ANALYSIS OF FLUID-SATURATED POROUS MEDIA IN TWO DIMENSIONS UNDER EARTHQUAKE LOAD

Transcription

1 ANALYI O LI-ATATE POO MEIA IN TWO IMENION NE EATHQAKE LOA Xoj QIN hol CHEN Ad Xh ZEN 3 MMAY The lss of d rse pheoe fld-sred poros ed s of gre eres geoehl egeerg d egeerg sesolog. I he prese pper he respose prole of fld-sred poros ed wo desos eed erhqke lod s desred. The fld sred poros ed s odeled s wo-phse sse ossg of els sold d opressle fld phse. Ths pproh ses he sold dsplee he fld dsplee d he pore pressre s he feld vrles. Bsed o he fld d d els sold eqos der he qs-roos o odo he pplo of fe elee spl dsrezo wh lerk s ehod elds se of opled ler r eqos. Te egro of he reslg se-dsree fe elee eqos s perfored sg Wlso- ehod. The he proedre s ppled o sple wo-desol prole of o-hoogeeos fld sred poros ed. oe olsos re ged fro he erl resls. Ihere perod s dffere ewee he wo-phse ed d he sgle- phse ed; The dpg effe of fld s sgf; 3 The respose of sold skeleo s ore sesve h h of pore pressre; 4 The effe of dffere poros of he lled eple s sgf. The lrger he poros The sller he respose of he pore pressre d he fld velo relve o sold skeleo; 5 The effe of dffere perel s sller h h of he poros. INTOCTION holrs hve ver erl developed he reserh of he poros lqd-sold wo-phse ed ehvor d properes. Bo hs eslshed he d eqo of he sred poros ed 956 d hs eslshed o he fodo for he wve d heor he reserh heerogeeos poros ed. Owg o he hel dffl h he ople fere of he sold lqd wo-phse d eqo of sred sol der he erhqke eg d he o- hoogeeos hrer of sred sol he solo e ged der ol few spel odo. Me l 98[] hve gve soe solo wh er odr odo. e wh he sold skeleo ppers der he erhqke effe srogl oler d kes hs prole eoe ore opled reserhers hve doped he erl ehod o ep o solve. Chefl go o orde wh hoogeeos sred sol of wo desos d he o-hoogeeos sred sol of oe deso esg reserh. The fe elee ehod s og he pplg ore ehods. hoss d Wlso 97[] hve frsl eslshed vro forl d leds he fe elee eqo o he fodo of Bos d eqo d s vrles s he sold d lqd dsplee. Negleg he oplg erl e Bos eqo Zekewz d o 984 e [7] [4] [5] hs eslshed severl kds of fe elee eqos of dffere for desred he dffere vrles wh lerks ehod. Ther llg he lss eple s oe deso. The dh e 990[3] hve gve o fe elee eqo d erl llo ehod desred feld vrle of sold dsplee lqd relvel dsplee of skeleo d poros pressre he d lss of he sred poros ed s ol goe o oe deso. Ygos d Prevos 99[6] hve rred o he erhqke respose lss of log d whh s oposed of he horzol els-pls wo-phse sol ler wh he fe elee ehod wo desos. 3 Assoe Prof. Ise of esolog e esologl Bre Wh P.. Ch. qj@pl.wh.h.. rd. sde of ser degree Ise of esolog e esologl Bre Wh P.. Ch. Prof. of Cvl Egeerg reor of Egeerg esolog Ceer Ise of esolog e esologl Bre

2 I he prese pper he sred sol s odeled s wo-phse poros d sse ossg of els skeleo d opressle fld phse. Ths pproh ses he sold dsplee he fld dsplee d he pore pressre s he feld vrles. sed o he wo-phse opled dfferel eqos he pplo of lerks prple d Wlso - ehod elds hree-feld fe elee egro proedre. The proedre o ol lle he respose of sold dsplee d fld dsplee lso gve o he respose of pore pressre. The he proedre s ppled o sple wo-desol eple of o-hoogeeos fld-sred poros ed. BAIC EQATION AN IT ICETIZATION. fferel eqo of sred ed wo desos If dsregrds grv he dfferel eqo of sred perre ed s. As for he sold phse τ τ 0 0 As for he lqd phse τ The o eqo s fe w 3 Whe lqd s opressle he eqo 3 eoes 0 4 Where esor τ s sold sress esor s verge ve wer pressre γ f s lqd dsplee esor γ f s lqd ss of lk sold ed f f g k Φ s he oeffe of perel. f k Φ lk of sold f s he poros lqd Whe he lqd s opressle he osve eqo s s sold dsplee s ss of lk of sold γ s ss des of γ s ss des of lk of e e e e e ψ 5 Where e e e e e e 6

3 3 Here s Le s os s sher odls.. The pplo of lerks prple Iser 5 d 6 o s goe he sold d eqo epressed dsplee Where The odr odo of dsplee s 8 The odr odo of sress s X τ Y τ p p 8 The Approe solo s hose s 9 Where s er fo or he preer s elog o se of oplee fo d s hose s le ssf odr odo 8. Iser he o 7 d 4 s g:

4 4 Where s he error e f s rl solo hese s ossel eql o zero he lose rego Γ s he whole re Γ s s odr eerll s o eql o zero. I order o deere rres o he rghg egro o 0 o d goes o he egro of prs he g 5 ed eqos of. Γ Γ d P X d ] [ 3 Γ Γ d P Y d ] [ 3 Γ Γ P d d ] [ 4 Γ Γ d P d ] [ 4 d 0 ] [ 5 Here followg odr odos s sed X τ 6 Y τ 6 P P 7 Where; s respevel he dreo ose o X d Y le of oer orl of odr. Bese s oplee fo se whe ; he pproe solo wll ed owrds o re solo..3 e elee dsrezo of hree feld vdg he spe o fe for eple M s-re or elee he shpe of hese s-res s

5 deered se of odes loo opleel. I eh elee he sold dsplee feld d lqd dsplee feld d he verge pore pressre feld s deered he vle of ode where po { }{ }{ }{ } T T { Φ } { } { Φ } { } T T { Φ } { } { Φ } { } T { Φ } { } 8 s respevel he sold d lqd dsplee of elee whh loes s verge wer pore pressre { } { } verge pore pressre veor he ode. elo 6 of sr - sress e wre s Φ s shpe fo se s respevel he dsplee veor of sold d lqd d he T T [ e e e ] [ ] L { Φ }{ } B { } 9 Where L s he dffereo operor r of ple prole d B s r r. L 0 The sold sress e goe he eqo 5 where; B 0 L { Φ } { } [ 0] [ Φ ]{ } { } E { } T [ ] B s he els r d T 0 s lled he sress r. or ode j of elee kes he rod sese dsplee for for j j j j j { } [ ] T j B Ψ P 8 o 3 4 d 5 d go o he egro of prs g he eqo s follow [ M ]{ Ψ } [ C]{ Ψ } [ K]{ Ψ } { } Where [K] s sffess r [C] s dpg r [M ] s ss r [] s lod r. EXAMPLE O NON_HOMOENEO ATATE OIL IN TWO IMENION Aordg o he forl eoed ove he oper progr hs ee de wh OTAN lgge. Choose he llo odel show g. s oposed of 48 elees 36 odes. All preers of sol re hose s follows 8 Pr of sol: Les os her odls I :.0 0 N 5

6 I : N old des 3 3 si :.0 0 g Lqd des fi : g Pr of sol: 8 Les os her odls II : N II :. 0 8 N 3 3 old des Lqd des sii :.5 0 g fii : g The p wve s show g.. The perod of p wve s hose o e d 0.8 seod. The d respose lss s rred o respevel for sred wo-phse ed d sgle-phse ed. Pr of lled resls re show g. 3 o g. 6. g. Clled odel of g. Iped lod o-hoogeeos sred sol B he fgres see h.. The g.3 s he horzol elero respose rve of skeleo whe poros s f I 0. f II d perel s..ro he fgre shows h:. The K I / s resl shows he s feres of fored vro of odel;. The reo qkl ees whle he p lod eoe sller; 3. The gfg lple of reo s dffere ordg o he dffere perod of p wve. 4. The dfferee of he respose phse fere of sred sol s qe sgf whe he p lods perod T s 0.4s or 0.s 0.8s. B oprg h dfferee of he sgle-phse sol s sller.5 Afer lodg he eo of sred sols respose s slower h h of he sgle-phse sol. Ths des h he flee of he ero dp of wo-phse ed.. g. 4 s he respose rve of fld velo reled o skeleo d g.5 s he respose rve of pore 3 3 pressre perel K I.0 0 / s K II / s d lods perod T 0.8s. As for he sgle-phse sol he poros elrges he respose of relve velo d pore pressre rede oherwse re elrged. As for he sred sol he reo hs he dfferee log wh he dffere poros d he dfferee poso. The vro hrer of ode 4 d ode 9 s dffereshow g g.6 s he respose rve of pore pressre poros f I 0.4 f II 0. d lods perod T 0.8s. Beg show sh s he fgre he flee of dffere perel s o so ler o he reo of pore pressre. 4. CONCLION. Ihere perod s dffere ewee he wo-phse ed d he sgle- phse ed.. The dpg effe of fld s sgf. 3. The respose of sold skeleo s ore sesve h h of pore pressre. 4. The effe of dffere poros of he lled eple s sgf. The lrger he poros The sller he respose of he pore pressre d he fld velo relve o sold skeleo. The effe of dffere perel s sller h h of he poros. 6

7 EEENCE [] hossj. d WlsoE.L. 97 Vrol forlo of ds of fld-sred poros els solds J. Eg. Meh. v. ACE [] Me l 98 The wve propgo he fld-sred els ed eophss Trso Vol.4 No.. [3] dh.. e l. 990 A hree-feld fe elee proedre for lss of els wve propgo hrogh fld-sred sol ol d Erh. Eg. Vol. 9 No.. 7

8 [4] o B... E l. 986 Evlo of - d - fe elee ehods for he d respose of sred poros ed sg oe-desol odels I. J. N. Al. Meh. eo. Vol. 0 No. 5. [5] o B.. e l. 986 Evlo of hgher order ed d here fe elee proedres for d lss of sred poros ed sg oe-desol odels I. J. N. Al. Meh. eo. Vol. 0 No. 5. [6] Ygos. N. e l. 99 Two-phse els-pls ses respose of erh ds Theor ol s d Erh. Eg. Vol. 0 No. 7..Zekewz O.C. d ho T. 984 ehvor of sred poros ed: he geerlzed Bo forlo d s erl solo I. J. N. Al. Meh. eo. Vol. 8 No.. 8