Effect of Pile Soil Structure Interaction on the Input Ground Motion for Base Surface of High-rise Building in Shanghai ABSTRACT INTRODUCTION

Transcription

1 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada Augut 1-6, 24 Paper o Effect of Pile Soil Structure Interaction on the Input Ground Motion for Bae Surface of High-rie Building in Shanghai Xiao WEI 1 Hong SU 2 Tian TIA 3 Guoxin CHE 4 ABSTRACT High-rie building in Shanghai are prone to be impacted by great earthquake in Taiwan and South of the Yellow Sea, China. In thi paper, the effect of oil and pile-upported high-rie building interaction i invetigated by uing an integral analyi method. Firtly, the oftware program of FLUSH wa redeveloped, replacing it conitent boundary with decoupling tranmitting boundary. Secondly, baed on the deign ground motion level of bae rock for exceedance probability 63.2, 1 and 3 percent in 5 year conidering the effect of oil nonlinear property uing an equivalent linerization model and tectonic earthquake background in area of Shanghai, which taking input ground motion with variable frequency content induced by near-field earthquake, right-beneath city type earthquake and far-field earthquake on bae rock urface, the effect of pile-oil-tructure interaction on the input ground motion for bae urface of high-rie building in hanghai, which ha thick and oft oil, i analyzed in detail. Finally, ome ueful reult for tructure deign are obtained. ITRODUCTIO Shanghai i a eahore city. Since development of Pudong new area, a number of high-rie building have been contructed, and more and more high-rie building will be continually contructed. With deep covering oil layer, the foundation of oil in Shanghai i typically oft and weak. Shanghai i mainly influenced by the eimic belt of the mouth of the Yangtze River and outh of the Yellow Sea, which i periodically calm and active by turn. For the moment the eimic belt i till in the active period of current activity cycle, in the future of ten of year ome earthquake above 6. magnitude even 7. magnitude will probably occur, and the level of eimic activity of the eimic belt in the following one hundred year will a little higher than long-term average level in the pat. Furthermore high-rie building (HB) in hanghai are prone to be impacted by great earthquake in Taiwan. However, real etate developer and tructure deigner have not yet paid highly attention to the eimic rik in Shanghai. The regulation of Chinee a eimic tandard are paid little attention to the effect the pile-oil-tructure interaction (PSSI) of HB, and can not meet the demand of the eimic deign of HB. Therefore, a tudy on the effect of the PSSI on the input ground motion for bae urface of high-rie building will help to improve the eimic deign of HB and inure the afety level of HB in eimic load tate. 1 Ph.D. and Senior Engineer, Seimological Bureau of Shanghai, Shanghai, China, 262. Wei@bn.net 2 Chief Engineer, Earthquake Office of Zhabei Ditrict, Shanghai, China, Technician, Seimological Bureau of Shanghai, Shanghai, China, Profeor, Intitute of Geotechical Engineering, anjing Univerity of Technology, anjing, 219, China 1

2 Computation Model and Analyi Method Simplification of pile-oil-upertructure ytem For practical purpoe, two dimenional finite element method and compound reaction analyi technique are adopted to perform the eimic analyi in PSSI analyi. In the model, the upertructure i implified to be a lumped ma ytem, and the pile were modeled a beam element; Furthermore, oil element were recognized a four-node element. The node of pile element have three freedom degree, and both node of oil element have two freedom degree, and the node diplacement of the pile i compatible with oil element. For the purpoe of determination of the input eimic motion of upertructure, the lumped-ma model i applicable. Thi method wa verified in ASCE-4-86(ASCE, 1986). Auming that upertructure and pile under the earthquake are in the elatic tate, the equivalent linearization method i applied to conider the nonlinear dynamic property of oil, which are one parameter and two curve: maximum hear module G max, the declining relationhip curve of G/G ma ~γ (ecant hear module G decreaing while hear train γincreaing), the acending relationhip curve of λ~γ( the damp ratio of the oil λincreaing while hear train γincreaing). G max can be obtained by hear velocity V of oil. Tranmitting boundary method The method of the multi-tranmitting boundary [Liao, 1996], i a pretty good artificial boundary for PSSI tudying. Suppoe that X axi i perpendicular to artificial boundary, eeing Figure 1, and incident wave project from the left to the boundary joint j with velocity C a. the diplacement of point j at the time of p i decribed a = u( p t, j t), j and p are integer number. t i pace tep, and t = x / c, u jp a Figure 1 Geometry relationhip of multi tranmitting boundary formula thu, u jp may be determined with the diplacement of interior node which were in the direction perpendicular to artificial boundary, a follow: p + = k 1 p k u j ( 1) ck u j k (1) 1 in which: =! C K, = 1,2,KK ( k)! k! (2) equation(2) i o called Multi-Tranmitting Formula (MTF). For the tationary tate wave motion, auming: p u j = U j exp( iω p t) (3) Expreion (3) ubtituted into equation (1) and it can be obtained: k+ 1 ( 1) Ck U j k exp( iω k t) = (4) which may be expreed in a imply formulation: a k U j k = (5) 2

3 in which: k+ 1 k ak = ( 1) Ck b (6) b = exp( iω x / ca ) (7) equation(5) i MTF in tationary tate. In two dimenion model of oil-tructure interaction, U l ( l = j k) in equation (5) mean diplacement of diemination wave reulting form tructure-foundation interaction influenced by incident wave. Furthermore, ul = utl u fl and u tl i component diplacement of joint l, u fl i component diplacement of joint l in free field ituation. Thu, equation (5) can be rewritten a follow: ak ( U tl U fl ) = (8) Complex Repone Motion Equation Complex motion equation in two dimenion of FLUSH program i expreed a follow [Lymer, 1975]: 2 ([ K] ω S [ M ] + [ R] + [ L] ){ U (9) = { m Y&& + ([ G] + [ R] + [ L] ){ U in which, [ K ] i complex tiffne matrix, {m ha related to ma matrix {M and ma motion direction under input wave. { u i joint diplacement relative to the urface at the bottom of oil where incident wave input. [ R ] i right boundary tiffne matrix and [ L] i left boundary tiffne matrix according to energy diemination tranmitting. Thoe tiffne matrixe can be exactly obtained according to layer medium elatic wave motion theory [Lymer and Drake. L]. [ G ]{ U f i the load force matrix that wa produced by outide medium acting on boundary, excluding the part of diemination wave energy. Y & i amplitude of acceleration correponding to ω, and { U f i diplacement matrix relative to rigid urface at the bottom of oil. { U f can be decribed a follow: { U f = { Af Y& =,1, 2, LL, 2 (1) in which { A f i the amplified vector of layered oil diplacement relative to that of acceleration at oil urface of rigid bottom. Replacing expreion (9) with (1), it can be obtained: [ K ] { U = { P Y & (11) in which, [ K] i tiffne matrix which ha relation to frequency, and { P repreent load vector of identify amplitude on rigid bottom motion. [ K] = [ K] + [ R] + [ L] ω 2 [ M ] (12) { P = ([ G] + [ R] + [ L] ) { Af { m (13) Thu, according to the node number decribed in fig 2, Equation (11) can be rewritten a [ L] b { U Lb { PLb [ K ] i { U i = { Pi (14) [ R] b { U kb { Pkb in which, b and i are repectively defined a the joint on boundary and interior node of oil. Furthermore, [ L] b and [ R] b repectively defined a tiffne matrix of the left and right boundary. { U Lb and{ U Rb are repectively defined a boundary diplacement of the left and the right, { P Lb and f 3

4 { P are repectively defined a load matrix acting on the left and right boundary. Rb tructure 1 j M+j 2M+j Soil urface 2M+j M+j j rigid Figure 2 Two dimenion model for oil-tructure interaction In order to reformation of program FLUSH, replacing conitent boundary with MTF boundary, and [ L b ] [ R b ] { P Lb and { P Rb in equation(14) mut be reformed. It can be obtained from equation (5): aku tl = { PLb (15) { PLb = aku fl (16) To deal with { P Lb { PLb, and [ a k ] [ L b ], equation (15) of the left and right ide of equation may be obtained with the ame way. Thu, equation (14) can be reformulated a: [ ak ] { U Lb { Pib [ K] i { U i = { Pi (17) { U Rb { PRb [ a k ] in which, the coefficient matrix [ a k ] in the condition of tranmitting boundary i 2 M 2 order matrix. UMERICAL AALYSIS AD DISCUSSIOS Supertructure parameter One high-rie building (HB) in Shanghai wa modeled. It i a frame-hear wall ytem building, and 15 floor. It i a 54.3 meter high, 68.4 meter long and 18 meter wide building. It foundation i box-pile foundation, thick at the bottom of box bae plate i 1.2 meter, and that of the top board i.2m thick. The baement into the ground ha 6.2m depth; the precat quare pile ection i 4 4mm in ize; Each floor from 1 to12 i 3.6m high, and height of floor 13 i 4.7m, but height both of floor 14 to floor 15 i 3.2m. The parameter of the implified tructure were howed in Table 1. The period of the firt to third mode period i and.2, repectively;the mode period of original tructure i calculated by program SAP2 in pace three dimenion method. The reult of period are and.25, repectively. It i indicated that the implified lumped ma tructure i harmonic with that of original tructure in repone characteritic. 4

5 Table 1: Parameter of lumped-ma tructure Floor o. Ma ( 1 3 kg) Moment of inertia(m 4 ) Table2: Soil layer and parameter Soil depth Soil Shear velocity H(m) type V (m/ 2 ) -6.2 clayey andy andy clayey 18 >3.2 andy H Parameter of oil It i uppoed that hear velocity V of oft oil change with depth H, a how in Table 2. The relationhip between the dynamic hear module ratio of the oil G/G max and the damping ratio λ with hear train i hown in Figure 3. hear module ratio clay oil andy oil damoing ratio.2 clay oil andy oil. 1E-6 1E-5 1E-4 1E-3 1E-2 1E-1 hear train Fig 3 Relationhip between hear module ratio, damping ratio of oil and hear train Geometry dimenion of pile There are two kind of pile with different length, 15m and 9m. The pile ection ize of 15m length i 4 4mm, and the ection of the 9m length pile i converted from the 15m length pile according to the ame volume principal. The main purpoe i to compare the eimic property of hort and fat pile with that of long and thin pile. Input eimic motion The component of frequency pectrum and duration time of input wave have great influence on tructure. According to eimic rik analyi, Shanghai i prone to be impacted by the earthquake near field earthquake, right-beneath city type earthquake and far field earthquake (earthquake in the outh of the Yellow ea and great earthquake in Taiwan). The four typical eimic motion are choen, repectively. Thoe are the Qianan wave which wa recorded on rock in Tanghan earthquake (ee Figure 4), EI Centro wave which wa recorded on the ground urface of oft deep oil, ee Figure 5, and two manmade wave conidering far-field earthquake (with the ame repone pectrum of acceleration (RSA), Figure 6), and another two manmade wave conidering right-beneath city-type earthquake factor (with the ame RSA, Figure 7). The peak value of acceleration(pva) of the input eimic wave i adjuted to.35g.9g and.125g, approximately correponding to the rock deign acceleration with the exceedance probability of 63.2%, 1%, 3% for fifty year, according to earthquake rik analyi in Shanghai [Wei and Shen,1998]. 5

6 Acce. g 16 Qianan wave Time Frequency Hz Fig 4 Acceleration time hitory and it Fourier pectrum of Qianan wave El Centro Fourier Spectrum(cm/) Qianan wave 14 El Cen t r o Acce. g Fourier Spectrum cm/ Time Figure 5 Acceleration time hitory and it Fourier pectrum of El Centro wave Manmade wave o Frequency (Hz) 2 mammade wave conidering far-field earthquake Acce. g) Fourier pectrum (cm/) Time () Frequency (Hz) Figure 6 Acceleration time hitory and it Fourier pectrum of manmade wave conidering far field EQ 1 conidering right-beneath type earthquake manmade wave o.1 3 Manmade wave conidering right-beneath type earthquake 5 Acc. g Fourier Spectrum (cm/) Time Frequency Hz Figure7 Acceleration time hitory and it Fourier pectrum of manmade wave conidering near field EQ 6

7 Supertructure Baement Pile Figure 8 Model of pile-oil-tructure interaction Calculation reult and dicuion The calculation model for PSSI analyi i hown in Figure 8. The pile are 15m long. Table 3 and Table 4 repectively give the reult of the PVA and maximum RSA of ground in free field and urface of bae. It can be founded that the acceleration peak value of the bae urface i lightly more than that of free field under Qianan wave input, which contain abundant content of high frequency and equivalent to the exceedance probability of 63.2% and 1% in fifty year (it peak value are.35g and.9g repectively). Under the eimic wave with the exceedance probability of 3% for fifty year (PVA i.125g), PSSI lead to the reult that PVA of the bae urface i about 11%-13% le than that of urface in free field. The maximum RSA of the bae urface i le than that of ground urface in free field under the condition of.35g,.9g and.125g peak value acceleration of input wave which containing much low frequency component conidering far field earthquake factor, and the PVA of bae urface i 37%-65% bigger than that of ground in free field model. Acceleration i effect on the maximum of the repone pectrum of acceleration (RSA), and the maximum RSA of the bae urface i 6%-16% bigger than that of ground urface in free field, the exceedance decline with increaing in the motion level. Although two wave have the ame RSA value and maximum of acceleration, the eimic repone of the oil and that of tructure i different from each other. Under the right-beneath city type eimic wave, the PSSI of two manmade wave i different to ome extent. For o.2 manmade wave with three level of intenity, the PVA of the bae urface conidering PSSI effect i le than that of the free field ground urface. When the PVA of input wave i.35g and.9g, it decreae in 4.4~1.8 percent. While the PVA i.125g, PVA on bae urface decreae 23 percent than that of free field urface; For o. 1 manmade eimic wave under the condition of PVA.9g, calculating reult in PSSI model how that PVA on the bae urface i bigger than that of on the free field ground urface with 14~3 percent. When the eimic PVA of input wave i.35g, conidering PSSI the PVA of the bae urface i lightly le than that of the free field urface, however for the eimic motion with the exceedance probability of 3% for fifty year, PSSI effect are relevant to the length of the pile. When the pile i 9 meter long, the PVA of the bae urface i 1% bigger than that of on free field urface, while the pile i 15m long, both are the ame. For the Max repone pectrum of acceleration, PSSI i relatively uncertain, becaue the trend i difficult to conclude. For notable El Centro wave, which contain abundant content of low frequency, PSSI effect i not prominent under the condition that the PVA of the input wave i.35g, and the PVA and the maximum RSA on the bae urface are almot the ame a thoe on the free field urface. Under the eimic motion intenity with the exceedance probability of 3% in fifty year, PSSI effect i prominent, becaue the reult how that the PVA on the bae urface i 27%~31% bigger than that of the free field ground urface, however, the maximum of RSA on the bae urface i 77%-13% bigger than that of the free field ground urface. For the ituation of different length of pile model, in general, RSA and PVA on bae 7

8 urface conidering PSSI effect are not almot the ame a that of on free field ground urface. Table3 Comparion max. acceleration on free field urface with that of bae urface(unit:g) The peak acceleration of input wave (g) Wave Type Free field Surface of bae Free field Surface of bae Free field Surface of bae Surface Pile length Surface Surface Pile length Surface Surface Pile length Surface 9m 15m 9m 15m 9m 15m Qianan O Right beneath{ O O Right beneath { O EI Centro Table4 Comparion max. acceleration on free field urface and that of bae urface (unit:g) The peak value acceleration of input wave (g) Wave Type Freefiel Surface of bae Freefield Surface of bae Freefield Surface of bae Surface Pile length Surface Surface Pile length Surface Surface Pile length Surface 9m 15m 9m 15m 9m 15m Qianan O Right beneath{ O O Right beneath { O EI Centro centor Figure 9 how computation reult of the tructure with pile length 15m under Qianan wave (it peak value of acceleration i.125g). Compared with the RSA of the free field urface, the value of the RSA on the bae urface obviouly decreae at hort period part, but the value on the range of the period above.3 are remarkably amplified. It can be found that the value of RSA i prominently amplified around the period point of Free field Surface of bae.125g Peak value Acc. of Qianan Wave Acce. peak value.9g with pile length 9m input manmade wave conidering far field earthquake frequency content Surface of free field ground urface of bae ormalized RSA ormalized RSA Period (S).1 Period () Figure 9 Reult under input.125g PVA of Qianan wave, 15m pile length Figure 1 Reult under input.9g PVA o.1 manmade wave conidering far field EQ, 9m pile length Figure 1 i the reult of the tructure with 9m long pile under o. 1 manmade eimic wave far field 8

9 earthquake with it PVA.9g. Compared with the RSA of the free field ground urface, the value of the RSA on bae urface drop down evidently nearby the period point of 1.5. On the contrary, RSA wa bigger than that of free field urface at the point of.43. Thoe period point repectively correpond to the firt and econd mode period of the upertructure. COCLUSIOS Conidering the eimic urrounding and the characteritic of high-rie building in Shanghai, ome ueful reult can be obtained by numerical analyi of PSSI: (1) The influence on the bae urface of high-rie building i related to the characteritic of the frequency pectrum and intenity of the input eimic motion conidering PSSI. Under the near field earthquake with abundant component of high frequency content, uch a Qianan recorded wave, with it low intenity condition, the peak value acceleration(pva) on the bae urface i lightly bigger than that of free field ground urface; On the contrary, the PVA on the bae urface i 1% above le than that of free field ground urface under high intenity of input wave motion;under the eimic action of far field earthquake with much component of low frequency content, the PVA of the bae urface i 37%~65% bigger than that of the free field ground urface. Under the right-beneath city type earthquake wave, it i difficult to find out the trend whether the PVA of the bae urface i more or le than that of ground urface in free field model. (2) Compared with the eimic motion characteritic of the free field, it can found that PSSI change the eimic repone characteritic on bae urface of high-rie building. Under the near field earthquake the component of high frequency pectrum content decreae, on the contrary, that of the low frequency pectrum content can be amplified. Under the eimic motion of far field earthquake, it i probably that pectrum in low frequency can be amplified, which i approximately equal to the firt and econd order mode of high-rie building. (3) It i different that the effect on the vibration of the high-rie building bae urface conidering PSSI under the different manmade wave with the ame RSA, Epecially indicated in PVA and maximum of RSA on bae urface. But it i not obviou different in the hape of RSA curve. The above concluion are obtained by the analyi of pecified tructure and with limited eimic wave, Therefore, effort hould be made to enure the concluion widely practicable. REFERECE 1 ASCE Standard 4-86,Seimic Analyi of Safety-Related uclear Structure and Commentary on Standard for Seimic Analyi of Safety-Related uclear Structure. American Society of Civil Engineer, Sept., Liao Zhenpeng, Introduction to Engineering Wave Motion Theory, Science Pre [Chinee], Lymer, J. et al, FLUSH,A Computer Program for Approximate 3-D Analyi of Soil-Structure Interaction Problem, UCB/EERC 75-3, Lymer, J. and Drake L. A.. A Finite Element Method For Seimology, Method in Computational Phyic, Vol.11, edited by Bolt, B. A.. 5 Xiao, Wei, Jianwen Shen, High-rie building eimic repone analyi conidering pile-oil-upertructure interaction. Report of eimological bureau of Shanghai, 1998.(in Chinee). 9