Effective Subgrade Coefficients for Seismic Performance Assessment of Pile Foundations

Transcription

1 Effctiv Subgrad Cofficints for Sismic Prformanc Assssmnt of Pil Foundations W.L. Tan, S.T. Song & W.S. Hung National Chung-Hsing Unuvrsity, Taiwan,.O.C. SUMMAY: ( Th soil subgrad cofficints availabl in currnt practics ar not suitabl for assssing th prformanc of pil foundations undr larg dformation. Th primary goal of this study is to dtrmin th soil subgrad cofficints appropriat for limit stat analysis of concrt pils. A st of modification factor is also obtaind to modify th stiffnss of th soil-pil systm aftr th formation of th plastic hing at th pil-had. sults indicat that th subgrad cofficint and stiffnss modification factors suitabl for limit stat analysis of soil-pil systms is dpndnt on th soil proprtis as wll as th rinforcmnt ratio and th abov ground hight of th pil. Th outcom of th study is validatd using finit lmnt analysis of soil-pil systms. Th comparison shows that th subgrad cofficint obtaind in this study can rasonably stimat th latral stiffnss of soil-pil systms subjctd to larg dformation. Kywords: pil foundation, subgrad cofficint, push-ovr analysis, soil-foundation intraction 1. INTODUCTION Th sismic prformanc of bridg structurs is significantly influncd by th strngth and ductility of th foundation. Following th capacity dsign principl, th foundations of bridgs ar normally dsignd for a highr latral strngth, comparing th columns, to prvnt undsird inlastic dformation occurring blow th ground lvl. Howvr, post-arthquak inspctions in rcnt sismic vnts hav suggstd that pil foundations ar highly suscptibl to damag from arthquak load. Sinc th inlastic dformation of pil foundations may b difficult to avoid during a svr arthquak vnt, th non-linar bhaviour of th soil-pil systm must b carfully assssd, particularly if a crtain lvl of prformanc is to b guarantd for th structur. For soil-pil systm subjctd to horizontal sismic motion, th larg latral loading may rsult in squntial yilding along th lngth of pil until a plastic mchanism is fully dvlopd. Fig. 1.1 shows th dflctd shap and th associatd bnding momnt distribution at various limit stats of a latrally loadd fixd-had pil. Th first yild limit stat of th pil, which is shown in Fig. 1.1(a), is charactrizd by a maximum bnding momnt at th pil/pil-cap connction whr th flxur M u of th pil is rachd. A plastic hing is thn assumd to form at th pil had with th strngth cntr of th rotation occurring at th ground lvl. Furthr displacmnt byond th first yild limit stat involvs a concntratd rotation of th plastic hing, which is accompanid by a rdistribution of intrnal forc in th pil. Th rdistribution incrass th bnding momnt in th non-yilding portion of th pil until th formation of a scond plastic hing, as shown in Fig. 1.1(b). Continud latral displacmnt aftr th scond plastic hing formation is facilitatd by inlastic rotations in both plastic hings until th pil rachs th ultimat limit stat. In currnt practics, many tchniqus ar availabl to invstigat th bhaviour of pil foundations subjctd to latral loads. An accptabl and convnint approach is to analyz th latrally loadd soil-pil systm as a flxural mmbr supportd by Winklr foundations. In such approach, th soil is

2 modlld as a sris of springs with a constant stiffnss, which is commonly charactrizd as th soil subgrad cofficint. Sinc most foundations ar traditionally dsignd for lastic rspons, th subgrad cofficint availabl in currnt practics is intndd for soil-pil systm undr small dformation and may not b suitabl for analyzing th rspons of pil foundations raching thir yild limit. Morovr, pil dformation byond th first yild limit stat inducs furthr softning of th surrounding soil and thrfor significantly rducs th latral stiffnss of th soil-pil systm. In ordr to carfully assss th prformanc of th pil foundations undr larg dformation, a st of subgrad cofficints and modification factors is obtaind in this study. Th subgrad cofficint is tabl for valuating th ffctiv stiffnss of th soil-pil systm at th first yild limit stat. Th rducd stiffnss of th soil-pil systm aftr th formation of th first plastic hing is stimatd by applying th modification factor into th solution of a flxural mmbr on Winklr foundation modl. In this study, th subgrad cofficints and modification factors ar validatd using th finit lmnt analysis of soil-pil systm. Th rsult shows that th obtaind cofficints can b usd to rasonably stimat th stiffnss of soil-pil systm subjctd to latral dformation. 2. LATEAL LOAD-DISPLACEMENT ELATION OF SOIL-PILE SYSTEMS Th load-displacmnt rlation and significant yild limit stat of latrally loadd pil is illustratd in Fig Th rspons can b furthr idalizd as a tri-linar curv, charactrizd by an initial linar lastic rspons with a stiffnss K 1, followd by a rducd stiffnss K 2 du to a first yilding of th pil-had, and thn by a fully plastic mchanism aftr th formation of th scond plastic hing. Th first and scond limit stats ar dfind by th latral yilding displacmnt y1 and y2, rspctivly. Th latral forc associatd with th first and scond yild limit stat ar dnotd as V y and V u, rspctivly. Idntifying th latral loads and displacmnts at th two yild limit stats allows th tri-linar load-displacmnt curv, as wll as th stiffnss of soil-pil systm to b dtrmind. In this papr, th latral stiffnss calculatd using a flxural mmbr on Winklr foundation modl is compard with th latral stiffnss assssd by a computr simulation of a latrally loadd soil-pil systm. Th comparison provids th ffctiv subgrad cofficint at th yild limit stat of th soil. 3. LATEAL STIFFNESS OF SOIL-PILE SYSTEM 3.1. Cohsiv Soils Analytical approach A common approach to stimat th latral stiffnss of a soil-pil systm involvs using th clos-form solutions of a flxural mmbr on lastic Winklr foundation modl. For cohsiv soils, th stiffnss of th soil is assumd to b indpndnt of th dpth, rsulting in a constant horizontal subgrad raction k h (in units of forc/lngth 2 ). Th govrning quation of th modl is givn by: (Poulos and Davis, 198) 4 d y k 4 hy dx (3.1) whr is th ffctiv flxural rigidity of th pil, y is th latral dflction of th pil, and x is th dpth blow th ground surfac. In ordr to solv th govrning Eqn. 3.1, th charactristic lngth of th soil-pil systm is first dfind as: k c 4 (3.2) h

3 Figur 1.1. Dflctd shap and bnding momnt distribution of a fix-had pil loadd at th ground lvl (a) first limit stat and (b) scond limit stat Figur 2.1. Idalizd load-displacmnt curv and significant limit stats of latrally loadd pils Th solution of Eqn. 3.1, in conjunction with appropriat boundary conditions, and th idalizd initial stiffnss 1 K of pils with a rotational rstraint at th pil-had is givn by: (Song, 25) K 1 V y y ξa 3 2ξa ξa 3 c (3.3) whr y1 and V y ar th latral displacmnt and th latral forc at th first yild limit stat, is th ffctiv flxural rigidity of th pil, and ξ a La / c is th abov ground hight cofficint, dfind as th abov ground hight L a of th pil normalizd by th charactristic lngth c of th soil-pil systm. Aftr th formation of th first plastic hing, th idalizd post-yild stiffnss K 2 of th soil-pil systm could b obtaind by: K 2 V V ξ 3 2ξ ξ u y y2 y1 a a a c (3.4) whr y2 is th latral displacmnt at th scond yild limit stat, and V u is th latral forc at th scond yild limit stat. Th latral stiffnss K 1 and K 2, as charactrizd in Eqn. 3.3 and Eqn. 3.4, rquir th dtrmination of th charactristic lngth c of th pil, which in turn rquirs an stimation of th modulus of horizontal subgrad raction k h. In currnt practics, th valu of k h is commonly stimatd basd on th undraind shar strngth s u of cohsiv soils. An xprssion for

4 k h is proposd by Davisson (197), i..: k h 67 su (3.5) whr s u is th undraind shar strngth of th cohsiv soil, which may b dtrmind from fild tsts or b stimatd dirctly from sit classifications in currnt building cods Computr simulation In this study, th non-linar bhaviour of a soil-pil systm subjctd to latral loads is simulatd using th computr program LPILE (s t al, 24). Th soil prssur inducd by pil dformation is givn by th non-linar p-y rlations widly usd in gotchnical nginring practics. For cohsiv soils, th p-y rlation proposd by Matlock (197) is usd. Th pil is modld as a flxural mmbr with its flxural rigidity and momnt-curvatur rlation of th pil sction spcifid. Outcoms of th simulation givs th latral load-displacmnt rlations at th first yild limit stat, dnotd as V y and y1, and at th scond yild limit stat, dnotd as V u and y2 in Fig To this nd, th initial stiffnss K 1 can b calculatd by K1 Vy / y1 and th post-yild stiffnss K 2 K2 Vu Vy / y2 y1. is givn by In ordr to stimat th ffctiv subgrad cofficint at th first yild limit stat, th initial stiffnss K 1 stimatd by th simulation is first substitutd into Eqn. 3.3 to calculat th charactristic lngth c of th soil-pil systm. Th ffctiv subgrad cofficint k h can thn b dtrmind using Eqn As mntiond arlir, pil dformation byond th first yild limit stat inducs furthr softning of surrounding soil. Th soil softning affcts th charactristic lngth of th soil-pil systm and thrfor rducs th post-yild stiffnss. To valuat th ffct of soil softning du to th larg dformation aftr th first yild limit stat, th post-yild stiffnss K 2 suggstd by th simulation is compard with Eqn. 3.4 from th analytical modl. A modification factor κc can thn b introducd to modify th charactristic lngth for stimating th post-yild stiffnss of soil-pil systms. Mor spcifically, th modifid charactristic lngth κc c, dnotd as th charactristic lngth c multiplid with a modification factor, is giv by rorganizing Eqn. 3.4 to: κ c c ξ 3 2ξ ξ 2 3 a a a K 2 (3.6) whr ξa is th abov ground hight cofficint, is th ffctiv flxural rigidity of th pil, and K 2 is th rducd stiffnss suggstd by th simulation Cohsionlss Soils Analytical approach Lik cohsiv soils, a similar approach to stimat th latral stiffnss of a soil-pil systm involvs using th clos-form solutions of a flxural mmbr on lastic Winklr foundation modl. For cohsionlss soils, th stiffnss of th soil is assumd to b th constant rat of incras of th horizontal subgrad raction, and may b dfind as nh kh x (in units of forc/lngth 3 ). Th govrning quation of th modl is givn by: (Poulos and Davis, 198) 4 d y n 4 hxy dx (3.7) whr is th ffctiv flxural rigidity of th pil, y is th latral dflction of th pil, and x is th dpth blow th ground surfac. Th charactristic lngth of th soil-pil systm is usd to solv Eqn. 3.7, and dfind as following quation.

5 n n 5 (3.8) h From solving Eqn. 3.7 with appropriat boundary conditions, th idalizd initial stiffnss K 1 of pils with a rotational rstraint at th pil-had is givn by: (Song, 25) Vy 1 K ξ.44ξ.83ξ y1 a a a n (3.9) whr V y and y1 ar th latral forc and th latral displacmnt at th first yild limit stat, is th ffctiv flxural rigidity of th pil, and ξ a La / n is th abov ground hight cofficint, dfind as th abov ground hight L a of th pil normalizd by th charactristic lngth n of th soil-pil systm. From th first limit stat to scond limit stat, th idalizd post-yild stiffnss K 2 of th soil-pil systm could b dvlopd by: K 2 V V ξ 5.24ξ ξ u y y2 y1 a a a n (3.1) whr V u is th latral forc at th scond yild limit stat, and y2 is th latral displacmnt at th scond yild limit stat. Using Eqn. 3.9 and Eqn. 3.1 to valuat th latral stiffnss K 1 and K 2, rquir th dtrmination of th modulus of th horizontal subgrad raction n h, which usd to stimat th charactristic lngth n of th soil-pil systm for chsionlss soils. In currnt practics, th valu of n h is commonly stimatd basd on th friction angl of cohsionlss soils. An xprssion for n h is proposd by ATC-32(1996), as shown in Fig NEHP (21) Soil profil Figur 3.1. Subgrad cofficints of cohsionlss soils rcommndd by ATC-32(1996)

6 Computr simulation Lik cohsiv soils, th non-linar bhaviour of a soil-pil systm subjctd to latral loads is simulatd using th computr program LPILE (s t al, 24). Th pil is modld as a flxural mmbr with its flxural rigidity and momnt-curvatur rlation of th pil sction spcifid. Th soil prssur inducd by pil dformation is givn by th non-linar p-y rlations usd in gotchnical nginring practics. For cohsionlss soils, th p-y rlation proposd by API (1993) is usd. Outcoms of th simulation givs th latral load-displacmnt rlations at th first yild limit stat, dnotd as V y and y1, and at th scond yild limit stat, dnotd as V u and y2 in Fig For th purpos in th study, th initial stiffnss K 1 can b calculatd by K1 Vy / y1, and th post-yild stiffnss 2 K2 Vu Vy / y2 y1. K is givn by As with cohsiv soils, in ordr to stimat th ffctiv subgrad cofficint at th first yild limit stat, th initial stiffnss K 1 stimatd by th simulation is first substitut into Eqn. 3.9 to calculat th charactristic lngth n of th soil-pil systm. Using Eqn. 3.8, th ffctiv subgrad cofficint n h can thn b obtaind. Additionally, surrounding soil bcam softn bcaus of pil dformation byond th first yild limit stat. Th soil softning influncs th charactristic lngth of th soil-pil systm and thrfor rducs th post-yild stiffnss. In ordr to assss th influnc of soil softning du to th larg dformation aftr th first yild limit stat, th post-yild stiffnss K 2 obtaind by th simulation is compard with Eqn. 3.1 from th analytical modl. A modification factor κn can b dvlopd to modify th charactristic lngth for valuating th post-yild stiffnss of soil-pil systms. Lik th cohsiv soil, th modifid charactristic lngth κn n, dnotd as th charactristic lngth n multiplid with a modification factor, is giv by rorganizing Eqn. 3.1 to: κ n n ξ 5.24ξ ξ 2 3 a a a K 2 (3.11) whr ξa is th abov ground hight cofficint, is th ffctiv flxural rigidity of th pil, and K 2 is th rducd stiffnss suggstd by th simulation. 4. SUBGADE COEFFICIENTS AND MODIFICATION FACTOS Twnty-svn pils with diffrnt diamtrs D, longitudinal stl ratios ρl and abov ground hights L a ar considrd for th study. Th undraind shar strngth s u of th soil is takn to vary from 2 kpa for soft clays to 2 kpa for vry stiff clays. Th friction angl of th soil is takn to vary from 29 for soft sands to 42 for vry stiff sands. Th corrlation btwn th ffctiv soil subgrad cofficint k h and th undraind shar strngth s u is illustratd in Fig. 4.1(a). For comparison, th subgrad cofficint givn by Eqn. 3.5 is also shown in th figur. It can b sn from th figur that th ffctiv subgrad cofficint incrass with th incrasing undraind shar strngth of th soil. Th subgrad cofficints suggstd by th p-y curvs ar significantly largr than thos calculatd from Eqn. 3.5 for mdium and stiff clays. Th corrlation btwn th ffctiv soil subgrad cofficint n h and th friction angl is illustratd in Fig. 4.1(b). For comparison, th subgrad cofficint givn by ATC-32 (1996) is also shown in th figur. Additionally, th subgrad cofficints suggstd by th p-y curvs ar significantly smallr than thos calculatd from ATC-32 (1996) for mdium and stiff sands. Not that sinc th ffctiv subgrad cofficint is corrlatd to th yild limit stat of th pil lmnt, th valu of th subgrad cofficint is rlatd to th longitudinal stl ratio and abov ground hight of th pil. For a givn undraind shar strngth or friction angl, th subgrad cofficint for pils with low longitudinal stl ratios is largr than that for pils with high longitudinal stl ratios. Additionally, th subgrad cofficint incrass with th incrasing abov ground hight. Howvr, for a givn undraind shar strngth or friction angl, pils with th sam longitudinal stl ratios and abov ground hight tnd to hav similar subgrad

7 cofficints for all diamtrs. Fig. 4.2(a) shows th corrlation btwn th modification factor κc and th undraind shar strngth s u of cohsiv soils. Th modification factor κc dcrass with incrasing undraind shar strngth. Fig. 4.2(b) shows th corrlation btwn th modification factor κn and th friction angl of cohsionlss soils. Th modification factor κn dcrass with incrasing friction angl for stiff sand and incrass with incrasing friction angl for soft sand. Additionally, th valu of κc or κn is dpndd on th abov ground hight but only slightly influncd by th longitudinal stls ratio ρl. It can also b sn from Fig. 4.2 that all modification factors ar gratr than unity, indicating an incras in charactristic lngth or a furthr dcras of latral stiffnss. Subgrad Cofficint (kn/m 2 ) k h Subgrad Cofficint (kn/m 2 ) k h Subgrad Cofficint k (kn/m 2 h ) L a = 2D Davisson (197) Undraind Shar Strngth s u (kn/m 2 ) L a = 4D Undraind Shar Strngth s u (kn/m 2 ) L a = 6D Davisson (197) Undraind Shar Strngth s u (kn/m 2 ) (a) Davisson (197) Subgrad Cofficint n (kn/m 3 h ) Subgrad Cofficint n (kn/m 3 h ) Subgrad Cofficint n (kn/m 3 h ) Friction Angl ATC lativ Dnsity D r (%) Friction Angl ATC lativ Dnsity D r (%) Friction Angl ATC lativ Dnsity D r (%) (b) Figur 4.1. Effctiv subgrad cofficint for pils with diffrnt abov ground hights (a) cohsiv soils and (b) cohsionlss soils

8 Modification Factor κ c L a = 2D L a = 6D L a = 4D Modification κ n L a = 2D L a = 4D L a = 6D Undraind Shar Strngth s u (kn/m 2 ) (a) Friction Angl (dgr) (b) Figur 4.2. Charactristic lngth modification factors for (a) cohsiv soils and (b) cohsionlss soils 5. COMPAISON WITH FINITE ELEMENT MODEL In ordr to nsur th confidnc in th applicability of th ffctiv subgrad cofficint, th tri-linar load-displacmnt rlationship from th analytical modl is compard with th pil rspons prdictd by th finit lmnt analysis. Th analytical modl has bn adjustd with th ffctiv subgrad, th stiffnss cofficint k h or n h, and th post-yild modification factor κc or κn. Th finit lmnt analysis is carrid out using th analysis platform OpnSs (McKnna t al, 28). Th gnral schmatic of th finit lmnt modl is shown in Fig In th modl, th pil sction is th fibr sction, and th rsistanc of th soil is modld by th non-linar p-y springs proposd by Matlock (197) for cohsiv soils and API (1993) for cohsionlss soils. To illustrat th mthod outlind in this papr, considr an xtndd pil-shaft with a diamtr of 2 D.91m, th ffctiv flxural rigidity of 4464 kn-m, and th longitudinal stl ratio of ρl 2%. Th abov ground hights L a ar 2D, 4D, and 6D. Th proprty of th soils is summarizd in Tabl 5.1. And th rsults ar shown in Fig Th data for th comparison with cohsiv soil is illustratd in Fig. 5.2(a). It can b sn from th figur that th tri-linar load displacmnt rlation givn by th analytical modl with th modifid soil stiffnss compars wll with th rspons from th finit lmnt analysis. Th analytical modl is abl to captur th initial scant stiffnss of th soil-pil systm prior to th first yild limit stat. Th post yild stiffnss prdictd from th analytical modl also tracks wll th slop of th load-displacmnt curv of th finit lmnt modl wll, th ultimat strngth stimatd by both modls is in clos agrmnt with ach othr. Th data for th comparison of cohsionlss soil is illustratd in Fig. 5.2(b). Th analytical modl, again, is abl to captur th initial scant stiffnss of th soil-pil systm bfor th first yild limit stat. Th post yild stiffnss prdictd from th analytical modl paths wll th slop of th load-displacmnt curv from th finit lmnt modl for th soft sand. Howvr, th ultimat strngth valuatd by both modls is rally diffrnt with ach othr. Th rason is that th p-y rlations proposd by diffrnt approach in th two modls. Th ultimat soil prssur rcommndd by API (1993), which is usd for th soil lmnts in th finit lmnt modl, is significantly largr than that proposd by Broms (1964), which is adoptd in th kinmatic modl. Tabl 5.1. Th proprtis of soils Soil typ Soil proprty S E S D S C Cohsiv Effctiv unit wight γ (kn/m 3 ) soils Undraind shar strngth s u (kn/m 2 ) Cohsionlss Effctiv unit wight γ (kn/m 3 ) soils Friction angl (dgr)

9 Figur 5.1. Gnral schmatic of th finit lmnt modl for latrally loadd fixd-had concrt pils Kinmatic Modl (with modifid soil Finit Elmnt Analysis L-PILE sult Soil Proprtis: S E cohsiv soil γ' = 15.5 kn/m 3 s u = 4 kn/m Latral Displacmnt (mm) Finit Elmnt Analysis L-PILE sult Latral Displacmnt (mm) Finit Elmnt Analysis L-PILE sult Kinmatic Modl (with modifid soil stiffnss) Soil Proprtis: S D cohsiv soil γ' = 17.5 kn/m 3 Kinmatic Modl (with modifid soil stiffnss) s u = 85 kn/m Latral Displacmnt (mm) (a) Soil Proprtis: S C cohsiv soil γ' = 18.5 kn/m 3 s u = 125 kn/m Finit Elmnt Analysis L-PILE sult Kinmatic Modl (with modifid soil Soil Proprtis: S E cohsionlss soil γ' = 17 kn/m 3 Φ = Latral Displacmnt (mm) Finit Elmnt Analysis L-PILE sult Kinmatic Modl (with modifid Soil Proprtis: S D cohsionlss soil γ' = 18.5 kn/m 3 Φ = Latral Displacmnt (mm) L-PILE sult Finit Elmnt Analysis Kinmatic Modl (with modifid soil Soil Proprtis: Sc cohsionlss soil γ' = 2 kn/m 3 Φ = Latral Displacmnt (mm) Figur 5.2. Comparison of th latral load-displacmnt rsponss of soil-pil systms (a) cohsiv soils and (b) cohsionlss soils (b)

10 6. CONCLUSIONS During a svr arthquak, th inlastic dformation of pil foundations may b difficult to avoid. In ordr to carfully assss th nonlinar bhaviour of latrally loadd soil-pil systm, a st of ffctiv subgrad cofficints, which corrlatd to th yild limit stat of th pil, is obtaind in this study. sults of th study show that th valu of th ffctiv subgrad cofficint is dpndnt on th longitudinal stl ratio and abov ground hight of th pil. Anothr st of modification factors is also calculatd to adjust th charactristic lngth and modify th post-yild stiffnss of th soil-pil systm. Th valu of th modification factors ar also rlatd to abov ground hight of th pil. Th outcoms obtaind in this study ar validatd using th finit lmnt analysis. For cohsiv soils, th rsult indicats that with th modifid soil stiffnss, quations providd by th bam on Winklr foundation modl ar capabl of capturing th stiffnss of a soil-pil systm subjctd to a larg latral dmand. For cohsionlss soils, th initial stiffnss prdictd from th analytical modl is abl to captur th initial scnt stiffnss of th soil-pil systm. Howvr, th ultimat strngth providd by th analytical modl is rally diffrnt from th ultimat strngth proposd by finit lmnt modl. Th rason is that th p-y rlations of th two modls ar rcommndd by diffrnt approach. Actually, it mans that th ffctiv subgrad cofficints providd from this study can b usd wll to valuat th first limit stat of soil-pil systms subjctd to a larg dformation. AKCNOWLEDGEMENT This study was supportd by National Scinc Council of Taiwan (undr Grant Nos. NSC E-5-1 -MY2). Th assistanc providd by Mr. Chun-Yao Wang and Mr. Po-Hung Liu, mastr studnt at National Chung-Hsing Univrsity, in procssing th push-ovr analysis ar highly apprciatd. Any conclusion xprssd in this articl ar thos of th authors and do not rflct th viw of th sponsor. EFEENCES Amrican Ptrolum Institut API. (1993). API commndd Practic for Planning, Dsigning and Constructing Fixd Offshor Platforms, API commndd Practic 2A (P2A), Twntith dition, Washington D.C. Applid Tchnology Council ATC-32. (1996). Improvd Sismic Dsign Critria for California Bridgs: Provisional commndations, dwood City, California. Broms, B. B. (1964). Latral rsistanc of pils in cohsionlss soils. Journal of th Soil Mchanics and Foundations Division, Amrican Socity of Civil Enginring, VOL.9: SM3, pp Davisson M. T. (197). Latral load capacity of pils, Highway sarch cord, NO.333, pp Matlock H. (197). Corrlation for dsign of latrally loadd pils in soft clay. Procdings, 2nd Annual Offshor Tchnology Confrnc, OTC 124(1), Houston, Txas. McKnna F., Fnvs G. L., Jrmic B. and Scott M.H. (28). Opn Systm for Earthquak Enginring Simulation, < NEHP. (21) NEHP rcommndd provisions for sismic rgulations for nw buildings and othr structurs, FEMA 368. Washington, D.C. Poulos H. G. and Davis E. H. (198). Pil Foundation Analysis and Dsign, Willy-Intrscinc, Nw York. s L. C., Wang S. T., Isnhowr W. M., Arrllaga J. A. and Hndrix J. (24). LPILE Plus Vrsion 5.-A Program for th Analysis of th Pils and Drilld shafts undr Latral Loads. Ensoft, Inc Austin Txas. Song S. T. (25). Limit Stat Analysis and Prformanc Assssmnt of Fixd-Had Concrt Pils undr Latral Loading, PH.D. Thsis Univrsity of California, Davis.