Simplified Approach for the Seismic Response of a Pile Foundation

Pseudostatic approaches for the seismic analysis of pile foundations are attractive for practicing engineers because they are simple when compared to difficult and more complex dynamic analyses. To evaluate the internal response of piles subjected to earthquake loading, a simplified approach based on the “p-y” subgrade reaction method has been developed. The method involves two main steps: first, a site response analysis is carried out to obtain the free-field ground displacements along the pile. Next, a static load analysis is carried out for the pile, subjected to the computed free-field ground displacements and the static loading at the pile head. A pseudostatic push over analysis is adopted to simulate the behavior of piles subjected to both lateral soil movements and static loadings at the pile head. The single pile or the pile group interact with the surrounding soil by means of hyperbolic p-y curves. The solution derived first for the single pile, was extended to the case of a pile group by empirical multipliers, which account for reduced resistance and stiffness due to pile-soil-pile interaction. Numerical results obtained by the proposed simplified approach were compared with experimental and numerical results reported in literature. It has been shown that this procedure can be used successfully for determining the response of a pile foundation to “inertial” loading caused by the lateral forces imposed on the superstructure and “kinematic” loading caused by the ground movements developed during an earthquake.     

Strain Wedge Model Capability of Analyzing Behavior of Laterally Loaded Isolated Piles, Drilled Shafts, and Pile Groups

This paper demonstrates the application of the strain wedge (SW) model to assess the response of laterally loaded isolated long piles, drilled shafts, and pile groups in layered soil (sand and/or clay) and rock deposits. The basic goal of this paper is to illustrate the capabilities of the SW model versus other procedures and approaches. The SW model has been validated and verified through several comparison studies with model- and full-scale lateral load tests. Several factors and features related to the problem of a laterally loaded isolated pile and pile group are covered by the SW model. For example, the nonlinear behavior of both soil and pile material, the soil-pile interaction (i.e., the assessment of the p-y curves rather than the adoption of empirical ones), the potential of soil to liquefy, the interference among neighboring piles in a pile group, and the pile cap contribution are considered in SW model analysis. The SW model analyzes the response of laterally loaded piles based on pile properties (pile stiffness, cross-sectional shape, pile-head conditions, etc.) as well as soil properties. The SW model has the capability of assessing the response of a laterally loaded pile group in layered soil based on more realistic assumptions of pile interference as compared to techniques and procedures currently employed or proposed.     

Liquefaction-Induced Softening of Load Transfer between Pile Groups and Laterally Spreading Crusts

Laterally spreading nonliquefied crusts can exert large loads on pile foundations causing major damage to structures. While monotonic load tests of pile caps indicate that full passive resistance may be mobilized by displacements on the order of 1–7% of the pile cap height, dynamic centrifuge model tests show that much larger relative displacements may be required to mobilize the full passive load from a laterally spreading crust onto a pile group. The centrifuge models contained six-pile groups embedded in a gently sloping soil profile with a nonliquefied crust over liquefiable loose sand over dense sand. The nonliquefied crust layer spread downslope on top of the liquefied sand layer, and failed in the passive mode against the pile foundations. The dynamic trace of lateral load versus relative displacement between the “free-field” crust and pile cap is nonlinear and hysteretic, and depends on the cyclic mobility of the underlying liquefiable sand, ground motion characteristics, and cyclic degradation and cracking of the nonliquefied crust. Analytical models are derived to explain a mechanism by which liquefaction of the underlying sand layer causes the soil-to-pile-cap interaction stresses to be distributed through a larger zone of influence in the crust, thereby contributing to the softer load transfer behavior. The analytical models distinguish between structural loading and lateral spreading conditions. Load transfer relations obtained from the two analytical models reasonably envelope the responses observed in the centrifuge tests.     

Effect of Soil Permeability on Centrifuge Modeling of Pile Response to Lateral Spreading

This paper presents experimental results and analysis of six model centrifuge experiments conducted on the 150?g-ton Rensselaer Polytechnic Institute centrifuge to investigate the effect of soil permeability on the response of end-bearing single piles and pile groups subjected to lateral spreading. The models were tested in a laminar box and simulate a mild infinite slope with a liquefiable sand layer on top of a nonliquefiable layer. Three fine sand models consisting of a single pile, a 3×1 pile group, and a 2×2 pile group were tested, first using water as pore fluid, and then repeated using a viscous pore fluid, hence simulating two sands of different permeability in the field. The results were dramatically different, with the three tests simulating a low permeability soil developing 3–6 times larger pile head displacements and bending moments at the end of shaking. Deformation observations of colored sand strips, as well as measurements of sustained negative excess pore pressures near the foundations in the “viscous fluid” experiments, indicated that an approximately inverted conical zone of nonliquefied soil had formed in these tests at shallow depths around the foundation, which forced the liquefied soil in the free field to apply its lateral pressure against a much larger effective foundation area. Additional p-y and limit equilibrium back-analyses support the hypothesis that the greatly increased foundation bending response observed when the soil is less pervious is due to the formation of such inverted conical volume of nonliquefied sand. This study provides evidence of the importance of soil permeability on pile foundations response during lateral spreading for cases when the liquefied deposit reaches the ground surface, and suggests that bending response may be greater in silty sands than in clean sands in the field. Moreover, the observations in this study may serve as basis for realistic practical engineering methods to evaluate pile foundations subjected to lateral spreading and pressure of liquefied soil.     

Numerical Analysis of Laterally Loaded 3 × 3 to 7 × 3 Pile Groups in Sands

The coupled bridge foundation-superstructure finite-element code FLPIER was employed to predict the lateral response of the single piles and 3 × 3 to 7 × 3 pile groups founded in both loose and medium dense sands. The p-multiplier factors suggested by McVay et al. for laterally loaded pile groups with multiple pile rows were implemented for the predictions. The soil parameters were obtained through a back-analysis procedure based on single pile test results. The latter, as well as the numerical predictions of both the single and group tests, are presented. It was found that the numerical code FLPIER did an excellent job of predicting the response of both the single piles and the 3 × 3 to 7 × 3 pile groups. The latter involved the predictions of lateral load versus lateral deflection of the group, the shears and bending moments developed in the individual piles, and the distributions of the lateral loads in each pile row, which were all in good agreement with the measured results.     

Pseudostatic Approach for Seismic Analysis of Single Piles

This paper evaluates a simple approximate methodology for estimating the maximum internal forces of piles subjected to lateral seismic excitation. The method involves two main steps: computation of the free-field soil movements caused by the earthquake and the analysis of the response of the pile to the maximum free-field soil movements (considered as static movements) plus a static loading at the pile head, which depends on the computed spectral acceleration of the structure being supported. The applicability of this approach has been verified by an independent benchmark analysis developed by the writers. It is demonstrated that the proposed method yields reasonable estimates of the pile maximum moment and shear. The methodology is then used to obtain the response of the Ohba-Ohashi bridge in Japan to one of the earthquakes that occurred in the 1980s. Good agreement is found between the computed and measured pile moments.     

Soil–Pile Response to Blast-Induced Lateral Spreading. I: Field Test

Two full-scale experiments using controlled blasting were conducted in the Port of Tokachi on Hokkaido Island, Japan, to assess the behavior of a single pile, a four-pile group, and a nine-pile group subjected to lateral spreading. The test piles were extensively instrumented with strain gauges to measure the distribution of bending moment during lateral spreading which allowed the backcalculation of the loading conditions, as well as the assessment of damage and performance of the piles. Based on the test results, it was concluded that using controlled blasting successfully liquefied the soil, and subsequently induced lateral spreading in the 4–6% surface slope test beds. The free-field soil displacements in the vicinity of the test piles were over 40 cm for both tests. When compared with the results from the single pile case, the effect of pile head restraint from the pile cap improved overall pile performance by decreasing the displacement of the pile groups and lowering the maximum moments in individual piles within each group. Finally, backcalculated soil reactions indicated that the liquefied soil layer imparted insignificant force to the piles. In the companion to this paper (Part II), an assessment of the potential of using the p–y analysis method for single piles and pile groups subjected to lateral spreading is presented.     

Failure Mechanisms of Pile Foundations in Liquefiable Soil: Parametric Study

This paper presents the response of piles in liquefiable soil under seismic loads. The effects of soil, pile, and earthquake parameters on the two potential pile failure mechanisms, bending and buckling, are examined. The analysis is conducted using a two-dimensional plain strain finite difference program considering a nonlinear constitutive model for soil liquefaction, strength reduction, and pile-soil interaction. The depths of liquefaction, maximum lateral displacement, and maximum pile bending moment are obtained for concrete and steel piles for different soil relative densities, pile diameters, earthquake predominant frequencies, and peak accelerations. The potential failure mechanisms of piles identified from the parametric analysis are discussed.     

Lateral Behavior of Pile Groups in Layered Soils

Assessment of the response of a laterally loaded pile group based on soil–pile interaction is presented in this paper. The behavior of a pile group in uniform and layered soil (sand and/or clay) is evaluated based on the strain wedge model approach that was developed to analyze the response of a long flexible pile under lateral loading. Accordingly, the pile’s response is characterized in terms of three-dimensional soil–pile interaction which is then transformed into its one-dimensional beam on elastic foundation equivalent and the associated parameter (modulus of subgrade reaction Es) variation along pile length. The interaction among the piles in a group is determined based on the geometry and interaction of the mobilized passive wedges of soil in front of the piles in association with the pile spacing. The overlap of shear zones among the piles in the group varies along the length of the pile and changes from one soil layer to another in the soil profile. Also, the interaction among the piles grows with the increase in lateral loading, and the increasing depth and fan angles of the developing wedges. The value of Es so determined accounts for the additional strains (i.e., stresses) in the adjacent soil due to pile interaction within the group. Based on the approach presented, the p–y curve for different piles in the pile group can be determined. The reduction in the resistance of the individual piles in the group compared to the isolated pile is governed by soil and pile properties, level of loading, and pile spacing.     

Permanent Strains of Piles in Sand due to Cyclic Lateral Loads

The strain superposition concept, proposed for ballast study, is applied here to evaluate strain accumulation for laterally loaded piles in sand. It is shown that the soil properties, types of pile installation, cyclic loading types, pile embedded length, and pile∕soil relative stiffness ratio are important factors that influence the pile behavior under mixed lateral loads. These factors are quantified by means of a degradation factor, t, which is derived from the results of 20 full-scale pile load tests and then verified using 6 additional full-scale pile load tests.     

Saturation and Preloading Effects on the Cyclic Behavior of Sand

In order to study pore water pressure response and liquefaction characteristics of sand, which has previously experienced liquefaction, two series of cyclic triaxial tests were run on medium dense sand specimens. In the first test series the influence of the soil saturation under undrained cyclic loading has been studied. It summarizes results of cyclic triaxial tests performed on Hostun-RF sand at various values of the Skempton’s pore-pressure coefficient. Analysis of experimental results gives valuable insights on the effect of soil saturation on sand response to undrained cyclic paths. In the second series of tests, the preloading influence on the resistance to the sands liquefaction has been realized on samples at various histories of loading. It was found that a large preloading induces a reduction of the resistance of sands to liquefaction.     

Behavior of Slender Piles Subject to Free-Field Lateral Soil Movement

Soil movements associated with slope instability induce shear forces and bending moments in stabilizing piles that vary with the buildup of passive pile resistance. For such free-field lateral soil movements, stress development along the pile element is a function of the relative displacement between the soil and the pile. To investigate the effects of relative soil-pile displacement on pile response, large-scale load tests were performed on relatively slender, drilled, composite pile elements (cementitious grout with centered steel reinforcing bar). The piles were installed through a shear box into stable soil and then loaded by lateral translation of the shear box. The load tests included two pile diameters (nominal 115 and 178?mm) and three cohesive soil types (loess, glacial till, and weathered shale). Instrumentation indicated the relative soil-pile displacements and the pile response to the loads that developed along the piles. Using the experimental results, an analysis approach was evaluated using soil p-y curves derived from laboratory undrained shear strength tests. The test piles and analyses helped characterize behavioral stages of the composite pile elements at loads up to pile section failure and also provided a unique dataset to evaluate the lateral response analysis method for its applicability to slender piles.     

Monotonic Lateral Loading of Piles in Calcareous Sand

This paper describes the results of a centrifuge modeling study of the response of piles embedded in calcareous sand under monotonic lateral loading. A number of features have been explored, including method of installation, rate of loading, and pile head restraint. The study has led to recommendations for load-transfer curves with the magnitude of lateral resistance linked to the soil strength through the cone resistance. Modification factors have been developed to allow for different methods of installation and for different rates of loading. The proposed load-transfer curves and resulting pile response are shown to provide an excellent match with the experimental data, and are compared with results derived using existing guidelines for terrigenous sands. Significant differences are demonstrated, confirming the need to treat calcareous sediments separately from other soil types with respect to lateral pile response.     

Modeling Lateral Soil-Pile Response Based on Soil-Pile Interaction

Although most designers prefer the p-y curve method as compared to elastic continuum or finite-element analysis of laterally loaded pile behavior, the profession has reached a state where it is time that closer scrutiny be given to the traditional “Matlock-Reese” p-y curves used in the analysis. The traditional p-y curves were derived from a number of well-instrumented field tests that reflect a limited set of conditions. To consider these p-y curves as unique is questionable. As important as such curves have been to advancing the practice from elastic to nonlinear beam on elastic foundation analysis, such calibrated∕verified p-y curves reflect the specific field test conditions (particularly the pile properties) encountered. As presented in this paper, there are additional influences such as pile bending stiffness, pile cross-sectional shape, pile-head fixity, and pile-head embedment that have an effect on the resulting p-y curves. It is argued that strain wedge (SW) model formulation can be used to characterize such effects. SW model analysis predicts the response of laterally loaded piles and has shown very good agreement with actual field tests in sand, clay, and layered soils. The advantage of the SW model is that it is capable of taking into account the effect of changes in soil and pile properties on the resulting p-y curves.     

Shaking Table Model Tests on Pile Groups behind Quay Walls Subjected to Lateral Spreading

This paper presents experimental results of 1-g shaking table model tests on a 3×3 pile group behind a sheet-pile quay wall. The main purpose was to understand the mechanisms of liquefaction-induced large ground deformation and the behavior of the pile group subjected to the lateral soil displacement. The sheet-pile quay wall was employed to trigger the liquefaction-induced large deformation in the backfill, and a study was made of the effect of several parameters such as soil density, amplitude and frequency of input motion, pile head fixity, and superstructure on the magnitude of soil lateral displacement and the maximum lateral force of liquefied soil. Furthermore, distribution of the maximum lateral force within the group pile was thoroughly studied. It was found that the force varies depending on the position of individual piles in the group. To evaluate the contribution of each pile in the total lateral force, a new two-dimensional parameter that is called contribution index was introduced and recommended values for each pile were suggested. Finally, it is concluded that displacement and velocity of soil are the most important parameters that affect the distribution of the lateral forces in the group pile, and these two parameters are highly dependent on the configuration of the ground (geometry).     

Liquefaction-Induced Settlement of Pile Groups in Liquefiable and Laterally Spreading Soils

The results of a series of dynamic centrifuge tests on model pile groups in (level) liquefied and laterally spreading soil profiles are presented. The piles are axially loaded at typical working loads, which has enabled liquefaction-induced settlements of the foundations to be studied. The development of excess pore pressures within the bearing layer (dense sand) was found to lead to a reduction in pile capacity and potentially damagingly large coseismic settlements. As the excess pore pressure increased, these settlements were observed to exceed postshaking downdrag-induced settlements, which occur due to the reconsolidation of liquefied sand around the pile shaft. In resisting settlement, the pile cap was found to play an important role by compensating for the capacity lost by the piles. This was shown to be achieved by the development of dilative excess pore pressures beneath the pile cap within the underlying loose liquefied sand which provide increasing bearing capacity with settlement. The centrifuge test data show good qualitative and quantitative agreement with the limited amount of model and full-scale data currently available in the literature. The implications of settlement for the design of piled foundations to serviceability conditions in both level and sloping ground are discussed, with settlement becoming an increasingly important consideration for laterally stiffer piles. Finally, empirical relationships have been derived from the test data to relate suitable static safety factors to given increases in excess pore pressure in the bearing layer within a performance-based design framework (i.e., based on limiting displacements).     

Single Piles in Lateral Spreads: Field Bending Moment Evaluation

The results of the six centrifuge models of instrumented single pile foundations presented in a companion paper, are used to calibrate two limit equilibrium (LE) methods to evaluate bending response and factor of safety against bending failure of piles in the field subjected to lateral spreading. These six models simulate single reinforced concrete piles in two- and three-layer soil profiles, mostly end bearing but including also one floating pile, with and without a reinforced concrete pile cap, and one model where the liquefiable sand layer was densified locally around the pile to simulate the effect of pile driving. The measured permanent maximum bending moments in the pile, Mmax, invariably occurred at the boundaries between liquefied and nonliquefied soil layers, and in most cases the moments at such boundaries reached their peak Mmax and then decreased during shaking. These values of Mmax before decrease, which were associated with failure of the soil against the deep foundation, are used to calibrate the two proposed LE engineering methods. For the piles where Mmax was controlled by the pressure of the liquefied soil, the measured prototype Mmax in the centrifuge tests ranged between about 100 and 200 kN?m. It is found that a lateral pressure per unit area of pile or pile cap constant with depth (pl) of 10.3 kPa, predicts Mmax of the single piles tested within 15%. For the cases where Mmax was controlled by passive failure of the shallow nonliquefied layer, the prototype Mmax measured at the upper and lower boundaries of the liquefied soil in the centrifuge tests ranged between 160 and 305 kN?m. The Mmax values of 160–270 kN?m measured at the upper boundary were reached during the shaking, and then observed to decrease towards the end of shaking. At the lower boundary, the measured Mmax of 305 kN?m was reached at the end of shaking. Use of passive pressure against the pile of the shallow nonliquefiable soil layer, obtained from the ultimate plateaus (pult) of p-y curves, in conjunction with basic pile kinematic considerations and parameters addressed herein, explains well the development of moments measured in the centrifuge at both the upper and lower boundaries of the liquefied layer. This good accord validates the simplified LE prediction of Mmax at the upper boundary. The two proposed simplified engineering LE methods are used to evaluate bending response and distress of end-bearing and floating piles in the Niigata Family Court House building during the 1964 Niigata earthquake, with good agreement between predicted and observed performance.     

Wedge Failure Analysis of Soil Resistance on Laterally Loaded Piles in Clay

A fundamental study of pile-soil systems subjected to lateral loads in clay soil was conducted by using experimental tests and a lateral load-transfer approach. The emphasis was on an improved wedge failure model developed by considering three-dimensional combination forces and a new hyperbolic p-y criterion. A framework for determining the p-y curve on the basis of both theoretical analysis and experimental load test results is proposed. The proposed p-y method is shown to be capable of predicting the behavior of a large-diameter pile under lateral loading. The proposed p-y curves with an improved wedge model are more appropriate and realistic for representing a pile-soil interaction for laterally loaded piles in clay than the existing p-y method.     

Soil-Pile Response to Blast-Induced Lateral Spreading. II: Analysis and Assessment of the p–y Method

This paper presents an assessment of the potential of using the p–y analysis method for single piles and pile groups subjected to lateral spreading. The computed responses were compared with the results from the full-scale lateral spreading tests in Japan as presented in the Part I companion paper. The responses of the single piles subjected to lateral spreading were determined by imposing the known free-field soil movement profile to the Winkler spring model. The soil springs of nonliquefied soils used in this study were based upon standard p–y springs whereas zero spring stiffness was used for liquefied soils. For the case of pile groups, they were modeled as an equivalent single pile with a rotational spring at the pile head to simulate effect of pile head restraint. A decrease of soil spring stiffnesses using the p-multiplier approach was used to account for pile group effects. Based on the results of analyses, the computed responses of all sets of the test piles using a single set of baseline soil properties were in good agreement with the measured responses. These results suggest that the p–y analysis method may be used to estimate the behavior of piles subjected to lateral spreading.     

Assessment of the Undrained Response of Sands under Limited and Complete Liquefaction

The technique presented deals with the assessment, based on drained test behavior and formulation, of the undrained postcyclic stress-strain behavior of sands under limited or complete (full) liquefaction and its associated strength. At present, there is no particular procedure that allows assessment of such undrained postcyclic behavior that could develop full (pore-water pressure ratio, ru = 1) or limited (ru<1) liquefaction. The prediction of the undrained postliquefaction (full or limited liquefaction) response presented here is based on basic properties of sand such as its relative density (Drc) [or (N1)60 blowcount], the effective angle of internal friction (φ), the roundness of the sand grains (ρ), and the drained axial strain at 50% stress level (ε50). The technique presented accounts for the excess pore-water pressure induced by cyclic loading (Δuc) and the postcyclic excess pore-water pressure generated under undrained monotonic loading (Δud).