THE EFFECT OF SHEAR STRENGTH NORMALISATION ON THE RESPONSE OF PILES IN LATERALLY SPREADING SOILS

Eathquake Geotechnical Engineeing Satellite Confeence XVIIth Intenational Confeence on Soil Mechanics & Geotechnical Engineeing 2-3.. 29, Alexandia, Egypt THE EFFECT OF SHEAR STRENGTH NORMALISATION ON THE RESPONSE OF PILES IN LATERALLY SPREADING SOILS Misko CUBRINOVSKI, Jennife HASKELL 2 and Bendon BRADLEY 3 ABSTRACT In the simplified pseudo-static analysis of piles, the ultimate lateal pessue fom the liquefied soil is commonly appoximated based on the esidual stength of liquefied soils. This stength does not have sound theoetical basis, but athe is estimated fom one of seveal empiical elationships between the esidual stength and penetation esistance. The two empiical elationships adopted in this study, even though oiginating fom the same database, esult in substantially diffeent stength pofiles (ultimate lateal pessues on the pile thoughout the depth of the liquefied laye. Seies of analyses wee conducted to investigate the effects of stength nomalisation on the pile esponse pedicted by the pseudo-static analysis. It was found that effects of stength nomalisation can be quite significant and that they depend on the elative stiffness of the pile and thickness of a non-liquefiable cust at the gound suface. Keywods: Liquefaction, lateal speading, pile, pseudo-static analysis INTRODUCTION The esponse of piles in liquefying deposits duing eathquakes is vey complex involving apidly vaying dynamic loads and significant eduction in soil stiffness and stength caused by liquefaction. Duing lateal speading of liquefied soils, the piles ae subjected to lage kinematic loads due to lateal movement of the speading soil and compaatively smalle inetial loads fom the diminishing vibation of the supestuctue. As illustated schematically in Figue, the liquefied soil and an ovelying cust at the gound suface povide diving foces fo the pile displacement in the diection of speading, while the base soil esists the pile movement. In the pseudo-static method of analysis, a elatively simple soil-pile model based on this mechanism is used to estimate the maximum defomation of the pile and its consequent damage due to speading. The simplified pseudo-static analysis is budened by significant uncetainties egading the chaacteization of lateal loads on the pile and popeties of the adopted soil-pile model. The uncetainties and difficulties in the modelling ae paticulaly ponounced fo the paametes of the liquefied soil, such as stiffness, stength and displacement of the liquefied soil. This pape focuses on one paticula aspect in the modelling of the lateal pessue fom the liquefied soil and its effects on the pile esponse. Namely, the appoximation of the ultimate pessue fom the liquefied laye on the pile based on the esidual stength of liquefied soils. A couple of well-known empiical elationships ae available fo estimating the esidual stength of liquefied soils, one using nonnomalised esidual stength (S and the othe using nomalised esidual stength (S /σ' vo. The key diffeence in the context of pile analysis is that these two elationships suggest vey diffeent distibutions of stength (ultimate lateal pessue fom the soil on the pile thoughout the depth of the liquefied laye. In this study, seies of pseudo-static analyses wee conducted to examine and quantify the effects of stess nomalisation on the pile esponse pedicted by the pseudo-static analysis. Models with diffeent cust thickness and piles of diffeent stiffness wee consideed in the analyses. Associate Pofesso, Univesity of Cantebuy, Chistchuch, New Zealand, misko.cubinovski@cantebuy.ac.nz 2 Reseach Student, Univesity of Cantebuy, Chistchuch, New Zealand, jjh64@student.cantebuy.ac.nz 3 PhD Student, Univesity of Cantebuy, Chistchuch, New Zealand, bab54@student.cantebuy.ac.nz

2 Effects of soil stength nomalization on pile esponse Figue. Schematic illustation of lateal loads on piles due to speading of liquefied soils and consequent damage PSEUDO-STATIC ANALYSIS OF PILES The pseudo-static method of analysis povides a pactical engineeing appoach fo seismic assessment of piles based on outine computations and use of elatively simple models. It aims at estimating the peak esponse of the pile (maximum stains o cuvatue of the pile due to eathquake shaking o lateal speading unde the assumption that complex dynamic loads can be idealized as static actions. Geneally, two appoaches ae used fo pseudo-static analysis of piles subjected to lateal speading: foce-based methods and displacement-based methods. These two appoaches diffe in the way in which the lateal load on pile due to gound movement (kinematic load is consideed. In foce-based methods, an equivalent static load epesenting the pessue fom the lateally speading soil is applied to the pile. Fo a typical thee-laye configuation with a liquefied laye sandwiched between a non-liquefied suface laye (cust and a non-liquefied base laye, the lateal eath pessues fom the cust and liquefied laye ae estimated and applied as diving loads (pushing the pile in the diection of speading, as shown in Figue 2a. One seious deficiency of this appoach is that it ignoes the dependence of the magnitude of the mobilized lateal soil pessue on the pile esponse (o elative displacement between the soil and the pile. In this context, the displacement-based methods offe moe igoous modelling that is compatible with the mechanism of soil-pile inteaction. In this appoach lateal gound displacements (epesenting fee field gound movement ae applied at the fee end of soil spings attached to the pile, as illustated in Figue 2b. In this case, the foces that develop in the soil spings ae compatible with the elative Figue 2. Pseudo-static methods fo analysis of piles: (a Foce-based appoach; (b Displacement-based appoach

M.Cubinovski, J.Haskell and B.Badley 3 displacement between the soil and the pile, and hence, the mobilized lateal soil pessue is compatible with the induced pile esponse. The displacement-based appoach allows scutiny of the behaviou of piles ove the entie ange of defomation, fom elastic (small lateal loads to failue (lage lateal loads, and theefoe was adopted in this study. Note howeve that, in pinciple, the conclusions with egad to the effects of shea stength nomalisation on the pile esponse (the subject of this study ae applicable to both displacement-based and foce-based methods. A typical beam-sping model epesenting the soil-pile system in the simplified pseudo-static analysis is shown in Figue 3. Since a key equiement of the analysis is to estimate the inelastic defomation and damage to the pile, simple but non-linea load-defomation elationships ae used fo the soil-pile model. The pile is modelled using a seies of beam elements with a tilinea moment-cuvatue elationship, while the soil is epesented by bilinea spings in which degaded stiffness and stength of the soil ae employed to account fo effects of nonlinea behaviou and liquefaction. Since the behaviou of piles in liquefying soils is extemely complex, involving vey lage and apid changes in soil stiffness, stength and lateal loads on the pile, one of the key questions in the implementation of the pseudo-static analysis is how to select appopiate values fo these paametes in the equivalent static analysis. In othe wods, what ae the appopiate values fo β, p L-max, U G and F in the model shown in Figue 3? While discussion on thei detemination, uncetainties in these paametes and the sensitivity of the pile esponse to thei vaiation can be found in Cubinovski et al. (29, Cubinovski and Badley (28 and Haskell et al. (29 espectively, the attention focus hee is one paticula aspect in the modelling of the lateal pessue fom the liquefied soil on the pile. LATERAL PRESSURE FROM LIQUEFIED SOILS The significant uncetainties associated with the stiffness and stength of liquefied soils esult in a lage anticipated vaiation of the bilinea p-δ elationship fo the liquefied soil, as illustated in Figue 4. The ultimate lateal pessue fom the liquefied soil (p L-max is often appoximated based on the esidual (shea stength of liquefied soils (S as p L max = α LS ( whee α L is a facto that accounts fo the volume of soil contibuting to the geneation of soil pessue on the pile (equivalent to the wedge-mechanism concept. a Coss section b Numeical scheme U G U P H C Non-liquefied cust laye Lateal load, F p kc p C-max δ H L Liquefied layes Fee field gound displacement M Y C p φ U β kl p L-max δ H B Non-liquefied base laye Soil sping Defomed pile Pile p k B p B-max Figue 3. Typical beam-sping model fo simplified pseudo-static analysis of piles δ

4 Effects of soil stength nomalization on pile esponse Figue 4. Schematic illustation of vaiation in the p-δ elationship fo the liquefied soil Thee ae seveal empiical elationships between the esidual stength of liquefied soils and penetation esistance established using back-calculations fom liquefaction case histoies. Based on an ealie wok by Seed (987, Seed and Hade (99 poposed an empiical elationship between S and SPT blow count (N 6cs, shown in Figue 5a. The elationship encompasses data of oughly 2 case histoies and is chaacteized by consideable scatte. Fo example, fo a nomalised equivalent-sand blow count of (N 6cs =, the esidual stength takes values between 5 kpa and 25 kpa. Using the same case histoy data, Olson and Stak (22 poposed an altenative elationship between the esidual stength and SPT esistance in which a nomalised esidual stength (S /σ' vo is coelated with (N 6, as shown in Figue 5b. Hee, the shea stength of the liquefied soil at depth z is nomalised by the espective effective ovebuden stess, σ' vo (z. Recently, Idiss and Boulange (28 eintepeted the same data set and poposed a pai of empiical elationships, disciminating between cases in which voids atio edistibution (loosening of the soil duing the liquefaction pocess occus o not. Again, they pesented thei elationships in two foms, non-nomalised S -(N 6, and nomalised (S /σ' vo -(N 6. The nomalisation (o not of shea stength of liquefied soils is an unesolved issue and ecommendation of one method in pefeence to the othe is beyond the scope of this pape. Rathe, this study investigates the effect of this nomalisation on the esponse of piles pedicted using the simplified pseudo-static analysis. INVESTIGATED SOIL-PILE MODELS Compehensive seies of paametic analyses wee conducted fo diffeent soil pofiles and piles encompassing a wide ange of soil popeties (vey loose to medium dense liquefied soil; vey soft Figue 5. Empiical elationships between esidual stength of liquefied soil and penetation esistance: (a Non-nomalised, Seed and Hade (99; (b Nomalised, Olson and Stak (22

M.Cubinovski, J.Haskell and B.Badley 5 to vey dense base laye and pile chaacteistics (flexible to stiff piles. Hee, analyses and esults fo one of these soil pofiles ae pesented in ode to illustate the effects of stength nomalisation on the pile esponse. As shown in Figue 6, a 2 mete-long pile is embedded in a deposit consisting of two layes, a loose sand laye (N =5 ovelying a non-liquefiable base laye of stiff gavel. Both layes have a thickness of m. Assuming that the soil above the wate table acts as a cust of non-liquefiable suface soil, five diffeent scenaios wee adopted fo the location of the wate table between z = and 2 m depth, defining a cust of thickness of H C =,.5,,.5 and 2 m espectively. The emaining pat of the loose sand laye below the wate table defined the thickness of the liquefiable laye, H L = - H C =, 9.5, 9, 8.5 and 8 m espectively. To account fo the effects of elative pile stiffness on the esponse, thee diffeent piles with diametes of 4, 8 and 2 mm wee consideed as epesentatives of a elatively flexible (F-Pile, intemediate (M-Pile and elatively stiff pile (S-Pile espectively. Tilinea moment-cuvatue elationships of actual einfoced concete piles wee adopted fo the piles. In total 5 computational models wee consideed, with five diffeent thicknesses of the cust and thee diffeent piles. Details about detemination of model paametes including ange of ealistic values, bestestimates o efeence values, and effects of uncetainties on the pile esponse ae given in Haskell et al. (29. In the analyses of the stength nomalisation effects pesented heein, models with efeence values of the paametes wee used. Fo example, fo the paamete α L a efeence value of α L = 3 was adopted fom a ange of expected ealistic values fom to 6. Fo each of the 5 computational models intoduced above, lateal speading displacements (U G anging fom. to 2. m wee applied as input in the pseudo-static analysis. Fo each case consideed, two analyses wee pefomed, one using non-nomalised stength fo the liquefied soil (as poposed by Seed and Hade, 99 and the othe using nomalised stength fo the liquefied soil (as poposed by Olson and Stak, 22. The esulting diffeence in the shea stength pofiles (and espective distibution of ultimate pessue on the pile fo the two methods is schematically illustated in Figue 7. Figue 6. Soil pofiles and piles adopted in the analyses Figue 7. Distibution of esidual soil stength (ultimate lateal pessue fom the liquefied soil fo the methods based on: (a Non-nomalised stength, S ; (b Nomalised stength, (S /σ' vo

6 Effects of soil stength nomalization on pile esponse ANALYSIS RESULTS Results of the analyses ae pesented in tems of the computed peak pile cuvatue along the length of the pile, because this cuvatue indicates both the size of the pile esponse and the level of damage to the pile. Figue 8 compaatively shows the peak pile cuvatues computed in the analyses using nomalised esidual stength (S /σ' vo and non-nomalised stength (S fo the liquefied soil. Thee ae thee phases in the elationship shown in this idealised plot that ae diectly elated to the load-defomation mechanism of the pile. Befoe initiation of soil yielding (fom the oigin to point A, both analysis methods poduce identical esults, because in this phase the pile esponse is not affected by p L-max (stength S. Howeve, once soil yielding is initiated (point A in Figue 8 the esponse deviates fom the : elationship. In the second phase (fom point A to point B, the ate of incease of cuvatue with applied gound displacement educes in the analysis using nomalised esidual stength as compaed to the analysis using non-nomalised esidual stength. In othe wods, fo a given gound displacement, a smalle cuvatue is computed in the analysis using nomalised esidual stength in the calculation of p L-max. To claify this esponse we need to compae the pocess of soil yielding fo the two methods. In the analysis with nomalised esidual stength, soil yielding fist occus at the top of the liquefied laye as this is the location whee the yield stess in the liquefied soil is the lowest, as appaent in Figue 7. The soil yielding effectively limits the lateal load fom the soil on the pile, esulting in a smalle pile displacement (U P and consequently, lage elative displacement between the soil and the pile, δ = U G U P. This in tun causes popagation of the soil yielding font fom the top of the liquefied laye towads the base of this laye. Eventually, the elationship levels off at point B, once soil yielding has been tiggeed thoughout the entie depth of the liquefied laye and the maximum lateal load fom the liquefied soil has been mobilized. The same pocess applies to the analysis with non-nomalised stength, except that it stats and ends at lage gound displacements and pile cuvatues. Compaative plots of computed peak pile cuvatues ae shown in Figues 9a, 9b and 9c fo piles with diametes of 4, 8 and 2 mm espectively. Fo each case, esults fo five diffeent thicknesses of the cust (H C =,.5,,.5 and 2 m ae pesented. Fo the flexible pile (F-Pile, vey lage effects of nomalisation ae seen fo the case without cust. Fo this case, the ultimate pile cuvatue ( was exceeded in the analysis using non-nomalised stength, wheeas in the coesponding analysis using nomalised stength, the computed cuvatue was below the cacking level. In othe wods, the nomalisation changed the pile pefomance fom failue to no damage. Much smalle effects of nomalisation ae seen fo a deposit with a.5 m thick cust, while no effects ae seen fo custs with thicknesses of,.5 and 2 m. Effects of nomalisation in educing the peak pile cuvatue ae also evident fo the M-Pile and S-Pile fo all cases with a cust thickness below 2 m. nomalized..5 Soil yielding is initiated in the S -nomalized analysis : Maximum soil pessue is mobilized in the S analysis A Maximum soil pessue is mobilized in the S -nomalized analysis.5. φ (S Figue 8. Typical elationship between peak pile cuvatues computed in the analyses with non-nomalised (S and nomalised stength (S /σ' vo B C

M.Cubinovski, J.Haskell and B.Badley 7 (a F-Pile (D o =.4m (b M-Pile (D o =.8 m.2. nomalized. nomalized.5..2 φ (S.5.. (c S-Pile (D o =.2 m nomalized.5 Cust thickness, H C (m m.5 m. m.5 m 2. m.5. Figue 9. Compaison of peak pile cuvatues computed in the analyses with non-nomalised (S and nomalised stength (S /σ' vo : (a F-Pile; (b M-Pile; (c S-Pile Clealy, the effects of nomalisation on the pile esponse pedicted by the pseudo-static analysis could be significant, and they depend both on the popeties of the pile and thickness of the cust laye. To summaize these effects, the atio of cuvatues φ A / is plotted against the thickness of the cust (H C in Figue. Hee, φ A and denote the peak pile cuvatue at which effects of nomalisation stat to influence the pile esponse (coesponding to point A in Figue 8 and the ultimate cuvatue of the pile espectively. The plot basically indicates whethe o not the nomalisation will affect the pe-failue esponse of the pile, as a function of pile stiffness and cust thickness. Fo example, fo elatively flexible piles (F-Pile, the stength nomalisation would affect the esponse of the pile only if the cust thickness is less than.9 m. On the othe hand, fo elatively stiff piles (S-Pile, the nomalisation will affect the pe-failue esponse of the pile when the thickness of the cust is less than.75 m. In othe wods, the load fom the cust would pactically goven the pile esponse and obscue the effects of stength nomalisation fo the liquefied soil when H C >.75m. Hence fo these cases, the nomalisation of the stength of the liquefied soil is not an issue. To illustate the magnitude of the nomalisation effects on the pile esponse, Figue shows the atio of the peak pile cuvatues computed by the two analysis methods as a function of the applied gound displacement. The figue depicts the amount of eduction in the pile esponse due to stength nomalisation fo diffeent pile stiffness and thicknesses of the cust. The eduction is vey ponounced (7-9% fo deposits without cust, and is still significant (3-4% fo medium-stiff to stiff piles with custs of up to.5 m thick.

8 Effects of soil stength nomalization on pile esponse.8 Relatively flexible pile F-Pile (D o =.4m Relatively stiff pile φ A /.6.4 M-Pile (D o =.8 m.2 S-Pile (D o =.2 m.5.5 2 Cust thickness, Η (m C Figue. Illustation of cuvatue levels (φ A / at which stength nomalisation stats to influence the pile esponse, as a function of pile stiffness and cust thickness (a F-Pile (D =.4m.2 o (b M-Pile (D o =.8 m.2 nomalized /.8.6.4.2 (S (S nomalized /.8.6.4.2.5.5 2 Gound displacment, U (m G.5.5 2 Gound displacment, U (m G nomalized / (c S-Pile (D =.2 m.2 o.8.6.4.2 Cust thickness, H C (m m.5 m. m.5 m 2. m Pile yielding (S analysis Pile 'failue' (S analysis.5.5 2 Gound displacment, U (m G Figue. Reduction in pile esponse due to stength nomalisation, fo diffeent pile stiffness and thicknesses of the cust: (a F-Pile; (b M-Pile; (c S-Pile

M.Cubinovski, J.Haskell and B.Badley 9 CONCLUSIONS Effects of soil stength nomalisation on the pile esponse pedicted by a simple pseudo-static analysis have been investigated in this pape. Two well-known empiical elationships fo esidual stength of liquefied soils, one non-nomalised (Seed and Hade, 99 and the othe nomalised (Olson and Stak, 22 wee adopted fo modelling the ultimate lateal pessue fom the liquefied soil on the pile, p L-max. Key findings fom a seies of paametic analyses can be summaized as follows: Effects of shea stength nomalisation of the liquefied soil could be significant fo the pile esponse pedicted by pseudo-static analysis. In the exteme case, the nomalisation educes the pile esponse fom the ultimate level (failue to the pe-cacking level (no damage. The magnitude of nomalisation effects depends on the elative stiffness of the pile and the thickness of the non-liquefied cust at the gound suface. Effects of stength nomalisation ae lagest in the absence of a cust, and decease with the thickness of the cust. Fo the m thick loose sand laye consideed, the effects of soil stength nomalisation wee eliminated once the thickness of the cust exceeded.75 m. It is impotant to ecognize that the nomalisation effects depend on the modelling of the ultimate load fom the cust, which in this study was adopted to be 4.5 times the Rankine passive pessue. Fo othe methods specifying smalle load fom the cust, the effects of nomalisation ae expected to be geate than those pesented heein. Similaly, one should note that the nomalisation effects and deived theshold values fo the thickness of the cust should be consideed in the context of the adopted m deposit of loose liquefiable soil. Acknowledgement The authos would like to acknowledge the financial suppot povided by the Eathquake Commission (EQC, New Zealand. REFERENCES Cubinovski, M. and Badley B.A. (28 Assessment of seismic pefomance of soil-stuctue systems, Invited Lectue, 8 th NZGS 28 Symposium, Auckland, -27. Cubinovski, M., Ishihaa, K., Poulos, H. (29 Pseudo-static analysis of piles subjected to lateal speading. Special Issue, Bulletin of NZ Society fo Eathquake Engineeing, 42(: 28-38. Haskell, J.J.M., Cubinovski, M., Badley B.A. (29 Citical uncetainties in the analysis of piles in liquefying soils Poc. 7 th ICSMGE, Alexandia, (in pint. Idiss, I.M. and Boulange, R.W. (28 Soil liquefaction duing eathquakes, Eathquake Engineeing Reseach Institute, MNO-2. Olson S.M. and Stak T.D. (22 Liquefied stength atio fom liquefaction flow case histoies, Canadian Geotechnical J. 39: 629-647. Seed H.B. (987 Design poblems in soil liquefaction, J. Geotechnical Eng. ASCE 3(8, 827-845. Seed, R.B. & Hade, L.F. (99 SPT-based analysis of cyclic poe pessue geneation and undained esidual stength, Poc. H. Bolton Seed Memoial Symposium, 2: 35-376.