KEY POINTS FOR NUMERICAL SIMULATION OF INCLINATION OF BUILDINGS ON LIQUEFIABLE SOIL LAYERS

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1 KY POINTS FOR NUMRICAL SIMULATION OF INCLINATION OF BUILDINGS ON LIQUFIABL SOIL LAYRS Jn Xu 1, Xaomng Yuan, Jany Zhang 3,Fanchao Meng 1 1 Student, Dept. of Geotechncal ngneerng, Inttute of ngneerng Mechanc, Harbn. Chna Profeor, Dept. of Geotechncal ngneerng, Inttute of ngneerng Mechanc, Harbn. Chna 3 Atant, Dept. of Geotechncal ngneerng, Inttute of Dater Preventon Scence and Technology, Sanhe. Chna mal: jxu86@gmal.com, yxmem@163.com, b53@163.com, emmfc@163.com ABSTRACT : The earthquake-nduced aymmetrcal ettlement of buldng on aturated ol layer one of the typcal phenomena n earthquake damage, whch wll lead to the nclnaton and the functon lo of the buldng. Developng numercal method for mulatng the lquefacton-nduced uneven ettlement of the buldng gnfcant for emc degn of buldng and engneerng dater reducton. However, mot reearche are focued on the mechanm of lquefacton and aement of lquefacton potental or the lateral preadng of lquefacton. The correpondng numercal mulaton method for the lquefacton-nduced uneven ettlement of the buldng are few. The reaon that the phycal proce of the problem not well undertood and the key pont for analyzng tll are not attaned. To earch for the key pont of the potental numercal method for calculatng the buldng nclnaton due to ol lquefacton, the relatonhp of the nputtng wave, the vertcal dynamc tree, the pore water preure and the buldng ettlement nvetgated by the hakng table tet n the paper. The tetng reult ndcate: (1) The pore water preure model ued n the potental method mut be utable for mulatng the proce of water preure rng durng the rregular load and can exactly calculate the dfference of the pore water preure under the ncdent load wth ame peak ampltude but dfferent form; () The pore water preure model hould be able to decrbe the pore water preure varaton due to the anotropc property of ol and can dtnguh the dfference of the water preure due to the compreon and extenon tree; (3) The pore water preure model hould be able to calculate the effect of the conoldaton rato on the pore water preure varaton and can attan the actual proce of water preure for the ol below the buldng; (4) The potental method hould be able to follow the track of the deformaton proce of the ol layer wth the ncreang of the pore water preure. KYWORDS: Lquefacton, Buldng, Inclnaton, Calculaton Method 1. INTRODUCTION The former reearch of ettlement on lquefable ol layer concernng the mpact of emc wave manly ued the method of equvalent range, whch mean takng.6 tme of the emc wave peak value a the range of mple harmonc wave. However, the mechanm of earthquake-nduced dfferental ettlement of buldng actually the ynergtc effect of everal mpact factor uch a foundaton ol layer, load dtrbuted on buldng, and nput of emc wave, among whch the mpact of aymmetry and rregularty of emc wave unneglectable. S.J. Meng ha ytematcally analyzed the mpact of emc wave on dfferental ettlement on clay layer, put forward a method that could analyze the dfferental ettlement concernng tme-htory repone of clay, and verfed by hakng table tet. R. Sun propoed a pore preure model that could alo reflect the tme-htory repone, and the relablty wa verfed by dynamc traxal tet. All thee reearch make poble analyzng the earthquake-nduced dfferental ettlement of buldng on lquefable and layer under earthquake wave.

2 Th paper apple the pore preure model propoed by Sun. Meanwhle baed on the relatonhp between pore preure varaton and and module varaton caued by pore preure propoed by W.L. Feng, the equaton about and module oftenng caued by pore preure ncreae, whch could reflect the tme-htory repone under rregularty effect, wa deduced and appled n the calculaton of dfferental ettlement.. TH MTHOD OF CALCULATING DIFFRNTIAL STTLMNTS ON SAND LAYRS.1. Pore Water Preure Model The pore preure model ued n th paper propoed by Sun. u u u 1,,... M 1 A C1, 4, C1, b u 1 C1, k 1 a c C, ( N ) eq The equvalent cycle number Where (.1) j j (.) N eq u the accumulated pore preure rato after the ()th tre cycle, u 1 the accumulated pore preure rato after the (-1)th tre cycle, u ncrement caued by the ()th tre cycle, the ()th effectve hear tre rato, C1, a, C1, b, A4,, C1,, C, are tet parameter, for the tuaton of looe, md-dene, and dene and, C 1,a are.38,.8, and.5, repectvely, C 1,b are.55,.47 and.38, repectvely. Th model could reflect the mpact of both dfferent conoldaton rato and rregular effect on the ncreae of pore preure... Varaton of Compreon Module along wth Varaton of Pore Water Accordng to Feng, the hear module C3 G A max 1 C3 (.3) N G G max N max N1 N 1 Where average effectve normal tre, C 3 tet parameter. Accordng to the relatonhp between compreon module and hear module G(1 ) (.4) Aumng that the total tre contant durng the proce of lquefacton, thu from (.3) and (.4) C3 C3 1 u 1 1 (.5) 1 u 1 1 u, baed on Z.J. Sh crtcal value When a certan and element determned havng lquefed, that 1. concept, for and, Thu, at th tme GLq Lq.15G (.6) max.15 (.7) Integrate (.5) and (.7), the relatonhp of the varaton of compreon module along wth the varaton of pore water

3 C3 1 u ( u 1) 1 1 u 1.15 ( u 1) (.8).3. Overall Flow and Calculatng Step Th paper mplfe the and-tructure ytem a a two-dmenonal problem, combned the earthquake-nduced dfferental ettlement analye wth the tatc and dynamc fnte element analy. The ntal tre tate of every ngle element can be acqured from tatc analy, whle the dynamc tre can be acqured from dynamc analy. A calculatng method can be gven by combnng the element dynamc tre wth the pore water preure model that ft for the rregular effect, alo atng wth the relatonhp of and element module decreae caued by lquefacton. The overall flow and calculatng tep are hown n fgure 1. Statc tet: Determne the ecant module varyng wth tre varaton Pore preure calculaton: Calculatng the pore preure of every element wth a adapted pore preure model Dynamc tet: Determne the module rato, dampng rato varyng wth tran varaton Statc fnte element analy (I): Determne the tatc prncpal tre, and conoldaton rato K of 1 3 c and element; calculate the dplacement U of every node and whch coordnated wth tran Dynamc fnte element analy: Determne the tme-htory baed dynamc prncpal tre; dcrete tme a actng number d ( 1, N) N total number. Module varaton of every element caued by pore preure ncreae: C3 1 u 1 ( u 1) 1 u 1.15 ( u 1) Statc fnte element analy (II): Determne the dplacement U of every node, and the ettlement U ( 1, ) p U U N Output the ettlement value and dfferental ettlement value after every acton Fgure 1 Overall flow and calculatng tep 3. NUMRICAL SIMULATION TST In th paper the computer program compled by Fortran Language ued, mulatng dfferent workng condton. Aume the foundaton and unform dtrbuted, and the load acted on the buldng are equvalent. Conder two workng condton: nput wave are (1) ne wave and () l Centro wave, hown n fgure. The calculatng model of and-tructure ytem hown n fgure 3. Th paper manly nvetgate

4 a a repone of two ymmetrc poton, namely NO.17 and NO.179 element n fgure 3. The calculatng parameter are hown n table 3.1 and table (m) Fgure Waveform of nput wave (m) Fgure 3 Model of and-tructure ytem 4. CALCULATION AND ANALYSIS The output reult are a lot, among whch th paper concern are three type of data: (1) The pore preure varaton of two ymmetrc poton (NO.17 and NO.179 element); () The module varaton of two ymmetrc poton; (3) The ettlement of two ymmetrc poton. Sol type K a (kpa) Table 3.1 Statc calculatng parameter Duncan parameter Lquefacton parameter Ф C n R (deg) (kpa) f C 1,a C 1,b C 1, C, A 4, Md-dene and Intal max hear module(kpa) Denty(g/cm 3 ) Md-dene and Brck Concrete Md-dene and Brck Concrete

5 Table 3. Dynamc calculatng parameter Shear Poon tran rato Sol type Module rato Sand Sand Buldng Brck Dampng rato. Sand concrete Buldng Input Sne Wave Two tet are executed, the range of nput wave are hown n fgure 4, 5, 6, and 7..1 / m,. / m, repectvely. The reult are In fgure 4 and 5 the and ha not lquefed yet, the pore preure ncreae and the module decreae of the two ymmetrc poton are ymmetrc; the foundaton ettlement are unform, too. Whle n fgure 6 and 7 the and ha already lquefed, however the pore preure ncreae and the module decreae of the two ymmetrc poton are tll ymmetrc, the module ha decreaed to about 1/8 of the ntal module, the foundaton ettlement are tll unform, too. 18. u/ Fgure 4 Left element repone under nput range m/ 18. u/ Fgure 5 Rght element repone under nput range m/ 4.. Input l Centro Wave Three tet are executed, the peak of nput wave are reult are hown n fgure 8, 9, 1, 11, 1, and / m,.7 / m,.1 / m repectvely. The In fgure 8 and 9 the and ha not lquefed nce the earthquake acceleraton mall. However the pore preure ncreae and the module decreae of the two ymmetrc poton preent the trend of aymmetrc, the foundaton ettlement are obvou uneven. In fgure 1 and 11, the left of the two ymmetrc poton the and ha lquefed, whle the rght one ha not. Both of the pore preure ncreae and the module decreae of the two

6 ymmetrc poton preent obvou aymmetrc, the foundaton ettlement are epecally notable. In fgure 1 and 13, both of the two ymmetrc poton have lquefed. Becaue the pore preure rato ncreae harply and mmedately reache 1., along wth the module decreae to 1/8 of the ntal module, the pore preure ncreae and the module decreae of the two ymmetrc poton preent eem ymmetrc agan. However the foundaton ettlement retan aymmetrc nce the tme-htory baed repone dfferent. The value of ettlement much more than whch before lquefacton, and wll go on ncreang harply along wth the ncreae of earthquake acceleraton. 18 u/ Fgure 6 Left element repone under nput range m/ u/ Fgure 7 Rght element repone under nput range m/ 4.3. Data Contrat and Analy Through the contrat of two group of numercal mulaton tet above the reult apparent. When the nput wave ymmetrc, the reacton of and foundaton, ncludng pore preure and ettlement, ymmetrc; When the nput wave obvou aymmetrc, the reacton of and foundaton not ymmetrc ether, and the ettlement wll be uneven due to the uneven ncreae of pore preure. In th paper n order to clearly analyze the tme-htory baed ol element reacton and the relaton between t and the dfferental ettlement, the acceleraton of nput wave are mall. Actually when the earthquake acceleraton large, the foundaton and layer wll be lquefed n a hort tme, and the ettlement wll be apparently uneven nce the dfferent ncreae progre of pore preure. 5. CONCLUSION (1) The pore water preure model ued n th paper and the equaton about and module varaton along wth the pore preure varaton deduced by th paper can uccefully preent the tme-htory repone of ol, and are adapted for the calculaton of dfferental ettlement of buldng. () The fnte element method ued n th paper can effectvely calculate the tme-htory repone of ol and ettlement, whch ft for any knd of nput wave, no matter ymmetrc or aymmetrc. (3)For the buldng on whch load are equvalent and the foundaton ol layer alo unform dtrbuted, t tll poble to appear the dfferental ettlement. Whether t happen related to the waveform and peak value of nput wave. When the nput wave ne wave, whch

7 unform, the reacton of and foundaton ymmetrc, o are the ettlement. When the nput wave aymmetrc, the reacton of and foundaton alo aymmetrc, leadng to the dfferental ettlement. u/ Fgure 8 Left element repone under nput peak.5 m/ u/ Fgure 9 Rght element repone under nput peak m/ u/ Fgure 1 Left element repone under nput peak m/ 18. u/ Fgure 11 Rght element repone under nput peak m/

8 18 u/ Fgure 1 Left element repone under nput peak -4.1 m/ u/ Fgure 13 Rght element repone under nput peak m/ RFRNCS [1] S.J. Meng. (). Study on Redual Deformaton of Sol under Irregular Dynamc Loadng and arthquake-nduced Dfferental Settlement of Buldng. Doctoral Dertaton. [] R. Sun. (6). Study on Semc Ground Moton on Lquefable Sol Layer and Ste Lquefacton Detecton. Doctoral Dertaton. [3] W.L. Feng, Z.J. Sh. (1987). Pore water preure analy method of nvetgatng horzontal ol layer lquefacton potental. Reearch Report of Inttute of ngneerng Mechanc. [4] S.J. Meng, X.M. Yuan. (4). Analy of nfluence factor for earthquake-nduced dfferental ettlement of buldng. arthquake ngneerng and ngneerng Vbraton 4:1, [5] X.M. Yuan, R. Sun, S.J. Meng. (3). ffect of aymmetry and rregularty of emc wave on earthquake-nduced dfferental ettlement of buldng on natural ubol. Sol Dynamc and arthquake ngneerng 3:, ACKNOWLDGMNT Th reearch wa upported by the Specal tem for Fundamental centfc reearch outlay of Natonal Commonweal Inttute, Grant No.6B3, and Natonal Natural Scence Foundaton of Chna, Grant No Th upport gratefully acknowledged.