Nonlinear analysis of laterally loaded rigid piles in cohesive soil

This article presents a method for the nonlinear analysis of laterally loaded rigid piles in cohesive soil. The method considers the force and the moment equilibrium to derive the system equations for a rigid pile under a lateral eccentric load. The system equations are then solved using an iteration scheme to obtain the response of the pile. The method considers the nonlinear variation of the ultimate lateral soil resistance with depth and uses a new closed‐form expression proposed in this article to determine the lateral bearing factor. The method also considers the horizontal shear resistance at the pile base, and a bilinear relationship between the shear resistance and the displacement is used. For simplicity, the modulus of horizontal subgrade reaction is assumed to be constant with depth, which is applicable to piles in overconsolidated clay. The nonlinearity of the modulus of horizontal subgrade reaction with pile displacement at ground surface is also considered. The validity of the developed method is demonstrated by comparing its results with those of 3D finite element analysis. The applications of the developed method to analyze five field test piles also show good agreement between the predictions and the experimental results. The developed method offers an alternative approach for simple and effective analysis of laterally loaded rigid piles in cohesive soil. Copyright © 2011 John Wiley & Sons, Ltd.     

Nonlinear analysis of laterally loaded rigid piles in cohesionless soil

In this paper, a method is developed for nonlinear analysis of laterally loaded rigid piles in cohesionless soil. The method assumes that both the ultimate soil resistance and the modulus of horizontal subgrade reaction increase linearly with depth. By considering the force and moment equilibrium, the system equations are derived for a rigid pile under a lateral eccentric load. An iteration scheme containing three main steps is then proposed to solve the system equations to obtain the response of the pile. To determine the ultimate soil resistance and the modulus of horizontal subgrade reaction required in the analysis, related expressions are selected by reviewing and assessing the existing methods. The degradation of the modulus of horizontal subgrade reaction with pile displacement at ground surface is also considered. The developed method is validated by comparing its results with those of centrifugal tests and three-dimensional finite element analysis. Applications of the developed method to laboratory model and field test piles also show good agreement between the predictions and the experimental results.     

分布荷载推力桩计算的p-y曲线法研究

为提高现有水平梯形分布荷载推力桩设计计算水平,提出了地基系数按非线性土抗力.水平位移(p-y)曲线抗力模式表达的水平梯形分布荷载推力桩位移和内力计算的有限差分数值分析方法,并详细推导了桩身位移的差分格式.基于这些公式,编制了全桩位移、内力及侧土抗力的计算和图形处理程序,可适用于滑坡抗滑桩和深基坑悬臂支护桩的设计计算.结合新型桩型现浇混凝土薄壁管桩(PCC桩)作为滑坡抗滑桩进行对比分析,算例表明:该方法方便可靠.当有限差分段划分得足够小时,可使数值解接近于真实解.     

Load transfer approach for laterally loaded piles

A two‐parameter model has been proposed previously for predicting the response of laterally loaded single piles in homogenous soil. A disadvantage of the model is that at high Poisson's ratio, unreliable results may be obtained. In this paper, a new load transfer approach is developed to simulate the response of laterally loaded single piles embedded in a homogeneous medium, by introducing a rational stress field. The approach can overcome the inherent disadvantage of the two‐parameter model, although developed in a similar way. Generalized solutions for a single pile and the surrounding soil under various pile‐head and base conditions were established and presented in compact forms. With the solutions, a load transfer factor, correlating the displacements of the pile and the soil, was estimated and expressed as a simple equation. Expressions were developed for the modulus of subgrade reaction for a Winkler model as a unique function of the load transfer factor. Simple expressions were developed for estimating critical pile length, maximum bending moment, and the depth at which the maximum moment occurs. All the newly established solutions and/or expressions, using the load transfer factor, offer satisfactory predictions in comparison with the available, more rigorous numerical approaches. The current solutions are applicable to various boundary conditions, and any pile–soil relative stiffness. Copyright © 2001 John Wiley & Sons, Ltd.     

Nonlinear response of laterally loaded piles and pile groups

In spite of extensive studies on laterally loaded piles carried out over years, none of them offers an expedite approach as to gaining the nonlinear response and its associated depth of mobilization of limiting force along each pile in a group. To serve such a need, elastic–plastic solutions for free‐head, laterally loaded piles were developed recently by the author. They allow the response to be readily computed from elastic state right up to failure, by assigning a series of slip depths, and a limiting force profile. In this paper, equivalent solutions for fixed‐head (FixH) single piles were developed. They are subsequently extended to cater for response of pile groups by incorporating p‐multipliers. The newly established solutions were substantiated by existing numerical solutions for piles and pile groups. They offer satisfactory prediction of the nonlinear response of all the 6 single piles and 24 pile groups investigated so far after properly considering the impact of semi‐FixH restraints. They also offer the extent to ultimate state of pile groups via the evaluated slip depths. The study allows ad hoc guidelines to be established for determining input parameters for the solutions. The solutions are tailored for routine prediction of the nonlinear interaction of laterally loaded FixH piles and capped pile groups. Copyright © 2008 John Wiley & Sons, Ltd.     

水平受荷长桩弹塑性计算解析解

当考虑桩侧土体非线性本构关系时对水平受荷桩的计算一般需采用数值方法,解析结果相对较少。基于Winkler地基模型和桩侧土体简化的弹塑性本构关系,对均质地基中水平荷载作用下桩头嵌固的长桩进行了解析推导,得到了桩身最大挠度及最大弯矩与荷载关系的统一解析表达式,并采用相同的方法求得高桩情形下桩头挠度的计算式。计算表明,联合荷载作用下桩身泥面处的挠度和转角不等于单个荷载作用时的线性叠加,采用常规的线性叠加法计算将偏于不安全。所求解析式借助计算器即可进行最大挠度和最大弯矩的计算,大大方便了工程的计算应用。     

Analysis of laterally loaded piles with rectangular cross sections embedded in layered soil

An analysis is developed to determine the response of laterally loaded rectangular piles in layered elastic media. The differential equations governing the displacements of the pile–soil system are derived using variational principles. Closed‐form solutions of pile deflection, the slope of the deflected curve, the bending moment and the shear force profiles can be obtained by this method for the entire pile length. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. The new analysis allows insights into the lateral load response of square, rectangular and circular piles and how they compare. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

水平荷载下桩身侧阻抗力矩的作用机制与计算模型研究

为探讨摩阻力增强效应影响下的水平受荷桩承载机制,建立了水平荷载作用下考虑增强效应影响的桩侧摩阻力τ-s曲线模型,并在此基础上推导了桩身单位长度侧阻抗力矩数值解。随后开展了桩径、临界位移、极限侧摩阻力等因素影响下Ms,ini/Msu,ini-θ/θref,ini无量纲化曲线规律分析。结合摩阻力增强效应理论进而分别建立了线弹性-塑性、双曲线、API规范砂土与黏土τ-s曲线模型作用下的桩身侧阻抗力矩简化理论解,并基于传递矩阵法原理,解得了考虑桩侧摩阻力作用时基桩水平承载力半解析解。通过多组验证工况和工程实例分析验证了所建立的侧阻抗力矩简化解以及考虑侧阻抗力矩影响的基桩水平承载力方法的正确性,同时也证明了摩阻力增强效应对基桩水平承载力的影响不能忽略,并得出如下结论:无试验数据参考时,砂土、黏土与桩接触面的刚度指数可分别取0.725和0.600;桩身侧阻抗力矩随着桩径、极限摩阻力的增加以及临界位移的减小而增加,其中桩径对侧阻抗力矩影响更为明显。     

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.     

A study of the effect of driving on pre‐bored piles

A finite element model for pile‐driving analysis is developed and used to investigate the behaviour of pre‐bored piles, which are then driven the last 1.25 or 2.25 m to their final design depth. The study was conducted for the case of saturated clays. The model traces the penetration of the pile into the soil and accommodates for large deformations. The non‐linear behaviour of the clay in this study is predicted using the bounding‐surface‐plasticity model, as applied to isotropic cohesive soils. The details of the 3‐D numerical modelling and computational schemes are presented. A significant difference was observed in the pile displacement during driving, and in the computed soil resistance at the pile tip, particularly at the earliest driving stages. No difference in soil resistance at the soil pile interface along the pile shaft was detected between the pre‐bored piles whether driven 1.25 or 2.25 m. Copyright © 2002 John Wiley & Sons, Ltd.     

Predicted ultimate capacity of laterally loaded piles in clay using support vector machine

The determination of ultimate capacity of laterally loaded pile in clay is a key parameter for designing the laterally loaded pile. The available methods for determination of ultimate resistance of pile in clay are not reliable. This study investigates the potential of a support vector machine (SVM)-based approach to predict the ultimate capacity of laterally loaded pile in clay. The SVM, which is firmly based on statistical learning theory, uses a regression technique by introducing an ?-insensitive loss function. A sensitivity analysis has been carried out to determine the relative importance of the factors affecting ultimate capacity. The results show that SVM has the potential to be a practical tool for prediction of the ultimate capacity of pile in clay.     

考虑桩土侧移的被动桩中土拱效应数值分析

被动桩对侧向位移的土层起到遮拦作用的机制主要是土拱效应。采用土工有限元软件Plaxis Tunnel 3D 1.2,对堆载荷载作用下邻近桩基中的土拱效应产生机制和性状进行三维数值分析,指出目前被动桩中土拱效应二维有限元分析存在的问题。考虑桩土侧移与相对位移,再利用土工有限元软件Plaxis2D 8.2详细地研究了侧向土体位移大小、桩身水平位移大小、土体性质以及桩土接触面性质等影响因素对土拱效应性态和桩土荷载分担比的影响。     

嵌岩桩嵌岩段侧阻和端阻综合系数研究

现行行业标准《建筑桩基技术规范》（JGJ94－2008）[1]采用嵌岩段侧阻和端阻综合系数?r与基岩单轴抗压强度frk来计算嵌岩桩嵌岩段的总承载力。该方法较简单且工程意义明确,便于工程设计使用。然而规范中综合系数的取值存在一定的局限性。采用ABAQUS通用有限元软件对武汉绿地中心等4个背景工程共20余根现场试桩试验成果进行了数值拟合,取得了较合理的岩（土）参数取值;利用前述参数,建立不同岩性条件下的嵌岩桩数值计算模型,对综合系数进行了计算分析,并建立其与基岩岩性、嵌岩深径比的关系,提出了综合系数建议取值表。相比于规范取值方法,该方法对不同岩石强度分类和嵌岩深径比两个维度上进行了扩充与细化。通过背景工程嵌岩桩试桩承载力的验算表明,采用综合系数比按规范计算的综合系数更接近试桩实测结果。     

被动桩中土拱效应问题的数值分析

被动桩对侧向位移的土层起到遮拦作用的机理主要是土拱效应。采用有限元软件Plaxis 8.1,详细地研究了被动桩中土拱效应的产生机理,分析了导致侧向位移的荷载大小、土体性质、群桩以及桩土接触面性质等影响因素对土拱效应性态和桩土应力分担比的影响,分析表明,桩间距是影响土拱效应的最主要因素。     

多层地基中PCC水平荷载桩的数值解

针对目前多层地基中水平荷载桩计算方法存在的问题,提出了一种基于弹性力学理论,根据桩-土应力应变关系,借助于变分原理和最小势能原理导出桩身位移控制方程,利用有限差分法对方程进行解答的方法,并编制了全桩位移和内力计算程序。算例结果表明,该方法分别同试验结果和有限元计算结果吻合较好,较现行地基系数法具有较高的计算精度和计算效率,对现浇混凝土大直径水平荷载管桩（PCC）的设计计算和分析具有一定的指导意义。     

单桩不同加载条件下有限元模拟及侧摩阻力分析

采用弹塑性有限元法,结合岩土体结构特征,应用接触单元模拟桩土之间的不连续面,分别对单桩传统静载加载方式和自平衡加载方式进行数值模拟。自平衡加载方式的数值模拟结果与实际自平衡测试结果吻合较好,说明选取的模型和参数比较合理。进而采用此模型和参数,对传统静载加载方式进行数值模拟,得出桩上部荷载传递过程中桩及桩周岩土体应力及位移,求出各单元的应力应变,确定出桩侧法向应力,结合桩土之间摩擦试验的参数,根据莫尔-库仑理论求出桩侧摩阻力。最后将有限元数值模拟和自平衡实测侧摩阻力值进行对比,验证了在选用合理的模型和物理力学参数的基础上,有限元计算的侧摩阻力值和实测值较吻合,通过有限元方法计算获得的单桩侧摩阻力值具有一定的可借鉴性和实用性。     

水平受荷桩的弹性有限元虚拟加载上限分析

基于将塑性上限分析等效为弹性迭代计算的总量虚拟加载上限分析理论,在商业化有限元软件ABAQUS中实现了弹性有限元虚拟加载上限方法（弹性有限元T-EMSD）。应用弹性有限元T-EMSD法分析了不排水黏土中的二维水平受荷桩,其获得的荷载-位移曲线与弹塑性有限元分析结果一致,其极限承载力与塑性解相近。在极限位移加载量下弹性有限元T-EMSD法对应的上限机构从弹性始速度场开始随迭代逐渐演化,迭代收敛后的速度场和解析塑性破坏机构相似。与其他基于可变强度概念（MSD）的方法相比,弹性有限元T-EMSD法对水平受荷桩桩身的分析具有更高的精度。弹性有限元T-EMSD法最大的优势在于可在计算中自然地获得塑性机构,因而可被用于研究一些塑性机构难以构造的复杂问题,并对弹塑性数值方法进行验证。     

岩溶地区桩基的有限元分析

岩溶地区长桩存在着遇洞率的问题。为了研究岩溶地区桩的受力特点,采用有限元法模拟岩溶地区桩基的工作方式,分析了岩层厚度对桩的影响以及桩的受力状态,并研究了去桩的可能性。计算结果表明:岩层厚度对桩的影响较大,岩层的位置对桩的应力不产生影响,仅对桩的位移产生影响。     

嵌岩桩尺寸效应的有限元分析

基于非线性有限元计算,分析了桩的尺寸效应对嵌岩桩承载性状的影响。结果表明：在其他条件一定时,随着桩径的增加,嵌岩深径比减小,桩的承载力有增大的趋势,其主要原因是增强了桩端承载力;另一方面,嵌岩深度也对桩的承载性状有影响,桩嵌入深度越短,桩端承担的荷载就越大。设计时可适当考虑通过增大桩径的办法来提高桩的承载力。