DYNAMIC EXPERIMENTS AND ANALYSES OF A PILE-GROUP-SUPPORTED STRUCTURE

Transcription

1 DYNAMIC EXPERIMENTS AND ANALYSES OF A PILE-GROUP-SUPPORTED STRUCTURE By Christina J. Curras, 1 Ross W. Boulanger, 2 Bruce L. Kutter, 3 and Daniel W. Wilson, 4 Members, ASCE ABSTRACT: Experimental data on the seismic response of a pile-group-supported structure was obtained through dynamic centrifuge model tests, and then used to evaluate a dynamic beam on a nonlinear Winkler foundation (BNWF) analysis method. The centrifuge tests included a structure supported on a group of nine piles founded in soft clay overlying dense sand. This structure was subjected to nine earthquake events with peak accelerations ranging from 0.02 to 0.7g. The centrifuge tests and dynamic analysis methods are described. Good agreement was obtained between calculated and recorded structural responses, including superstructure acceleration and displacement, pile cap acceleration and displacement, pile bending moment and axial load, and pile cap rotation. Representative examples of recorded and calculated behavior for the structure and soil profile are presented. Sensitivity of the dynamic BNWF analyses to the numerical model parameters and site response calculations are evaluated. These results provide experimental support for the use of dynamic BNWF analysis methods in seismic soil-pile-structure interaction problems involving pile-group systems. INTRODUCTION Soil-pile-structure interaction can be an important consideration in evaluating the seismic performance of pile-groupsupported structures, particularly in soft clay or liquefying sand. Methods of analyzing semismic soil-pile-structure interaction have included 2D and 3D modeling of the pile and soil continuum using finite element or finite difference methods, dynamic beam on a nonlinear Winkler foundation (BNWF) methods, and simplified two-step methods that uncouple the superstructure and foundation portions of the analysis. The accuracy of these dynamic analysis methods under soft soil conditions has not been fully evaluated because the available case histories and physical model studies are limited in number and detail. The first goal of this study is to perform a series of dynamic centrifuge model tests of pile-supported structures in soft ground and document the results for use by other researchers. These centrifuge experiments were performed using the 9-m radius centrifuge at the University of California-Davis. Structural models were designed to be representative of select bridge structures, and included two structures supported by single piles and one structure supported by a nine-pile group, all founded in a profile of soft clay over dense sand. These structures were subjected to nine different earthquake motions having peak base accelerations of g. The experimental data are available in Wilson et al. (1997a,b). The second goal of this study is to evaluate a dynamic BNWF analysis method against the experimental data. Dynamic BNWF analysis methods, as depicted in Fig. 1, are considerably less complex than continuum methods and yet provide a practical tool for incorporating the essential mechanisms of the dynamic system. BNWF analyses of the two singlepile-supported structures, as described in Boulanger et al. 1 Asst. Prof., Dept. of Civ. and Envir. Engrg., Univ. of Wisconsin, Platteville, WI Assoc. Prof., Dept. of Civ. and Envir. Engrg., Univ. of California, Davis, CA Prof., Dept. of Civ. and Envir. Engrg., Univ. of California, Davis, CA Facility Mgr., Ctr. for Geotech. Modeling, Univ. of California, Davis, CA Note. Discussion open until December 1, To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on March 3, 2000; revised February 5, This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering, Vol. 127, No. 7, July, ASCE, ISSN /01/ /$8.00 $.50 per page. Paper No (1999), showed that reasonably good agreement between calculated and recorded responses could be obtained for all nine shaking events. Extending the BNWF analysis method to the pile-group-supported structure required including the effects of rocking motions (and hence the axial response of the piles), pile group effects, and the lateral resistance of the pile cap. This paper presents the evaluation of the BNWF analysis method against the recorded responses of the pile-group-supported structure. Brief descriptions of the centrifuge experiments and the dynamic analysis procedures are presented; more detailed descriptions are available in Boulanger et al. (1999). Calculated and recorded responses are compared for all nine earthquakes, and the sensitivity of the results to the numerical model parameters is assessed. The results provide an evaluation of the analysis method s ability to reliably capture the many aspects of soil-pile-structure interaction effects for a structure supported on a pile group over a wide range of earthquake motions. CENTRIFUGE EXPERIMENTS Tests were performed on the 9-m radius centrifuge at the University of California-Davis in a flexible shear beam container at a centrifugal acceleration of 30g. All results presented herein are in prototype units unless otherwise stated. The soil profile, structural models, and instrumentation for the tests are schematically illustrated in Fig. 2. The lower soil layer was fine, uniformly graded Nevada sand (C u = 1.5, D 50 = 0.15 mm) at a relative density D r of about 75 80%. The upper soil layer was 6 m of normally consolidated reconstituted Bay mud (liquid limit 88, plasticity index 48). The structural models included one structure supported by a pile group (referred to as the PG33 structure) and two structures supported by single piles. The pile group for PG33 consisted of nine piles spaced at four diameters on center in a 3 3 grid. The pile cap was m in plan, 2.3 m thick, and had a mass of 318 Mg. PG33 had a superstructure mass of 468 Mg centered 10.7 m above the pile cap. The resonant frequency of the PG33 superstructure with its pile cap fixed against movement was measured as 2 Hz (60 Hz model scale); the prototype column can therefore be represented by an average flexural stiffness of kn m 2 over the 7.4 m column height (from top of pile cap to bottom of superstructure mass). Each pile was approximately equivalent to a m diameter steel pipe pile with a 19 mm wall thickness. The pile group was installed at 1g (prior to spinning the centrifuge), and remained elastic during all earthquake events. Two centrifuge model configurations, hereafter referred to JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JULY 2001 / 585

2 FIG. 1. Schematic of Dynamic BNWF Analysis Method TABLE 1. Earthquake Events in Csp4 and Csp5 Series Event Motion a max base input (g) (a) Csp4 Series A Kobe a B Kobe C Kobe D Kobe 0.20 E Kobe 0.58 (b) Csp5 Series A Santa Cruz B Santa Cruz 0.12 C Santa Cruz 0.30 D Santa Cruz 0.60 E Kobe 0.70 a Event B is a repeat of this event so that only event B was analyzed. FIG. 2. Schematic of Layout and Instrumentation as containers Csp4 and Csp5, were each shaken with five simulated earthquake events, as summarized in Table 1. Note that there are only nine different events in total because event B duplicated event A in Csp4, and the recorded responses for these two events were essentially identical. Each event was a scaled version of a time history prepared by filtering and integrating strong motion records from Port Island in the 1995 Hyogoken-Nambu (Kobe) earthquake or from Santa Cruz in the 1989 Loma Prieta earthquake. Each earthquake event was separated by sufficient time for dissipation of any shakinginduced excess pore pressures. The same soil model was used in both configurations, but after all shaking events for Csp4 were completed, the centrifuge was spun down (stopped) and the single pile structures were relocated (Boulanger et al. 1999). Test details and all time histories are available in data reports by Wilson et al. (1997a,b). The undrained shear strength c u of the soft clay was measured using a small torvane immediately after the centrifuge stopped spinning. The c u profile increased from about 1 to 13.4 kpa over the clay layer s full depth. These strengths were found to be consistent with normalized undrained shear strength ratios expected for normally consolidated or slightly overconsolidated clay. The sequence of earthquake shaking events imposed on the physical models produces a loading history that can be expected to progressively affect the soil properties and the lateral and axial loading behavior of the piles and pile cap. There are, however, insufficient data to define how prior loading followed by reconsolidation might affect p-y, t-z, or q-z behavior. Consequently, the baseline set of input parameters described in the analysis sections can be considered as representing average conditions across all shaking events. The sensitivity of the analysis results to variations in the input parameters is evaluated for all shaking events, and this allows a qualitative evaluation of whether a progressive evolution of input parameters would or would not have improved the accuracy of the numerical modeling. In addition, examination of the force, moment, and displacement time histories, as shown in subsequent figures, shows that the residual loads and displacements in the structure after each shaking event were negligible relative to the transient loads and displacements (for these level ground conditions). DYNAMIC BNWF ANALYSES Finite-Element Model The dynamic BNWF analyses were performed using the finite-element platform GeoFEAP (Bray et al. 1995) with the 586 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JULY 2001

3 added elements described below. The pile group was modeled as a single row of three piles, parallel to the direction of shaking, with the appropriate tributary masses, column stiffness, and soil resistances. As shown in Fig. 1, each of the pile nodes below ground was connected to a horizontal p-y element and a vertical t-z element. The nodes at the pile tips were connected to q-z elements as well. The pile cap was modeled as a rigid frame with the piles fixed into its base, and was connected to p-y elements representing the lateral soil resistance. Horizontal free-field motions were input to the free-field ends of all p-y elements. The free-field ends of the t-z and q-z elements were fixed because vertical ground motions were not being considered. In reality, rocking of the container will impose some vertical motion on the models, but the magnitude is reasonably small and can be neglected for the purposes of this study (Wilson et al. 1997c). The solution technique involved Newton-Raphson iteration with a line search, the Newmark method with = 0.6 and = , and the use of the deformed mesh geometry (to incorporate P-delta effects). Nonlinear p-y Elements Nonlinear p-y behavior was modeled using the element described in Boulanger et al. (1999), which accounts for gapping and radiation damping. The general behavior of the p-y element is illustrated in Fig. 3(a). The p-y parameters for the soft clay were based on Matlock s (1970) recommendations, and the p-y parameters for the underlying sand were based on [American Petroleum Institute (API) 1993] recommendations with modifications as described in Boulanger et al. (1999). A p-multiplier (Brown et al. 1988) was used to account for group effects on the lateral load behavior of the piles. An average p-multiplier of 0.7 for piles at a four-diameter spacing was used for all piles regardless of their location in the group; this simplifies the numerical model because the front and rear rows alternate between being the leading and following row during cyclic loading. An average p-multiplier is considered appropriate for obtaining the global dynamic response of the system, after which the demands on the individual piles could be estimated by performing a pseudostatic (pushover) analysis for the peak global loading condition and with different p-multipliers assigned to each pile. This last step was not necessary for the PG33 structure because the recorded bending moments at the heads of the inner and other piles (the heads of four piles were instrumented) showed no notable differences during earthquake shaking. This latter observation is attributed to the very soft soil conditions, the framing action of the pile group, and other characteristics particular to these tests. Lateral soil resistance against the pile cap was also modeled using p-y elements, with appropriate adjustments. Lateral resistance may develop as passive pressure on the front, active pressure on the back, and skin friction on the sides and base. Passive and active pressures were estimated using Rankine theory, although it is recognized that the calculated passive pressure would be greater if wall friction and 3D effects were included, smaller if cyclic degradation was included, and alternately increased and decreased by inertia effects since the soil and pile cap motions varied in phase. Skin friction on the sides was estimated using the method ( f s = c u ) with = 1. Skin friction on the base was neglected because the clay appeared to settle slightly more than the pile cap, which likely reduced or eliminated the base contact stress. The cumulative lateral resistance on the pile cap was represented by p-y elements having the same backbone as the soft clay p-y elements along the piles. These pile-cap p-y elements had an initial stiffness that was based on an elastic solution and were set to develop about 95% of their ultimate resistance at a lateral displacement of 46 mm (2% of the pile cap height). Gapping behavior was based on the assumption that active and passive pressures would not act within gaps that formed on the front and rear faces while side skin friction would always act. Nonlinear t-z and q-z Elements Nonlinear t-z elements for skin friction on the pile were modeled as elastic and plastic components in series. The ultimate skin friction resistance of the t-z elements in the clay was calculated using the method with = 1. For the sand, it was calculated using f s = K v tan( ) with K = 0.8, v = effective vertical stress, and =30. Coupling of the t-z elements to the p-y elements is neglected. A typical response of a t-z element is shown in Fig. 3(b). Nonlinear q-z elements for the pile tip resistance were modeled as elastic, plastic, and gap components in series. The q-z element allowed for different capacities in compression and uplift, as illustrated by the typical response in Fig. 3(c). The ultimate resistance in compression was calculated as q u = N* q v,t, where v,t = effective vertical stress at the tip elevation, and N* q = 300 based on an estimated effective friction angle of 38 for the dense sand. A nominal uplift capacity of 100 kpa on the tip was used to represent any effects of suction during rapid uplift of the pile tip. The initial stiffnesses of the t-z and q-z elements were based on recommendations by Randolph (1991). Yield displacement values were taken as 0.5% of the pile diameter for shaft resistance and 2.5% of the pile diameter for tip resistance. These values were chosen from the stiffer range of Randolph s recommendations to account for dynamic earthquake effects. Radiation Damping Radiation damping for the different nonlinear elements was modeled by a dashpot in parallel with the elastic component (i.e., p-y e, t-z e,orq-z e ), with the dashpot coefficient approximating elastic theory solutions for lateral or vertical pile vibration (Gazetas and Dobry 1984). This dashpot arrangement was termed series hysteretic/viscous damping by Wang et al. (1998) because the hysteretic damping from the plastic component is in series with the viscous damping on the elastic component. Having the dashpot in parallel with the entire nonlinear element ( parallel hysteretic/viscous damping ) can result in excessive dashpot forces when the element is loaded into the highly nonlinear range (Wang et al. 1998; Randolph FIG. 3. Typical Behavior of: (a) p-y Element; (b) t-z Element; (c) q-z Element JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JULY 2001 / 587

4 1991), although the effect of using series versus parallel damping is small when the element behavior is mostly elastic. FREE-FIELD SITE RESPONSE The free-field response of the soil profile, which is input to the dynamic BNWF analyses of the structure, was obtained in two different ways. Details for both approaches, as well as input parameters, are described in detail in Boulanger et al. (1999). One approach was to use the 1D equivalent-linear site response program SHAKE91 (Schnabel et al. 1972; Idriss and Sun 1991) to calculate a free-field site response. Parametric studies showed that the equivalent-linear procedure was unable to consistently match the intensity and frequency content of the recorded ground motions at all depths for the strongest shaking events. This limitation was attributed to the fact that the shear strength of the clay was likely exceeded during the stronger shaking events, reducing the accuracy of the equivalent linear model. The other approach involved developing interpolated recorded displacement time histories by double integration of the acceleration time histories recorded by the free-field vertical array, using the signal processing procedures described by Wilson et al. (1998). Input motions for the finite-element nodes were then obtained by linearly interpolating displacements between adjacent accelerometers. Linear interpolation of displacements will attenuate high frequency motions if the distance between accelerometers is significant relative to the wavelengths of interest. This effect will vary with each earthquake because the wavelengths depend on the level of shaking as well as on the frequency content of the motions. Evaluations showed that the interpolated motions provided an excellent overall representation of the free-field soil motions for periods greater than about 1 s and reasonably good representation to periods as low as 0.1 s. The advantage of using the recorded motions as inputs to the dynamic BNWF analyses is that any differences between calculated and recorded structural responses can be more directly attributed to shortcomings in the BNWF analysis rather than to the site response analysis. TYPICAL RECORDED AND CALCULATED RESPONSES Typical Kobe Motion Recorded and calculated responses of the soil profile during a large-scaled Kobe motion (event E in Csp5, 0.7g maximum base acceleration) are shown in Figs. 4 and 5. Acceleration time histories at eight depths in the soil profile are shown in Figs. 4(a) (recorded) and 4(b) (calculated equivalent-linear site response). Acceleration response spectra (ARS) for these eight depths are compared in Fig. 5. The accelerations are generally amplified up through the lower sand layer and then attenuated in the upper clay. The calculated and recorded ARS agree relatively well in the longer period range (greater than about 1 s), but have significant differences in the lower period range. The dynamic response of the PG33 structure was calculated using the two different approaches for specifying the free-field soil profile motions. Acceleration time histories and ARS for the superstructure and pile cap are shown in Fig. 6 for the case when the interpolated-recorded soil profile motions are used as inputs to the BNWF analyses. The same plots are shown in Fig. 7 for the case when the free-field motions are obtained from the equivalent-linear site response analyses. In either case, the greatest amplification of motions in the structure occurred at periods of about 0.35 and 1.2 s. These two dominant modes of structural vibration arise from the large masses concentrated at the pile cap and superstructure, such that the system acts largely as a two-degree-of-freedom system. The cal- FIG. 4. Accelerations in Soil Profile during Event E (Kobe Motion) in Csp5: (a) Recorded; (b) Equivalent-Linear Site Response Calculations 588 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JULY 2001

5 FIG. 5. Acceleration Response Spectra (5% Damping) at Various Depths during Event E (Kobe Motion) in Csp5; Recorded and Calculated (Equivalent- Linear Site Response) Motions culated structural responses are generally in good agreement with the recorded responses in Figs. 6 and 7, with the exception that the pile cap motions are overpredicted by about 50% when the input motions for the BNWF analysis are obtained from the site response analysis. This overprediction occurs because the site response analysis overestimates the soil profile motions in the 0.3- to 0.4-s period range, and thus tends to overexcite the second mode of the PG33 structure (which is strongly present in the pile cap motion). Other response characteristics that are important for design purposes include superstructure displacements, pile cap displacements, bending moments, axial forces, and pile cap rotations. Recorded and calculated time histories of some of these responses, along with base input acceleration, are shown in Fig. 8 for the case in which the interpolated-recorded soil profile motions are used as inputs. Note that the superstructure and pile cap displacements are taken as relative to the pile tips, that the bending moment and axial force time histories are for the head of a corner pile (north end of the group), and that only the transient component of the axial force is shown. Good agreement was obtained for all aspects of the structural response during this scaled Kobe earthquake event. Typical Santa Cruz Motion Recorded and calculated responses of the soil profile during a scaled Santa Cruz motion (event C in Csp5, maximum base acceleration of 0.30g) are compared in Fig. 9, which shows ARS for the same eight depths in the soil profile. For this motion, the site response analysis clearly overestimated the higher frequency motions in the clay layer. The calculated dynamic response of the PG33 structure is again compared for the two different approaches used to specify free-field soil profile motions. Acceleration time histories and ARS for the superstructure and pile cap are shown in Fig. 10 for the case when the interpolated-recorded soil profile mo- JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JULY 2001 / 589

6 FIG. 6. Accelerations and ARS (5% Damping) for Superstructure and Pile Cap of PG33 during Event E (Kobe Motion) in Csp5 Using Interpolated- Recorded Soil Profile Motions FIG. 7. Accelerations and ARS (5% Damping) for Superstructure and Pile Cap of PG33 during Event E (Kobe Motion) in Csp5 Using Soil Profile Motions from Site Response Analysis tions are used, and in Fig. 11 for the case when the equivalentlinear site response analysis was used. When the interpolatedrecorded motions are used as inputs to the BNWF analyses (Fig. 10), good agreement is obtained between the calculated and recorded structural responses, with both showing that the second mode plays a greater role during this scaled Santa Cruz earthquake than during the scaled Kobe earthquake. When the equivalent-linear site response analysis was used to define the free-field soil profile motions for the BNWF analyses (Fig. 11), the second mode is overexcited and the structural response is overestimated, e.g., the maximum pile cap acceleration is overestimated by a factor of about two. Similar results were presented by Curras et al. (1999) for the slightly smaller shaking event B in Csp5 (scaled Santa Cruz motion with maximum base acceleration of 0.12g). Results for other response characteristics are shown in Fig. 12 for the case where the interpolated-recorded free-field motions were used as inputs to the BNWF analysis. These recorded and calculated time histories are in good agreement, with both showing that the second mode had a stronger influ- 590 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JULY 2001

7 FIG. 8. Calculated and Recorded Response Time Histories of PG33 Structure for Event E (Kobe Motion) of Csp5 Using Interpolated-Recorded Soil Profile Motions ence on the structural response (e.g., there are stronger higherfrequency components) than was observed for the Kobe motion (Fig. 8). Effect of Approach for Specifying Free-Field Motions The two different approaches for specifying free-field soil profile motions sometimes had a significant effect on the calculated behavior of the PG33 structure, as illustrated by the typical results presented above. The equivalent-linear site response analyses did an adequate job of matching the recorded soil response for periods greater than about 1 s, but generally overestimated the higher frequency motions in the upper clay layer during the stronger shaking events. The PG33 structure was affected because its second modal period was only about s and this second mode was important to the global response. The pile cap was thus overexcited, which resulted in calculated pile cap accelerations up to two times the recorded values. The interpolated-recorded motions provided a better representation of the higher frequency motions in the soil, resulting in more reasonable pile cap behavior. It is interesting to note that calculated responses of the two single-pile-supported structures, as previously analyzed by Boulanger et al. (1999), were less affected by the differences in these two approaches for specifying free-field soil profile motions. The reason for this was that the single-pile-supported structures were dominated by a single mode of vibration at a period greater than about 1 s. Therefore, the overestimation of higher frequency motions by the equivalent-linear site response analyses did not have as significant an effect. The interpolated-recorded free-field soil profile motions are used for the remainder of the BNWF analyses presented herein. The advantage of using the interpolated-recorded motions as inputs to the dynamic BNWF analyses is that any differences between calculated and recorded structural responses can be more directly attributed to shortcomings in the dynamic BNWF analysis, rather than potentially being due to shortcomings in the site response analysis. This was particularly important for the PG33 structure because the dynamic analysis of the pile-group-supported structure is more complex than that of a single-pile-supported structure. EFFECTS OF SHAKING LEVEL AND EARTHQUAKE MOTION Recorded and calculated structural responses for PG33 were compared for the nine different earthquake events listed in Table 1. Maximum values of structural responses (both calculated and recorded) are plotted versus peak base (input) acceleration in Fig. 13 results are shown for superstructure acceleration, superstructure displacement (relative to the pile tips), pile cap acceleration, pile cap displacement (relative to the pile tips), pile cap rotation, pile bending moment, and pile axial force (transient component). Overall, calculated maximum responses are in reasonably good agreement with recorded maximum structural responses. The nonlinear response of the PG33 structure is illustrated in Fig. 14 showing recorded and calculated ARS for the superstructure during four of the scaled Kobe motions. The first modal period (or period of maximum amplification) increases from about 0.8 s for the smallest shaking level to about 1.2 s for the largest shaking level due to increased yielding in the p-y, t-z, and q-z elements. These changes in the structure s modal periods, together with the nonlinear site response (which alters the frequency content of the soil profile motions), are why the structural responses shown in Fig. 13 vary nonlinearly with peak base acceleration. The frequency content of the earthquake motion (i.e., Kobe versus Santa Cruz) had a dominant effect on the calculated and recorded structural response, with the Santa Cruz motions generally producing much lower responses. The main reason that the PG33 structure responded less strongly to the Santa JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JULY 2001 / 591

8 FIG. 9. Acceleration Response Spectra (5% Damping) at Various Depths during Event C (Santa Cruz Motion) in Csp5; Recorded and Calculated (Equivalent-Linear Site Response) Motions Cruz motions than to the Kobe motions was that the Santa Cruz free-field motions had smaller spectral accelerations at the first modal period ( s) of the PG33 structure, i.e., compare the free-field ARS in Figs. 5 and 9. The exception to this behavioral pattern, as shown in Fig. 13(d), was that the maximum pile cap accelerations were similar for both earthquake motions at the same peak base acceleration level. This is because the pile cap acceleration is strongly affected by the structure s second mode, which is in the 0.3- to 0.4-s period range where the Kobe and Santa Cruz motions have similar spectral accelerations. SENSITIVITY OF BNWF RESULTS TO FOUNDATION STIFFNESS Sensitivity of the analysis results to the translational and rotational stiffnesses of the foundation substructure was evaluated, and some results are presented herein. As mentioned previously, the PG33 structure responded essentially as a twodegree-of-freedom system with its two dominant modes dictated by the two concentrated masses (pile cap and superstructure), the bending stiffness of the superstructure column, the translational stiffness of the substructure, and the rotational (rocking) stiffness of the substructure. The translational stiffness depends primarily on the lateral stiffness of the piles (py and pile properties) and the soil resistances against the pile cap (passive and active pressures, side and base shears). The rocking stiffness depends primarily on the axial stiffness of the piles (t-z, q-z, and pile properties) and their geometric layout. In addition, the translational and rotational stiffnesses of the substructure are cross-coupled and vary with shaking level because of their nonlinear characteristics. The translational and rotational stiffnesses of the substructure were found to be of roughly equal importance in their effects on the first modal period for the PG33 structure. This can be illustrated by considering the results of a pseudostatic pushover analysis of the superstructure. For a pseudostatic horizontal force of 0.2g times the superstructure mass, the superstructure was displaced by 29 mm with 28% due to translation of the pile cap, 30% due to rotation of the pile cap, and 42% due to bending of the superstructure column. When the pseudostatic force is increased to 0.5g times the superstructure mass, the superstructure displacement increased to 84 mm and the contributions changed to 32% due to pile cap translation, 592 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JULY 2001

9 FIG. 10. Accelerations and ARS (5% Damping) for Superstructure and Pile Cap of PG33 during Event C (Santa Cruz Motion) in Csp5 Using Interpolated-Recorded Soil Profile Motions FIG. 11. Accelerations and ARS (5% Damping) for Superstructure and Pile Cap of PG33 during Event C (Santa Cruz Motion) in Csp5 Using Soil Profile Motions from Site Response Analysis 31% due to pile cap rotation, and 37% due to bending of the superstructure column. Two cases are used to illustrate the results of the sensitivity studies. In the first ( stiffer ) case, the translational and rotational stiffnesses of the pile cap were both increased by 33%. In the second ( softer ) case, the translational and rotational stiffnesses of the pile cap were both decreased by 33%. For both cases, these relative changes refer to the secant stiffness under loads produced by an inertial force on the superstructure of 0.4g times its mass. These changes in stiffness were obtained by stiffening (or softening) the various parameters by reasonably consistent amounts. For example, the stiffer case was achieved by making the following changes to the p-y, t-z, and q-z parameters: p-multiplier of 1.0, =40 for the sand, N* q = 400, yield displacement for t-z elements of 0.25%D, yield displacement for q-z elements of 2%D, and uplift resistance of 200 kpa at the pile tip. The response of the PG33 structure to all nine earthquakes was then reanalyzed for JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JULY 2001 / 593

10 FIG. 12. Calculated and Recorded Structural Response Time Histories for Event C (Santa Cruz Motion) of Csp5 Using Interpolated-Recorded Soil Profile Motions FIG. 14. Calculated and Recorded Superstructure ARS (5% Damping) for Four Kobe Motions FIG. 13. Calculated and Recorded Structural Response for PG33 Structure Using Interpolated-Recorded Soil Profile Motions the stiffer and softer cases using the interpolated-recorded soil profile motions. The results obtained for these two cases are illustrated in Fig. 15 showing the maximum superstructure displacement and maximum pile cap rotation versus the maximum base acceleration. This figure compares the recorded response values to those calculated for the baseline case, the stiffer case, and the softer case. The range of calculated responses obtained between the stiffer and softer cases generally enveloped the recorded structural responses (displacements, accelerations, moments, axial forces, and rotations) for all nine earthquake motions. Interestingly, the stiffer case tended to provide the best agreement with recorded responses during the scaled Kobe motions, and the softer case tended to provide the best agreement for the scaled Santa Cruz motions. This observation may be related to the earthquake shaking sequence (Table 1). The pipe cap displacements during event E (scaled Kobe motion) in Csp4 were greater than those produced during any of the four Santa Cruz motions that came after it. Prior larger pile cap displacements (with associated cyclic degradation or gapping) would be expected to reduce the substructure stiffness, while reconsolidation of the soil (to lower void ratios) between shaking events would be expected to cause strength gains that might increase the substructure stiffness. The net effect of loading history on substructure stiffness is difficult to 594 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JULY 2001

11 FIG. 15. Sensitivity of Calculated Response to Foundation Substructure Stiffness: (a) Superstructure Horizontal Displacement; (b) Peak Pile Cap Rotation quantify, but the analysis results in Fig. 15 are consistent with a net softening of the substructure stiffness for the Santa Cruz events. The baseline set of analyses did not explicitly model the effects of load history, and instead appear to have produced a substructure stiffness that was like an average across all events, e.g., underestimating the stiffness for the Kobe responses and overestimating the stiffness for the Santa Cruz responses. The effect of these stiffer and softer parameter sets on the dominant modes of response varied slightly with the level of shaking. On average, the stiffer case produced first and second modal periods that were about 7 and 11% shorter than the baseline case, respectively. The softer case produced first and second modal periods that were about 13 and 17% longer than the baseline case, respectively. In both cases, the second modal period was more strongly affected by the change in BNWF parameters, as would be expected for this system. DISCUSSION The set of nine earthquake events provided a much more thorough evaluation of the analysis methods than could have been achieved with any single event. Parametric studies, beyond those shown herein, showed that considerably different parameter sets could produce generally good agreement for one or more shaking events, but could then do poorly for other events. Such results were always well explained by examining how the different parameter sets affected the translational and rotational stiffness of the pile cap over the full range of imposed loads. For example, one such parameter set overestimated the rocking stiffness and underestimated the translational stiffness, and yet produced a good match on the first modal period for some earthquake events. This resulted in good agreement on the peak superstructure acceleration, peak superstructure displacement, and peak axial forces in the piles (which are closely related to the overturning moment produced by the superstructure s inertia). Slightly poorer agreement was obtained for other aspects of structural response in the same events, with the clearest disagreement obviously being for the pile cap s rotation and translation. The limitations of that parameter set became clearer for other events when the errors in system stiffness influenced the response more strongly. These results demonstrate how poor agreement in some structural responses can be an indication that a parameter set may perform less satisfactorily under a significantly different earthquake loading. At the same time, good agreement in all aspects of structural response during one earthquake was still not sufficient to expect good agreement during significantly different earthquakes. One example of this is the rocking response of the PG33 structure. The uplift capacity of the piles controlled an important aspect of system nonlinearity during stronger shaking events, but had little effect on system response during smaller shaking events. In this regard, the centrifuge modeling tests proved valuable by providing detailed structural response data over a wide range of shaking intensities and earthquake motions. The dynamic BNWF analyses were able to reasonably model the recorded responses of the PG33 structure in all nine earthquakes despite the many approximations in the analysis methods and the potential uncertainties in the centrifuge data. Furthermore, the recorded responses were generally within the envelope of analysis results that were obtained when the rotational and translational stiffnesses of the pile cap were softened or stiffened by reasonable amounts. In practice, uncertainty in the translational and rotational stiffness of a pile cap can be greater because of the many complications presented by natural soil heterogeneity, soil characterization, and construction effects. Another issue in seismic design practice is that plastic hinging in the superstructure column can limit the inertial loads transmitted from the superstructure to the pile cap and thereby reduce some components of nonlinearity in the foundation substructure, e.g., avoiding uplift of the outer piles. In any event, the designer invariably must evaluate how the uncertainty in the pile cap stiffness affects the superstructure response. Such effects can be small or large depending on how much deformation the foundation contributes to the global system deformation in the various modes of response. Given that the designer must allow for these uncertainties in the translational and rotational stiffness at the pile cap level, the approximations involved in the BNWF analysis method appear to be acceptable for design purposes. SUMMARY AND CONCLUSIONS Dynamic centrifuge model tests of a pile-group-supported structure were performed to provide physical data against which numerical modeling methods could be evaluated. The centrifuge tests involved a structure supported on a group of nine piles (PG33 structure) and two other structures supported by single piles. These structures were founded in a profile of soft clay overlying dense sand, and subjected to nine earthquake shaking events with peak base accelerations of g. Descriptions of the test data and electronic copies of the instrument recordings are available in Wilson et al. (1997a,b). A beam on nonlinear Winkler foundation (BNWF) analysis method for soil-pile-structure interaction problems was evaluated against the centrifuge test data, providing one of few such evaluations to date. The BNWF analysis method and the baseline set of analysis parameters were developed using pro- JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JULY 2001 / 595

12 cedures commonly used in practice. Free-field soil profile motions were obtained in two ways: (1) one approach involved interpolating recorded soil accelerations; and (2) the second involved using 1D equivalent linear site response analyses. Calculated and recorded responses for the single-pile-supported structures, as previously described in Boulanger et al. (1999), showed that good agreement could be obtained for both structures in all nine earthquakes. The BNWF analyses of the PG33 structure, presented in this paper, were more complicated than the single-pile-supported structures because it involved rocking motions (axial pile behavior), lateral resistances on the pile cap, and group effects. Reasonable agreement was obtained between calculated and recorded responses in all nine earthquakes when the interpolated recorded soil profile motions were used. The 1D site response analyses tended to overestimate the higher frequency component of motions in the clay and thus tended to overexcite the second mode of the PG33 structure. The results of this study provide experimental support for the use of dynamic BNWF analysis methods in seismic soilpile-structure interaction problems involving pile groups. Physical model data for other soil-pile-structure configurations are still needed to further evaluate the reliability and potential usefulness of these dynamic analysis methods. ACKNOWLEDGMENTS CALTRANS supported this research project under Contract No. 65V495. A National Science Foundation Graduate Research Fellowship and GAANN Fellowship provided support for the first writer. However, the contents of this paper do not necessarily represent a policy of either agency or endorsement by the state or federal government. The centrifuge shaker was designed and constructed with support from the National Science Foundation, Obayashi Corp., CALTRANS, and the University of California. Abbas Abghari provided valuable comments and suggestions, and Tom Kohnke assisted with the centrifuge model testing. The above support and assistance is greatly appreciated. REFERENCES American Petroleum Institute (API). (1993). Recommended practice for planning, designing and constructing fixed offshore platforms. API RP 2A-WSD, Washington, D.C. Boulanger, R. W., Curras, C. J., Kutter, B. L., Wilson, D. W., and Abghari, A. (1999). Seismic soil-pile-structure interaction experiments and analyses. J. Geotech. and Geoenvir. Engrg., ASCE, 125(9), Bray, J. D., Espinoza, R. D., Soga, K., and Taylor, R. L. (1995). GeoFEAP Geotechnical finite element analysis program. Dept. of Civ. and Envir. Engrg., University of California, Berkeley, Calif. Brown, D. A., Morrison, C., and Reese, L. C. (1988). 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