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.     

多向荷载作用下层状地基刚性桩筏基础分析

提出一种多向荷载作用下层状地基中刚性桩筏基础的计算方法。基于剪切位移法,采用传递矩阵形式分析了竖向荷载下桩顶面-桩顶面相互作用;引入修正桩侧地基模量,采用有限差分法分析了水平荷载下桩顶面-桩顶面相互作用;基于层状弹性半空间理论,分析了多向荷载下桩顶面-土表面、土表面-桩顶面、土表面-土表面的相互作用关系。建立了桩土体系柔度矩阵,得到了多向荷载下层状地基中刚性桩筏基础的受力和变形的关系以及桩的内力和变形沿桩身分布规律。通过与有限元对比,验证了该方法的合理性和修正地基模量的优越性,并对多向荷载作用下的桩筏基础进行了计算分析,计算结果表明,水平力将会引起桩筏基础的倾斜。     

复杂地基反力模式下高承台嵌岩灌注桩的屈曲稳定分析

为探讨桩侧地基土反力对高承台嵌岩灌注桩桩身屈曲稳定的影响,假定地基反力系数呈更为复杂的幂分布,基于弹性地基梁理论建立桩土体系总势能方程,采用最小势能原理,导出了桩身屈曲临界荷载与稳定计算长度的解析解,并据此获得了地基反力系数分布模式、桩身自重及桩侧摩阻力等对桩身屈曲稳定的影响规律。工程应用分析结果表明,考虑地基反力系数为一般幂分布时,桩身屈曲分析结果更趋合理。     

横向载荷作用下刚性桩变位规律研究

目前对横向受载刚性桩的研究主要集中在其承载力方面,对变化规律研究很少。为此提出了利用刚性桩上两点位移求桩上任意一点位移、桩回转中心位置及转角的方法。通过对粉质黏土中的刚性桩进行模型试验与数值计算发现,回转中心位置随位移和载荷的增大,先是急剧下降,然后变缓,最后基本趋于稳定,而且桩埋置参数与土力学参数对回转中心位置的变化规律影响很小;而桩的转角随位移增大近似线性变化。比较发现,由试验和数值计算得到的回转中心极限位置与由极限地基反力法得到的结果相差不大     

水平荷载下纵截面异形桩承载特性试验

针对纵截面异形桩（扩底桩和楔形桩）、等混凝土用量常规等直径桩的水平向承载特性进行对比模型试验研究,测得不同水平荷载等级下扩底桩和楔形桩的内力、变形、极限承载力和桩侧土压力分布等变化规律特性;初步探讨3种桩型的水平极限承载特性和桩侧土压力分布规律。考虑纵向截面异形效应,基于水平土抗力与水平位移（p-y）曲线法建立纵截面异形桩水平向承载特性理论计算方法,进一步分析弯矩分布规律,并开展影响因素分析。研究结果表明,在当前试验条件下,等混凝土用量楔形桩的水平向承载力比等直径桩的高,砂性土和黏性土中楔形桩水平向极限承载力约分别为等直径桩的1.25倍和1.33倍。相关研究成果可为今后类似土层下水平受荷纵截面异形桩的设计与计算提供参考依据。     

刚性桩加固软土路基失稳破坏数值模拟

为控制路堤的整体稳定性,刚性桩现已常用于软土路基的加固。本文引入了桩体的断开机制,采用有限元软件ABAQUS对刚性桩加固软土路基的失稳破坏模式进行分析,相较于传统的数值模拟方法,体现了路堤荷载作用下,刚性桩的渐次失稳破坏过程。在此基础上,考虑桩体可能优先发生的弯曲破坏,提出将临界比例n作为判断桩体优先发生剪切破坏或弯曲破坏的临界值,并将其作为本文桩体断开机制的终止判别条件,合理地规避了数值模拟软件定量计算存在的较大误差。最后,将本文数值模拟与传统的数值模拟、等效砂桩法的数值模拟进行对比,结果反应出本文数值模拟方法的合理性与可靠性,工程上可通过增大前排桩的抗弯强度或限制桩体的水平位移,提高路堤的整体稳定性。     

ANALYSIS OF PILES USED FOR SLOPE STABILIZATION

Piles used for the stabilization of slopes have to be adequately designed to resist the induced lateral loads due to the movement of the unstable slope. In this paper, a numerical method is presented for the analysis of this problem. In this approach, the piles are modelled using beam finite elements. The soil response at the individual piles is modelled using the modulus of subgrade reaction and pile–soil–pile interaction considered using the theory of elasticity. Two case histories, one for single pile and the other for pile group, are analysed which show that the numerical model can predict the general characteristics of the piles reasonably well. The study suggests that the design of the piles based on the computed response from single pile analysis, ignoring group effects, may be unduly conservative.     

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.     

海洋工程中大直径管桩垂直水平荷载试验研究

通过海洋环境条件下大直径管桩的垂直和水平荷载试验,分析了管桩在垂直和水平荷载作用下的受力特点,得到了管桩的垂直极限承载力、侧摩阻力及端承力、轴向反力系数等结果,以及水平荷载作用下桩顶位移和转角关系、弯矩分布、土抗力、水平地基反力系数的比例系数和最大弯矩点等参数。试验结果表明：垂直荷载作用下,极限承载力可达12000kN,在沉桩过程中部分桩有一定程度的闭塞;大直径管桩能够抵抗水平荷载的作用,弹性长桩的受力性质主要受上部土层的影响。根据试验结果计算的水平地基抗力比例系数m值,对本工程及同类地质条件的桩基设计具有参考价值。     

BEM analysis of the interaction factor for vertically loaded dissimilar piles in saturated poroelastic soil

This paper focuses on an analysis by the boundary element method (BEM) of the pile-to-pile interaction for pile groups with dissimilar piles of different pile lengths embedded in saturated poroelastic soil. The behaviour of the poroelastic homogeneous soil is governed by Biot’s consolidation equations. The pile–soil system is decomposed into extended soil and fictitious piles. Considering the compatibility of vertical strain between fictitious piles and soil, the second kind of Fredholm integral equations were obtained to predict the axial force and settlement along pile shafts numerically. For the analysis of the interaction factor, two loading conditions for a two-dissimilar-pile system were proposed: (a) only one pile is loaded and (b) each pile is subjected to a load proportional to the pile length. Furthermore, the two-pile system was extended to pile groups with a rigid cap to capture the optimum design where each pile shares the same loading at the pile heads. The optimum results require shortening the peripheral piles and elongating internal piles, and the consolidation effect needs to be considered due to the adjustment of loading distribution among piles.     

旋喷群桩复合地基承载特性的数值分析

旋喷桩加固软土地基在各种地基处理工程中得到了广泛应用。对旋喷桩的研究多数集中在其施工工艺的改进上,或者针对单桩的承载特性进行研究,而对旋喷群桩的承载特性则研究不多。根据工程实际情况,采用基于MIDAS-GTS的三维有限元分析技术,通过改变旋喷群桩的布置方式、桩弹性模量、桩长、桩径、桩距等设计参数及桩-土接触面等参数对旋喷群桩复合地基承载特性的影响进行了研究。研究表明：旋喷桩加固软土地基主要减小了地表至桩底深度范围内土体的竖向沉降,对桩底下方的土体沉降基本无影响;提高旋喷桩桩径及材料强度会提高复合地基承载能力;不同旋喷桩布置方式、桩-土之间是否设置Goodman接触面单元对地基承载能力基本无影响。     

刚性桩复合地基桩土应力比计算及承载特性分析

分析了刚性桩复合地基中垫层、桩及桩间土的共同作用机理,考虑复合地基中桩、土变形协调,提供一种计算复合地基桩土应力比的方法;在此基础上研究复合地基中垫层模量、桩端持力层模量、桩土相对刚度比、桩长径比、面积置换率等因素对复合地基桩土应力比的影响,分析刚性桩复合地基的承载特性。     

纵横向受荷基桩变形内力的矩阵传递解

针对地基的土体屈服性状,将桩侧土体分为弹性变形区域与塑性变形区域两种情况。假定地基反力系数为3参数的一般形式,同时考虑桩身 效应并计入桩身自重、桩侧摩阻力的影响,根据地基反力法分别建立桩身弹性段和塑性段挠曲线微分方程。在解微分方程的过程中,采用矩阵传递法结合Laplace正逆变换的方法解得桩顶作用轴向力、水平力、弯矩时桩身内力和变形的矩阵传递解,并用Fortran语言编制了相应计算程序。最后将试验数据对上述方法进行验证,结果表明计算值与模型试验的实测值吻合很好,采用文中3参数地基反力法反算所得的地基参数离散性很小,研究结果具有较高的应用价值。     

基于传递矩阵法的层状土中管桩水平动力阻抗分析

在考虑土体分层特性的基础上,分别建立了管桩桩周土体和桩芯土体的水平振动控制方程。通过引入势函数并考虑桩周土和桩芯土径向位移和环向位移的边界条件及其奇偶性,求得了管桩-土动力相互作用的刚度系数和阻尼系数。将土体模拟为连续分布的弹簧-阻尼器,并考虑桩芯土和桩周土的作用,建立了层状土中管桩的水平振动方程。借助初参数法和传递矩阵法求解了管桩的水平振动,得到了管桩桩顶的水平动力阻抗。通过数值分析,得到了土层剪切模量、管桩壁厚、桩周土和桩芯土剪切模量比、土层厚度等对管桩桩顶动力阻抗的影响规律。土层剪切模量、管桩壁厚、桩周土和桩芯土剪切模量比对层状土中管桩水平振动的影响主要在低频处,土层厚度在较宽的频率范围内对管桩水平振动有影响;管桩壁越厚,桩周土的剪切模量越大时,管桩水平动力阻抗的绝对值越大。     

Settlement analysis of rectangular piles in nonhomogeneous soil using a Winkler model approach

An analytical approach using a Winkler model is investigated to provide analytical solutions of settlement of a rectangular pile subjected to vertical loads in nonhomogeneous soils. For a vertically loaded pile with a rectangular cross section, the settlement influence factor of a normal pile in nonhomogeneous soils is derived from Mindlin's solution for elastic continuum analysis. For short piles with rectangular and circular cross sections, the modified forms of settlement influence factors of normal piles are produced taking into account the load transfer parameter proposed by Randolph for short circular piles. The modulus of subgrade reaction along a rectangular pile in nonhomogeneous soils is expressed by using the settlement influence factor related to Mindlin's solution to combine the elastic continuum approach with the subgrade‐reaction approach. The relationship between settlement and vertical load for a rectangular pile in nonhomogeneous soils is available in the form of the recurrence equation. The formulation of settlement of soils surrounding a rectangular pile subjected to vertical loads in nonhomogeneous soils is proposed by taking into account Mindlin's solution and both the equivalent thickness and the equivalent elastic modulus for layers in the equivalent elastic method. The difference of settlement between square and circular piles is insignificant, and the settlement of a rectangular pile decreases as the aspect ratio of the rectangular pile cross section increases. The comparison of results calculated by the present method for a rectangular pile in nonhomogeneous soils has shown good agreement with those obtained from the analytical methods and the finite element method. Copyright © 2014 John Wiley & Sons, Ltd.     

超长桩荷载传递性状研究

根据超长桩的现场静载荷试验资料,分析了超长桩的单桩荷载传递特性。结果表明,超长桩表现出端承摩擦桩的特性,桩顶以下l/3桩长及桩端以上l/6范围内的桩侧摩阻力极限值接近规范推荐值,而中间部分的桩侧摩阻力远远大于规范值,表现出强化效应,桩端注浆桩的侧摩阻力强化效应更加明显。根据其荷载传递特性,提出了单桩极限承载力的估算公式,实例计算结果和实测结果较吻合。     

轴向荷载对斜桩水平承载特性影响试验及理论研究

斜群桩受水平荷载作用时,群桩中的基桩受到径向荷载、轴向荷载和弯矩的共同作用。为研究轴向荷载对斜桩水平承载特性的影响,完成了3根单桩以及1组1×2斜桩的大尺寸模型试验。试验结果表明：轴向拉力作用会降低斜桩的水平刚度和极限承载力;而轴向压力作用则会使其水平刚度和极限承载力提高。基于桩侧浅层土体楔形破坏假定,推导了考虑轴向荷载影响的斜桩水平极限土抗力计算公式,提出了桩侧土抗力的p-y曲线方法,并通过模型试验及现场试验验证其合理性。     

Soil resistances for laterally loaded rigid piles in multi-layered elastic soil

ABSTRACT

Short stubby piles like monopiles and large diameter drilled shafts undergo rigid body translation and rotation when subjected to a lateral force and/or a moment at the head. A method of analysis for these piles embedded in multi-layered elastic soil is developed using the variational principles of mechanics. Using this analysis, the soil resistance against pile movement can be rigorously related to the soil elastic constants, and the pile head displacement and rotation can be quickly calculated. The equilibrium equations for pile and soil displacements are obtained using the principle of virtual work and solved using an iterative algorithm. Pile responses obtained from the analysis match well with those obtained from three-dimensional finite element analyses in which the same inputs of loads, geometry, and material properties are given. Based on the new analysis, fitted equations for soil resistance parameters are developed, which can be used to directly calculate the pile head displacement and rotation without the use of the iterative algorithm. Numerical examples are provided that demonstrate how the method can be used to analyse practical problems.     

Shaft and base resistance of non-displacement piles in sand

This paper presents the results of three-dimensional, finite element analyses performed with an advanced, two-surface-plasticity, constitutive sand model to investigate the response of non-displacement piles to axial loading. The analysis domain is carefully meshed such that the formation and evolution of shear bands next to the pile shaft and near the pile base can be properly captured. Analyses considering various soil profiles and pile geometries show that the mobilized lateral earth pressure coefficient K along the pile shaft increases with increasing relative density and decreasing initial confining stress. The ultimate unit base resistance is independent of pile diameter, increasing with increasing relative density and increasing initial confining stress at the pile base. Based on the analysis results, design equations are proposed to estimate the limit shaft resistance and ultimate base resistance of non-displacement piles in sandy soil. In proposing these relationships, the pile slenderness ratio is considered. The effect of layer proximity to the base of the pile or pile base embedment in a layer is also considered.     

砂土中水平受荷桩非线性分析

对水平受荷桩的非线性分析,多采用p-y曲线法。现行p-y曲线模型很多,曲线形式和选用的参数各不相同。分析各桩土参数对现有p-y曲线的影响,并选择合理的标准化参数将各p-y曲线归一化,采用双曲线模型拟合归一化曲线。总结目前对地基反力模量和土体极限抗力的研究,并考虑桩径、施工等因素的影响,选择合理的双曲线模型参数。通过实例对比分析,证明了双曲线模型以及参数选取的有效性和适用性。双曲线模型形式简洁,符合理想土体的应力-应变关系,并能近似拟合现有的砂土p-y曲线,可广泛用于工程中砂土水平受荷桩基的非线性分析