics of soil. No crack appears on the superstructure when excitation is slight, and the crack on the superstructure is slight even when the excitation is moderate. There have many horizontal bending cracks distributing along the pile. (2) Comparison of dynamic characteristics shows that the natural frequency of the SSI system under the liquefiable soil condition is lower than that of the structure on the fixed base by 20~60 percent, and the damping ratio of the system is 1.5~6 times of that of the structure material. Table 1 shows the frequency and damping ratio of some test results measured in test. (3) Due to the effect of SSI, the mode shape of the SSI system under the liquefiable soil condition is greatly different from that of the structure on the fixed base. There have rocking and

swing at the foundation.

Fig. 6 Sand boil in the test

Fig.4 Sketch of measuring point arrangement

SZDSD

P8E10 P7E9

E1

H4E2

E6E5

H5E3

H6 E8E7

P2S2 S5P1

H1S1

S3 H3

H2

P3E4 P4

P5S4 P6S6

S7

S10S9R2R1 A1

S8

AZ7

A2AZ2

AZ3A3

A4AZ4

AZ5A5

AZ6A6

A7

Pore Pressure Gauge

Shaking Direction

Accelerometer

Strain Gauge

Soil Pressure Gauge

X

Y

Z

Fig.5 Photograph of container and model

5

(4) It is commonly considered that field soil will magnify vibration transformed from bedrock. But it is observed in tests that liquefiable soil can filter and isolate vibration. When the vibration wave travels upwards, liquefiabel soil filters most of the high-frequency components, leaves behind the low-frequency components and minimizes the peak value of the acceleration.

Table 1 Frequency and damping ratio SSI System

No. Excitation Code

Freq. (Hz)

Damping Ratio (％)

Freq. of Structure on

Fixed Base(Hz)

1 1WN 2.643 9.816 3.273 10 10WN 2.139 12.586 3.147 16 16WN 1.636 16.616 2.895 22 22WN 1.384 15.964 2.644 28 28WN 1.258 17.198 2.267 34 34WN 1.133 21.770 2.014 40 40WN 1.133 18.636 1.762

(5) The whole system response of the acceleration amplitude is shown in Fig.7. In this figure, EL2 denotes the unidirectional excitation of El Centro wave, whose peak value of acceleration is 0.266g. The conclusion that may be drawn from the figure is as follows. The magnification or reduction of vibration transferred by soil is related to the soil characteristics and the magnitude of the excitation. The amplification factor of acceleration of the medium sand layer is bigger than 1.0, which demonstrates that vibration is transmitted effectively by the bottom medium sand. The intermediate layer of sandy silt attenuates and isolates the vibration, while the upper layer of clay magnifies the vibration. With the increasing of the input acceleration, the amplification factors of peak acceleration are reduced due to the nonlinearity of soil and increasing of the pore pressure. (6) The distribution of the strain amplitude along the pile shows that the strain is large at the top of the pile and small at its tip. This is in agreement with the crack distribution observed in the test. (see Fig.8) The distribution of the contact pressure on the soil-pile interface shows that the pressure is smaller at the middle of the pile and larger at both ends. With the increasing of the input acceleration, the contact pressure amplitude increases on the soil-pile interface. (see Fig.9)

Fig.8 Distribution of the strain amplitude on pile (excited by different Shanghai Artificial Wave)

1200

800

400

00 300 600 900 1200

桩身应变幅值(× 10 6－ )

SH1 SH2 SH3 SH4 SH5 SH6

测点与桩顶距离

(mm

)

Strain amplitude on pile (10 P

-6P)

Dep

th (m

m)

Fig.9 Distribution of the contact pressure amplitude on the pile-soil interface (excited by

different Shanghai Artificial Wave)

1200

1000

800

600

400

200

00 8 16 24 32 40

粘土

粉土

砂土

桩土接触压力幅值(kPa)

SH1 SH2 SH3 SH4 SH5 SH6 EL7

测点与桩顶距离

(mm

)

Contact pressure amplitude (kPa)

Dep

th (m

m)

Fig.7 Distribution of the amplification factors of the

acceleration amplitude (excited by different El Centro Wave)

0.0

0.8

1.6

2.4

3.2

4.0

4.8

0.0 0.5 1.0 1.5 2.0 2.5

砂土

粉土

粘土

土表面

EL1 EL2 EL3 EL4 EL5 EL6 EL7

加速度峰值放大系数

测点与底面距离

(m)

Hei

ght (

m)

Amplification factor

6

(7) The liquefaction phenomena of sandy silt under building footing are reproduced with shaking table tests on dynamic soil-structure interaction. Based on these tests, the issues of the development of excess pore water pressure in soft soil under simulated earthquake excitations are investigated. Excess pore water pressure in soil increases with the increasing of excitations. And variation of excess pore water presure is related to the situation of measuring point, soil characteristics, the spectral characteristics of seismic excitation, and so on. (See Fig.10~Fig.11) Excess pore water pressure does not always dissipate in short time immediately after the excitations, but it may keep on increasing too. (8) The response of the system under the excitation of Shanghai artificial wave is obviously larger than that under the excitation of El Centro wave and Kobe wave. Vertical excitations have little effect on the response of the dynamic interaction system of the soil-structure. Through the test, abundant experimental data are obtained, which can be used to verify the results of theoretical and analytical research, and improve or put forward better computational models and analytical methods. The present work provides the basis for further research.

TWO-DIMENSIONAL EFFECTIVE STRESS ANALYSIS ON THE TEST Constitutive Model of Soil In this paper, Drucker-Prager model is adopted as static constitutive model of sand. And the soil’s skeleton curve of Davidenkov model is applied as dynamic constitutive model of soil. As shown in Fig.12, the dynamic shear modulus and shear intensity of saturated soil declined under excitation of cycle load. The decline may be caused by increasing of pore water pressure and can be described by decreasing the GBmax B and τ Bmax B. Supposing the decreased maximum shear modulus and shear intensity as GBmt B andτ Bmt B, then:

( )21

*max 1 uGGmt −= (1)

)(( )vmt u*

max 1−= ττ (2) *u is the pore water pressure ratio. v is a constant and the value of v is usually taken as 3.5~5.0.

The hysteresis loop of soil D/DBmax B－γBd B is expressed as following empirical formula.

β)1(max mtG

GD

D−= (3)

DBmax B is the max damping ratio of soil. βis the shape factor of curve D/DBmax B－γBd B, and 1.0 is chosen as β for soft soil of Shanghai area. The value of DBmax B is taken as 0.30 for clay, 0.25 for sand soil, 0.25

Fig.10 Excess pore water pressure in different load case

0 5 10 15 20 25 30 35 400

2

4

6

8

10

12

14 H6 H3 H5 H2 H4 H1

超孔隙水压力

(kPa

)

工况序号

Exce

ss p

ore

wat

er p

ress

ure

(kPa

)

Load case

7

for silt. Pore Water Pressure Mode of Sand Soil The increment mode of pore water pressure of Shanghai sand soil could be expressed as follows:

( ) θπασ 210

* arcsin2)1(/ fs NNmuu −=′= (4)

θ

θπθα

σ21

10

* )()(1

)1(

ff

s

NN

NNNNmuu

−

∆−=

′∆

=∆ (5)

u∆ is pore water pressure induced by seismic vibration within the time of T∆ . 0σ ′ is initial average effective stress.

m is a constant from test, and the value is usually taken between 1.0 and 1.2.

Fig. 11 Time history of excess pore water pressure（excited by Shanghai Artificial Wave,the peak acceleration is 0.532g）

Fig. 12 Stress-strain curve under excitation of cyclic load

Initial hysteresis loop

Following hysteresis loop

Following skeleton curve

Initial skeleton curve

G Bmax B

G BmtB

τ

γ

8

sα is the level of static stress, and can be figured out by equation 7. N∆ is equivalent vibration times in every time interval, and can be figured out by equation 10.

N is total vibration times, and ∑∆= NN . θ is a constant, and Seed deems that 0.7 can be chosen as the value for most soil.

fN is the vibration times when liquefaction occur. And it can be calculated from equation 6.

0στ ′=−d

bfaN (6)

dτ is peak value of cycle shear stress . a and b are constant from test. Assuming the destroyed area is the maximum cycle shear area under plain strain state, initial static shear ratio αBs B and dynamic shear stress ratioαBd B can be drawn from following equations (Chen et al. 1995).

xycyxxys22 4)2(2 τσσστα −+′+′= (7)

yxxycyx

dxydd

σστσσσ

τ

στα

′−′+−+′+′=

′=

22

,

4)2(

2 (8)

xσ ′ , yσ ′ and xyτ is static normal effective stress and static shear stress on horizontal area,

respectively. ϕσ ′⋅′= ctgcc , c′ and ϕ′ is cohesive strength and internal friction angle, respectively. The value of c′ is zero for pure sand soil. dxy,τ is equivalent cycle peak value of seismic shear stress on horizontal area.

N∆ is equivalent vibration times in every time interval, and can be figured out as follows. First, the duration time dT and the effective vibration time eqN is looked up in Table 2. Then, the ratio

between energy of the seismic wave in time interval of iT∆ and the corresponding energy in the whole duration time dT is calculated:

∫∫−

=∆di

i

Tt

ti dttadttaTSA0

22 )()()(1

(9)

)( ieq TSANN ∆⋅=∆ (10) Table 2 The value of NBeq B and T Bd B

Earthquake Magnitude N BeqB（time） TBdB（second）

5.5～6 5 8 6.5 8 14 7 12 20

7.5 20 40 8 30 60

Dynamic Analysis Method with Effective Stress by Step by Step Iteration in Every Time Interval. The analysis method is shown in detail as follows. (1) The static effective stress xσ ′ , yσ ′ and xyτ are worked out through static analysis. (2) The whole period of the seismic wave is divided into some equal intervals. The initial dynamic shear modulus and the initial damping ratio are determined for each of element. And analysis using the above-mentioned dynamic constitutive model of sand soil is carried out by step by step iteration

9

method in the first time interval. (3) N∆ in this time interval and the accumulative value N are figured out. (4) *u∆ in this time interval and the accumulative value *u are figured out using equation 4 for each of element. (5) GBmt B and DBmt B considering the effect of the pore water pressure are figured out for each of element. And the calculated value is used as the initial value for the next time interval. (6) Using the restart function of ANSYS program, the dynamic shear modulus and damping ratio are changed into the value worked out in the step (5). And the calculation of next time interval is carried out without exiting the program. In this way, the continuity of result can be ensured. The above step (2)~(6) should be repeated for each of time interval until the seismic wave finishes. The magnitude of time interval has an effect on the calculation result. Reasonable magnitude of time interval relates with the site condition and the property of inputted seismic wave. Generally, the pore water pressure should have at least one whole cycle in each time interval. Two-dimensional Effective Stress Analysis on the Test The effective stress method of considering the soil as equivalent linear material in divided time intervals is introduced. And the method is realized in ANSYS program by using the ANSYS Parameter Design Language (ANSYS Inc. 2000). Furthermore, the method of equivalent linearity is improved to the method of calculating nonlinearity step by step. Nonlinear model and computer simulation method of high-rise building considering liquefiable soil-structure interaction is established through comparison between shaking table test and theoretic analysis. The constitutive model of soil, the equation of damping and some other parameters in the calculation can refer to corresponding item mentioned above. The soil and pile are simulated by two-dimensional plain strain element. The column and beam are simulated by two-dimensional beam element. Simple truncation boundary is used as the lateral boundary. The time interval is 0.194 second. The meshing of test model is shown in Fig.13. Selected acceleration time-histories of the computed and test results are given in Fig.14. SH4 denotes the excitation of Shanghai artifical wave, with a peak acceleration of 0.532g. Fig. 6 shows that the acceleration time-history curves in the soil match reasonably well. The increment curve on pore water pressure of soil is shown in Fig.15. Comparing the caculating curve with the test, we can draw the following conclusion. The rule drawn from the calculation is agreed with those from the tests, though there have some difference between the calculation and tests in quantity. Such as: The increment curve on pore water pressure of the point under the structure is higher than the point not under the structure in the same height. And the point H2 is the highest. From this comparison it can be said that the computational model is rational and appropriate for further studies of the SSI effects.

TCONCLUSIONS Shaking table scale model tests of soil-structure interaction in ground of liquefaction soil and its comparative calculation have been carried out. Issues drawn from the study are as follows. 1) In the tests, macro-phenomena of soil liquefaction and structure failure due to natural earthquake

Fig.13 Meshing of test model

10

are reproduced well, such as sand boil, water to be emitted, foundation and structure sink. The failure status of scale model agree with the actual failure phenomena of prototype.

2) The effective stress method of considering the soil as equivalent linear material in divided time

intervals is introduced. And the method is realized in ANSYS program by using the Ansys Parameter Design Language. Nonlinear model and computer simulation method of high-rise

0 4 8 12 16-0.6

-0.3

0.0

0.3

0.6

Acc

eler

atio

n (g

)

Time (s)

A1_Effective stress analysis A1_Test

0 4 8 12 16-0.8

-0.4

0.0

0.4

0.8

Acc

eler

atio

n (g

)

Time (s)

A3_Effective stress analysis A3_Test

0 4 8 12 16-1.2

-0.6

0.0

0.6

1.2

Acc

eler

atio

n (g

)

Time (s)

A7_Effective stress analysis A7_Test

0 4 8 12 16-1.2

-0.6

0.0

0.6

1.2

Acc

eler

atio

n (g

)

Time (s)

S2_Effective stress analysis S2_Test

0 4 8 12 16-0.6

-0.3

0.0

0.3

0.6

Acc

eler

atio

n (g

)

Time (s)

S3_Effective stress analysis S3_Test

0 4 8 12 16-0.6

-0.3

0.0

0.3

0.6

Acc

eler

atio

n (g

)

Time (s)

S4_Effective stress analysis S4_Test

0 4 8 12 16-1.2

-0.6

0.0

0.6

1.2

Acc

eler

atio

n (g

)

Time (s)

S5_Effective stress analysis S5_Test

0 4 8 12 16-1.6

-0.8

0.0

0.8

1.6

Acc

eler

atio

n (g

)

Time (s)

S6_Effective stress analysis S6_Test

0 4 8 12 16-1.2

-0.6

0.0

0.6

1.2

Acc

eler

atio

n (g

)

Time (s)

S7_Effective stress analysis S7_Test

0 4 8 12 16-0.8

-0.4

0.0

0.4

0.8

Acc

eler

atio

n (g

)

Time (s)

S8_Effective stress analysis S8_Test

Fig.14 Comparison between calculation and test result (under excitation of SH4)

11

building considering liquefiable soil-structure interaction is established through comparison between shaking table test and theoretic analysis. The rule drawn from the calculation is agreed with those from the tests, though there have some difference between the calculation and tests in quantity.

ACKNOWLEDGEMENT

This project is carried out under the sponsorship of the key project (No.50321803) and the project (No.50578124) of National Natural Science Foundation of China.

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Fig.15 The increasing curve of excess pore pressure

0 4 8 12 160

1

2

3

4

5

6

7

孔隙水压力 (kPa)

时间 (s)

H6

Time (s)

Exce

ss p

ore

pres

sure

(kPa

)

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1

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6

孔隙水压力 (kPa)

时间 (s)

H4

Time (s)

Exce

ss p

ore

pres

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孔隙水压力 (kPa)

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H1

Time (s)

Exce

ss p

ore

pres

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孔隙水压力 (kPa)

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Exce

ss p

ore

pres

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孔隙水压力 (kPa)

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Time (s)

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ss p

ore

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孔隙水压力 (kPa)

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H3

Time (s)

Exce

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ore

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(kPa

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12

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