Lateral Loaded Pile Response in Liquefiable Soil

This paper provides a new analysis procedure for assessing the lateral response of an isolated pile in saturated sands as liquefaction develops in response to dynamic loading such as that generated during earthquake shaking. This new procedure predicts the degradation in pile response and soil resistance due to the free-field excess porewater pressure generated by the earthquake, along with the near-field excess porewater pressure generated by lateral loading from the superstructure. The new procedure involves the integration of the developing (free- and near-field) porewater pressure in the strain wedge (SW) model analysis. The current SW model, developed to evaluate drained response (a nonlinear three-dimensional model) of a flexible pile in soil, has been extended in this paper to incorporate the undrained response of a laterally loaded pile in liquefied sand. This new procedure has the capability of predicting the response of a laterally loaded isolated pile and the associated modulus of subgrade reaction (i.e., the p–y curve) in a mobilized fashion as a result of developing liquefaction in the sand. Current design procedures assume slight or no resistance for the lateral movement of the pile in the liquefied soil which is a conservative practice. Alternatively, if liquefaction is assessed not to occur, some practitioners take no account of the increased free-field porewater pressure, and none consider the additional near-field porewater pressure due to inertial interaction loading from the superstructure; a practice that is unsafe in loose sands.     

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.     

Numerical Solution for Laterally Loaded Piles in a Two-Layer Soil Profile

Piles are often embedded in a layered soil profile, such as sand or clay layer underlain by rock. Several existing solutions are available for laterally loaded piles in a layered soil system. However, these solutions are only applicable to constant soil stiffness for each layer. In this paper, a variational approach is employed to numerically solve the problem of laterally loaded piles in layered soils using beam on an elastic foundation model. The soil stiffness can be either constant with depth or linearly varying with depth. The numerical solution is validated against an existing solution for linearly varying soil stiffness in a single soil layer system and an existing solution for a two-layer soil system with constant soil stiffness. Case studies using the proposed solution for field lateral load tests on full size drilled shafts embedded in weak rock with an overlying sand layer are presented. The simplicity and the relative ease of using the solution make it a good alternative approach for estimating the deflection and moment responses of a laterally loaded pile in a two-layer soil profile.     

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.     

Analysis of Laterally Loaded Piles in Soil with Stiffness Increasing with Depth

This article reports a variational solution and its spreadsheet calculation procedure for the analysis of laterally loaded piles in a soil with stiffness increasing with depth. The aim of the paper is to provide solutions that can be used simply with recourse only to spreadsheet calculation to solve the displacement and bending moment of laterally loaded piles, so that they can be easily applied in practice as an alternative approach to analyze the response of laterally loaded piles.     

Practical Solution for Group Stiffness Analysis of Piles

This paper presents a practical solution for group stiffness estimate of vertically loaded piles. The solution is based on a variational approach for pile groups in a soil modeled using a load–transfer curve method. Using the present method, the group stiffness of piles can be easily obtained based on spreadsheet calculation and this is very useful for practical purpose. The paper also presents comparison between results from modeling the soil using load–transfer curves and as an elastic half space. Their difference in estimating the group stiffness of piles is addressed.     

Kinematic Pile Response to Vertical P-wave Seismic Excitation

An analytical solution based on a rod-on-dynamic-Winkler-foundation model is developed for the response of piles in a soil layer subjected to vertical seismic excitation consisting of harmonic compressional waves. Closed-form solutions are derived for: (1) the motion of the pile head; (2) the peak normal strain in the pile, and (3) the group effect between neighboring piles. The solutions are expressed in terms of a dimensionless kinematic response factor Iv, relating pile-head motion and free-field soil surface motion, a dimensionless strain transmissibility factor Iε, relating pile and soil peak normal strains, and a pile-to-pile interaction factor α measuring group effects. It is shown that a pile foundation may significantly reduce the vertical seismic excitation transmitted to the base of a structure.     

Laterally Loaded Pile Study in Permafrost of Northern Québec, Canada

This paper describes a study undertaken at Umiujaq, in northern Québec, on laterally loaded piles in permafrost subject to a constant displacement rate. Test results of bending moments, shear load, soil reaction, and pile displacements demonstrate the complex nature of creep of frozen soils. FEM simulations show a good concurrence with field test results and confirm a clear distinction between stationary and nonstationary creep.     

Experimental Load–Transfer Curves of Laterally Loaded Piles in Nak-Dong River Sand

This paper describes the results of a model testing of the piles embedded in Nak-Dong River sand, located in south Korea, under monotonic lateral loadings. A number of features were studied, including the lateral resistance of piles, the effect of the installation method, and the pile head restraint condition. The study has led to recommendations of the load–transfer curves (p–y curves) for laterally loaded piles. Modification factors were developed to allow for both a different pile installation method and different pile head restraint conditions by comparison to existing model load tests. The proposed p–y curves were compared to the existing curves and were evaluated with the experimental data. The ultimate lateral soil resistance and subgrade modulus were investigated and discussed. It is revealed that the proposed p–y curves show significant differences in shapes and magnitudes when compared with existing p–y curve models. The accuracy of the proposed p–y curve model, considering the effect of installation method and pile head restraint condition, is very reasonable as shown by comparing measured and predicted lateral behavior of the pile.     

Seismic Behavior of Batter Piles: Elastic Response

Several aspects of the seismic response of groups containing nonvertical piles are studied, including the lateral pile-head stiffnesses, the “kinematic” pile deformation, and the “inertial” soil-pile-structure response. A key goal is to explore the conditions under which the presence of batter piles is beneficial, indifferent, or detrimental. Parametric analyses are carried out using three-dimensional finite-element modeling, assuming elastic behavior of soil, piles, and superstructure. The model is first used to obtain the lateral stiffnesses of single batter piles and to show that its results converge to the available solutions from the literature. Then, real accelerograms covering a broad range of frequency characteristics are employed as base excitation of simple fixed-head two-pile group configurations, embedded in homogeneous, inhomogeneous, and layered soil profiles, while supporting very tall or very short structures. Five pile inclinations are considered while the corresponding vertical-pile group results serve as reference. It is found that in purely kinematic seismic loading, batter piles tend to confirm their negative reputation, as had also been found recently for a group subjected to static horizontal ground deformation. However, the total (kinematic plus inertial) response of structural systems founded on groups of batter piles offers many reasons for optimism. Batter piles may indeed be beneficial (or detrimental) depending on, among other parameters, the relative size of the overturning moment versus the shear force transmitted onto them from the superstructure.     

Nonlinear Analysis of Torsionally Loaded Piles in a Two-Layer Soil Profile

This paper presents a method for predicting the nonlinear response of torsionally loaded piles in a two-layer soil profile, such as a clay or sand layer underlain by rock. The shear modulus of the upper soil is assumed to vary linearly with depth and the shear modulus of the lower soil is assumed to vary linearly with depth and then stay constant below the pile tip. The method uses the variational principle to derive the governing differential equations of a pile in a two-layer continuum and the elastic response of the pile is then determined by solving the derived differential equations. To consider the effect of soil yielding on the behavior of piles, the soil is assumed to behave linearly elastically at small strain levels and yield when the shear stress on the pile-soil interface exceeds the corresponding maximum shear resistance. To determine the maximum pile-soil interface shear resistance, methods that are available in the literature can be used. The proposed method is verified by comparing its results with existing elastic solutions and published small-scale model pile test results. Finally, the proposed method is used to analyze two full-scale field test piles and the predictions are in reasonable agreement with the measurements.     

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.     

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.     

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.     

Analytical Solution for Piles Supporting Combined Lateral Loads

Analytical solutions of normalized maximum deflection and normalized maximum moment for laterally loaded long piles in homogeneous elastoplastic soil under combined loads are presented in this paper. Both the normalized deflection surface and normalized moment surface are continuous and increasing constantly with normalized applied force and moment with various slopes. It shows that the normalized applied force and moment have different contributions to the deflection and moment. In general, the variation of normalized moment surface is relatively moderate compared to normalized maximum deflection. Due to the nonlinear effect, the deflections and moments using superposition approach will be on the unsafe side. The analytical solutions can be used for any elastic materials, any type of soil, and any shapes of pile cross section. Above all, the analytical solutions may be easily applied to calculate the maximum deflection or moment of lateral long piles subject to combined loads accurately using a calculator.     

Pile Spacing Effects on Lateral Pile Group Behavior: Analysis

Using the results from three full-scale lateral pile group load tests in stiff clay with spacing ranging from 3.3 to 5.65, computer analyses were performed to back-calculate p multipliers. The p multipliers, which account for reduced resistance due to pile–soil–pile interaction, increased as pile spacing increased from 3.3 to 5.65 diameters. Extrapolation of the test results suggests that group reduction effects can be neglected for spacings greater than about 6.5 for leading row piles and 7–8 diameters for trailing row piles. Based on analysis of the full-scale test results, pile behavior can be grouped into three general categories, namely: (1) first or front row piles; (2) second row piles; and (3) third and higher row piles. p multiplier versus normalized pile spacing curves were developed for each category. The proposed curves yield p multipliers which are higher than those previously recommended by AASHTO in 2000, the US Army in 1993, and the US Navy in 1982 based on limited test data, but lower values than those proposed by Reese et al. in 1996 and Reese and Van Impe in 2001. The response (load versus deflection, maximum moment versus load, and bending moment versus depth) for each row of the pile groups computed using GROUP and Florida Pier generally correlated very well with measurements from the full-scale tests when the p multipliers developed from this test program were employed.     

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.     

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.     

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.     

Behavior of Model Rafts Resting on Pile-Reinforced Sand

Piles in a pile raft are sometimes considered as settlement reducers, not load-carrying members. In design, one often tries to minimize the number of piles. This often results in a high axial stress in the piles that may deter their use due to the limits on pile stress in practice. An alternative is to consider the pile as reinforcement in the base soil, and not as a structural member. Serving as a soil stiffener, the pile can tolerate a lower safety margin against structural failure without violating building codes. Previous numerical studies on the use of disconnected piles as settlement reducers have shown the effectiveness of such piles. This study aims to verify experimentally the effectiveness of such piles through load tests of model rafts resting on pile-reinforced sand. By varying factors such as raft stiffness, pile length, pile arrangement, and pile number, results of the investigation indicate that structurally disconnected piles are effective in reducing the settlement and bending moments in the model rafts.