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FIG. 1. Schematic of Dynamic p-y Analysis Model

physical model studies are too limited in number and de-Consequently, the purpose of this study was to perform a

es of dynamic centrifuge model tests of pile-supportedctures in soft ground and then to evaluate the ability of theamic p-y analysis method to reliably capture the observed

ssoc. Prof., Dept. of Civ. and Envir. Engrg., Univ. of California,s, CA 95616.rad. Student, Dept. of Civ. and Envir. Engrg., Univ. of California,

s, CA.rof., Dept. of Civ. and Envir. Engrg., Univ. of California, Davis, CA.ac. Mgr., Ctr. for Geotech. Modeling, Univ. of California, Davis,

r. Materials and Research Engineer, Ofc. of Struct. Found., Califor-ept. of Transp., Sacramento, CA 94273.

ote. Discussion open until February 1, 2000. To extend the closingone month, a written request must be filed with the ASCE Managerurnals. The manuscript for this paper was submitted for review and

ible publication on August 28, 1998. This paper is part of the Journaleotechnical and Geoenvironmental Engineering, Vol. 125, No. 9,ember, 1999. qASCE, ISSN 1090-0241/99/0009-07500759/$8.00.50 per page. Paper No. 19133.SEISMIC SOIL-PILE-STRUCTURAND AN

By Ross W. Boulanger,1 Member, ASCE, ChBruce L. Kutter,3 Member, ASCE, Daniel

Abbas Abghari,

ABSTRACT: A dynamic beam on a nonlinear Winklanalyzing seismic soil-pile-structure interaction was evamodel tests. The centrifuge tests included two different searthquake events with peak accelerations ranging frooverlying dense sand. Site response and dynamic p-ybased on existing engineering practices. Reasonably gcorded responses for both structural models in all eartmodel parameters and site response calculations are evthe use of dynamic p-y analysis methods in seismic so

INTRODUCTION

Soil-pile-structure interaction can be an important consid-eration in evaluating the seismic response of pile-supportedstructures, particularly in soft clay or liquefying sand. Methodsof analyzing seismic soil-pile-structure interaction have in-cluded 2D and 3D modeling of the pile and soil continuumusing finite-element or finite-difference methods, dynamicbeam on a nonlinear Winkler foundation (i.e., dynamic p-y)methods, and simplified two-step methods that uncouple thesuperstructure and foundation portions of the analysis. Dy-namic p-y methods, as depicted in Fig. 1, are considerably lesscomplex than finite-element or finite-difference modeling ofthe pile and soil continuum and yet offer several potentialadvantages over the simplified two-step methods when dealingwith soft soil conditions. In fact, dynamic p-y analyses havea long history of development and application to seismic andoffshore problems [e.g., Matlock et al. (1978), Kagawa andKraft (1980), Novak and Sheta (1980), and Nogami et al.(1992)] and can be performed with a number of different com-puter codes. Wang et al. (1998) compared several implemen-tations of the dynamic p-y method and showed that calcula-tions can be sensitive to the details of the nonlinear springsand dashpots but that different codes did produce similar re-sults when similar modeling details were used.

The validity and reliability of dynamic p-y analysis methods(or any other method) has not, however, been fully evaluatedfor soft ground conditions because the available case historiesDownloaded 12 Oct 2009 to 128.120.194.194. Redistribution subjeE INTERACTION EXPERIMENTSALYSES

ristina J. Curras,2 Student Member, ASCE,. Wilson,4 Associate Member, ASCE, and

Member, ASCE

r foundation (or dynamic p-y) analysis method foruated against the results of a series of dynamic centrifugeingle-pile-supported structures subjected to nine differentm 0.02 to 0.7g. The soil profile consisted of soft clayanalyses are described. Input parameters were selectedod agreement was obtained between calculated and re-quake events. Sensitivity of the results to dynamic p-yaluated. These results provide experimental support forl-pile-structure interaction problems.

soil-pile-interaction effects. Centrifuge experiments were per-formed using the earthquake simulator on the 9-m-radius cen-trifuge at the University of California at Davis. The soil profileconsisted of soft clay overlying dense sand. Structural modelcomponents were designed to be representative of select Cal-trans bridge structures and included single-pile- and pile-group-supported structures. The models were subjected to ninedifferent earthquake motions, each a scaled version of a recordprepared from strong motion accelerograms. Peak base accel-erations ranged from 0.02 to 0.7g. In this paper, the responsesof the two single-pile-supported structures to these nine earth-quake events were analyzed in detail using a dynamic p-ymethod. Analysis results for the pile-group-supported structurecan be found in Curras et al. (1999). The response of the soilprofile was analyzed using a 1D equivalent-linear site responseprogram. A nonlinear p-y element with gapping capability wasimplemented in a finite-element program for the dynamic p-yanalyses. Details of the free-field site response analyses, thenonlinear p-y element formulation, and the dynamic p-y anal-yses are described. Using a single baseline set of input param-eters, the calculated and recorded responses of the single-pile-supported systems and soil profile are compared for allearthquake events. Sensitivity of the analysis results to dy-namic p-y parameters and site response calculations is evalu-ated by numerical parameter studies. The results provide anevaluation of the analysis procedures ability to reliably cap-ture soil-pile-structure interaction effects over a wide range ofct to ASCE license or copyright; see http://pubs.asce.org/copyright

shaking intensities and earthquake motions. Findings from thecentrifuge experiments and numerical analyses and their im-plications for design practice are discussed.

CENTRIFUGE EXPERIMENTSTests were performed using the large servohydraulic shak-

ing table on the 9-m-radius centrifuge at the University ofCalifornia at Davis (Kutter et al. 1994). Models were tested ina flexible shear beam (FSB) container at a centrifugal accel-eration of 30g. The FSB container consists of a series ofstacked aluminum rings separated by soft rubber that enablesthe container to deform with the soil. The inside dimensionsof the container are 1.7 m long, 0.7 m deep, and 0.7 m wide.The shaker performance, FSB container behavior, and mod-eling procedures were evaluated in Wilson et al. (1997a). Allresults presented herein are in prototype units unless otherwisestated; an overview of scaling relationships can be found inKutter (1992).

The soil profile, structural models, and instrumentation forthe tests described herein are illustrated in Fig. 2. The soilprofile consisted of two horizontal soil layers. The lower layerwas fine, uniformly graded Nevada sand (Cu = 1.5 and D50 =0.15 mm) at a dry density of 1.66 Mg/m3, which correspondsto a relative density Dr of about 7580%. The sand was airpluviated, flushed with carbon dioxide, and saturated undervacuum. The upper layer was reconstituted Bay Mud (liquidlimit 88, plasticity index 48) placed as a slurry (watercontent 140%) in four equal layers, with each layer sepa-rated by filter paper to accelerate consolidation. Each layer wasindividually preconsolidated under an applied vertical stress.The pore fluid was water (as opposed to a higher viscositypore fluid), and saturation was confirmed by measuring p-waves velocities before testing.

The two single-pile-supported systems (SP1 and SP2) ana-lyzed in this paper consisted of a superstructure mass attachedto an extension of the pile. The superstructure masses, theirheights from the ground surface, and their fixed-base periods(i.e., as if perfectly fixed at the ground surface) are summa-rized in Table 1. The aluminum pile (including its above-ground extension) had a mass per unit length of 0.37 Mg/mand a flexural stiffness EI of 417 MN?m2, which is approxi-mately equivalent to a 0.67-m-diameter steel pipe pile with a19 mm wall thickness. The piles were installed at 1g (prior tospinning the centrifuge) and remained elastic during all earth-quake events. Results for the pile-group-supported structurecan be found in Wilson et al. (1997b,c) and Curras et al.(1999).

Two centrifuge model configurations, hereafter referred toas containers Csp4 and Csp5, were each shaken with severalsimulated earthquake events, as summarized in Table 2. Notethat each model was shaken by five earthquake events, butbecause Event B duplicated Event A in Csp4 there are onlynine different events in total. Each event was a scaled versionof a record prepared by filtering and integrating strong motionrecords from Port Island in the 1995 Hyogoken-Nambu (Kobe)earthquake or Santa Cruz in the 1989 Loma Prieta earthquake.Each earthquake event was separated by sufficient time fordissipation of any shaking-induced excess pore pressures. Thesame soil model was used in both containers, but the modelstructures and instrumentation were rearranged between Csp4and Csp5. After all shaking events for Csp4 were completed,the centrifuge was spun down (stopped) and the single-pile-supported structures pulled out of the soil profile. The pileswere then redriven in different locations within the containerand the centrifuge was spun up for the subsequent series ofshaking events (Csp5). This procedure was followed becausethe soil around the piles was progressively disturbed by soil-pile interaction during each shaking event. The effect of thisJOURNAL OF GEOTECHNICA

Downloaded 12 Oct 2009 to 128.120.194.194. Redistribution subjeFIG. 2. Schematic of Layout and Instrumentation

TABLE 1. Prototype Characteristics of Single-Pile-SupportedStructures

Characteristic(1)

SP1(2)

SP2(3)

Superstructure mass (Mg) 49.1 45.1Height of mass from ground surface (m) 3.81 7.32Fixed-base period of structure (s) 0.29 0.75

Notes: Both piles were 0.67 m in diameter, weighed 0.37 Mg/m, andhad an EI of 417 MN ?m2.

TABLE 2. Earthquake Events for Containers Csp4 and Csp5

Event(1)

Motion(2)

amax base input(g)(3)

(a) Container Csp4A Kobe 0.055aB Kobe 0.055C Kobe 0.016D Kobe 0.20E Kobe 0.58

(b) Container Csp5A Santa Cruz 0.035B Santa Cruz 0.12C Santa Cruz 0.30D Santa Cruz 0.60E Kobe 0.70

aEvent B is a repeat of this event so that only Event B was analyzed.

disturbance on the structural response for a given series of tests(i.e., Csp4 or Csp5) is expected to be small as each earthquakeevent was generally stronger than all prior events. Moving thepiles between Csp4 and Csp5 allowed a second series of shak-ing events to restart at low shaking levels without any priordisturbance from local soil-pile interaction. Detailed documen-tation of the tests, including all recorded time histories, areavailable in Wilson et al. (1997b,c).

The undrained shear strength cu of the Bay Mud layer versusdepth is shown in Fig. 3. Strengths were measured using asmall torvane after Csp5 immediately after the centrifugestopped spinning. The elapsed time between the start of cen-trifuge shutdown and torvane measurements was shorter thanthe time required to consolidate any of the layers. Thus, thetorvane measurements are believed to reasonably represent thestrength of the clay in the centrifuge tests. Also shown in Fig.3 are estimated profiles of cu for before and after earthquakeshaking conditions. The before-shaking profile was calcu-lated asL AND GEOENVIRONMENTAL ENGINEERING / SEPTEMBER 1999 / 751

ct to ASCE license or copyright; see http://pubs.asce.org/copyright

752 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENG

FIG. 3. Undrained Shear Strength in Soft Clay Layer Esti-mated from Stress History and Measured by Torvane Tests

0.8c = 0.35s9 OCR (1)u vcwhere = effective vertical consolidation stress, OCR = thes9vcoverconsolidation ratio (OCR = and = vertical pre-s9/s9 ), s9p vc pconsolidation stress. The after-shaking profile was calcu-lated using the same expression, but with the value of OCRincreased by a factor of 1.3 to represent the estimated effectsof earthquake-induced consolidation. The after-shaking cu pro-file is in reasonable agreement with the torvane measurements.For simplicity, a single cu profile was adopted for all analysesof the centrifuge models (sensitivity studies presented later inthis paper suggest that more detailed refinements would havebeen unwarranted). The adopted cu profile was calculated asthe average of the before and after static cu profiles in Fig. 3,plus an increase of 15% to account for the combined effectsof different loading rates and stress paths between the torvanetests and the seismic shaking tests in the centrifuge. The re-sulting cu profile for seismic loading involves some uncertaintybut reflects our judgment based on the various factors in-volved.

FREE-FIELD SITE RESPONSE ANALYSES

Free-field site response analyses were performed using the1D equivalent linear site response program SHAKE91 (Schna-bel et al. 1972; Idriss and Sun 1991). For the sand, the low-strain shear modulus Gmax was calculated from the dimension-less form of the equation by Seed and Idriss (1970)

G s9max m= 21.8K (2)2,max P Patm atm

with K2,max = 65; = (1 1 and K0 = 0.6. The uppers9 2K )s9 /3;m 0 vcrange modulus reduction G/Gmax and median equivalent damp-ing ratio b versus shear strain g relationships for sand by Seedand Idriss (1970) were used.

For the clay, Gmax was calculated using Gmax/cu = 380 andthe seismic cu profile described earlier. This Gmax/cu ratio wasbased on matching the soil profiles fundamental period at verylow strain levels (smallest shaking events in Table 2) and isslightly less than implied by correlations for undisturbed nat-Downloaded 12 Oct 2009 to 128.120.194.194. Redistribution subjeINEERING / SEPTEMBER 1999

FIG. 4. Normalized p-y Curves for Soft Clay and Sand

ural Bay Mud (Dickenson 1994). The G/Gmax and b versus grelationships recommended by Vucetic and Dobry (1991) fora plasticity index of 50 were used. The G/Gmax curve at largestrains was modified to limit the peak shear stress to the seis-mic cu value [i.e., tpeak = gpeakG, giving G/Gmax = cu/(Gmaxgpeak)].

The mass of each container ring was distributed over theenclosed soil by increasing the soils unit weights, as sug-gested by Van Laak et al. (1994). This corresponded to anaverage increase in soil unit weight of about 25%. The un-derlying elastic half-space was treated as essentially rigid, andthe recorded base motion was used as the input base motionfor each event.

DYNAMIC p-y ANALYSES

Nonlinear p-y Element

A nonlinear p-y element was developed that can model arange of desired p-y behaviors and was implemented into afinite-element program for this study. The nonlinear p-y be-havior is conceptualized as consisting of elastic (p-ye), plastic(p-yp), and gap (p-yg) components in series. Equations describ-ing the p-y behavior are presented in Appendix I.

The backbone of the p-y curves for the Bay Mud was basedupon Matlocks (1970) recommendations for soft clay. Theresulting p-y curves match Matlocks within a few percent overthe entire range of y as shown in Fig. 4. For this study, theinput parameters pult and y50 were also based upon Matlocks(1970) equations

p = c BN (3)ult u pg9x Jx

N = 3 1 1 # 9 (4)p S Dc Bu

y = 2.5Be (5)50 50where B = pile diameter; Np = lateral bearing capacity factor;g9 = average buoyant unit weight; x = depth; cu = undrainedshear strength; and e 50 = strain corresponding to a stress of50% of the ultimate stress in a laboratory stress-strain curve.e 50 was taken as 0.005 based on published laboratory test datafor reconstituted Bay Mud, and J was taken as 0.5 accordingto Matlocks recommendations for soft clay.

The effects of gapping are modeled similar to the procedureby Matlock et al. (1978). The gapping behavior includes aresidual resistance that may be thought of as a drag force onthe sides of the pile as it moves within the gap. This residualresistance is specified by a parameter Cd that is defined as theratio of the residual resistance to the ultimate resistance pult.Back-calculated p-y curves from these centrifuge experiments(Wilson 1998) suggest that Cd 0.3 would be reasonable, andct to ASCE license or copyright; see http://pubs.asce.org/copyright

t C

hysteretic damping from the plastic (p-y ) and gap (p-y ) com-p(utPchcMd

Calculated and recorded accelerations and ARS for the pileJOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / SEPTEMBER 1999 / 753

onents are in series with the viscous damping on the elasticp-ye) component. Another dashpot arrangement that has beensed by others is parallel hysteretic/viscous damping wherehe dashpot is placed in parallel with the entire p-y element.arallel hysteretic/viscous damping can, however, result in ex-essive dashpot forces when the p-y element is loaded into theighly nonlinear range unless some special precautions orhecks are made (Wang et al. 1998). For example, Badoni andakris (1996) recognized that parallel hysteretic/viscous

amping could produce excessive damping forces and chose

head and superstructure of SP1 are shown in Fig. 9. Calculatedand recorded peak bending moments and displacements (rel-ative to the pile tip) are plotted versus depth in Fig. 10 (alongwith results for the other events in Csp4). The calculated p-ybehavior at a depth of 2.1 m was shown in Fig. 5, along withresults for the same depth in Events D and E for comparison.These results show excellent agreement between the calculatedand recorded structural response of SP1 for this one shakingevent.

The centrifuge and analysis results shown in Fig. 510 il-FIG. 5. Calculated p-y Behavior at 2.1 m Depth in Sof

this value was adopted for the baseline analyses presentedlater. The importance of Cd and the other p-y parameters isinvestigated in subsequent parametric studies.

Behavior of the p-y element during cyclic loading at threelevels of displacement is shown in Fig. 5. The inclusion of thegap component permits simulation of inverted s-shaped p-ycurves that may represent the influence of a physical gap and/or the undrained hysteretic behavior of the soil. For example,similar inverted s-shaped p-y behavior was back-calculated forsaturated sands by Wilson et al. (1999), with the behavior be-ing attributed to the undrained stress-strain behavior of satu-rated sand and not to a physical gap.

The backbone of the p-y curves for the lower sand layerwas based on American Petroleum Institute (API) (Recom-mended 1993) recommendations for sand. The resulting p-ycurve closely reproduces the API curve over the entire rangeof y, as shown in Fig. 4. For this study, the input parameterspult and kx were also based on API recommendations but withmodifications for the increase in stiffness with depth and theeffect of the overlying soft clay. API recommendations assumethat the initial p-y stiffness increases linearly with depth anddefine the initial stiffness as the product of depth x and theinitial modulus of subgrade reaction coefficient k. API rec-ommendations for k were derived from lateral loading teststhat were controlled by drained soil behavior at relatively shal-low depths. A constant k value overestimates the p-y stiffnessat depths larger than a few pile diameters (Lam and Law 1996)because the stiffness of sand generally increases in proportionto the square root of confinement, not in proportion to con-finement. In this study, the initial p-y stiffness for the under-lying sand layer was estimated using the elastic theory of Vesic(1961), the Gmax adopted in the site response analyses, and thejudgment that a G/Gmax ratio of about 25% was appropriatefor working load levels. The influence of the soft clay on thepult values in the sand was accounted for using the proceduresuggested by Georgiadis (1983). These approximate correc-tions to capacity and stiffness of the deep sand p-y elementsprovide at least a first-order compensation for the acceptedshortcomings of these common p-y formulations.

Radiation damping was modeled by a dashpot in parallelwith the elastic (p-ye) component, with the dashpot coefficientbased on the recommendations of Gazetas and Dobry (1984).This dashpot coefficient is used to represent the loss of energydue to outgoing stress waves that the pile transmits to the soil.This dashpot arrangement, discussed in detail in Wang et al.(1998), is termed series hysteretic/viscous damping because

p gDownloaded 12 Oct 2009 to 128.120.194.194. Redistribution subjeclay for SP1 in Csp4: (a) Event B; (b) Event D; (c) Event E

to circumvent this possibility by placing a limit on the mag-nitude of the parallel viscous dashpot force. Nonetheless, se-ries hysteretic/viscous damping is preferred over parallel hys-teretic/viscous damping because it is a conceptually moreattractive analogy, and it avoids the possibility of excessivedashpot forces that might unrealistically dominate the p-y be-havior (Wang et al. 1998).

Finite-Element AnalysesThe dynamic p-y analyses were performed using the finite-

element platform GeoFEAP (Bray et al. 1995) with the addedp-y element described above. The single-pile structures weremodeled with 17 linear-elastic beam elements (15 belowground and 2 above). Each of the 16 pile nodes below theground surface was connected to one of the nonlinear p-y el-ements described earlier (and in detail in Appendix I). Dis-placement time histories from the free-field site response anal-yses were input to the free-field ends of the p-y elements. P-Deffects were included by using the deformed (updated) mesh.The solution technique involved Newton-Raphson iterationand the Newmark method with g = 0.6 and b = 0.3025. Itshould be noted that high frequency noise can develop in thepile accelerations when using the energy conserving form ofthe Newmark method (i.e., g = 0.5 and b = 0.25). Parameterstudies showed that such high frequency noise could be effec-tively reduced using numerical damping with the Newmarkmethod or by switching to a Hilber-Hughes-Taylor technique(Hilber et al. 1977). More importantly, superstructure accel-erations, pile bending moments, and pile displacement timehistories were essentially unaffected by the numerical noise orthe techniques used to control it. This finding is consistent withtheoretical expectations because the time steps are small rel-ative to the range of periods (or frequencies) dominant in thepile response [e.g., Zienkiewicz and Taylor (1991)].

TYPICAL SET OF RECORDED AND CALCULATEDRESPONSES

A typical set of centrifuge and analysis results are presentedin Figs. 610 for SP1 during a scaled Kobe earthquake motion(Event B in Csp4). Recorded accelerations at eight depths inthe soil profile (Fig. 6) show a progressive amplification ofmotions up through the soil profile. Calculated motions are ingood agreement with the recorded response as shown by theacceleration time histories in Figs. 6 and 7 and the accelerationresponse spectra (ARS) in Fig. 8.t to ASCE license or copyright; see http://pubs.asce.org/copyright

FIG. 6. Recorded Accelerations in Soil Profile during Event B(Kobe Motion) in Csp4

FIG. 7. Calculated Accelerations in Soil Profile during Event B(Kobe Motion) in Csp4

lustrate the type of experimental data that was recorded, thegeneral features of the soil profile and structural responses,and the ability of the analysis method to reproduce those re-sponses for this one shaking event.754 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGIN

Downloaded 12 Oct 2009 to 128.120.194.194. Redistribution subjecFIG. 8. Acceleration Response Spectra (5% Damping) in SoilProfile during Event B (Kobe Motion) in Csp4

EFFECTS OF SHAKING LEVEL AND EARTHQUAKEMOTION

Calculated and recorded responses for the soil profile andstructural models (SP1 and SP2) were compared for the nineearthquake events listed in Table 2. All analyses used onebaseline set of input parameters selected using the engineeringprocedures described earlier. These comparisons are summa-rized in Figs. 11 and 12 showing both calculated and recordedpeak superstructure accelerations and displacements versuspeak base (input) acceleration. Results for SP1 are shown inFigs. 11(a) and 12(a) and for SP2 in Figs. 11(b) and 12(b).Calculated responses are in reasonably good agreement withrecorded structural responses, with a limited number of excep-tions and a slight overall tendency to underestimate the su-perstructure response. For example, calculated peak super-structure accelerations were within 225 to 110% of therecorded values in 16 of the 18 cases (nine events, two struc-tures), and were about 35% smaller than recorded values inthe remaining two cases. On average, the peak superstructureaccelerations were underestimated by about 1520%. Simi-larly, calculated peak superstructure displacements were within225 to 125% of the recorded values in 16 of the 18 casesand were 28 and 43% smaller than recorded values in theremaining two cases. On average, peak superstructure dis-placements were also underestimated by about 1520%.

Differences between calculated and recorded peak bendingmoments in the piles were similar to the differences betweencalculated and recorded peak superstructure responses dis-cussed above. This is because the peak bending moment ap-peared to be dominated by inertial loading from the superstruc-tures in all events (Wilson 1998). As expected, the calculatedand recorded peak bending moment distributions in Fig. 10EERING / SEPTEMBER 1999

t to ASCE license or copyright; see http://pubs.asce.org/copyright

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / SEPTEMBER 1999 / 755

FIG. 9. Accelerations and ARS (5% Damping) for Pile Head and Superstructure of Structure SP1 during Event B (Kobe Motion) inCsp4

FIG. 10. Calculated and Recorded Peak Bending Moments and Displacements for SP1 in Csp4, Events BE: (a) Peak Bending Mo-ments; (b) Peak Relative Displacements

show that the depth to maximum moment increases with in-creasing loading level.

Amplification ratios, in terms of peak superstructure re-sponse relative to peak base motion, generally decreased withincreasing peak base acceleration (Figs. 11 and 12). This trendis consistent with the expected effects of nonlinearity for therange of structural periods, soil profile periods, and input fre-quency contents involved in these tests. The nonlinear re-sponse is illustrated in Fig. 13 showing calculated and re-corded ARS for the superstructure of SP1 during Events BEin Csp4. The equivalent fundamental period of this struc-tural model increased from about 1.0 s under the smallestshaking level to about 2.0 s under the strongest shaking level,and this effect was captured by the analyses.

Calculated and recorded superstructure response wasstrongly affected by the frequency content of the earthquakemotion (i.e., Kobe versus Santa Cruz) as well as by the level

of shaking (Figs. 11 and 12). The frequency content of theseearthquakes is illustrated in Fig. 14 showing ARS for baseinput motions with similar peak accelerations. The Santa Cruzinput motion had smaller spectral accelerations in the 1- to 2-speriod range than did the Kobe input motion. This is the mainreason that the structural models (with fundamental periods ofbetween 1 and 2 s) responded less strongly to the Santa Cruzmotions.

The combined effects of shortcomings in site response anddynamic p-y portions of the analyses contribute to the dis-crepancies between calculated and recorded responses in thepreceding analyses (which used a single baseline set of param-eters). Consequently, the sensitivities of the results to the siteresponse and dynamic p-y portions of the analyses were eval-uated separately, as described in the following two sections,to gain insight into the possible causes of these discrepanciesand to investigate the influence of various parameters.Downloaded 12 Oct 2009 to 128.120.194.194. Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright

FIG. 11. Calculated and Recorded Peak SuperstructureAccel-erations for: (a) SP1; (b) SP2

FIG. 12. Calculated and Recorded Peak Superstructure Dis-placements for: (a) SP1; (b) SP2

SENSITIVITY TO SELECT DYNAMIC p-yPARAMETERS

The sensitivity of analysis results to select dynamic p-y pa-rameters was evaluated by reanalyzing the response of SP1756 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGI

Downloaded 12 Oct 2009 to 128.120.194.194. Redistribution subjecFIG. 13. Calculated and Recorded Superstructure ARS (5%Damping) for SP1 during Events BE in Csp4

FIG. 14. Recorded Base Input Motion ARS (5% Damping) forKobe and Santa Cruz Motions at Comparable Shaking Levels

during Events BE in Csp4. Select results are summarized inTable 3 in terms of their effect on the peak superstructuredisplacement (effects on peak superstructure acceleration andpeak bending moments were similar). Results are presentedfor the following cases:

Residual resistance of the gapping element Cd was re-duced from 0.3 to 0.1.

Gapping behavior was excluded from the p-y element. Radiation damping coefficients were doubled. Radiation damping coefficients were set to zero. The p-y curves in the clay were softened by increasing

e 50 by a factor of 4. The Georgiadis (1983) correction of the effect of the soft

clay layer on the p-y curves in the sand was neglected. The cu profile was increased by 30%, resulting in corre-

sponding changes in the site response parameters (Gmax/cuwas held constant) and the pult values for the p-y elements.

P-D effects were omitted.

The percent change in peak superstructure displacement forthese parameter variations ranged from 226 to 124 but wasonly greater than 610% for 6 out of the 32 cases summarizedin Table 3.

The sensitivity of the calculated structural response to in-dividual parameters for each case was qualitatively consistentwith the effects that the parameter had on total energy dissi-pation (hysteretic plus viscous) or on the fundamental periodof the structural system relative to the frequency content ofthe ground motions. In some cases, the magnitude of the sen-sitivity varied considerably with shaking intensity, illustratingthe complexity of the interaction between the free-field mo-tions (e.g., frequency content and intensity) and the nonlinearsoil-pile-structure system. These results serve as a remainderthat the selection of softer or weaker properties, which maybe conservative for a static analysis, is not necessarily conser-vative for a nonlinear dynamic response analysis.NEERING / SEPTEMBER 1999

t to ASCE license or copyright; see http://pubs.asce.org/copyright

aresponse analysis was used to calculate the free-field motionsJOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / SEPTEMBER 1999 / 757

the recorded motions as inputs to the dynamic p-y analysesis that any remaining differences between calculated and re-corded structural responses can be more directly attributed toshortcomings in the dynamic p-y analysis.

Superstructure responses for all 18 cases were recalculatedusing the recorded input motions and the same baseline set ofinput parameters. Results are summarized in Fig. 15 in termsof the calculated and recorded peak superstructure displace-ments versus the peak base acceleration. Peak superstructureaccelerations were overestimated by about 510% on average,with the calculated accelerations within 28 to 119% of therecorded values in 16 of the 18 cases, and 125 and 131% inthe remaining 2 cases. Peak superstructure displacements (Fig.

(e.g., compare Figs. 12 and 15). The fact that better agreementin structural responses is obtained when the free-field motionsare well represented indicates that the dynamic p-y portion ofthe analyses is reasonably accurate for the range of conditionsinvolved in this study.

Using recorded motions rather than site response calcula-tions as the inputs to the dynamic p-y analyses caused thecalculated peak superstructure displacements to change by 27to 164%, with an average of 125% over all 18 cases. Theeffect of changing input motions tended to increase with in-creasing shaking level, although the correlation was poor. Onaverage, the use of recorded input motions rather than thebaseline site response analysis results had a greater effect onTABLE 3. Effect of Select Parameters on Calculated Pe

Shakingevent

(1)

Basemotionrecorded,

amax(g)(2)

Peak SuperstructureDisplacement Dmax

RecordedDmax(mm)(3)

Calculatedbaselinecase Dmax

(mm)(4)

Change in Calc

ReduceCd to 0.10

(5)

Nogappingin p -y

element(6)

C 0.016 20 17 0 0B 0.055 70 64 1 25D 0.20 299 169 21 7E 0.58 733 585 6 216

SENSITIVITY TO SITE RESPONSE ANALYSIS

The sensitivity of the structural response to variations in thesite response was evaluated by (1) repeating the site responseanalyses with select soil parameter variations; and (2) derivinginput motions for the dynamic p-y analyses directly from therecorded motions within the soil profile. The site response pa-rameter study showed significant effects on the calculatedstructural response, as expected, but no one set of parameterscould be found that resulted in consistently better agreementwith the recorded motions (in terms of intensity and frequencycontent) at all depths for the strongest shaking events. Thisresult is not surprising as the calculated soil shear stressesreached the shear strength of the clay in these stronger events,reducing the accuracy of the equivalent-linear soil model.

The second approach was to bypass the site response cal-culations by using the recorded free-field motions as inputsto the dynamic p-y calculations. Displacement time historiesfor the soil profile were obtained by filtering and integratingthe acceleration time histories recorded by the free-field ver-tical array using the procedures described by Wilson et al.(1998). Input motions for the finite-element nodes were ob-tained by linearly interpolating displacements from the adja-cent accelerometers. Linear interpolation of displacements willattenuate high frequency motions if the distance between ac-celerometers is significant relative to the wavelengths of in-terest. This effect will vary with each earthquake because thewavelengths depend on the level of shaking as well as on thefrequency content of the motion. The potential loss of higherfrequency motion was evaluated using the results of site re-sponse analyses for several earthquakes. Calculated motionsat accelerometer depths were used to interpolate motions atintermediate depths, and then these interpolated motions werecompared with the actual site response calculations at thosedepths. These evaluations showed that the interpolationmethod worked excellently in the sand but filtered some higherfrequency motions in the clay (lower shear-wave velocities andhence smaller wavelengths). Nonetheless, these evaluationssuggest that the interpolated (recorded) motions provide anexcellent overall representation of the free-field soil motionsfor the range of periods of interest (>1 s) and a reasonablygood representation at shorter periods. The advantage of usingDownloaded 12 Oct 2009 to 128.120.194.194. Redistribution subjk Superstructure Displacement for SP1 in Container Csp4

ulated Superstructure Dmax for Specified Parameter Change (%)

Doubleradiationdamping

(7)

Zeroradiationdamping

(8)

Increasee 50 to 0.02

(9)

Stiffer/stronger

p -y curvesin sand

(10)

Increasecu by 30%

(11)

Omit P-Deffects

(12)22 10 210 0 24 2225 7 226 0 224 321 2 13 0 7 2223 3 22 14 23 21

FIG. 15. Calculated and Recorded Peak Superstructure Dis-placements for Dynamic p-y Analyses Using Recorded Motionsas Inputs for: (a) SP1; (b) SP2

15) were also overestimated by about 510% on average, withthe calculated displacements within 27 to 128% of the re-corded values in 16 of the 18 cases and within 131 to 149%in the remaining 2 cases (with both being events with peakbase accelerations

peak superstructure response than did most of the dynamicp-y parameter variations summarized in Table 3.

DISCUSSIONThe above comparisons of calculated and recorded re-

sponses illustrate the value of evaluating any analysis/designmethod against a wide range of conditions as opposed to asingle agrees/disagrees comparison for one set of data. In fact,good agreement could have been fortuitously obtained for anyone structure and earthquake, as illustrated by the parametricstudy presented herein. A more thorough evaluation was pro-vided by seeing if the dynamic p-y analysis method could,using one set of baseline properties, reliably capture the ob-served soil-pile-structure interaction effects over a wide rangeof shaking intensities and earthquake motions. In this regard,the centrifuge modeling tests performed in this study provedparticularly valuable.

The dynamic p-y and site response analyses were able toreasonably model the recorded responses despite the many ap-proximations in the analysis methods and the potential uncer-tainties in the centrifuge data. Notable approximations in theanalyses include the assumption of equivalent-linear soil be-havior in the free-field, the uncoupling of site response andstructural response, the use of independent p-y springs, and theuncertainties in soil properties and p-y characterizations. Po-tential uncertainties or errors in the experimental data includethe effects of soil-container interaction, influence of the pilefoundations on the soil profile motions, limitations in the sig-nal processing, and scale effects. With these factors in mind,it should be noted that these experiments involved very highlevels of nonlinearity in the soil profile and around the pilesand thus provided a difficult test of these analysis methods.The sensitivity analyses suggest that the dynamic p-y modelwas able to reasonably capture the experimental model behav-ior, but combining the site response and dynamic p-y analysesreduced the agreement due to differences between the recordedand calculated site responses.

SUMMARY AND CONCLUSIONSA dynamic beam on a nonlinear Winkler foundation (or dy-

namic p-y) analysis method was evaluated against a set ofcentrifuge model tests involving pile-supported structures in aprofile of soft clay (6 m thick) overlying dense sand. Ninedifferent earthquake shaking events were performed on twomodel configurations, including five scaled Kobe motions (amax= 0.020.7g at the base) and four scaled Santa Cruz motions(amax = 0.040.6g at the base). A baseline set of analysis pa-rameters was selected using procedures commonly used inpractice. The analyses consisted of performing 1D equivalent-linear site response analyses to calculate the dynamic responseof the free-field soil profile and then dynamic p-y analyses tocalculate the dynamic response of the structural models. Im-portant features of the dynamic p-y analyses include the useof series hysteretic/viscous damping to represent radiationdamping (Wang et al. 1998) and the inclusion of gapping ef-fects (after Matlock et al. 1978). Calculated and recorded re-sponses of the two single-pile-supported systems and soil pro-file were compared for all earthquake events.

Reasonable agreement was obtained between the dynamicp-y analyses and the centrifuge model data over the wide rangeof shaking intensities and earthquake motions covered in thisstudy. Peak superstructure motions (accelerations and displace-ments) were underestimated on average by about 1520%when using the baseline set of analysis parameters. Similardifferences were obtained for peak pile bending momentsalong the pile length. When the recorded free-field motionswere used as inputs to the dynamic p-y model, bypassing the758 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENG

Downloaded 12 Oct 2009 to 128.120.194.194. Redistribution subjFIG. 16. Characteristics of Nonlinear p-y Element: (a) Com-ponents; (b) Behavior of Components

site response analysis, peak superstructure motions were over-estimated on average by about 510%. The results of theseand other sensitivity studies suggest that the site response cal-culations were a greater source of uncertainty than the dy-namic p-y calculations in the prediction of superstructure re-sponse for the range of conditions involved in this study.

The results of this study provide experimental support forthe use of dynamic p-y analysis methods in seismic soil-pile-structure interaction problems. Additional physical model datafor other soil-pile-structure configurations and systematic eval-uations of such data are still needed to further evaluate thereliability of dynamic p-y analysis methods and their extensionto pile groups.

APPENDIX I. EQUATIONS DESCRIBING p-yELEMENT

The equations used to describe p-y behavior were chosen asa versatile means of approximating established p-y relationsand structured to be relatively easy to implement in a displace-ment-based finite-element program. The nonlinear p-y behav-ior is conceptualized as consisting of elastic (p-ye), plastic (p-yp), and gap (p-yg) components in series. Radiation dampingis modeled by a dashpot in parallel with the elastic (p-ye) com-ponent. The gap component consists of a nonlinear closurespring (pc-yg) in parallel with a nonlinear drag spring (pd-yg),as shown in Fig. 16. The characteristics of the p-y spring com-ponents are illustrated in Fig. 16. Note that y = ye 1 y p 1 ygand that p = pd 1 pc.

The plastic spring has an initial range of rigid behavior be-tween 2Crpult < p < Crpult, where Cr = ratio of p/pult whenplastic yielding first occurs in virgin loading. The rigid rangeof p, which is 2Crpult, remains constant and translates withplastic yielding (kinematic hardening). Beyond the rigid range,loading of the plastic (p-y p) spring is described by

n

cy50p = p 2 (p 2 p )ult ult 0 F Gp pcy 1 uy 2 y u50 0where pult = ultimate resistance of the p-y element in the cur-INEERING / SEPTEMBER 1999

ect to ASCE license or copyright; see http://pubs.asce.org/copyright

rent loading direction; p0 = p at the start of the current plasticloading cycle; = y p at the start of the current plastic loadingpy 0cycle; c = constant to control the tangent modulus at the startof plastic yielding; and n = exponent to control sharpness ofthe p-yp curve.

The closure (pc-yg) spring is described byy y50 50cp = 1.8p 2ult F G1 g 2 gy 1 50(y 2 y ) y 2 50(y 2 y )50 0 50 0

where = memory term for the positive side of the gap; and1y0= memory term for the negative side of the gap. The initial2y0

values of and were set as y50/100 and 2y50/100, respec-1 2y y0 0tively. The factor of 1.8 brings pc up to pult during virgin load-ing to (or Enlargement of the gap follows logic similar1 2y y ).0 0to that of Matlock et al. (1978) with and representing1 2y y0 0the maximum past y values (positive and negative) for thenear-field component (y p 1 yg) minus an unloading displace-ment at a slope of p50/y50. This closure spring allows for asmooth transition in the load-displacement behavior as the gapopens or closes.

The nonlinear drag (pd-yg) spring is described byy50d dp = C p 2 (C p 2 p )d ult d ult 0 F Gg gy 1 2uy 2 y u50 0

where Cd = ratio of the maximum drag force to the ultimateresistance of the p-y element; = pd at the start of the currentdp0loading cycle; and = yg at the start of the current loadinggy0cycle.

Matlocks (1970) recommended backbone for soft clay isclosely approximated using c = 10, n = 5, and Cr = 0.35.Values of pult, y50, and Cd must then be specified to define thep-y behavior.

APIs recommended backbone for drained sand is closelyapproximated using c = 0.5, m = 2, and Cr = 0.2. Values ofpult, kx, and Cd must then be specified to define the p-y behav-ior. Note that kx is the initial virgin p-y spring stiffness andthat the corresponding y50 value is calculated automatically foruse in the preceding equations.

ACKNOWLEDGMENTSCaltrans supported this research project under contract number

65V495. Support for C. J. Curras was provided by a Graduate ResearchFellowship from the National Science Foundation, Washington, D.C. Thecontents of this paper do not necessarily represent a policy of eitheragency or endorsement by the state or federal government. The centrifugeshaker was designed and constructed with support from the National Sci-ence Foundation, Obayashi Corp., Caltrans, and the University of Cali-fornia at Davis. Tom Kohnke assisted with the centrifuge model testing.I. M. Idriss offered valuable comments throughout the study. JonathanBray provided the GeoFEAP program, and Thomas Lok provided adviceon implementation issues. The above support and assistance is greatlyappreciated.

APPENDIX II. REFERENCESBadoni, D., and Makris, N. (1996). Nonlinear response of single piles

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Curras, C. J., Boulanger, R. W., Kutter, B. L., and Wilson, D. W. (1999).Seismic soil-pile-structure interaction in soft clay. Proc., 2nd Int.Conf. on Earthquake Geotech. Engrg., Balkema, Rotterdam, The Neth-erlands, in press.

Dickenson, S. E. (1994). Dynamic response of soft and deep cohesivesoils during the Loma Prieta earthquake of October 17, 1989, PhDthesis, University of California, Berkeley, Calif.

Gazetas, G., and Dobry, R. (1984). Simple radiation damping model forpiles and footings. J. Engrg. Mech., ASCE, 110(6), 937956.

Georgiadis, M. (1983). Development of p-y curves for layered soils.Proc., Geotech. Pract. in Offshore Engrg., ASCE, New York, 536545.JOURNAL OF GEOTECHNICAL

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ct to ASCE license or copyright; see http://pubs.asce.org/copyright