Seismic Earth Pressure Development in Sheet Pile Retaining Walls: A Numerical Study

Transcription

1 8 th Australasan Congress on Appled Mechancs, ACAM November 014, Melbourne, Australa Sesmc Earth Pressure Development n Sheet Ple Retanng Walls: A Numercal Study P Raeev 1*, H Bu, N Svakugan 3 1 Department of Cvl and Constructon Engneerng, Swnburne Unversty of Technology, Australa Department of Cvl Engneerng, Monash Unversty, Australa 3 School of Engneerng & Physcal Scences, James Cook Unversty, Townsvlle, Qld, Australa *Correspondng author Emal: praeev@swneduau Abstract: The desgn of retanng walls requres the complete knowledge of the earth pressure dstrbuton behnd the wall Due to the complex sol-structure effect, the estmaton of earth pressure s not an easy task; even n the statc case The problem becomes even more complex for the dynamc (e, sesmc) analyss and desgn of retanng walls Several earth pressure models have been developed over the years to ntegrate the dynamc earth pressure wth the statc earth pressure and to mprove the desgn of retanng wall n sesmc regons Among all the models, Mononobe- Okabe (M-O) method s commonly used to estmate the magntude of sesmc earth pressures n retanng walls and s adopted n desgn practces around the world (eg, EuroCode and Australan Standards) However, the M-O method has several drawbacks and does not provde relable estmate of the earth pressure n many nstances Ths study nvestgates the accuracy of the M-O method to predct the dynamc earth pressure n sheet ple wall A D plane stran fnte element model of the wall-sol system was developed n DIANA The backfll sol was modelled wth Mohr-Coulomb falure crteron whle the wall was assumed behave elastcally The numercally predcted dynamc earth pressure was compared wth the M-O model predcton Further, the pont of applcaton of total dynamc force was determned and compared wth the statc case Fnally, the applcablty of M-O methods to compute the sesmc earth pressure was dscussed Keywords: Sesmc earth pressure, retanng wall, elasto-plastc, Mohr-Coulomb, Mononobe-Okabe 1 Introducton Regardless the multtude of studes that have been carred out over the years, the dynamc response of earth-retanng walls s far from beng well understood There s, n current engneerng practce, a lack of conclusve nformaton that can be used n desgn method The most commonly used methods to desgn earth-retanng structures under sesmc condtons are force-based equlbrum approaches lke the pseudo-statc analyss (eg Mononobe-Okabe [1]) and pseudo-dynamc technques (Steedman and Zeng []), and dsplacement-based procedures such as the sldng block method (eg Rchards and Elms [3]) In the lmt-state methods of analyses, the wall s consdered to dsplace or deform suffcently at the base to fully moblze the shearng strength of the backfll Even under statc condtons, predcton of actual retanng wall pressures and deformatons consttute a complcated sol-structure nteracton problem The dynamc response of even the smplest type of retanng wall s therefore a qute complex phenomenon It depends on the mass and stffness of the wall, the backfll and the underlyng ground, as well as the nteracton among these components and the nature of the sesmc motons The purpose of ths study was to develop a fnte element model to shed lght nto understandng the dynamc behavour of sheet ple wall, n partcular to fnd the dstrbuton of dynamc lateral earth pressures In all the analyses, the sol was assumed to behave as a homogeneous, elasto-plastc medum wth a Mohr-Coulomb falure crteron The wall was assumed to behave as a lnear elastc materal The numercal model for the wall and surroundng sol have been developed usng DIANA [4], a commercally avalable fnte element program

2 The results obtaned wth DIANA were compared wth results obtaned from pseudo-statc analyss usng the procedure by Mononobe-Okabe and Wood analytcal solutons Mononobe-Okabe Earth Pressure Models Okabe [5], Mononobe and Matsuo [1] were the poneers to obtan the actve and passve earth pressure coeffcents under sesmc condtons It was an extenson of Coulomb s method n the statc case for determnng the earth pressures by consderng the equlbrum of a trangular falure wedge The method s now commonly known as Mononobe-Okabe method For actve and passve cases, planar rupture surfaces were assumed n the analyss Fgure (1) shows the falure surfaces at actve and passve states, and the forces consdered n the analyss The Mononobe-Okabe approach s valuable n provdng a good assessment of the magntude of the peak dynamc force actng on a retanng wall However, the method s based on three fundamental assumptons: 1 The wall has already deformed outwards suffcently to generate the mnmum (actve) earth pressure; A sol wedge, wth a planar sldng surface runnng through the base of the wall, s on the pont of falure wth a maxmum shear strength moblzed along the length the surface; and 3 The sol behnd the wall behaves as a rgd body so that acceleraton can be assumed to be unform throughout the backfll at the nstant of falure kvw khw plane falure surface ah=khg av=kvg Actve AE P a kvw P p PE khw plane falure surface Passve Fgure 1: Falure surfaces and the forces consdered by Mononobe-Okabe The expresson for computng the sesmc actve and passve earth force, P ae,pe, s gven by K ae, pe cos cos 1 (1) P ae, pe H (1 kv ) K ae, pe cos ( ) sn( )sn( cos( ) 1 cos( ) cos( ) where, γ s the unt weght of sol, H s the vertcal heght of the wall, K ae,pe s the sesmc actve and passve earth pressure coeffcent, φ s the sol frcton angle, δ s the wall frcton angle, β s the wall nclnaton wth respect to vertcal, s the ground nclnaton wth respect to horzontal on both sdes of the wall, k h s the sesmc acceleraton coeffcent n the horzontal drecton, and k v s the sesmc acceleraton coeffcent n the vertcal drecton k h tan 1 (3) 1 kv In Mononobe-Okabe analyss, the pont of applcaton of the total sesmc actve or passve force s consdered to be at H/3 from base of the wall, but expermental results (Jacobse 1939, Matsuo 1941) 05 ()

3 [6] show t s slghtly above H/3 from base of the wall for sesmc actve case Prakash and Basavanna [7] have made an analyss to determne the heght of the resultant force n the Mononobe-Okabe analyss Seed and Whtman [8] recommended that the dynamc component be taken as actng at 06H Mononobe-Okabe analyses show that k v, when taken as one-half to two-thrds the value of k h, affects the total actve or passve pressure by less than 10% Seed and Whtman [8] concluded that vertcal acceleratons can be gnored when the Mononobe-Okabe method s used to estmate the total pressure for typcal wall desgns The Mononobe-Okabe method s very smple and straghtforward, has been used by desgners for long, because expermental and theoretcal studes have shown that t gves satsfactory results n cases where the backfll deforms plastcally and the wall movement s large and rreversble (Whtman [9]) However, there are many practcal cases, such as massve gravty walls or basement walls braced at top and bottom, where the wall movement s not suffcent to nduce a lmt state n the sol 3 Sheet Ple Wall-Sol System Fgure shows the sol-wall system that has been studed n ths paper The heght of the flexble wall s 60 m, wth 5 m of embedment The backfll and foundaton sol s assumed to be medum-dense, coheson-less, compacted fll Its geotechncal propertes are as follows: unt weght: γ s = 196 kn/m 3 ; effectve angle of nternal frcton: φ = 40 The water table s assumed located well below the bottom of the wall and thus the analyses are performed assumng dry sol It s a plane stran problem The propertes of the concrete and of the renforcng steel used for desgnng the wall are as follows: concrete unt weght : γ c = 36 kn/m 3 ; concrete compressve strength: f c = 76 MPa; steel yeld strength: f y = 4134 MPa 05 m Retanng Wall 6 m 5 m Fgure : Dmensons of the sheet ple retanng wall The prmary parameters governng the dynamc response of the system are the relatve flexblty of the wall and retaned medum and relatve flexblty of the rotatonal pont constran gven by retaned sol The characterstcs of the base moton also affect the response 4 Numercal Model The DIANA fnte element model conssts of the upper 15 m of the wall-sol system; contanng wall and backfll and 4 m of the underlyng natural sol below the base of the wall Laterally, the model s approxmately 385 m, to nclude 1 m of exstng sol n front of the wall, approxmately 6 m of the backfll/exstng sol behnd the wall and 05 m wall thckness (Fgure 3) The sol and wall are modelled usng eght-node quadrlateral soparametrc plane stran elements These elements are based on quadratc nterpolaton of dsplacement and Gauss ntegraton An elasto-plastc consttutve model, n conuncton wth Mohr-Coulomb falure crteron, s used to model the sol Plane-stran elements are also used to model the concrete retanng wall as a lnear elastc materal The wall/backfll was numercally constructed n DIANA smlar to the way an actual wall would be constructed The sol n front of the wall s excavated n two steps, each of 3 m, wth the

4 model beng brought to statc equlbrum after each excavaton Such excavaton allowed realstc earth pressure to develop as the wall deformed durng the excavaton 1 m 6 m 15 m 9 m 385 m Fgure 3 Annotated DIANA model of the wall-sol system The small stran natural frequency of the DIANA model of the retanng wall-sol system s estmated to be 48 Hz ( 50 Hz) At hgher stans, t s expected that the natural frequency of the system wll be less than 5 Hz The cut-off frequency for dynamc analyss was set at 15 Hz All along the model, the sze of the elements vared from 05 to 10 m n both drectons, whch was less than one eghth of the shortest wave length that corresponds to the hghest frequency of 15 Hz consdered n the transent analyss (Kuhlemeyer and Lysmer [10]) Total of 806 elements was used n the model 41 Model Parameters for the Sol The stress-stran behavour of the sol was modelled usng the Mohr-Coulomb consttutve model The sol nput parameters used n the fnte element model are gven n Table 1 Table 1 DIANA nput propertes of sand Parameters value Posson s rato 06 At-rest pressure coeffcent 036 Small stran Young s modulus (MPa) Effectve frcton angle 40º Densty (kg/m 3 ) Model Parameters for the Wall The concrete wall s modelled to behave lnear elastcally durng the whole analyss The parameters are requred to defne the mechancal propertes of the wall: densty (ρ), elastc modulus (E c ), and Posson s rato (ν) E c s calculated usng followng equaton: where f c s compressve strength of concrete 43 Dampng ' Ec 5000 fc MPa (4) Table DIANA nput propertes of concrete Parameters Value Elastc modulus of concrete (MPa) 30,000 Yeld strength of steel (MPa) Young s modulus of steel (GPa) 00 Densty of concrete (kg/m 3 ) 400 As stated before, the sol was modelled as an elasto-plastc Mohr-Coulomb materal Inherent n ths model s that once the nduced dynamc shear stresses exceed the shear strength of the sol, the plastc deformaton of the sol ntroduced consderable hysteretc dampng However, for dynamc stresses less than the shear strength, the sol behaves elastcally, wthout any dampng In order to avod over dampng n large deformaton stuatons, a lower bound dampng rato of one percent of

5 Raylegh dampng was set to the sol at frst natural frequency of the system and the predomnant frequency of the exctaton 5 Ground Moton To perform the dynamc analyss, three real earthquake acceleraton tme-hstores were selected wth varyng levels of ntensty and they nclude the 1940 Imperal Valley earthquake (Calforna), the 1999 Ch-Ch earthquake (Tawan), and the 1995 Hyogoken-Nambu (Japan), correspondng to low, medum and hgh Peak Ground Acceleraton (PGA), respectvely The response of nonlnear dynamc solstructure system may be strongly affected by the tme-doman character (eg, frequency content, shape, number of pulses of tme-hstory, and response spectrum characterstc) of tme-hstores even f the spectra of dfferent tme-hstores are nearly dentcal 6 Results and Dscusson Dynamc analyses were performed usng the acceleraton tme-hstores descrbed above The results obtaned from DIANA were compared wth those determned usng a pseudo-statc method (e followng the approach by Mononobe-Okabe) Followng Green and Ebelng [11] approach, the dynamcally-nduced lateral earth pressures actng on the wall were computed by assumng constant stresses wthn the element The correspondng lateral earth pressure coeffcent (K,DIANA) could then be back-calculated at tme ncrement from DIANA results usng the followng expresson: K, DIANA P, DIANA (5) H 1 k where, P,DIANA s the resultant of force computed by DIANA and actng on the wall, γ t s the total unt weght of the backfll, H s the heght of the wall, and k v, s the vertcal nertal coeffcent (assumed n ths study equal to zero) Equaton (5) s used to compute K DIANA values at tmes correspondng to the peaks n the tme-hstory of the horzontal nertal coeffcent (k h ), whch s calculated from acceleraton tme-hstory recorded at the mdpont of the sldng wedge n both the actve and passve sdes The drecton of k h s opposte to drecton of the acceleraton and acts towards and away from the backfll (more detal can be found n Raeev [1]) A plot of the computed K,DIANA values versus k h s shown n Fgure 4 The calculaton of K,DIANA was carred out at the preselected tmes, where the maxmum acceleraton occurs n all three tme-hstores to cover the entre range of k h Also shown n ths fgure are the lateral dynamc earth pressure coeffcents (actve: K AE ; Passve: K PE ) computed usng the Mononobe-Okabe expressons for the wall-sol system (Okabe [5]; Mononobe [1]) and Wood [1] soluton for rgd wall Followng observatons were made from the Fgure 4 1 Actve pressure coeffcent: v, a K DIANA K Mononobe-Okabe, for moderate levels of shakng b K DIANA < K Mononobe-Okabe, for larger levels of shakng c K away from backfll > K towards backfll d The computed K values show a general scatter around the curve for the Mononobe-Okabe dynamc actve earth pressure curve Passve pressure coeffcent: e The computed K DIANA values for lower levels of shakng show values sgnfcantly lower than the K Mononobe-Okabe f The computed K DIANA ncreases wth level of shakng g The computed K DIANA values do not show a general scatter around the curve for the Mononobe-Okabe dynamc passve earth pressure curve

6 Fgure 4 Comparson of actve and passve lateral earth pressure coeffcents (K DIANA ) backcalculated from DIANA results wth values computed usng the Mononobe-Okabe and Wood expressons At larger levels of shakng, the Mononobe-Okabe expressons for actve pressures faled to predct the nduced stresses on the wall The computed dynamc stresses from numercal analyss are hgher than those computed by the Mononobe-Okabe equaton for actve pressures n the range of small to moderate levels of shakng At the lower levels of shakng, the passve pressures are not fully moblzed, therefore the K values computed from the DIANA results are smaller than those calculated from the Mononobe-Okabe expressons When the level of shakng ncreases, the moblzaton of passve pressure also ncreases, and consequently the K values ncrease The ponts of applcaton of the total and ncremental dynamc resultant forces are also mportant parameters for desgn and stablty assessment of sheet ple wall Therefore, the vertcal dstances (Y ) from the base of the retanng wall to the ponts of applcaton of total dynamc forces (P )actng on the wall were computed usng the followng relaton: Y h, h where, Y s the vertcal dstance from the base of the retanng wall to the pont of applcaton of the total resultant force actng on the wall at tme ncrement, y s the vertcal dstance from the base of the retanng wall to the centre of element,, s the average stress actng on the element and at tme ncrement, and h s the length of element Fgure 5 compares the pont of applcaton of total dynamc force together wth pont of applcaton of statc force calculated at the end of the constructon of the wall The pont of applcaton of statc force (095%) calculated was below the value (033%) calculated usng trangular stress dstrbuton along the heght, because the stresses below the pont of rotaton of wall had very large passve stresses Further, the ponts of applcaton of dynamc forces for lower levels of shakng show a scatter around 05% (H/4), but for larger level of shakng t showed bg range of devaton y, (6)

7 Fgure 5 Pont of applcaton of total actve dynamc force on sheet ple wall 7 Summary and Conclusons Ths paper llustrates a prelmnary nvestgaton onto the sesmc behavour of flexble sheet ple wall, retanng a dry granular backfll A fnte element model of the system s bult usng DIANA fnte element program For the sol surroundng the sheet ple was modelled as elasto-plastc materal wth Mohr-Coulomb falure crteron The results from ths study show that usng the Mononobe-Okabe equaton to desgn the sheet ple wall wll provde good estmate for dynamc stresses on the actve sde Conversely, t wll overestmate dynamc stresses n the passve sde Further, the pont of applcaton of total dynamc forces n actve sde s below the pont of applcaton of statc forces, around 05H, because of the large passve pressure beyond the pont of rotaton of the wall The conclusons drawn from ths study may not apply to retanng wall system of dfferng geometry and/or materal propertes Further research s requred to draw more general conclusons regardng the approprateness of the Mononobe-Okabe method to evaluate the dynamc pressure nduced under sesmc condtons on the sheet ppe walls References 1 Mononobe, N, and Matuo, H, 199, On the determnaton of earth pressures durng earthquakes, Proc World Engrg, Congr, Tokyo, Japan, vol9, paper no388 Steedman, RS, and Zeng, X, 1990, The nfluence of phase on the calculaton of pseudo-statc earth pressure on a retanng wall, Geotechnque, 40 (1), , 3 Rchard, R, and Elms, DG, 1979, Sesmc behavor of gravty retanng walls, JGeotec Engrg, ASCE, 105 (GT4)Hassots, S, Khodar, Y, Roman, E, Dehne, Y, 006, Lateral Earth Pressure Behnd Integral Abutment Walls, Evaluaton of Integral Abutments, Vol 1, pg DIANA fnte element analyss User s manual Release 9 TNO DIANA BV 5 Okabe, S, 194, General theory of earth pressure and sesmc stablty of retanng wall and dam, JJapan Soc Cv Engrs, Tokyo, Japan, 1(1) 6 Nason J McCullough, and Dckenson, S E, 1998, Estmaton of sesmcally nduced lateral deformatons for anchored sheetple bulkheads, Conference proceedngs of Geotechncal Earthquake Engneerng and Sol Dynamcs III, August 3-6, 1998, Seattle, WA, USA pp Prakash, S, and Basavanna, B M, 1969, Earth pressure dstrbuton behnd retanng wall durng earthquake, Proc, 4 th world Conf on Earthquake Engrg, Satago, Chle 8 Seed, HB, and Whtman, RV, 1970, Desgn of earth retanng structures for dynamc loads, ASCE SpecConf Lateral Stresses n the ground and desgn of retanng structures,cornell,pp

8 9 Whtman, R, V, 1990, Sesmc desgn and behavor of gravty retanng walls, Proc, Spec Conf on Des And Constr Of Earth Retanng Struct, ASCE, New York, NY, Kuhlemeyer, R L, and Lysmer, J, 1973, Fnte Element Method Accuracy for Wave Propagaton Problems, Journal of the Sol Mechancs and Foundatons Dvson, ASCE, Vol 99, No SM5, Proc Paper 9703, May, 1973, pp q J Sol Mech and Found Dv 11 Green, RA, and Ebelng, RM, 00, Sesmc analyss of cantlever retanng walls, Phase I, ERDC/ITL TR-0-3, Informaton technology laboratory, US army corps of engneers, Engneer research and development center, Vcksburg, MS, 00 1 Raeev, 007, Numercal modelng of sesmc behavour of earth-retanng walls, MSc thess, ROSE School, Unversty of Pava, Italy 13 Wood, J H, 1973, Earthquake-nduced sol pressures on structures, Rep EERL 73-05, Earthquake Engneerng Research Laboratory, Calforna Inst of Technol, Pasadena, Calf