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

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1 TP TP TP PT Associate PT Professor, PT Professor, PT an 4th International Conference on Earthquake Engineering Taipei, Taiwan October 1-13, 6 Paper No. 31 STUDY AND ANALYSIS ON SHAKING TABLE TESTS OF DYNAMIC INTERACTION OF SOIL-STRUCTURE CONSIDERING SOIL LIQUEFACTION 1 Peizhen LiTP PT, Xilin LuTP 3 Yueqing ChenTP PT ABSTRACT Shaking table moel tests an analysis on soil-structure interaction system with liquefaction soil are escribe in this paper. A flexible container is fabricate to minimize the box effect. Pile founation is use in the test. A 1-story cast-in-place R.C. frame moel are use as superstructure, an Shanghai soft soil is employe as moel soil. In the tests, macro-phenomena of soil liquefaction an structure failure ue to natural earthquake are reprouce well, such as san boil, water to be emitte, founation an structure sink. The failure status of scale moel agrees with the actual failure phenomena of prototype. Some important finings from the present tests an calculation are as follows. Base on these tests, the issues of the evelopment of excess pore water pressure in soft soil uner simulate earthquake excitations are investigate. Excess pore water pressure in soil increases with the increasing of excitations. An variation of excess pore water pressure is relate to the situation of measuring point, soil characteristics, the spectral characteristics of seismic excitation, an so on. The effective stress metho of consiering the soil as equivalent linear material in ivie time intervals is introuce. An the metho is realize in ANSYS program by using the ANSYS Parameter Design Language. Furthermore, the metho of equivalent linearity is improve to the metho of calculating nonlinearity step by step. Nonlinear moel an computer simulation metho of high-rise builing consiering liquefiable soil-structure interaction is establishe through comparison between shaking table test an theoretic analysis. The rule rawn from the calculation is agree with those from the tests, though there have some ifference between the calculation an tests in quantity. Key wors: shaking table test; interaction; high-rise builing; liquefaction; earthquake resistance INTRODUCTION Dynamic test an analysis on soil-structure interaction (SSI) in groun of liquefaction soil is one highlight of soil-structure interaction stuy, also is recognize ifficulty. Abroa scholars have got a lot of valuable conclusions on shaking table scale moel test of soil-structure ynamic interaction in groun of liquefaction soil (Hatsukazu et al., Funahara et al., Yasua et al., Takahiro et al. 4). An omestic scholars have begun to stuy on this theme (Chen et al. 1995, Ling et al. 6). With the evelopment of moel similitue theory an structural seismic testing technology, 1 Professor, State Key Lab. for Disaster Reuction in Civil Eng., Tongji Univ., Shanghai, China. State Key Lab. for Disaster Reuction in Civil Eng., Tongji Univ., Shanghai, China. lxlst@mail.tongji.eu.cn Wuhan Urban Construction Investment & Development Group Co. Lt, Wuhan, China. 3 1

2 shaking table moel test has playe more an more important role on the research of SSI. However, this kin of test is rather ifficult ue to its complexity. This paper presents shaking table scale moel tests of soil-structure interaction in groun of liquefaction soil an its comparative calculation. In the tests, macro-phenomena of soil liquefaction an structure failure ue to natural earthquake are reprouce well, such as san boil, water to be emitte, founation an structure sink. The failure status of scale moel agree with the actual failure phenomena of prototype. The effective stress metho of consiering the soil as equivalent linear material in ivie time intervals is introuce. An the metho is realize in ANSYS program by using the Ansys Parameter Design Language. Nonlinear moel an computer simulation metho of high-rise builing consiering liquefiable soil-structure interaction is establishe through comparison between shaking table test an theoretic analysis. The rule rawn from the calculation is agree with those from the tests, though there have some ifference between the calculation an tests in quantity. Similitue Design of Moels SHAKING TABLE TESTS AND RESULTS To stuy the seismic characteristics an response of the ynamic SSI system, the similitue esign of test moels is base on the following principles (Sabnis et al.1983, Lu et al. 1999). (1) The same similitue relation is applie to soil, founation an superstructure. () Distortion of gravity is permitte. The metho of aing aitional weight is not aopte in present stuy in that it is almost impossible to be realize in soil an pile founations. (3) Parameters of ynamic loas are controlle to meet the performance requirements of shaking table. (4) Requirements of construction an capacity of equipment must be accessible in laboratory. Consequently, non-gravity moel with similitue rules controlle materials is aopte in present test. Similitue formulas an similitue factors of all physical quantities are inuce from Bockingham theorem. A 1-story cast-in-place frame is use as prototype superstructure, an Shanghai soft soil is selecte as prototype soil. Thus, the prototype system can be regare as a typical small high-rise builing system of Shanghai. The scales of moels are 1/1. The similitue factor of mass ensity is 1, an the similitue factors of elasticity moulus for both soil an structure are 1/4. Simulation of Soil Bounary Conition In the shaking table moel test, the moel soil shoul be hel in a box of reasonable size. Due to wave reflection on the bounary an variation of vibration moe of the system, an error calle bounary effects will affect the test results. In orer to reuce the bounary effect, a flexible container an proper constructional etails are esigne in the moel test, an the ratio between the groun plane iameter D an the structural plane size is taken as 5 by controlling the size of the structural plane. The cylinrical container is 3 mm in iameter an its lateral rubber membrane is 5mm in thickness. Reinforcement loops of 4 mm in iameter space at 6 mm are use to strengthen the outsie of the container in the tangential irection. Fig.1 shows the flexible container use in present test. Design an Fabrication of the Moels Fig.1 Sketch of flexible container use in present test Having taken the test purpose, test conition, moel material, an construction technique into account, three layers of Shanghai soft soil are use for the soil moel. The top layer consiste of silty clay, the

3 mile layer is sany silt an the bottom layer is meium san. For the founation of the superstructure, a 33 group-pile founation is use. The superstructure is a 1-story reinforce concrete frame structure with a single bay an a single span. Founation an soil are esigne accoring to the similitue relation. The scaling factors is 1/1. The layout an reinforcement etails of the moels are shown in Fig.. H h3 h1 h4 h U11 U U44 U33 1/1 H 16 h1 36 h 1 h3 1 h4 3 E 45 F1 3 F 6 G1 5 G 6 L1 6 B3.11 B4.9@15 B6.11 B7.9@ B8.11 B9.9@15 B1.9@15 B11.9@15 The superstructure an founation is mae of micro-concrete an fine steel bar. Shanghai soft soil is use as moel soil. Properties of all materials are measure by material tests before the shaking table test. Fig.3 is typical G G ~ γ an D ~ γ curves of Shanghai soft soil in this test, where G, G, D, γ is ynamic shear moulus, initial ynamic shear moulus, amping ratio an shear Fig. Moel layout an reinforcement etail strain. Nonlinear properties of soil can be seen clearly in the figure. Arrangement of Measuring Points 1. 5 Accelerometers an strain gauges are use to measure the ynamic response of the superstructure, the founation an the soil. Pore pressure gauges are embee in soil to measure the change of pore pressure. Pressure gauges are use to measure the contact pressure between piles an the surrouning soil. The arrangement of measuring points of the test is shown in Fig.4. Test Loaing Scheules G / G E-6 1E-5 1E-4 1E-3 1 Fig.3 Typical G-γ sany silt silty clay meium san G D-γ γ G ~ γ D ~ γ an curves of Shanghai soft soil D(%) Groun shaking is simulate as uniirectional (X irection of the shaking table), as well as bi-irectional (X an Z irections of the shaking table) motions. The recors selecte for the stuy inclue a) the 194 El Centro earthquake; b) a synthetically generate recor (SHW) that matches the Shanghai esign spectrum; an one of the recors from the 1995 Kobe earthquake (N-S an vertical irection from oceanic observatory station). Acceleration peak value, which is etermine accoring to the corresponing epicentral intensity in the seismic coe of China, an time interval, are ajuste to 3

4 accor with the similitue relation.seven levels of excitation are use in this stuy. From level 1 to level 6 the peak acceleration is, respectively, 93g, 6g,.399g,.53g, 65g,.798g an.931g. The time interval of the test is 388s (Lu et al. ). A7 AZ7 A6 AZ6 A5 AZ5 Accelerometer Pore Pressure Gauge Strain Gauge Soil Pressure Gauge Summary of Test Results The container an moel fixe on the shaking table is shown in Fig.5. The summary of some important finings from SSI system tests is presente as follows. It shoul be note that only parts of test eviences are escribe here ue to the limitation of paper length. (1) The macro-phenomena of soil liquefaction an structure failure ue to natural earthquake are reprouce well, such as san boil (see Fig.6), water to be emitte, founation an structure sink. The failure status of scale moel agree with the actual failure phenomena of prototype. The settlement of the structure occurs uring excitation. The incline of structure is little for SSI system with pile founation. The egree of settlement an incline has close relation with characteristics of soil. No crack appears on the superstructure when excitation is slight, an the crack on the superstructure is slight even when the excitation is moerate. There have many horizontal bening cracks istributing along the pile. () Comparison of ynamic characteristics shows that the natural frequency of the SSI system uner the liquefiable soil conition is lower than that of the structure on the fixe base by ~6 percent, an the amping ratio of the system is 1.5~6 times of that of the structure material. Table 1 shows the frequency an amping ratio of some test results measure in test. (3) Due to the effect of SSI, the moe shape of the SSI system uner the liquefiable soil conition is greatly ifferent from that of the structure on the fixe base. There have rocking an H6 H5 H4 R1 E9 E1 P7 E7 E8 S4 P5 E5 E6 S3 H3 P3 E3 E4 H E1 S P1 E S1 H1 A4 AZ4 A3 AZ3 A AZ R A1 S9 P8 P6 P4 P S8 S7 S6 S5 S1 Fig.4 Sketch of measuring point arrangement Y Shaking Direction Z X SD SZD Fig. 6 swing at the founation. San boil in the test Fig.5 Photograph of container an moel 4

5 (4) It is commonly consiere that fiel soil will magnify vibration transforme from berock. But it is observe in tests that liquefiable soil can filter an isolate vibration. When the vibration wave travels upwars, liquefiabel soil filters most of the high-frequency components, leaves behin the low-frequency components an minimizes the peak value of the acceleration. Table 1 Frequency an amping ratio SSI System Freq. of No. Excitation Freq. Damping Structure on Coe (Hz) Ratio Fixe Base(Hz) () 1 1WN WN WN WN WN WN WN (5) The whole system response of the acceleration amplitue is shown in Fig.7. In this figure, EL enotes the uniirectional excitation of El Centro wave, whose peak value of acceleration is 6g. The conclusion that may be rawn from the figure is as follows. The magnification or reuction of vibration transferre by soil is relate to the soil characteristics an the magnitue of the excitation. The amplification factor of acceleration of the meium san layer is bigger than 1., which emonstrates that vibration is transmitte effectively by the bottom meium san. The intermeiate layer of sany silt attenuates an 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 reuce ue to the nonlinearity of soil an increasing of the pore pressure. (6) The istribution of the strain amplitue along the pile shows that the strain is large at the top of the pile an small at its tip. This is in agreement with the crack istribution observe in the test. (see Fig.8) The istribution of the contact pressure on the soil-pile interface shows that the pressure is smaller at the mile of the pile an larger at both ens. With the increasing of the input acceleration, the contact pressure amplitue increases on the soil-pile interface. (see Fig.9) (m) Height (m) Amplification factor EL1 EL EL3 EL4 EL5 EL6 EL7 Fig.7 Distribution of the amplification factors of the acceleration amplitue (excite by ifferent El Centro Wave) Depth (mm) (mm) Strain amplitue on pile (1P ( Fig.8 Distribution of the strain amplitue on pile (excite by ifferent Shanghai Artificial Wave) ) -6 P) SH1 SH SH3 SH4 SH5 SH6 (mm) Depth (mm) Contact pressure amplitue (kpa) (kpa) SH1 SH SH3 SH4 SH5 SH6 EL7 Fig.9 Distribution of the contact pressure amplitue on the pile-soil interface (excite by ifferent Shanghai Artificial Wave) 5

6 (7) The liquefaction phenomena of sany silt uner builing footing are reprouce with shaking table tests on ynamic soil-structure interaction. Base on these tests, the issues of the evelopment of excess pore water pressure in soft soil uner simulate earthquake excitations are investigate. Excess pore water pressure in soil increases with the increasing of excitations. An variation of excess pore water presure is relate to the situation of measuring point, soil characteristics, the spectral characteristics of seismic excitation, an so on. (See Fig.1~Fig.11) Excess pore water pressure oes not always issipate in short time immeiately after the excitations, but it may keep on increasing too. (8) The response of the system uner the excitation of Shanghai artificial wave is obviously larger than that uner the excitation of El Centro wave an Kobe wave. Vertical excitations have little effect on the response of the ynamic interaction system of the soil-structure. Through the test, abunant experimental ata are obtaine, which can be use to verify the results of theoretical an analytical research, an improve or put forwar better computational moels an analytical methos. The present work provies the basis for further research. Excess pore water pressure (kpa) (kpa) TWO-DIMENSIONAL EFFECTIVE STRESS ANALYSIS ON THE TEST Constitutive Moel of Soil Fig.1 H6 H5 H4 H3 H H1 Excess pore water pressure in ifferent loa case In this paper, Drucker-Prager moel is aopte as static constitutive moel of san. An the soil s skeleton curve of Davienkov moel is applie as ynamic constitutive moel of soil. As shown in Fig.1, the ynamic shear moulus an shear intensity of saturate soil ecline uner excitation of cycle loa. The ecline may be cause by increasing of pore water pressure an can be escribe by ecreasing the GBmaxB an BmaxB. Supposing the ecrease maximum shear moulus an shear intensity as GBmtB anbmtb, then: G mt ( 1 * ) v ) = G 1 u max (1) ( ( ) τ = τ max 1 () mt u * * u is the pore water pressure ratio. v is a constant an the value of v is usually taken as 3.5~5.. The hysteresis loop of soil D/DBmaxBBB is expresse as following empirical formula. D G β = (1 ) (3) D G max Loa case DBmaxB is the max amping ratio of soil. is the shape factor of curve D/DBmaxBBB, an 1. is chosen as for soft soil of Shanghai area. The value of DBmaxB is taken as.3 for clay,.5 for san soil,.5 mt 6

7 Fig. 11 Time history of excess pore water pressureexcite by Shanghai Artificial Wave, the peak acceleration is.53g τ GBmaxB GBmtB Initial hysteresis loop Following hysteresis loop Following skeleton curve γ Initial skeleton curve for silt. Fig. 1 Stress-strain curve uner excitation of cyclic loa Pore Water Pressure Moe of San Soil The increment moe of pore water pressure of Shanghai san soil coul be expresse as follows: * u = u / σ α π ( ) 1 θ = (1 m s ) arcsin N N f (4) * u (1 mα s ) N N 1 θ u = = ( ) (5) σ 1 θ πθn 1 ( N N ) N f u is pore water pressure inuce by seismic vibration within the time of T. σ is initial average effective stress. m is a constant from test, an the value is usually taken between 1. an 1.. f 7

8 an α s is the level of static stress, an can be figure out by equation 7. N is equivalent vibration times in every time interval, an can be figure out by equation 1. N is total vibration times, an N = N. θ is a constant, an See eems that.7 can be chosen as the value for most soil. N is the vibration times when liquefaction occur. An it can be calculate from equation 6. f b an = τ σ f (6) τ is peak value of cycle shear stress. a an b are constant from test. Assuming the estroye area is the maximum cycle shear area uner plain strain state, initial static shear ratio BsB ynamic shear stress ratiobb can be rawn from following equations (Chen et al. 1995). α τ α = = σ s = τ xy ( σ x + σ y + σ c ) 4τ xy (7) ( σ + σ + σ ) x y τ c xy, 4τ xy + σ σ σ x, σ y an τ xy is static normal effective stress an static shear stress on horizontal area, respectively. σ = c ctgϕ c, c an ϕ is cohesive strength an internal friction angle, respectively. The value of c is zero for pure san soil. τ xy, is equivalent cycle peak value of seismic shear stress on horizontal area. N is equivalent vibration times in every time interval, an can be figure out as follows. First, the uration time T an the effective vibration time N eq is looke up in Table. Then, the ratio between energy of the seismic wave in time interval of Ti an the corresponing energy in the whole uration time T is calculate: t T i SA( Ti ) = a ( t) t a ( t) t ti 1 (9) N = N eq SA( Ti ) (1) Table The value of NBeqB an TBB Earthquake Magnitue NBeqBtime TBBsecon Dynamic Analysis Metho with Effective Stress by Step by Step Iteration in Every Time Interval. The analysis metho is shown in etail as follows. (1) The static effective stress σ x, σ y an τ xy are worke out through static analysis. () The whole perio of the seismic wave is ivie into some equal intervals. The initial ynamic shear moulus an the initial amping ratio are etermine for each of element. An analysis using the above-mentione ynamic constitutive moel of san soil is carrie out by step by step iteration x y (8) 8

9 metho in the first time interval. (3) N in this time interval an the accumulative value N are * figure out. (4) u in this time interval an the accumulative value u * are figure out using equation 4 for each of element. (5) GBmtB an DBmtB consiering the effect of the pore water pressure are figure out for each of element. An the calculate value is use as the initial value for the next time interval. (6) Using the restart function of ANSYS program, the ynamic shear moulus an amping ratio are change into the value worke out in the step (5). An the calculation of next time interval is carrie out without exiting the program. In this way, the continuity of result can be ensure. The above step ()~(6) shoul be repeate for each of time interval until the seismic wave finishes. The magnitue of time interval has an effect on the calculation result. Reasonable magnitue of time interval relates with the site conition an the property of inputte seismic wave. Generally, the pore water pressure shoul have at least one whole cycle in each time interval. Two-imensional Effective Stress Analysis on the Test The effective stress metho of consiering the soil as equivalent linear material in ivie time intervals is introuce. An the metho is realize in ANSYS program by using the ANSYS Parameter Design Language (ANSYS Inc. ). Furthermore, the metho of equivalent linearity is improve to the metho of calculating nonlinearity step by step. Nonlinear moel an computer simulation metho of high-rise builing consiering liquefiable soil-structure interaction is establishe through comparison between shaking table test an theoretic analysis. The constitutive moel of soil, the equation of amping an some other parameters in the calculation can refer to corresponing item mentione above. The soil an pile are simulate by two-imensional plain strain element. The column an beam are simulate by two-imensional beam element. Simple truncation bounary is use as the lateral bounary. The time interval is.194 secon. The meshing of test moel is shown in Fig.13. Selecte acceleration time-histories of the compute an test results are given in Fig.14. SH4 enotes the excitation of Shanghai artifical wave, with a peak acceleration of.53g. Fig. 6 shows that the acceleration time-history curves in the soil match reasonably well. Fig.13 Meshing of test moel The increment curve on pore water pressure of soil is shown in Fig.15. Comparing the caculating curve with the test, we can raw the following conclusion. The rule rawn from the calculation is agree with those from the tests, though there have some ifference between the calculation an tests in quantity. Such as: The increment curve on pore water pressure of the point uner the structure is higher than the point not uner the structure in the same height. An the point H is the highest. From this comparison it can be sai that the computational moel is rational an appropriate for further stuies of the SSI effects. TCONCLUSIONS Shaking table scale moel tests of soil-structure interaction in groun of liquefaction soil an its comparative calculation have been carrie out. Issues rawn from the stuy are as follows. 1) In the tests, macro-phenomena of soil liquefaction an structure failure ue to natural earthquake 9

10 are reprouce well, such as san boil, water to be emitte, founation an structure sink. The failure status of scale moel agree with the actual failure phenomena of prototype. ) The effective stress metho of consiering the soil as equivalent linear material in ivie time intervals is introuce. An the metho is realize in ANSYS program by using the Ansys Parameter Design Language. Nonlinear moel an computer simulation metho of high-rise A1_Effective stress analysis A1_Test A3_Effective stress analysis A3_Test A7_Effective stress analysis A7_Test S_Effective stress analysis S_Test S3_Effective stress analysis S3_Test S5_Effective stress analysis S5_Test S4_Effective stress analysis S4_Test S6_Effective stress analysis S6_Test S7_Effective stress analysis S7_Test S8_Effective stress analysis S8_Test -.8 Fig.14 Comparison between calculation an test result (uner excitation of SH4) 1

11 builing consiering liquefiable soil-structure interaction is establishe through comparison between shaking table test an theoretic analysis. The rule rawn from the calculation is agree with those from the tests, though there have some ifference between the calculation an tests in quantity. Excess pore pressure (kpa) Excess pore pressure (kpa) Excess pore pressure (kpa) Excess pore pressure (kpa) Excess pore pressure (kpa) Excess pore pressure (kpa) Fig.15 The increasing curve of excess pore pressure ACKNOWLEDGEMENT This project is carrie out uner the sponsorship of the key project (No.53183) an the project (No ) of National Natural Science Founation of China. REFERENCES ANSYS Inc., (), User s Manual for ANSYS 5.7. Chen G.X., Xie J.F., Zhang K.X. (1995), Effect of Founation Soil Liquefaction on Earthquake Response of 11

12 Pile-supporte High-rise Builing System, Earthquake Engineering an Engineering Vibration, 15(4), Funahara H., Fujii S. an Tamura S., (), Numerical simulation of pile failure in liquefie soil observe in large-scale shaking table test, 1th Worl Conference on Earthquake Engineering, Aucklan, New Zealan, No.97. Hatsukazu M., Michio S. an Toshihiro M., et al. (), Dynamic behavior of pile founation in liquefaction process-shaking table tests utilizing big shear box, 1th Worl Conference on Earthquake Engineering, Aucklan, New Zealan, No Ling X.Z., Guo M.Z., Wang D.S. et al. (6), Large-scale shaking table moel test of seismic response of brige of pile founation in groun of liquefaction, Rock an Soil Mechanics. 7(1): 7-1, (in China). Lu, X.L., Zhang, H.Y., Hu, Z.L. an Lu W.S. (1999), Shaking table testing of a U-shape plan builing moel, Canaa Journal of Civil Engineering, 6(6): Lu, X.L., Chen, Y.Q., Chen, B. an Li, P.Z., et al. (), Shaking table moel test on ynamic soil-structure interaction system, Journal of Asian Architecture an Builing Engineering, 1(1): Sabnis, G.M., Harris, H.G., White, R.N., an Mirza, M.S. (1983), Structural moeling an experimental techniques, Prentice-Hall, Inc., Englewoo Cliffs, N.J. Takahiro K., Yoichi Y., Naoki T., Fusanori M., Masayuki H., an Norimasa Y., (4), Shaking table testing of liquefiable groun improve by multi-layer soli, 13th Worl Conference on Earthquake Engineering, August 1-6, Vancouver, Canaa, Paper No Yasua & Susumu et al, (), Large-scale shaking table tests on pile founations in liquefie groun, 1th Worl Conference on Earthquake Engineering, Aucklan, New Zealan, No