Applicability of Conventional p-y Relations to the Analysis of Piles in Laterally Spreading Soil

This paper presents a kinematic analysis of a single pile embedded in a laterally spreading layered soil profile and discusses the relevancy of conventional analysis models to this load case. The research encompasses the creation of three-dimensional (3D) finite-element (FE) models using the OpenSees FE analysis platform. These models consider a single pile embedded in a layered soil continuum. Three reinforced concrete pile designs are considered. The piles are modeled using beam-column elements and fiber-section models. The soil continuum is modeled using brick elements and a Drucker-Prager constitutive model. The soil-pile interface is modeled using beam-solid contact elements. The FE models are used to evaluate the response of the soil-pile system to lateral spreading and two alternative lateral load cases. Through the computation of force density-displacement (p-y) curves representative of the soil response, the FE analysis (FEA) results are used to evaluate the adequacy of conventional p-y curve relationships in modeling lateral spreading. It is determined that traditional p-y curves are unsuitable for use in analyses where large pile deformations occur at depth.     

Three-Dimensional Analysis of Performance of Laterally Loaded Sleeved Piles in Sloping Ground

Development of urban cities in hilly terrain often involves the construction of high-rise buildings supported by large diameter piles on steep cut slopes. Under lateral loads, the piles may induce slope failure, particularly at shallow depths. To minimize the transfer of lateral load from the buildings to the shallow depths of the slope, an annulus of compressible material, referred to as sleeving, is usually constructed between the piles and the adjacent soil. However, the influence of the sleeving on the pile performance in a sloping ground is not fully studied and understood. To investigate the influence, a 3D numerical analysis of sleeved and unsleeved piles on a cut slope is described in this paper. The influences of relative soil stiffness on the response of sleeved piles are also examined. The load transfer from the laterally loaded sleeved pile to the sloping ground is primarily through a shear load transfer mechanism in the vertical plane. Under small lateral loads, the sleeving can lead to a significant reduction in subgrade reaction on the sleeved pile segment and may considerably increase the pile deflection and bending moments. Under large lateral loads, the influence of the sleeving on pile performance appears to diminish because of the widespread plastic zones developed around the pile.     

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.     

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.     

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.     

Inelastic Analysis of Pile–Soil Interaction

In this paper, inelastic pile–soil interaction is analyzed by using a hybrid type of numerical method. Piles are modeled as linear finite elements and the soil half-space is modeled using boundary elements. Inelastic modeling of the soil media is introduced by a rational approximation to a continuum with nonlinear interface springs along the piles. For this purpose, a modified ?zdemir’s nonlinear model is implemented and systems of equations are coupled for piles and pile groups at interacting nodes. To verify the proposed algorithm, three experimental results from previously conducted tests on piles under static axial and lateral loads are compared with those obtained from the present analysis.     

Simplified Lateral Load Analyses of Fixed-Head Piles and Pile Groups

The characteristic load method (CLM) can be used to estimate lateral deflections and maximum bending moments in single fixed-head piles under lateral load. However, this approach is limited to cases where the lateral load on the pile top is applied at the ground surface. When the pile top is embedded, as in most piles that are capped, the additional embedment results in an increased lateral resistance. A simple approach to account for embedment effects in the CLM is presented for single fixed-head piles. In practice, fixed-head piles are more typically used in groups where the response of an individual pile can be influenced through the adjacent soil by the response of other nearby piles. This pile–soil–pile interaction results in larger deflections and moments in pile groups for the same load per pile compared to single piles. A simplified procedure to estimate group deflections and moments was also developed based on the p-multiplier approach. Group amplification factors are introduced to amplify the single pile deflection and bending moment to reflect pile–soil–pile interaction. The resulting approach lends itself well to simple spreadsheet computations and provides good agreement with other generally accepted analytical tools and with values measured in published lateral load tests on groups of fixed-head piles.     

Dynamic Soil–Structure Interaction of Bridge Substructure Subject to Vessel Impact

The paper describes the in situ investigation, site stratigraphy, field monitoring, data reduction, and subsequent time-domain analysis of soil–structure interaction from a full scale vessel impact loading of a bridge pier at the St. George Island Causeway. The in situ investigation included standard penetration testing, electric cone, dilatometer, and pressuremeter testing to identify soil stratigraphy, engineering properties (strength and moduli), and axial and lateral static pile resistance (T–z, and P–y). Field instrumentation included soil total stress and pore pressure gauges in front of and behind the pile cap, a fully instrumented pile (strain gauges along length), dynamic load cells to monitor barge impact loads, and accelerometers to monitor pier accelerations, velocities, and displacements. Analyses of the field data reveal significant dynamic forces within the soil–structure system as a result of the duration and magnitude of the loading. Inertia from the piers, cap, and piles provide significant resistance in the early portion of the impact. However, postpeak inertia (i.e., pier deceleration) resulted in maximum deformations of the pier. Soil damping provided most of the resisting force at the peak barge loading, whereas static soil resistance dominated at the peak lateral displacement. Time-domain finite element analysis of an impact event employing viscous soil dashpots, nonlinear P–y and T–z springs with nonlinear beam, and shell elements for the pier, cap, and piles resulted in reasonable load displacement predictions.     

Evaluation of Rotational Stiffness of Elastomeric Bearing Pad-Anchor Bolt Connections on Deep Foundation Bents

Experimental tests are performed on a bearing pad-anchor bolt connection to study rotational stiffness and moment transfer capabilities of a typical bridge configuration. The experimental program is divided in two phases. The first phase consisted of shear and compression properties of two types of bearing pads. The second phase consisted of a total of 42 full-scale tests of a bearing pad-anchor bolt connection. The tested bridge-bent configuration includes two AASHTO Type II girders made continuous with a slab and diaphragm, bearing pads, pile caps, and piles. Variables included axial loads applied to the piles and bearing pads, two different sets of bearing pads, and three different pile types. The bridge connection is subjected to lateral cyclic reversed loading in one-cycle displacement increments. Test results show the potential for this type of connection to sustain lateral loads and flexural moments, and to develop the full strength of the pile elements. Shear and compression modulus are also obtained for the bearing pad types used in this study. Rotational stiffness values for the connection are determined as a function of varying axial loads.     

Observed Seismic Lateral Resistance of Liquefying Sand

This paper presents results from a study of the dynamic response of pile foundations in liquefying sand during seismic loading. The study included a series of dynamic centrifuge tests of pile-supported structures and the back-calculation of time histories for the lateral resistance p and relative displacement y between a pile and the free-field soil. Details of the centrifuge experiments and the procedures used to back-calculate p and y time histories are described. The back-calculated p-y time histories provide a concise representation of the experimental results and can be compared to the equivalent p-y behavior predicted by soil-pile interaction analysis methods. The observed p-y behavior provides insight into the mechanisms of soil-pile interaction in liquefying sand, showing characteristics that are consistent with the undrained cyclic loading behavior of saturated sand, including the effects of relative density, cyclic degradation, pore-pressure generation, prior displacement (strain) history, and phase transformation behavior.     

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.     

Application of Periodic Boundary for Large Pile Group

Full-scale testing of a large pile group is economically not feasible. A concept based on a periodic boundary has been used to study lateral behavior of a large pile group. The approach and findings from anchorage design of a major suspension bridge in California are presented here. Using the repeating nature of soil's displacement field within infinite number of piles arranged in a regular grid pattern, soil-pile interaction phenomenon from the finite area enclosed by one periodic soil boundary effectively represents behavior of the entire pile group. A 3D finite-element analysis was used to create the soil-pile models in which the boundary conditions mimic the repeating nature of the infinite number of piles by slaving the boundary nodes. The soil resistance, as calculated from the finite-element method employing the periodic boundary, is compared with the empirical p-y curve approach for a single isolated pile to determine the group effects. Values of p-multiplier and y-multiplier have been obtained for different pile spacings.     

Behavior of Step Tapered Bored Piles in Sand under Static Lateral Loading

The behavior of step tapered bored piles in sand, under static lateral loading, was examined by field tests at one site in Kuwait. A total of 14 bored piles including two instrumented piles were installed for lateral loading. The soil profile consists of medium dense sand with weak cementations and no groundwater was encountered in the boreholes. Laboratory tests were carried out to determine the basic soil characteristics and the strength parameters. Both the ultimate lateral capacity and the deflections at applied loads were examined. The results indicate increased lateral load carrying capacity and decreased deflections at different applied loads for the step tapered piles due to the enlargement or strengthening of the upper section of the piles. The advantages of using this type of pile is emphasized including the cost saving resulting from an economical design.     

Experimental Evaluation of Lateral-Load Resistance of Pile Caps

Although pile caps have considerable ability to resist lateral loads, this resistance is often neglected in design. Published cases involving a variety of pile and cap sizes, soil conditions, and loading conditions indicate that the lateral-load resistance of pile caps can be significant, but it is difficult to generalize on the basis of these results because of the variations in conditions involved in the tests. To develop a more systematic basis for evaluating cap resistance, a field test facility was constructed to perform full-scale lateral-load tests on single piles and pile groups, with the pile caps embedded in the stiff natural soil at the site and with the pile caps backfilled with granular soil. Thirty-one tests were conducted to evaluate the lateral-load resistance of pile caps by comparing the response of pile groups with caps fully embedded and with soil removed from around the caps. The results of the tests show that pile caps provide significant resistance to lateral load. This resistance depends primarily on the stiffness and strength of the soil in front of the cap and the depth of cap embedment.     

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.     

Response of Laterally Loaded Large-Diameter Bored Pile Groups

This paper presents results of full-scale lateral load tests of one single pile and three pile groups in Hong Kong. The test piles, which are embedded in superficial deposits and decomposed rocks, are 1.5 m in diameter and approximately 30 m long. The large-diameter bored pile groups consist of one two-pile group at 6 D (D = pile diameter) spacing and one two-pile and one three-pile group at 3 D spacing. This paper aims to investigate the nonlinear response of laterally loaded large-diameter bored pile groups and to study design parameters for large-diameter bored piles associated with the p-y method using a 3 D finite-element program, FLPIER. Predictions using soil parameters based on published correlations and back-analysis of the single-pile load test are compared. It is found that a simple hyperbolic representation of load-deflection curves provides an objective means to determine ultimate lateral load capacity, which is comparable with the calculated values based on Broms' theory. Lateral deflections of bored pile groups predicted using the values of the constant of horizontal subgrade reaction, suggested by Elson and obtained from back-analysis of the single pile load test, are generally in good agreement with the measurements, especially at low loads.     

Simple Energy-Based Method for Nonlinear Analysis of Incompressible Pile Groups in Clays

This note presents a method for predicting nonlinear response of pile groups in clays, subjected to vertical loads. The method is based on mobilizable strength design (MSD) concepts, in which the mobilized strength is associated with the shear strains developed in the soil. The suggested procedure is incremental, and requires evaluation of a displacement field. A simple procedure of superposition of pattern functions is suggested for the construction of a complete displacement field. The incremental procedure allows for the variation of the displacement field throughout the loading process, according to principles of minimum energy and compatibility requirements among the piles. Essentially, the procedure allows consideration of a nonlinear continuum between the piles. The pattern functions are an adaptive form of the logarithmic function suggested by Randolph and Wroth in 1979. Under small load levels, when the soil is essentially elastic, the procedure yields values comparable to those from the elastic solution of Randolph and Wroth. At larger strain levels, nonlinear pile group response is simulated based on the soil constitutive models specified by the practitioner. The method is applicable to cases where shaft loading does not induce volume changes in the soil. The method is compared with three dimensional finite difference simulation of undrained loading of pile groups with a nonlinear soil constitutive model. Fair agreement is observed.     

Employment of the P-Multiplier in Pile-Group Analysis

This paper discusses the variation of the P-multiplier (Pm) used with the p-y curve to assess the response of a pile group under lateral loads, which is a crucial topic for the design of bridge pile foundations. Pm is influenced by the site geotechnical conditions (i.e., soil profile, type and properties), pile front and side spacings, and pile-group deflection. The presented study shows the needs to incorporate these factors with the recommended sets of Pm to avoid any compromise or uncertainty when Pm is treated as a single (unique) value based only on pile spacings. The current study addresses these influential elements using the strain wedge (SW) model technique, suggested Pm values, and data collected from full-scale pile-group load tests. The experimental results show that Pm is not unique and must be assessed based on the site geotechnical conditions along with the pile-row front and side spacings. Because the employed Pm values must be a function of these influential factors, additional full- and model-scale load tests with different pile spacings and soil types might be required. The paper also emphasizes that using other techniques, such as the SW model, in addition to the P-multiplier could increase the confidence in the predicted pile-group lateral response.     

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.     

Centrifuge Model Study of Laterally Loaded Pile Groups in Clay

A series of centrifuge model tests has been conducted to examine the behavior of laterally loaded pile groups in normally consolidated and overconsolidated kaolin clay. The pile groups have a symmetrical plan layout consisting of 2, 2×2, 2×3, 3×3, and 4×4 piles with a center-to-center spacing of three or five times the pile width. The piles are connected by a solid aluminum pile cap placed just above the ground level. The pile load test results are expressed in terms of lateral load–pile head displacement response of the pile group, load experienced by individual piles in the group, and bending moment profile along individual pile shafts. It is established that the pile group efficiency reduces significantly with increasing number of piles in a group. The tests also reveal the shadowing effect phenomenon in which the front piles experience larger load and bending moment than that of the trailing piles. The shadowing effect is most significant for the lead row piles and considerably less significant for subsequent rows of trailing piles. The approach adopted by many researchers of taking the average performance of piles in the same row is found to be inappropriate for the middle rows, of piles for large pile groups as the outer piles in the row carry significantly more load and experience considerably higher bending moment than those of the inner piles.