Development of p–y curves for undrained response of piles near slopes

The response of laterally loaded piles placed near the crest of clay slopes is analysed. Three-dimensional finite element analyses are presented for piles of different geometries, installed at several distances from slopes of various inclinations. The results of these analyses are used to establish the pattern of lateral load distribution along the pile length in relation to slope inclination and pile to slope distance. Subsequently, p–y curves are developed for the case of undrained lateral loading of piles near the crest of clay slopes, a case for which no such curves exist so far. The proposed p–y curves are implemented into a commercial subgrade reaction computer code and used to perform a series of parametric numerical analyses. The results of these analyses show that the predicted response of piles near slopes with the proposed p–y curves is in good agreement with the response observed in some pile tests reported in the literature.     

Nonlinear three-dimensional analysis of pile group supported columns considering pile cap flexibility

A numerical method that takes into account the coupling between the rigidities of the piles, the cap, and the column has been developed for analyzing the response of pile group supported columns. Special attention is given to consideration of pile cap flexibility. A load transfer approach using t–z/q–z and p–y curves is used for the analysis of single piles. The finite element technique is used to combine the pile stiffness with the stiffness of the cap and column. The numerical method developed has been verified by comparing the results with other numerical methods for pile groups. Through comparative studies, it has been found that the maximum load on the individual piles in a group is highly influenced by pile cap flexibility. The prediction of the lateral loads and bending moments in the pile cap is much more conservative in the present analysis than in FBPier 3.0 and shows a definitely larger lateral load and bending moment for various cap thicknesses.     

Explicit extension of the p–y method to pile groups in sandy soils

The method of “p–y” curves has been extensively used, in conjunction with simplified numerical methods, for the design and response evaluation of single piles. However, a straightforward application of the method to assess the response of pile groups is questionable when the group effect is disregarded. For this reason, the notion of p-multipliers has been therefore introduced to modify the “p–y” curves and account for pile group effect. The values proposed for p-multipliers result from pile group tests and are limited to the commonly applied spacing of 3.0 D and layout less than 3 × 3, restricting the applicability of the method to specific cases. With the aim of extending the applicability of the “p–y” method to pile groups, the authors have already proposed a methodology for estimating the “p _G–y _G” curves of soil resistance around a pile in a group for clayey soils. A complementary research allowing for the estimation of the “p _G–y _G” curves for sandy soils is presented in this paper. The well-known curves of soil resistance around the single pile in sandy soils are appropriately transformed to allow for the interaction effect between the piles in a group. Comparative examples validate the applicability and the effectiveness of the proposed method. In addition, the method can be straightforwardly extended to account for varying soil resistance, according to the particular location of a pile in a group. It can therefore be used in a most accurate manner in estimating the distribution of forces and bending moments along the characteristic piles of a group and therefore to design a pile foundation more accurately.     

Numerical analysis of pile behaviour under lateral loads in layered elastic–plastic soils

This paper presents results from a finite element study on the behaviour of a single pile in elastic–plastic soils. Pile behaviour in uniform sand and clay soils as well as cases with sand layer in clay deposit and clay layer in sand deposit were analysed and cross compared to investigate layering effects. Finite element results were used to generate p–y curves and then compared with those obtained from methods commonly used in practice. Copyright © 2002 John Wiley & Sons, Ltd.     

A modulus‐multiplier approach for non‐linear analysis of laterally loaded pile groups

A modulus‐multiplier approach, which applies a reduction factor to the modulus of single pile p–y curves to account for the group effect, is presented for analysing the response of each individual pile in a laterally loaded pile group with any geometric arrangement based on non‐linear pile–soil–pile interaction. The pile–soil–pile interaction is conducted using a 3D non‐linear finite element approach. The interaction effect between piles under various loading directions is investigated in this paper. Group effects can be neglected at a pile spacing of 9 times the pile diameter for piles along the direction of the lateral load and at a pile spacing of 6 times the pile diameter for piles normal to the direction of loading. The modulus multipliers for a pair of piles are developed as a function of pile spacing for departure angle of 0, 90, and 180sup>/sup> with respect to the loading direction. The procedure proposed for computing the response of any individual pile within a pile group is verified using two well‐documented full‐scale pile load tests. Copyright © 2006 John Wiley & Sons, Ltd.     

Explicit extension of the p–y method to pile groups in cohesive soils

Although simplified numerical methods are reliable for evaluating the response of a single pile under horizontal load, their application is questionable for assessing the response of pile groups. The notion of “p–y” curves has been considered with the aim of establishing a transformation relationship able to provide the “p_G–y_G” curves of soil resistance around a pile in a group from the well-known curves of soil resistance around the single pile.This transformation extends the applicability of the “p–y” method to pile groups, without the need for time consuming numerical computations, rendering the proposed method efficient and attractive. Comparative examples demonstrated the applicability and the effectiveness of the proposed method. In addition, the method can be straightforwardly extended to account for varying soil resistance, according to the particular location of a pile in a group. It can therefore be used to estimate accurately force and bending moment distributions along the characteristic piles of a group, which are required for the efficient design of foundations.     

Uncoupled analysis of stabilizing piles in weathered slopes

This paper describes a simplified numerical approach for analyzing the slope/pile system subjected to lateral soil movements. The lateral one-row pile response above and below the critical surface is computed by using load transfer approach. The response of groups was analyzed by developing interaction factors obtained from a three-dimensional nonlinear finite element study. An uncoupled analysis was performed for stabilizing piles in slope in which the pile response and slope stability are considered separately. The non-linear characteristics of the soil–pile interaction in the stabilizing piles are modeled by hyperbolic load transfer curves. The Bishop's simplified method of slope stability analysis is extended to incorporate the soil-pile interaction and evaluate the safety factor of the reinforced slope. Numerical study is performed to illustrate the major influencing parameters on the pile-slope stability problem. Through comparative studies, it has been found that the factor of safety in slope is much more conservative for an uncoupled analysis than for a coupled analysis based on three-dimensional finite element analysis.     

Seismic Response Analysis of Pile Foundations

A quasi-3D continuum method is presented for the dynamic nonlinear effective stress analysis of pile foundation under earthquake excitation. The method was validated using data from centrifuge tests on single piles and pile groups in liquefiable soils conducted at the University of California at Davis. Some results from this validation studies are presented. The API approach to pile response using p–y curves was evaluated using the quasi-3D method and the results from simulated earthquake tests on a model pile in a centrifuge. The recommended API stiffnesses appear to be much too high for seismic response analysis under strong shaking, but give very good estimates of elastic response.     

Analysis of soil resistance on laterally loaded piles based on 3D soil–pile interaction

The load distribution and deflection of large diameter piles are investigated by lateral load transfer method (p–y curve). Special attention is given to the soil continuity and soil resistance using three-dimensional finite element analysis. A framework for determining a p–y curve is calculated based on the surrounding soil stress. The appropriate parametric studies needed for verifying the p–y characteristic are presented in this paper. Through comparisons with results of field load tests, the three-dimensional numerical methodology in the present study is in good agreement with the general trend observed by in situ measurements and thus, represents a realistic soil–pile interaction for laterally loaded piles in clay than that of existing p–y method. It can be said that a rigorous numerical analysis can overcome the limitations of existing p–y methods to some extent by considering the effect of realistic three-dimensional combination of pile–soil forces.     

A Winkler model approach for vertically and laterally loaded piles in nonhomogeneous soil

An investigation is made to present analytical solutions provided by a Winkler model approach for the analysis of single piles and pile groups subjected to vertical and lateral loads in nonhomogeneous soils. The load transfer parameter of a single pile in nonhomogeneous soils is derived from the displacement influence factor obtained from Mindlin's solution for an elastic continuum analysis, without using the conventional form of the load transfer parameter adopting the maximum radius of the influence of the pile proposed by Randolph and Wroth. The modulus of the subgrade reaction along the pile in nonhomogeneous soils is expressed by using the displacement influence factor related to Mindlin's equation for an elastic continuum analysis to combine the elastic continuum approach with the subgrade reaction approach. The relationship between settlement and vertical load for a single pile in nonhomogeneous soils is obtained by using the recurrence equation for each layer. Using the modulus of the subgrade reaction represented by the displacement influence factor related to Mindlin's solution for the lateral load, the relationship between horizontal displacement, rotation, moment, and shear force for a single pile subjected to lateral loads in nonhomogeneous soils is available in the form of the recurrence equation. The comparison of the results calculated by the present method for single piles and pile groups in nonhomogeneous soils has shown good agreement with those obtained from the more rigorous finite element and boundary element methods. It is found that the present procedure gives a good prediction on the behavior of piles in nonhomogeneous soils. Copyright © 2011 John Wiley & Sons, Ltd.     

Nonlinear Response of Single Piles in Sand Subjected to Lateral Loads using k hmax Approach

This paper presents results of analysis of full-scale pile load test data of 14 piles embedded in either loose or medium dense sands. The analysis was performed using two methods, p–y curve approach and a more recently developed k_hmax approach. Comparison of the results obtained using both the methods is also presented. A step-by-step analysis procedure is presented for predicting lateral load deflection response of single piles in sand using the k_hmax approach. The results presented show that the k_hmax approach has promise over the p–y curve approach because of its simplicity and the fact that it provides upper- and lower-bound curves, which are valuable guides to making engineering decisions. For loose sands, a new range of k_hmax values is recommended to better predict the lateral load–deflection response of single piles.     

考虑应力扩散时桩端土性对单桩沉降影响分析方法

基于虚土桩模型,分析了层状地基中桩端土性对单桩沉降特性的影响。首先,以虚土桩扩散角反映桩端土层应力扩散效应,将桩端一定锥角范围内由桩端至基岩面的土体视为虚土桩,并根据其变截面特性,将虚土桩沿纵向划分为有限个微元段。然后,对桩及虚土桩桩侧土体采用理想弹塑性荷载传递模型,利用荷载传递法,推导了层状地基中以桩侧土塑性发展深度为变量的单桩荷载-沉降递推计算方法,并进一步得到了桩身轴力及桩侧摩阻力递推计算式。在此基础上,给出了荷载传递模型参数选取方法,并分析了虚土桩临界深度的影响因素及由实测荷载-沉降曲线反演虚土桩扩散角的可行性。最后,利用该方法分析了桩端沉渣和软弱下卧层对荷载-沉降曲线的影响。结果表明,考虑桩端土层应力扩散效应时,通过计算得到的桩顶及桩端荷载-沉降曲线与实测曲线吻合较好;当桩端存在沉渣或软弱下卧层时,采用虚土桩模型的单桩沉降计算方法可以在一定程度上反映沉渣特性及软弱下卧层埋深等因素对桩顶荷载-沉降曲线的影响。     

Evaluation of Curve Fitting Techniques in Deriving p–y Curves for Laterally Loaded Piles

The p–y method is one of the most popular methods for the analysis and design of laterally loaded piles. The mathematical relationship it provides between the bending moment, which can be easily measured at strain gauges along the pile, and the soil resistance and lateral pile displacement, facilitates the construction of p–y curves. Numerical techniques are required to fit smooth continuous curves to the discrete bending moment data in order to improve the accuracy of subsequent differentiation and integration operations. Due to the lack of guidance on the optimum positioning of strain gauges and the reliability and accuracy of curve fitting methods, a unifying study, inclusive of small (0.61 m) and large (3.8 and 7.5 m) diameter piles in clay, was carried out using 18 strain gauge layouts and cubic spline, cubic to quintic B-spline and 3rd to 10th degree global polynomial techniques. Bending moment data was obtained using 3D finite element analysis. Through a comprehensive evaluation, the cubic and cubic B-spline methods were found to be consistently accurate in deriving p–y curves for both the small and large diameter piles.     

Numerical study of group effects for pile groups in sands

The OpenSees finite element framework was used to simulate the response of 3×3 and 4×3 pile groups founded in loose and medium dense sands. Several numerical static pushover tests were conducted to investigate the interaction effects for pile groups. The results were then compared with those from centrifuge study. It is shown that our simulations can predict the behaviour of pile groups with good accuracy. Special attention was given to the three dimensional distribution of bending moment. It was found that bending moment develops in the plane perpendicular to the loading direction. In addition, bending moment data from simulations was used to derive p–y curves for individual piles, which were used to illustrate different behaviour of individual piles in the same group. Copyright © 2003 John Wiley & Sons, Ltd.     

Variation of limiting lateral soil pressure with depth for pile rows in clay

Pile group interaction effects on the lateral pile resistance are investigated for the case of a laterally loaded row of piles in clay. Both uniform undrained shear strength and linearly increasing with depth shear strength profiles are considered. Three-dimensional finite element analyses are presented, which are used to identify the predominant failure modes and to calculate the reduction in lateral resistance due to group effects. A limited number of two-dimensional analyses are also presented in order to examine the behaviour of very closely spaced piles. It is shown that, contrary to current practice, group effects vary with depth; they are insignificant close to the ground surface, increase to a maximum value at intermediate depths and finally reduce to a constant value at great depth. The effect of pile spacing and pile–soil adhesion are investigated and equations are developed for the calculation of a depth dependent reduction factor, which when multiplied by the limiting lateral pressure along a single pile, provides the corresponding variation of soil pressure along a pile in a pile row. This reduction factor is used to perform p–y analyses, which show that, due to this variation of group effects on the lateral soil pressures with depth, the overall group interaction effects depend on the pile length. Comparisons are also made with approaches used in practice that assume constant with depth reduction factors.     

Scour effects on the response of laterally loaded piles considering stress history of sand

Scour is the removal of soils around pile foundations of bridges or offshore platforms, resulting in reduced capacity of the foundations in either lateral or vertical direction. A common way to analyze the scour-affected pile foundations is to remove the scoured soil layers while keeping the properties of the remaining soil unchanged. However, this approach ignores the fact that the remaining soil experiences different stress histories before and after scour, which can be expected to change the properties of the remaining soil. As a result, the resistance of the remaining soil provided to the pile foundation may be different. The present study focused on the response of laterally loaded pile foundations in sand under scour considering the stress history of the remaining sand. Relative density and coefficient of lateral earth pressure of the sand were evaluated when it changed from a normally consolidated (NC) soil to an over-consolidated (OC) soil due to scour. The relative density was then used to estimate other properties of sand, e.g., unit weight, friction angle, and modulus of subgrade reaction of the sand based on their correlation. The lateral load–deflection (p–y) curve for a pile in sand was modified and input into the computer software, LPILE Plus V 5.0, to account for the effect of the stress history induced by scour. A field test was referenced as an example to compare the calculated results from the modified p–y curves with those from the initially developed p–y curves for the tested sand. The results showed that the change in the over-consolidation ratio (OCR) resulted in the most significant effect on the lateral soil resistance among all the effects due to the changes in the properties of the remaining sand. The sand changing from an NC to OC state increased the lateral soil resistance to the pile foundation. Ignoring the stress history would result in a conservative design of laterally loaded piles under scour.     

Observed and predicted test pile behaviour

The results obtained from a loading test on a bored, cast-in-place pile instrumented with six pairs of load cells at different levels are compared with the results obtained from a non-linear finite element analysis based on the geotechnical parameters of the cohesive soils in which the pile was bored. Settlements computed using deformability parameters obtained by a standard laboratory test were much larger than the measured settlements. Satisfactory results are instead obtained assuming E_i=1000c_u and c_α=c_u. The distribution of the vertical stresses within the pile and of the shear stresses in the soil adjacent to the pile obtained by the numerical analysis are compared with the measured values. A fair agreement is found at loads below failure but differences between experimental and computed values are found at loads close to failure.     

A simplified analysis method for piled raft foundations in non‐homogeneous soils

A simplified method of numerical analysis based on elasticity theory has been developed for the analysis of axially and laterally loaded piled raft foundations embedded in non‐homogeneous soils and incorporated into a computer program “PRAB”. In this method, a hybrid model is employed in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are approximated based on Mindlin's solutions for both vertical and lateral forces with consideration of non‐homogeneous soils. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups and capped pile groups in non‐homogeneous soils. Thereafter, the solutions from this approach for the analysis of axially and laterally loaded 4‐pile pile groups and 4‐pile piled rafts embedded in finite homogeneous and non‐homogeneous soil layers are compared with those from three‐dimensional finite element analysis. Good agreement between the present approach and the more rigorous finite element approach is demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

海上风电桩基水平承载力循环衰减二维简化分析

海上风电的桩基在长期循环荷载作用下会引起承载力的衰减。针对软黏土中水平受荷单桩,通过引入累积塑性应变以考虑土体不排水强度的循环弱化,建立二维有限元数值模拟和简化p-y曲线简化方法,以分析水平循环荷载作用后单桩桩侧侧向抗力的衰减弱化。在小数目循环荷载下简化方法与有限元计算结果比较吻合,在此基础上,采用二维简化分析方法得到长期大数目循环荷载下桩侧水平抗力的衰减规律,发现如荷载幅值与初始极限抗力的比值小于土体灵敏度的倒数,单桩在长期水平循环荷载作用下承载力虽有所衰减,但桩基趋于稳定,不会发生破坏。