Accurate Prediction of Wave-induced Seabed Liquefaction at Shallow depths using Multi-Artificial Neural Networks

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1 Jural Casal Research SI ICS009 (Prceedigs) Prugal ISSN Accurae Predici Wave-iduced Seabed iqueaci a Shallw dephs usig Muli-Ariicial Neural Newrks D.H. Cha, H. Zhag, M. Blumesei ad D.S. Jeg Schl Schl irmai Divisi Civil Egieerig, ad Cmmuicai Egieerig Dudee Griih Uiversiy / Techlgy, Griih Uiversiy Gld Cas Ciy Uiversiy, Gld Cas Sclad Cucil, Gld Cas Ausralia Ausralia ABSTRACT CHA, D., ZHANG, H., BUMENSTEIN, M., ad JENG, D., 009. Accurae predici wave-iduced seabed liqueaci a shallw dephs usig muli-ariicial eural ewrks. Jural Casal Research, SI 56 (Prceedigs he 10h Ieraial Casal Sympsium), isb, Prugal, ISSN I pas decades, csiderable er has bee deved he pheme wave-iduced liqueaci, because i is e he ms impra acrs r aalysig he seabed ad desigig marie srucures. As waves prpagae ad lucuae ver he cea surace, eergy is carried wihi he medium he waer paricles. This eergy culd be rasmied i he seabed, which resuls i he raher cmplex mechaisms sil behaviur ad sigiicaly aecs he sabiliy he seabed. The predici wave-iduced seabed liqueaci has bee recgised by casal geechical egieers as a impra acr whe csiderig he desig marie srucures. All exisig mdels have bee based cveial appraches egieerig mechaics wih limied labrary wrk. I he auhrs previus sudy, a Sigle Ariicial Neural Newrk (SANN) was applied r he predici wave-iduced seabed liqueaci. I had bee demsraed ha SANN mdel s perrmace ca be acceped i egieerig pracice wih large liqueaci deph. Hwever, i ailed i he liqueied deph is very small such as less ha 1 m. Therere, i he prese sudy, he Muli Ariicial Neural Newrk (MANN) mdel was irduced. The simulai resuls idicae ha he MANN mdel ca prvide mre accurae predici he wave-iduced maximum liqueaci deph bewee 0 1m. This sudy has shw he capaciy he prpsed MANN mdel ad prvides casal egieers wih aher eecive l aalyse he sabiliy he marie sedime. ADITIONA INDEX WORDS: Sigle Ariicial Neural Newrks, Muli Ariicial Neural Newrks, Waveiduces seabed liqueacis INTRODUCTION Durig he pas decade, AI (Ariicial Ieligece) echlgies especially ANN (Ariicial Neural Newrk) skills have bee applied casal egieerig ields, such as predici waer qualiy parameers (Maier ad Dady, 1996), geerai wave equais based hydraulic daa (Yas e al 1998) ad iderecasig usig ariicial eural ewrks (ee & Jeg, 00). Wave-iduced seabed liqueaci is prud ieres marie geechical ad casal egieers because is iluece verical mveme sedime. This sedime mveme i he viciiy a srucure causes he isabiliy he srucure. Numerus ivesigais liqueaci have bee carried u i he pas. Bjerrum (1973) was pssibly he irs pers ha csidered he wave-iduced liqueaci ccurrig i sauraed seabed sedimes. aer, Naaraja e al. (1980) suggesed a simpliied prcedure r cea wave-iduced liqueaci aalysis. Recely, Rahma (1997) esablished he relaiship bewee liqueaci ad characerisics wave ad sil. He ccluded ha liqueaci peial icreases wih degree saurai ad icrease wave perid. Jeg (1997) examied he wave-iduced liqueied sae r several diere cases, icludig Ze & Yamazaki s (1991) ield daa. He ud ha liqueaci ccurs i a sauraed seabed, excep i very shallw waer wih large waves ad seabed wih very lw permeabiliy. Fr mre advaced pr-elasplasic mdels r wave-iduced liqueaci peial, he reader ca reer Sassa & Sekiguchi (001) ad Sassa e al. (001). All aremeied ivesigais have bee reviewed by Jeg (003). I summary, all previus ivesigais r wave-iduced liqueaci peial i a prus seabed have bee based varius assumpis egieerig mechaics, which limis he applicai he mdel i realisic egieerig prblems. The majr dierece bewee geeral egieerig mechaics appraches ad ANN mdels r he esimai he waveiduced liqueaci is he prcedure. Cveial mdels r wave-iduced liqueaci prcedures always ivlve cmplex mahemaical calculais wih umerus variables, such as shear Jural Casal Research, Special Issue 56,

2 Wave-iduced Seabed iqueaci Table 1: Ipu daa r he pr-elasic mdel Sil Characerisics Sil permeabiliy (k z ) 10-4, 5 x 10-4 (m/s) Seabed hickess (h) Frm 10 m r varius Shear mdules (G) 10 7 N/m Piss rai () 0.4 Prsiy () 0.35 Degree saurai (S) 0.95, 0.975, 0.99 ad 1 Wave Characerisics Wave perid (T) 8.00 sec r varius Wave heigh (H) 7.5 m r varius Waer deph (d) 50m r varius Figure 1. Deiii wave-seabed ieraci mdulus, degree saurai ad Piss rai ec. Hwever, ANN mdel ca be simply buil he lear kwledge a daabase wihu cmplex mahemaical prcedures. The ANN mdel ly requires accurae daa, which iclude ipu ad upu daa. Fr liqueaci csiderais, such as he predici seismic liqueaci peial, back-prpagai eural ewrks have bee widely used by Gh (1995). aer, Juag & Che (1999) prediced seismic liqueaci peial rm he ce peerai ield es daa. aely, Jeg e al. (003) prediced earhquake-iduced liqueaci usig he ANN mdel. I he auhrs previus sudy (Jeg e al 004), a Sigle Ariicial Neural Newrk (SANN) was applied r he predici waveiduced seabed liqueaci. Hwever, his sudy ccluded ha he SANN mdel ailed predic he liqueaci deph whe i is very shallw i.e. less ha 1 m. (Jeg e al 004). Therere, i he prese sudy, he Muli Ariicial Neural Newrk (MANN) mdel was applied. The simulai resuls idicae ha he MANN mdel ca prvide a mre accurae predici he wave-iduced maximum liqueaci deph bewee 0 1m. This sudy has shw he capabiliy he MANN mdel ad prvides casal egieers wih aher eecive l aalyse he sabiliy he marie sedime. WAVE-INDUECED SEABED IQUEFACTION I his sudy, we csider a cea wave prpagaig ver a prus seabed iiie hickess. The deiii he prblem is illusraed i Figure 1. Csiderig a w-dimesial waveseabed ieraci prblem, ad reaig he prus seabed as hydraulically isrpic wih he same permeabiliy. Bi (1956) preseed a geeral se equais gverig he behaviur a liear elasic prus slid uder dyamic cdiis. They are summarized i he esr rm belw u w (1) ij, j i i g p i u w i w (), i k z u i, i w ii k p where he subscrips i, j dee he derivai which respec he i- ad j- direcis, respecively, p is pre pressure, u ad w are he displacemes slid ad relaive displacemes slid ad luids; 1/k is he cmpressibiliy pre luid, which is deied by S. (4) 9 k 10 P w where S is he degree saurai, P w is he abslue waer pressure. Esimai iqueaci I has geerally bee acceped ha whe he verical eecive sress vaishes, he sil will be liqueied. Thus, he sil marix lses is sregh carry lad, ad csequely causes seabed isabiliy. Based he ccep excess pre pressure, Ze ad Yamazaki (1991) prpsed a crieri liqueaci, which has bee urher exeded by csiderig he eecs laeral ladig (Jeg, 1997) (3) 1 (1 K)( s w) z ( Pb p) 0 (5) 3 where K is he ceicie earh pressure a res, which is rmally varied rm , ad 0.5 is cmmly used r marie sedimes (Sc, 1968). I (5), s is he ui weigh sil, w is he ui weigh waer, ad P b is he wave pressure a he seabed surace, which is give by H P ( x, ) w b cs( kx ) (6) csh kd where, H is he wave heigh ad d is he waer deph. The ipu daa r he wave-iduced seabed liqueaci calculai which esablishes he ANN mdel, are shw i Table 1. As see i Table 1, he daabase was cmpiled rm he peial rage wave ad sil cdiis ms likely iduce seabed liqueaci. Jural Casal Research, Special Issue 56,

3 Cha e al MUTI NEURA NETWORK MODE FOR SHAOW DEPTH SEA BED IQUEFACTION A muli-ariicial eural ewrk (MANN) mdel was irduced, which exeds he sigle ariicial eural ewrk (SANN) mdel develped i he auhrs previus sudy (Jeg e al 004). The majr dierece bewee he SANN mdel ad he MANN mdel is he umber ewrks used. The SANN mdel is cmprised ly e ewrk which is used r he whle daabase, ad he MANN is cmpsed varius ewrks depedig he rage he daabase. Hece i is beer suied he predicai shallw liqueaci seabed deph. T evaluae he mdel perrmace, hree diere values were used disiguish he predici seabed liqueaci deph. These are R Mea Square Errr (RMSE), Scaer Idex (SI) ad Crrelai Ceicie (R). These parameers are deied as llws N 1 RMSE A P (7) N O i 1 RMSE SI (8) Figure. Cmparis he wave-iduced maximum liqueaci deph by he SANN mdel versus pr-elasic mdel (Kz = 10 4 m/sec) R ( ( ) )( ( ) ) (9) (10) (11) where is he maximum liqueaci deph rm he prelasic mdel, is he maximum liqueaci deph rm he ANN mdel ad is he umber maximum liqueaci deph. I geeral, he crrelai ceicie (R ) values are used r he accuracy he predici. Hwever, resuls i his sudy idicae ha i is very diicul evaluae he mdel usig ly he crrelai ceicie. Therere, he R Mea Square Errr (RMSE) was adped, as well as he Scaer Idex (SI) deied i Equais (7) ad (8). RESUTS A muli-ariicial eural ewrk (MANN) mdel was ivesigaed r he imprveme he accuracy he exisig ANN mdel, ad umerical experimes were cduced demsrae he capabiliy he prpsed MANN mdel r he predici wave iduced liqueaci. The MANN has a similar raiig prcedure he SANN mdel, bu he daa used r raiig is divided dierely depedig he rage he raiig daases. The ccurrece wave-iduced liqueaci depeds sil ad wave parameers. I is clearly shw ha he verall perrmace maximum liqueaci deph predici he seabed usig sigle ariicial eural ewrk (SANN) mdels are wrkig well (Figures ad 5). Hwever, whe we ivesigae he verall resuls he SANN mdel r shallw liqueaci rage deph secis as shw i Figures 3 ad 6, he SANN mdel ails predic values i he zer 1m liqueaci deph Figure 3. Cmparis he wave-iduced maximum liqueaci deph bewee 0 1 m by he SANN mdel versus pr-elasic mdel (K z = 10 4 m/sec) eve hugh his is e he ms accurae predici resuls i each sil permeabiliy case. Therere, he MANN mdel is applied deal wih he same rage as he SANN mdel cases rm 0 1 m. Nrmally, MANN experimes wuld iclude mre ha e eural ewrk r dealig wih each level liqueaci deph, hwever i his sudy, we are maily cceraig shallw deph. Hece apply he MANN his sudy, he SANN mdel r he rage 0-1 m was used r he esig prcedure. Figures 4 ad 7, clearly shw ha he resuls r each rage maximum liqueaci deph prediced r he MANN mdels agree wih he umerical calculai dephs. I is demsraed ha maximum liqueaci deph rages bewee 0 1 m have a gd agreeme bewee he MANN ad pr-elasic mdels whe cmpared he SANN mdel. I is als shw ha he crrelai he MANN mdel ad he pr-elasic mdel is ver 97% r ms rages ad RMSE values are dramaically decreased whe Jural Casal Research, Special Issue 56,

4 Wave-iduced Seabed iqueaci Figure 4. Cmparis he wave-iduced maximum liqueaci deph bewee 0 1 m by he MANN mdel versus pr-elasic mdel (K z =10 4 m/sec) Figure 6. Cmparis he wave-iduced maximum liqueaci deph bewee 0 1 m by he SANN mdel versus pr-elasic mdel (K z =5x10 4 m/sec) Figure 5. Cmparis he wave-iduced maximum liqueaci deph by he SANN mdel versus pr-elasic mdel (K z =5x10 4 m/sec) cmpared he SANN mdel. These igures illusrae ha he diereces i predicis he maximum dephs are wihi he ± 10% rage, which is accepable r a egieerig applicai. CONCUSION This paper discusses perrmace he sigle ariicial eural ewrk (SANN) mdel r he predici liqueaci deph. Eve i resuls he SANN mdel ca be acceped i he egieerig view, we are sill aced wih he prblem predici shallw liqueaci deph. Therere, we ivesigaed he use he Muli-Ariicial Neural Newrk (MANN) mdel r he liqueaci deph rage 0 1 m. where he SANN mdels ailed. The resuls clearly idicae ha he MANN mdel successully prediced he wave-iduced liqueaci deph r he rage 0 1 m, where he SANN mdel ailed achieve high accuracy. Figure 7. Cmparis he he wave-iduced maximum liqueaci deph bewee 0 1 m by he MANN mdel versus pr-elasic mdel (K z =5x10 4 m/sec) ITERATURE CITED Bi, M.A., Thery prpagai elasic waves i a luid-sauraed prus slid. Par I: w requecy rage; Par II. High requecy aalysis. Jural Acusics Sciey, 8: Bjerrum, J., Geechical prblem ivlved i udais srucures i he Nrh Sea. Geechique 3(3): Gh, A.T.C., Seismic liqueaci peial assessed by eural ewrks, Jural Geechical Egieerig, ASCE 10(9): Jeg, D.S., Wave-iduced seabed isabiliy i r a breakwaer. Ocea Egieerig 4(10): Jeg, D.S., 003. Wave-iduced sealr dyamics. Applied Mechaics Review, 56(4): Jeg, D.S.; Cha, D.H.; Blumesei, M., 004 Neural Newrk mdel r he predici he wave-iduced liqueaci peial i a prus seabed. Ocea Egieerig,;31(17-18): Jural Casal Research, Special Issue 56,

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