Chapter 34
Experimental and Numerical Investigations of Nonlinearity in Soils Using Advanced Laboratory-Scaled Models (ENINALS Project): From a Site-Test to a Centrifuge Model Francesca Bozzano, Salvatore Martino, Alberto Prestininzi, Gabriele Scarascia-Mugnozza, Luis Fabian Bonilla, Alberto Bretschneider, Jean Louis Chazelas, Sandra Escoffier, Luca Lenti and Jean-François Semblat
34.1
Introduction
The historical centre of 5RPHLV EXLOWIRU DJUHDWSDUWRQ DQDOOXYLDOSODLQILOOHG E\VHGLPHQWVIURPWKH7LEHUULYHUDQGLQSDUWRQKLOOVZKHUHS\URFODVWLFGHSRVLWV IURP WKH$OEDQL +LOO DQG 6DEDWLQR YROFDQLF GLVWULFWV DUH H[SRVHG )XQLFLHOOR DQG Giordano %R]]DQR HW DO 7KH /¶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ā)%R]]DQRā$3UHVWLQLQ]Lā*6FDUDVFLD0XJQR]]D 'HSDUWPHQWRI(DUWK6FLHQFHVDQG5HVHDUFK&HQWUHIRU*HRORJLFDO5LVNV &(5, ³6DSLHQ]D´ 8QLYHUVLW\RI5RPH3LD]]DOH$0RUR5RPD,WDO\ HPDLO VDOYDWRUHPDUWLQR#XQLURPDLW /)%RQLOODā//HQWLā-)6HPEODW 'HSDUWPHQWRI*HRWHFKQLFV(QYLURQPHQW1DWXUDOKD]DUGVDQG(DUWKVFLHQFHV)UHQFK,QVWLWXWH RI6FLHQFHDQG7HFKQRORJ\IRU7UDQVSRUW'HYHORSPHQWDQG1HWZRUNV ,)677$5 %RXOHYDUG 1HZWRQ&LWp'HVFDUWHV&KDPSVVXU0DUQH0DUQHOD9DOOpH)UDQFH $%UHWVFKQHLGHUā-/&KD]HODVā6(VFRIILHU 'HSDUWPHQWRI*HRWHFKQLFV(QYLURQPHQW1DWXUDOKD]DUGVDQG(DUWKVFLHQFHV)UHQFK,QVWLWXWH RI6FLHQFHDQG7HFKQRORJ\IRU7UDQVSRUW'HYHORSPHQWDQG1HWZRUNV ,)677$5 5RXWHGH %RXD\H&6%RXJXHQDLV&HGH[)UDQFH 6SULQJHU,QWHUQDWLRQDO3XEOLVKLQJ6ZLW]HUODQG )7DXFHU5$SRVWROVND HGV Experimental Research in Earthquake Engineering, *HRWHFKQLFDO*HRORJLFDODQG(DUWKTXDNH(QJLQHHULQJ '2, B
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34.2 The Rome Historical Centre Case Study 7KHDUHDRI5RPHKLVWRULFDOFHQWHU )LJ ZDVFKDUDFWHULVHGE\PDULQHVHGL PHQWDU\FRQGLWLRQVIURP3OLRFHQHWKURXJKHDUO\3OHLVWRFHQHWLPHV ±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¶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model of the Tiber al OXYLDLQWKHKLVWRULFDOFHQWUHRI5RPHIRXUVRLOFROXPQVZHUHVHOHFWHGWRUHSUHVHQW KRPRJHQHRXVVDQG\DQGFOD\H\GHSRVLWVKHWHURJHQHRXVGHSRVLWVDOWHUQDWLQJVDQG\ DQG FOD\H\ OHYHOV RI GLIIHUHQW WKLFNQHVV FRUUHVSRQGLQJ WR WKH FROXPQV$ DQG % )LJ
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34.3
Seismic Input
The dynamic input considered in this study represents the maximum expected seis mic action in 5RPH,WZDVUHSURGXFHGRQWKHVRLOFROXPQVE\G\QDPLFFHQWULIXJH PRGHOLQJIROORZLQJWKUHHDSSURDFKHV L DQDWXUDOVLJQDO LL DQHTXLYDOHQWVLQX VRLGDOVLJQDODQG LLL DPXOWLIUHTXHQWLDOHTXLYDOHQWVLJQDOGHULYHGE\WKHUHFHQWO\ SURSRVHG/(0$B'(6DSSURDFK7KHWKUHHVLJQDOVDUHKHUHGHVFULEHG
34.3.1
Natural Reference Input
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34.3.2
Cyclic Mono-Frequency Input
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34.3.3
LEMA_DES Multi-Frequency Input
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LEMA_DES signalREWDLQHGVWDUWLQJIURPWKHQDWXUDOVLJQDOLQWHUPVRIHTXLYDOHQW DFFHOHUDWLRQLVVKRZQRQ)LJF:LWKUHIHUHQFHWRWKHSURFHGXUHE\/HQWLDQG 0DUWLQR WKH &RQYHUJHQFH 5HODWLYH (UURU &5( IRU WKH KHUH REWDLQHG VLJQDOLVHTXDOWRFRUUHVSRQGLQJWRDPLGGOHUHOLDELOLW\RIWKHGHULYHGVLJQDO
34.4 34.4.1
Centrifuge Modelling Experimental Project
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34.4.2
Experimental Device
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34.4.3
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Experimental Setup
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34.4.3.1
Preparation of the Sample Boxes: Soil Columns #1 and #2
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([SHULPHQWDODQG1XPHULFDO,QYHVWLJDWLRQVRI1RQOLQHDULW\« )LJ )ORZFKDUWVKRZ ing the procedure adopted to prepare the multilayer soil FROXPQ
Consolidation of a 9 cm or 18 cm clay layer
Pluviation of 13.5 cm Fontainebleau sand - Id=57%
Saturation of the 1st layer of sand
Installation of the clay layer on the saturated sand layer
Pluviation of the 2nd layer of sand Id= 57%
Saturation of the 2nd layer of sand
E\DJHRWH[WLOHZDVVHWXSDWWKHERWWRPRIWKHER[)RUWKLVFOD\OD\HUGUDLQDJHZDV DOORZHGERWKDWWKHWRSDQGWKHERWWRPVXUIDFHV7KHVDWXUDWHGFOD\ZDVFRQVROL GDWHGIROORZLQJDUDPSRILQFUHDVLQJVWUHVVHVZLWKDILQDOYHUWLFDOVWUHVVRIN3D
34.4.3.2
Preparation of the Sample Boxes: Soil Columns #3 and #4
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³FXWDQGLQVWDOO´SURFHGXUHZDVH[SHULHQFHGWRUHDOL]HWKHPXOWLOD\HUVDPSOHV The process of installation of the consolidated clay layer used a suction pad and a FXWWLQJVNLUWPDGHRI39&VKHHWVIL[HGRQWKHSHULSKHU\RIDIODWVXFNHU7KHSURFHVV LVGHWDLOHGLQ)LJ
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)LJ Installation of the consolidated clay layer in the ESB box
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
34.4.4
Seismic Signals Analysis
34.4.4.1
Signal Reproduction
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natural signal )LJ ZDVYHU\ZHOOUHSURGXFHGE\ WKHVKDNHUDVFDQEHVHHQFRPSDULQJWKHDFFHOHUDWLRQERWKLQWLPHDQGIUHTXHQF\ GRPDLQV
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([SHULPHQWDODQG1XPHULFDO,QYHVWLJDWLRQVRI1RQOLQHDULW\«
240 mm
300 mm 200 mm
400 mm 200 mm
10 mm 135 mm
30mm
12
60 mm 30mm
120 mm
60 mm 30 mm
90 mm
360 mm
60 mm 120 mm
135 mm
30mm
90 mm
LEGEND B&K accelerometerstype 4517 Keller Pore pressure sensors
90 mm
3 2
Sand (S) Clay(C)
Potentiometer displacementsensors
)LJ 6NHWFKLOOXVWUDWLQJWKH(6%ER[LQVWUXPHQWHGZLWKWKHPRQLWRULQJV\VWHPLQWKHFDVHRI a multilayer sample
Some spurious accelerations are not completely negligible on the x direction be FDXVHWKHJOREDOOHYHOLVZHDNIRUWKHVKDNHUZKLOHWKH\DUHQHJOLJLEOHRQWKHz direc WLRQ$OOWKHIUHTXHQF\YDOXHVUHSRUWHGKHUHDIWHUDUHUHIHUUHGWRWKHSURWRW\SHVFDOH The LEMA_DES signal )LJ SUHVHQWV DQ H[FHOOHQW ILWWLQJ LQ WKH IUHTXHQF\ GRPDLQWLOO+]VRPHIUHTXHQF\KLJKHUWKDQWKHUHIHUHQFHFDQEHQRWHGDURXQG +]7KHVSXULRXVPRYHPHQWVRIWKHWDEOHDUHUHOHYDQWRQO\IRUVRPHIUHTXHQFLHV DURXQG+]EXWLQJHQHUDOWKHVLJQDOTXDOLW\LVJRRG7KHVKDNHUDOVRUHSURGXFHG YHU\ZHOOWKHsinusoidal signal )LJ ZLWKDQH[FHOOHQWFRUUHVSRQGHQFHRI WKHVLJQDOVXSWR+]6RPHIUHTXHQFLHVDURXQG+]JHQHUDWHVRPHWURXEOHVRQ WKHVLJQDO6SXULRXVDFFHOHUDWLRQVDUHQHJOLJLEOH7KHVSXULRXVPRYHPHQWVRIWKH WDEOHDUHUHOHYDQWRQO\IRUVRPHIUHTXHQFLHVDURXQG+]EXWLQJHQHUDOWKHVLJQDO TXDOLW\LVJRRG
34.4.4.2
Signal Transmission
,QRUGHUWRHYDOXDWHWKHHIILFLHQF\RIWKHWUDQVPLVVLRQRIWKHLQSXWUHSURGXFHGE\WKH shaking table to the bottom of the soil column the accelerations recorded at these SRVLWLRQVZHUHWDNHQLQWRDFFRXQW7KH)DVW)RXULHU7UDQVIRUPV ))7 RIWKHVLJQDOV
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)LJ Natural signal reproduced by the shaker upscaled to prototype scale: a))7 top-left b Arias Intensity of the natural signal top-right cDFFHOHURPHWULFWLPHKLVWRULHV bottom
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∑ i =1 ( xi − yi )2
ZKHUHiLVWKHVXPLQGH[PRYLQJIURPRQHXSWRWKHPD[LPXPQXPEHURISRLQWVLQ WKH))7xi and yiDUHWKHVSHFWUDODPSOLWXGHYDOXHVUHODWHGWRWKHUHFRUGVDWFKDQQHOV WZRDQGWKUHHDQGEWKHHVWLPDWLRQRIWKHHUURU1RQRUPDOL]DWLRQRQWKHWRWDOQXP EHURISRLQWVZDVDGRSWHGEHFDXVHWKH))7VZHUHFKDUDFWHUL]HGE\WKHVDPHWRWDO QXPEHURISRLQWVLQWKHIUHTXHQF\EDQG±+] 7KH HUURU YDOXHV DUH DQG PV UHVSHFWLYHO\ IRU WKH naturalWKHLEMA_DES and sinusoidal signalsIRUWKHZKROHIUHTXHQF\EDQGUH WDLQHGIRUWKHVXP,IRQO\WKHKLJKIUHTXHQF\EDQG LH±+] LVUHWDLQHGIRUWKH VXPWKHYDOXHVDUH DQG PVUHVSHFWLYHO\IRUWKHnatural LEMA_DES and sinusoidal signals7KLVYHU\SUHOLPLQDU\DQDO\VLVVXJJHVWVWKDWD better reproduction of the signal can be expected for the natural and for the LEMA_ DES signals$Q))7FRPSDULVRQ SRLQWYVRI)LJ ZDVDOVRSHUIRUPHG
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)LJ LEMA_DES signal reproduced by the shake upscaled to prototype scale: a))7 topleft b$ULDV ,QWHQVLW\ RI WKH ³QDWXUDO LQSXW´ VLJQDO top-right c accelerometric time histories bottom
WRHYDOXDWHWKHJHQHUDWLRQRIKLJKIUHTXHQFLHV ±+] ZLWKLQWKHPRGHOGXHWR WKHYLEUDWLRQRIWKHVWUXFWXUDOFRPSRQHQWVRIWKHVDPSOHER[,WUHVXOWHGLQDYHU\ VLPLODUHUURURIDERXWIRUWKHnatural and the LEMA_DES signalsZKLOHDORZHU HUURU DERXW UHVXOWHG IRU WKH sinusoidal signal EXW LQ WKLV FDVH LW VKRXOG EH taken into account that the sinusoidal signal FDQQRW UHSUHVHQW IUHTXHQFLHV KLJKHU WKDQ+] 7KLVRXWSXWGHPRQVWUDWHVWKHJRRGTXDOLW\RIWKHHTXLYDOHQWLEMA_DES signalZLWKUHVSHFWWRWKHnaturalRQH
34.5
Conclusions
7KHSUHOLPLQDU\UHVXOWVREWDLQHGLQWKHIUDPHRIWKH6(5,(6(1,1$/6SURMHFWDUH VXPPDUL]HGLQWKHIROORZLQJ DFHQWULIXJHPRGHOLQJZDVFDUULHGRXWE\XVLQJPXOWLOD\HUVDPSOHVFRPSRVHGRI DFOD\OHYHOZLWKLQVDQG\RQHV7RWKLVDLPVSHFLILF³FXWDQGLQVWDOO´WHFKQLFDO VROXWLRQVZHUHDGRSWHG
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)LJ Sinusoidal signal reproduced by the shaker upscaled to prototype scale: a))7 topleft b$ULDV ,QWHQVLW\ RI WKH ³QDWXUDO LQSXW´ VLJQDO top-right c accelerometric time histories bottom
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This application can represent a useful tool for mapping the susceptibility to HDUWKTXDNHLQGXFHGJURXQGHIIHFWVUHODWHGWRVKHDUVWUDLQGHIRUPDWLRQVLHIRUVHLV PLFPLFUR]RQDWLRQVWXGLHV:LWKSDUWLFXODUUHIHUHQFHWRWKHKHUHFRQVLGHUHG5RPH FDVHVWXG\LWLVZRUWKVWUHVVLQJWKDWWKLVDSSOLFDWLRQFDQUHSUHVHQWDFRPSOHPHQWDU\ WRROIRUWKHDSSOLFDWLRQRIWKH,WDOLDQRIILFLDOWHFKQLFDOUXOH³,QGLUL]]LH&ULWHUL GL0LFUR]RQD]LRQH6LVPLFD´ ,&06 Acknowledgments 7KHUHVHDUFKOHDGLQJWRWKHVHUHVXOWVKDVUHFHLYHGIXQGLQJIURPWKH(XURSHDQ &RPPXQLW\¶V6HYHQWK)UDPHZRUN3URJUDPPH>)3±@IRUDFFHVVWRWKH,)677$5&HQ WULIXJH1DQWHV)UDQFHXQGHUJUDQWDJUHHPHQWQ
References $PEURVLQL6&DVWHQHWWR6&HYRODQ)'L/RUHWR()XQLFLHOOR5/LSHUL/0ROLQ' 5LV SRVWDVLVPLFDGHOO¶DUHDXUEDQDGL5RPDLQRFFDVLRQHGHOWHUUHPRWRGHO)XFLQRGHO*HQQDLR 0HP6RF*HRO,W ± %DODNULVKQDQ$.XWWHU%/,GULVV,0 &HQWULIXJHWHVWLQJRIUHPHGLDWLRQRIOLTXHIDFWLRQDW EULGJHVLWHV7UDQVS5HV5HF ± /LTXHIDFWLRQ'LIIHU6HWWO)RXQG(QJ %RQLOOD)/HQWL/0DUWLQR61LFRODV-)5RYHOOL$6HPEODW-) )UDFWLRQDOGHULYDWLYHV DQ DOWHUQDWLYHDSSURDFKWRPRGHOVHLVPLFZDYHDWWHQXDWLRQDQGDPSOLILFDWLRQ,Q :RUOG&RQ IHUHQFHRQ(DUWKTXDNH(QJLQHHULQJ/LVERQ±6HSWHPEHU %R]]DQR)$QGUHXFFL$*DHWD06DOXFFL55RVD& $JHRORJLFDOPRGHORIWKHEXULHG 7LEHU5LYHUYDOOH\EHQHDWKWKHKLVWRULFDOFHQWHURI5RPH%XOO(QJ*HRO(QY ± %R]]DQR)&DVHUWD$*RYRQL$0DUUD)0DUWLQR6 6WDWLFDQGG\QDPLFFKDUDFWHUL]DWLRQ RIDOOXYLDOGHSRVLWVLQWKH7LEHU5LYHUYDOOH\ QHZGDWDIRUDVVHVVLQJSRWHQWLDOJURXQGPRWLRQ LQWKHFLW\RI5RPH-*5 ± %R]]DQR)*LDFRPL$&0DUWLQR6&RUSR1D]LRQDOH9LJLOLGHO)XRFR 6FHQDULRGLGDQ QHJJLDPHQWRLQGRWWRQHOODFLWWGL5RPDGDOODVHTXHQ]DVLVPLFDDTXLODQDGHO ,W-(QJ *HRO(QY ± %R]]DQR)%UHWVFKQHLGHU$*LDFRPL$& /HQWL/ 0DUWLQR 6 6FDUDVFLD0XJQR]]D * 6WHGLOH /7DFLWD-/ 8QGUDLQHGEHKDYLRXURIWKHVDQG\VLOW\OHYHOVRIWKH7LEHUULYHUDOOXYLDO GHSRVLWVLQ5RPH ,WDO\ ,W-(QJ*HRO(QY ± &DVHUWD$0DUWLQR6%R]]DQR)0DUUD)*RYRQL$ '\QDPLFSURSHUWLHVRIORZYHORFLW\ DOOXYLDOGHSRVLWVLQIOXHQFLQJVHLVPLFDOO\LQGXFHGVKHDUVWUDLQV WKH*URWWDSHUIHWWDYDOOH\WHVW VLWH 5RPH,WDO\ %XOO(DUWKT(QJ ± &DVHUWD$%RRUH'05RYHOOL$*RYRQL$0DUUD)'HOOD0RQLFD*%RVFKL( *URXQG PRWLRQVUHFRUGHGLQ5RPHGXULQJWKH$SULO /¶$TXLODVHLVPLFVHTXHQFH VLWHUHVSRQVHDQG FRPSDULVRQ ZLWK JURXQGPRWLRQ SUHGLFWLRQV EDVHG RQ D JOREDO GDWDVHW %66$ ± &RUD]]D$/DQ]LQL05RVD&6DOXFFL5 &DUDWWHULVWUDWLJUDILFLLGURJHRORJLFLHJHRWHFQLFL GHOOHDOOXYLRQLWLEHULQHQHOVHWWRUHGHOFHQWURVWRULFRGL5RPD,O4XDWHUQDULR ± 'RQDWL6)XQLFLHOOR55RYHOOL$ 6HLVPLFUHVSRQVHLQDUFKDHRORJLFDODUHDV WKHFDVHKLVWRU\ RI5RPH-$SSO*HRSK\V ± )XQLFLHOOR5*LRUGDQR* &DUWDJHRORJLFDGHOGL5RPD)RJOLRVFDOD 'LSDU WLPHQWR6FLHQ]HJHRORJLFKH8QLYHUVLW5RPD8IILFLRGLSURWH]LRQHFLYLOHH'LSDUWLPHQWR SURWH]LRQHGHOVXROR$3$7 *LDFRPL$& ,PSOLFDWLRQVRIULYHUV\VWHPRQUHFHQW7LEHU5LYHUDOOXYLXP,O4XDWHUQDULR ,W-4XDW6FL ±
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