Transactions, SMiRT-23 Manchester, United Kingdom - August 10-14, 2015 Division V, Paper ID 703

Transcription

1 Trasactos, SMRT-23 Machester, Uted Kgdom - August 10-14, 2015 Dvso V, Paper ID 703 SOIL-STRUCTURE INTERACTION UNDER STATIC LOADS ACCOUNTING FOR THE EFFECT OF ADJACENT BUILDINGS: DEFINITION AND USE OF A FLEXIBILITY MATRIX FOR THE SOIL MODELLING Perre-Lous Regazzo 1, Sébaste Reyaud 2, Va-Nga Nguye 3, Dao Pham-Th-Ah 4, Slvao Erlcher 5, Domque Allagat 6, Roberto Pto-Ward 7 1 PhD, Egeer, Egs Structures Evroemet Géotechque, Frace. 2 Seor Egeer, Egs Structures Evroemet Géotechque, Frace. 3 Egeer, Egs Idustres, Frace. 4 Seor Egeer, Egs Idustres, Frace. 5 PhD, Techcal Drector, Egs Idustres, Frace. 6 Techcal Drector, Egs Structures Evroemet Géotechque, Frace. 7 Egeer, EDF, Frace. ABSTRACT Durg the desg phase of uclear buldgs, the sol-structure teracto uder statc loads s ofte modelled usg Wkler sol-sprgs. I the smplest cases, the stffess of these depedet sprgs s defed by eglectg the effect of sol ad buldgs outsde the vertcal projecto of the studed foudato. Coversely, whe these effects have to be accouted for, the stffess ca be obtaed after several teratos volvg both the structural fte elemet models (provdg at each terato the reactos at the structure foudato odes) ad the sol model (gvg at each terato the sol settlemet). The reacto forces to sol settlemet rato (ode-by-ode) provde the stffess estmato at each ode for each terato. Whe the sol settlemets computed at two subsequet teratos are almost detcal, terato s stopped. The obtaed stffess values deped o the load case. Hece, a dfferet modellg approach, based e.g. o the sol flexblty matrx s preferable. A three-step procedure for the flexblty matrx calculato s preseted ths paper: () a complete geomechacal model of the ste wth geologcal layers, faults s desged wth the software GDM; () ths model s the mplemeted wth the software FLAC 3D; () usg the FLAC3D model, a ut load s appled o each pot of the sol surface uder the aalysed buldgs: the dsplacemets computed for each ut load o all pots become oe colum of the flexblty matrx. Ths matrx s fally tegrated as a superelemet wth the software ANSYS for the structural computato. The effectveess ad accuracy of ths procedure s dscussed wth referece to the case study of a uclear power plat. Keywords: Sol-structure teracto, flexblty matrx, substructurg method, superelemet INTRODUCTION The purpose of ths artcle s to preset the methodology used to defe the sol-structure teracto uder statc loads ad accoutg for the effect of adjacet buldgs of a uclear power plat. Nuclear facltes are characterzed by ther geometrcal complexty ad by the large sze of the buldgs. Ths has duced the eed for robust umercal tools ad the eed to develop a specfc three-step methodology. The frst phase was the mplemetato of the sol geometry, takg to accout the dfferet states of alterato, the fault etwork, the accurate lthology ad the exact geometry of buldg foudatos. Ths

2 23 rd Coferece o Structural Mechacs Reactor Techology Machester, Uted Kgdom - August 10-14, 2015 Dvso V was acheved usg specfc tools lke GDM ad AutoCAD. The secod aalyss step was the mplemetato of the sol model (lthology ad mechacal parameters) the software FLAC3D used for the sol mechacal computatos ad sol-structure teracto (SSI). The thrd phase was the SSI coducted to compute the sol flexblty matrx. Ths matrx s the used to represet the sol the buldg FE model used for the desg calculatos. Actually, structural calculatos the sol s usually represeted by lear sprgs defed at each ode of the model o the udersde of the raft. For the defto of ther stffess, a teratve process s used, a frst guess s made o sprg stffess the buldg model; ths gves the odal reactos uder the foudato, whch are appled o the sol model. The, the loadg s appled ad a frst couple force/dsplacemet o each ode of the model s calculated. Ths allows defg a ew set of stffess whch s mplemeted for the structural computato. A ew set of force appled to the sol s calculated ad the prevous process s reewed. After several teratos, a covergece crtero s reached. To smplfy ths process, ad uder codto of learty of the sol behavor, t s proposed to compute the sol flexblty matrx. The ma advatage s to facltate the tegrato of the sol stffess the software used for the structural calculatos. THE GEOLOGICAL 3D MODEL Geologcal cotext of the studed ste The layers of sol ecoutered are the followg, from the most recet to the older deposts: - Made groud (athropc deposts): clay ad sady clay (thckess: 1-2m); - Over burde deposts: clay less or more gravely (thckess: ~1m); - Blue Las formato: alterato of mudstoes ad lmestoes (thckess : 75m; - Llstock formato : lmestoes ad mudstoes (thckess : 1,3-3,4m); - Westbury formato : black shales wth lmestoes beds (thckess : 7 -,5m); - Blue Achor formato : grey to gree mudstoes ad sltstoes, wth ahydrte-gypsum levels (thckess : 26-36m); - Red Mudstoes formato: red ad gree mudstoes ad sltstoes wth odules ad levels of ahydrte -gypsum. The foudato raft level s maly the lower part of the Blue Las formato (mudstoes ad sadstoes). Three dfferet water levels are take to accout for desg computatos: ) the atural water level, ) the level for the costructo perod, 21m below the atural water level (after drawdow), ) the level for the explotato perod, at 2m below the atural water level (permaet water level drawdow). Numercal tool ad model costructo method The software used to buld the geologcal model s the geo-modeler GDM. It allows buldg a geologcal model based o the terpolato of data betwee boreholes. A computer-aded desg (CAD) wth AutoCAD software allowed supplemetg ad correctg strata calculated wth the software GDM. I order to buld a geometrcal model of the geologcal layers (3D geo-modeler), the sythess of the factual data (boreholes data) ad the terpreted data (geologcal map) s requred. All factual data ad geologcal rules are captured the GDM software. Some complemetary assumptos are doe order to complete the data-set. These assumptos cocered maly the layer thckess. Moreover, some codtos are mposed o the model. These codtos arse from geologcal processes appled by the software o the geometry of the strata. Data complemets are doe essetally the South-West ad Norther part of the model.

3 23 rd Coferece o Structural Mechacs Reactor Techology Machester, Uted Kgdom - August 10-14, 2015 Dvso V For terpolatg the data, a grd of 2mx2m s used. Ths grd sze allows a suffcet detal the umercal model of the sol for a reasoable computato tmes. For the terpolato computatos of the DTM (Dgtal Terra Model) of the ste topography, we use the ordary krgg (or lear krgg wthout dervatve). For the computatos of the geologcal surfaces, we use the uversal krgg (or krgg wth tred). Ths choce s justfed by the dp of the layers the Norther part of the model. Due to umercal dffcultes (spatal scatterg of the geologcal data), t was ot possble to buld the fault model wth GDM. Cosequetly, the GDM model has bee computed wthout faults. Based o the aalyss of a geologst, the faults are represeted to surface object wth software AutoCAD ad Covads. The GDM model ad the faults are the tegrated to AutoCAD. Ths esures the cotuty betwee the lthologcal model ad the faults system. To ft the geometrcal model to our geologcal aalyss, some redraw work has bee doe wth AutoCAD. The AutoCAD fles clude all the geometrcal formato cocerg the geologcal layers ad the fault system of the ste. A example of cross-secto s gve Fgure 1 o the rght. O the left of Fgure 1 also presets a extract of the geologcal map at the atural groud. Fgure 1 : Example of cross-secto of the umercal geologcal model (rght) ad extract of the geologcal map from the umercal geologcal model (left) The geologcal model (essetally lthology ad faults geometry) does ot clude all the formato o the sol behavor. Thus, several addtos have bee made o the geologcal model to prepare the geotechcal model (essetally mechacal behavor, ad addtoal layers) : - The layers of earth-flls ad the surface sol layers, ther base are defed as geometrcal surface. Ths two layers have specfc mechacal propertes. - The states of alterato of the rock that apply from the surface utl deep, regardless of the ature of the rock: the parameters are defed accordg to the depth. Geotechcally, the mechacal parameters are gve by the pot posto compared to the geologcal layer ad the alterato degrees. I summary, the umercal model, t s set 7 geotechcal layers: 5 rocky layers ad 2 sol layers. The rocky layer s dvded to 4 sub-layers accordg to degree of alterato. Model sze s about sol volume elemet (800m x 500m x 100m thck). THE SOIL MECHANICAL 3D MODEL Am of sol mechacal model ad umercal tool The sol mechacal model must allow represetg the correct behavor of sol uder the structure statc loads accoutg for the teracto effects due to eghborg buldgs. Ths model should allow a accurate represetato of the sol structure teracto (SSI) whch s cosdered as a put data for the structural models. The lthology ad the geo-mechacal parameters are mplemeted FLAC 3D code. Ths code allows the modelg of faults system ad the use of a wde choce of costtutve laws, partcularly the asotropy

4 23 rd Coferece o Structural Mechacs Reactor Techology Machester, Uted Kgdom - August 10-14, 2015 Dvso V of the rock formatos. Ths model takes to accout the phasg of costructo ad the correspodg water levels. Sol costtutve laws ad parameters As metoed above, two types of mechacal behavor are possble: rock behavor or loose sol behavor. The mechacal parameters are defed for the dfferet layers. I order to aalyse the mpact of olearty o the global groud behavor, two set of parameters are defed: oe set defes the behavour wthout falure (lear elastc costtutve laws), aother set defes the falure crtera. The o-learty comes from the falure model. Cosequetly, for each type of mechacal behavor, two set of parameters are used: 1- Sol: a. 1 st set: elasto-plastc behavour wth sotropc behavour (2 parameters) ad a Mohr- Coulomb crtero (3 parameters) b. 2 d set: elastc behavour, sotropc behavour; 2- Rock: a. 1 st set: elasto-plastc behavour wth sotropc elastcty ad a Hoek-Brow crtero (3 parameters) b. 2 d set: elastc behavour, trasversely sotropc model (5 parameters). The value of elastc modulus rages from roughly 10 MPa for the sols to MPa for the rocks. The mechacal parameters (modulus, Posso s rato, frcto agle) were adjusted accordg to the -stu tests (dlatometer, pressuremeter) ad laboratory data (traxal test, oedometer tests). Cocerg the fault system, the geometry of each prcpal fault s represeted accurately. The mechacal law cosdered for faults s a elastc law, taget ad ormal to the surface, ad a Mohr- Coulomb crtero. The base of the foudato rafts s modelled wth a CAD software three dmesos. The, the model s mplemeted the sol computato software. (a) (b) Fgure 2 (a) Vew of the tal sol computatoal model (FLAC 3D) wth the dfferet geotechcal layers wthout alterato layer ad faults; (b) Vew of the slab geometry wth the CAD software Assessmet of o-learty effects The sol mechacal 3D model was used to assess the overall behavour of groud uder the dead weght of all buldgs (log term behavour). Several tests were performed to check the model robustess. I partcular, the comparso betwee the dsplacemets calculated wth FLAC 3D ad those calculated wth aother smple computato method showed good complace. Ths model eables, frstly, to kow the detals of the sol behavour uder each buldg ad, secodly, to calculate the sol structure teracto comprehesvely (stress, stra, dsplacemet ).

5 23 rd Coferece o Structural Mechacs Reactor Techology Machester, Uted Kgdom - August 10-14, 2015 Dvso V The effect of o-learty s assessed by aalysg the occurrece of plastcty zoes ad by comparg the dsplacemet obtaed by the elasto-plastc model, wth that obtaed by the elastc model. Plastc zoes appear at the last load step; evertheless the movemet obtaed wth both models (elastc ad elasto-plastc model) are almost detcal. It s the cocluded that the sol behaves learly uder the operatg loads. Thus the computato of the flexblty matrx ca be performed. The followg secto explas the methodology. Fgure 3 O the left, map of Z-dsplacemet of the sol surface uder the deadweght (color-scale s meter); o the rght, vew of plastc volumes of sol ad represetato of the fault system (color-scale shows the occurrece of plastcty) COMPUTATION OF THE FLEXIBILITY MATRIX FROM FLAC 3D SOIL MODEL Sce the sol behavor s supposed lear, the force-dsplacemet relatoshp s descrbed by the followg equato: where: SF (1) : dsplacemet vector (model of the sol surface uder the buldgs) - - F : force vector - S : flexblty matrx of sol model The dsplacemet vector at each pot s obtaed by the multplcato of the force vector flexblty matrxs. F by a I order to compute the flexblty matrx from the FLAC 3D model, a utary force s appled at each pot uder the buldgs accordg to oe spatal drecto (X, Y or Z). Durg the process, the three spatal drectos are swept. The result of oe computato s the dsplacemet feld uder the buldgs for oe ut load. Ths vector s recorded as a structured text fle whch s easly readable by computer laguage. So, based o the text fle, the flexblty matrx may be bult ad formatted to be read by aother computer program, lke the ANSYS software. The ma advatages of ths method wth respect to more commoly used o depedet Wkler sprgs, are that the computed soluto s accurate (takg to accout the 3D effect), the effect of loads of eghbourg buldgs are take to accout at each pot of the model ad the aswer takes to accout the terms of couplg xz ad yz (o-dagoal terms).

6 23 rd Coferece o Structural Mechacs Reactor Techology Machester, Uted Kgdom - August 10-14, 2015 Dvso V The flexblty matrx [S] geerated by FLAC 3D software s a square matrx of sze 3x3, where s the umber of odes of sold sol model FLAC 3D at the terface wth the foudato raft of the structure (see equato (2)). The matrx s composed by 9 sub-matrces: - [Sxx], [Sxy],[Sxz]: correspodg to the dsplacemet of each ode the respectve drecto X, Y, Z uder the ut force of X drecto, - [Syx], [Syy],[Syz]: dem uder the ut force of Y drecto, - [Sxz], [Syz],[Szz]: dem uder the ut force of Z drecto. x,1 sxx x, sxx, y,1 syx y, syx, z,1 z,,1,1,1,1,1,1 S S S S S S S zx s xx,1, s s xx,, s yx,1, yx,, yy zy xy xz yz zz Fx Fx, Fy F y, Fz Fz,,1,1,1 (2) MODELLING THE SSI BASED ON THE SUBSTRUCTURING METHOD The substructurg method for statc aalyss cossts o codesg a group of fte elemets to oe reduced stffess matrx called superelemet (reduced model). The followg secto presets the costructo of the reduced stffess matrx represetg the sol. Reduced stffess matrx, case 1: all buldgs are modelled Cosder the fte elemet model G costtutes by the two substructures: A (structures model from 1 to ) ad B (sold sol model) as show the fgure below. The fte elemet model G (A+B) ca be subdvded the followg Degrees of Freedom (DOF s) sets: - a: teral DOF s of structures model (A), - b: teral DOF s of sol model (B), - : terface DOF s betwee sol ad structures. F a a a a structure 1 structure 2 structure A F G F b=0 b B sol Fgure 4: Structures from 1 to ad sol models The costructo of the reduced stffess matrx of the sol model (B) at the terface DOF s s totally depedet from the structural model (A) (see techcal paper of AJA about substructurg method). Thus, ths task ca be performed usg a separate sol model.

7 23 rd Coferece o Structural Mechacs Reactor Techology Machester, Uted Kgdom - August 10-14, 2015 Dvso V Cosder the fte elemet sold sol model as show fgure above. After applyg costrat codtos, statc aalyss equatos become flexblty submatrces form as follows: S S b S S b bb F Fb b I sol model, oly terface surface () of sol wth the structure s the loaded area (F 0). All the other parts of sol model are cosdered as uloaded (F b = 0). Thus, the equato (3) ca be smplfed: S (4) F 1 F (5) S Thus, the reduced stffess matrx s the verse of flexblty matrx at terfaces DOF s: red S 1 K (6) - S s computed as explaed the prevous secto To resume, order to perform a statc aalyss of structures by substructurg method, the followg tems are eeded (see Fgure 5): - fte elemet model of structures (A), - reduced stffess matrx of sol to terface DOF s calculated as the verse of the flexblty matrx at the terface DOF s betwee structure ad sol. (3) Structures ad full model of sol Structures ad reduced model of sol structure 1 structure 2 structure structure 1 structure 2 structure sol sol red K S 1 (superelemet) Fgure 5: Substructure method appled for SSI multple structures fouded o the sol Reduced stffess matrx, case 2: oly oe buldg s modelled I practce, a separate structure s studed wth ts ow load cases whch are depedet from the other structures. For stace, we cosder the model of structure 1 oly. The, the structures from 2 to are replaced by load felds correspod to the deadweght load at terface DOF s of these structures wth sol model. The terface DOF s betwee all structures from 1 to ad sol s subdvded two sets: - 1: terface DOF s betwee structure 1 ad sol, - 2: terface DOF s betwee structures 2 to ad sol. The equato (4) s wrtte by submatrces of two sets 1 ad 2 DOF s as below:

8 S S rd Coferece o Structural Mechacs Reactor Techology Machester, Uted Kgdom - August 10-14, 2015 Dvso V S S F1 1 F2 2 - S : sol flexblty submatrx of set 1 of terface DOF s (structure 1) - S 22 : sol flexblty submatrx of set 2 of terface DOF s (structures 2 to ) S , S 21 : couplg flexblty submatrces betwee set 1 ad 2 of terface DOF s, F : load path feld at set 1 of terface DOF s uder studed load case o structure 1, F : load path feld at set 2 of terface DOF s uder studed load case o structures 2 to. - 2 {F 2} (7) structure 1 structure 1 sol set 1 DOF s set 2 DOF s sol, K red S 1 (superelemet) 1 F S S ext 12 F 2 (exteral load appled at foudato raft odes) Fgure 6: Substructure method appled for SSI teracto betwee structures The equato (7) results followg equatos: red - K, S F 1 S 12 F 2 1 S F S F (8) (9) F 1S S 12 F2S 1, red K 1F 1F ext, red 1 1 K S F S S (10) () & ext 12 F 2 : reduced stffess matrx of terface DOF s betwee structure 1 ad sol, F : load feld at terface DOF s betwee structure 1 ad sol due to the deadweght of the - ext other buldgs. To resume, order to perform a statc aalyss of oe structure takg to accout the effect of adjacet buldgs by substructurg method, the followg tems are eeded (see Fgure 6): - fte elemet model ANSYS of cosdered structure (structure 1), red - reduced stffess matrx K,, that s the verse of flexblty matrx of sol at terface DOF s betwee structure 1 ad sol, tegrated ANSYS code as a superelemet matrx, - exteral forcef ext at foudato raft odes of cosdered structure ( 1), calculated from other structures 2 to, cosdered as a separated load case.

9 CASE STUDY: UK EPR NUCLEAR ISLAND 23 rd Coferece o Structural Mechacs Reactor Techology Machester, Uted Kgdom - August 10-14, 2015 Dvso V I ths secto, the results of SSI study for NI2 buldg are show (see fgure below). The reduced red stffess matrx K, at terface DOF s betwee sol ad NI2 buldg s calculated ad the tegrated ANSYS model as a superelemet. Ths matrx s appled for all statc loads. NI2 Fgure 7: Localsato of NI2 buldg ste The Fgure 8 presets the settlemet of foudato raft of NI2 buldg uder deadweght loads of eghbour buldgs (wthout deadweght of NI2 buldg). The settlemet observed o the rght sde of foudato raft, where may other buldgs are located, s more sgfcat tha the oe o the left sde, where oly oe buldg s located. Fgure 8: Settlemet feld of foudato raft uder deadweght of eghbour buldgs The followg fgure presets the settlemet of foudato raft of NI2 buldg uder deadweght of NI2 buldg (wthout fluece of deadweght of eghbour buldgs): Fgure 9: Settlemet feld of foudato raft uder self-weght load of NI2 buldgs

10 23 rd Coferece o Structural Mechacs Reactor Techology Machester, Uted Kgdom - August 10-14, 2015 Dvso V CONCLUSION I ths paper, a methodology has bee preseted for the accurate represetato of the sol by a flexblty matrx to a fte elemet model for statc structural calculatos. The ma assumpto s that the sol behavor s lear uder the cosdered loads. I detal, for the aalysed case study, the sol mechacal 3D model was bult wth several umercal tools: GDM ad Autocad for the geologcal model, whch has bee mplemeted FLAC3D wth the sutable mechacal laws of sol. Ths model was used to assess the overall behavour of groud uder the effect of the full structure deadweght. The effect of o-learty s assessed by aalysg the occurrece of plastcty zoes ad t was cocluded that the sol behaves learly. Thus the computato of the sol flexblty matrx has bee performed. We recall that the sol flexblty matrx s a trsc represetato of the sol, whch s totally depedet from the stffess, loadg, geometry of structures. The, ay modfcato of structures does ot requre the recosderato of the boudary codto (sol) ad the results are the same tha the oes obtaed wth the complete model. Ths cosderably mproves the usual methodology based o the use of depedet sol sprgs whose load depedet stffess s obtaed by a expesve teratve process. REFERENCES GDM verso 7.0, Bureau des recherches géologques et mères (BRGM), Frace. AutoDesk, AutoCAD 20, ITASCA, Fte Lagraga Approach of Cotua (F.L.A.C.3D) verso 5.0, P.G. Kelly (October 1998). Developmet ad teracto of segmeted fault systems, Uversty of Southampto, UK. Bowyer ad P.G. Kelly (1995). Stra ad scalg relatoshp of faults ad ves at Klve, Somerset, Aual Coferece of the Ussher Socety, M. O N. Prudde, H.C. (2005). Strke-slp faultg Somerset ad adjacet areas, The Ussher Socety. Egelder, T. ad Peacock Davd C.P (Jue 2000). Jot developmet ormal to regoal compresso durg flexural-flow foldg : the Llstock buttress atcle, Somerset, Eglad Joural of Structural Geology. Km, Y.S., Peacock, Davd C.P. ad Saderso, Davd J. (November 2002). Fault damage zoes, Joural of Structural Geology. Rves, T. (October 1992). Mécasmes de formato des daclases das les roches sédmetares, approche expérmetale et comparaso avec quelques exemples aturels, Uversté de Motpeller II, Motpeller, Frace. AJA, A. M. (2000). Sub-modellg techques for statc aalyss, MSC Software Frst South Europea Techology Coferece, Prcpauté de Moaco, 7-9 Jue ANSYS software: Reducto Techque, Part 2 : Substructurg Applcablty ad Examples