Differential Method of Thin Layer for Retaining Wall Active Earth Pressure and Its Distribution under Seismic Condition Li-Min XU, Yong SUN

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1 Itertol Coferece o Mechcs d Cvl Egeerg (ICMCE 014) Dfferetl Method of Th Lyer for Retg Wll Actve Erth Pressure d Its Dstrbuto uder Sesmc Codto L-M XU, Yog SUN Key Lbortory of Krst Evromet d Geologcl Hzrd Preveto of Mstry of Educto, Guzhou Uversty, Guyg , Ch xulm0010@163.com, suyog00188@163.com Keywords: Erthquke, Retg Wll, Actve Erth Pressure, Fllg by Lye. Abstrct. Ths pper studes the clculto of ctve erth pressure of retg structure uder the codto of erthquke. By comprg wth the Rke theory d Coulomb theory, we get very good result. The lytcl solutos of the prevous works re for sgle homogeeous sotropc fllg.but ths pper, the clculto formul d method re sutble for the clcultg of ctve erth pressure of retg wll whch s for dfferet multlyer ture fllg. I ths pper, the cocluso s the sme wth the cocluso of lterture before, mely the pot posto of pssve erth pressure s lower th the posto of Rke theory d Coulomb theory, whch should lso be otced. Itroducto Sce 190s, lot of scholrs t home d brod hve crryed o lot of reserch bout Retg wll ctve erth pressure d ts dstrbuto uder sesmc codto [1-5], whch most bout theory reserch d model test, put forwrd erly d up to ow stll wdely used s the Mooobe - Okbe theory, sce the umber of sesmc erth pressure clculto theory ws developed bsed o the theory. M-O theory ws bsed o Coulomb theory, whch ws see s the model of erth pressure clculto [-9].Ths pper use the method of pseudo sttc d horzotl lyer lyss method, get dfferetl sol studes testy dstrbuto formul the pot posto of totl erth pressure, rupture gle clculto formul of sol of homogeeous clyey sol retg structure ctve erth pressure uder sesmc codto. [, 3] The Alyss Model Pseudo-sttc Alyss The clculto process, the bsc ssumptos d horzotl d vertcl erthquke force of the pseudo-sttc lyss re the sme to [3]. Alyss the Model As show fgure 1,the heght of retg wll H,wll bck Agle, the fllg wll surfce behd wll. Cohesve force behd wll c, terl frcto gle, cohesve force betwee sol wll c, exterl frcto gle betwee sol wll, whe the rgd wll behd retg wll move devte from the fllg behd the wll d reches cert level, the fllg behd the wll wll move log BC whch course the wll heel d cuse to the vertcl drecto. We ssume tht the sldg surfce BC s ple. The we see the sol pressure cused by the sol wedge ABC. The Theoretcl Dervto Bsc Assumpto (1)The Fllg wll s lyered cohesve sols The uthors - Publshed by Atlts Press 6

2 ()The sol wedge Frcture surfce BC s ple. (3)The sol wedge ABC s movemet ws see s whole rgd body. (4)The ftesml body the frot d bottom ed d fg respectve by resultt force ther drecto s vertcl. (5) c d c log BC d AB dstrbuted uformly. ' The Bsc Formul of the Lyered Sol q, q d 1 The geometrcl reltoshp d power reltos of the ftesml body re the sme to [3]. Equto of Forces Equto of forces of horzotl drecto: Fg. 1 A Lyered Model of Actve Erth Pressure P ef cos( ) ' K w c ef s c gd s R gd cos( ) 0 h Equto of forces of vertcl drecto: P ef q q K w c ef c gd R gd ' s( ) 1 (1 v ) cos cos s( ) 0 Momet equlbrum equtos: ed fg ed fg P ef cos( ) s P ef s( ) cos ' ed fg s s ' ed fg c ef c ef cos cos Computto Process Strtg from the top, q q0 10kp, q s the mdpot of 0 AC, q d q re the mdpot 1 of ed d fg. We c get: c c p = q w K w(1 K ) h h h v 4 7

3 q h h cos cos h p s c cos q 1 K w +1 v c hcos cos w K s cos cos cos cos 1 =(H-h- h) s( + ) cos( - ) cos( + ) -(H-h-h) s( + ) cos cos( + + )-h cos( - ) s cos( + + ) =(H-h- h) s( + ) s( + - ) cos( + ) -(H-h-h) s( + ) cos s( )-h cos( - ) s s( ) 3 =cos( - ) cos [(H-h- h) s( + ) cos + hcos( - ) s ] 4=(H-h- h) s( + ) s( + - ) cos( + ) cos( + )-(H-h-h) ; s( + ) cos s( ) cos( + )-h cos( - ) s s( ) cos( + ) 5 =cos cos( + ) [cos( - ) s -s( + ) cos ] 6 =(H-h-h) s( + ) cos s( + ) cos + h cos( - ) s s( + ) cos +x t cos cos( + ) cos( + ) =(H-h-h) s( + ) cos cos( + ) cos 7 + h cos( - ) s cos cos( + )- x cos cos( + ) cos( + ) Compute Istce Clculto exmple referece Che Xzhe tsghu uversty "sol mechcs d foudto" d "retg wll clculto hdbook", d we c get tht the cocluso ths pssge s the sme wth the cocluso of lterture Rke theory d Coulomb theory. (1) The cocluso ths pssge s the sme wth the cocluso of Rke theory 3 [1] The questo s H 6.0 m, 0, 0, KN / m, 30, how to get the ctve erth pressure? We let c 0, c 0, kh 0, kv 0, q0 0, h = 0.5m,from the Rke theory, we c get , the Clculto results see the tble below. H/m Fg. Actve Sol Pressure Dstrbuto of Dfferet Clyey Sols uder Sesmc Codto 8

4 ( ) Tb.1 Clculto Results by Lyers of Actve Sol Pressure dw KN p ( KN / m) / m q ( ) 1 KN hm ( ) h( m) totl ctve sol pressure dstrbuto(mp) We c get the ctve pressure from tble 1: P KN / m, 1 We c get the ctve pressure from Rke theory H k H KN m P t (45 ) / P1 P %, P The result of tble 1 s greed well wth the Rke theory. As: Z 0 1 h p [ H ( h1 h h h )] cos 1 p Erth pressure resultt force pot heght Z H, lttle hgher th 1 3 H. ()The cocluso ths pssge s the sme wth the cocluso of Coulomb theory 9

5 3 []The questo s H 6.0 m, 10, 10, KN / m, 30,how to get the ctve erth pressure? 14 We let c 0, c 0, kh 0, kv 0, q0 0, h = 0.5m, we c get , the Clculto results see the tble below: Tb. Clculto Results by Lyers of Actve Sol Pressure dw ( KN ) p( KN / m) / m q ( ) 1 KN hm ( ) h ( m ) totl ctve sol pressure dstrbuto (MP) H/m Fg.3 Actve Sol Pressure Dstrbuto of Dfferet Clyey Sols uder Sesmc Codto We c get the ctve pressure from tble : P kn / m 30

6 We c get the ctve pressure from Coulomb theory: / P H K KN m P P %, P The result of tble 1 s greed well wth the Coulomb theory. As: Z 0 1 h p [ H ( 1h h h1 0.5 h )] cos 1 p Erth pressure resultt force pot heght Z H, lttle hgher th 1 3 H Cocluso (1)Ths pper studes the clculto of pssve erth pressure of retg structure uder the codto of erthquke. Assume tht every lyer h oly trsfer force dowwrd q,there s o frcto betwee the lyers,tht s the horzotl sesmc force fully bore by retg wll. ()The clculto formul d method re sutble for the clcultg of ctve erth pressure of retg wll whch s for dfferet multlyer ture fllg. (3)The cocluso s the sme wth the cocluso of lterture Rke theory d Coulomb theory. (4)The pot posto of ctve erth pressure s hgher th the posto of Rke theory d Coulomb theory, whch should lso be otced,becuse the rgdty of the retg wll problem s beefcl. Refereces [1]Wg Wezhg.The ew theory s formul d test verfy to the erth pressure dstrbuto behd retg wll[j].south Cetrl Trffc Techology, 1995, (): []L Yulg,Yg Guol, Zho Lheg. Actve erth pressure of cohesve sol behd retg wlls uder sesmc codto [J].Rock d Sol Mechcs, vol.3 No.8, 011. [3]Su Yog.Ufed soluto of sesm ctve erth pressure d ts dstrbuto o retg wll [J].Rock d Sol Mechcs, 01, 33(1): [4]Yg J.Actve erth pressure of cled retg wlls uder sesmc codto [J].Chese Jourl of Geotechcl Egeerg, 009, 31(9): [5]Wg Lqg.Dstrbuto of sesmc sol presssure o retg wll[j].ch Hrbour Egeerg, 007,(5):1-5. [6]Steedm R S,Zeg X,The fluece of phse o the clculto of pseudo-sttc erth pressure o retg wll[j].geotechque,1990,40(1): vol.8, [7]Yg J.Pssve erth pressure of cled retg wlls uder sesmc codto [J].Chese Jourl of Geotechcl Egeerg, 009, 31(9): [8]Lu Kul.Prelmry study of ctve erth pressure uder olmt stte[j].rock d Sol Mechcs,010,31():