Group interaction on vertically loaded piles in saturated poroelastic soil

The pile-to-pile interaction was obtained for vertically loaded piles embedded in homogeneous poroelastic saturated soil. Deduced from Biot’s theory, the fundamental functions of the quasi-static development for the force, displacement and pore pressure were acquired in cylindrical coordinates. The pile–soil system was decomposed into extended soil and fictitious piles, and the compatibility condition was set up between the axial strain of the fictitious piles and the corresponding average strain over the extended soil. This approach results in the governing equations, which consist of the Fredholm integral equations of the second kind and the basic unknowns of the axial forces along the fictitious pile shaft. The axial force and settlement along the pile shaft were calculated based on the axial forces of the fictitious piles. The interaction between the piles was investigated under different consolidation conditions through a two-pile model, and two pile interaction factors were obtained. Stemming from the two-pile analysis, numerical analyses on the settlement of the pile groups were conducted to probe pile interaction with consolidation. The conventional solutions for the single-phase soil-pile problem seem to underestimate the interaction factor if the consolidation effect is taken into account as pile settlement continues. The pile-to-pile interaction can also aggravate the percentage of consolidation settlement (PCS), and as the pile number increases, the value of the PCS will also increase. Several key factors, such as the pile stiffness, pile slenderness ratio and pile spacing, are investigated to better understand the impact of consolidation on pile analysis.     

Boundary element analysis of axially loaded piles embedded in a multi-layered soil

In a field, piles are likely installed in a multi-layered soil. Analysis of axially loaded piles in a multi-layered soil is complicated and deserves more attention. A boundary element method is used in this study to analyze an axially loaded single pile in a multi-layered soil using the solution for vertical and horizontal axisymmetric ring loads in a multi-layered elastic medium. Good and reasonable agreement is obtained between the proposed and published solutions for a single pile in a homogenous soil, a finite soil, and a Gibson soil. The proposed solution is also used to evaluate an axially loaded single pile in a multi-layered (8 layers) soil.     

Amplitude reduction of elastic waves by a row of piles in poroelastic soil

This paper studies the displacements behind a row of elastic piles in a homogeneous unbounded poroelastic soil after excitation by the passage of elastic waves. Biot’s theory is employed to describe soil behavior. Using a Fourier–Bessel series expansion with the aid of a translational addition theorem, closed-form expressions for the scattering coefficients are developed by imposing continuity conditions at the pile–soil interfaces. The influence of certain parameters, such as pile rigidity and soil permeability on the screening performance of the pile barrier is investigated. Particular attention is focused on the influence of the soil permeability on the screening effectiveness of a row of piles in the frequency domain.     

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.     

Study on interaction between dissimilar piles in layered soils

This paper, under the assumption that the pile–pile interaction showed elasticity, analyzed the pile–pile interaction between two dissimilar piles in layered soils using the shear displacement method and taking the sheltering effect into account to modify the conventional interaction factor between two dissimilar piles. The linear stiffness of single pile was adopted herein to analyze the influence of the pile stiffness factor, the pile length factor, and the diameter of shorter pile on the pile–pile interaction factor between two dissimilar piles. The interaction factor between two dissimilar piles drew from the present method was generally in good agreement with the interaction factor computed by Wong and Poulos. However, this paper intends to provide a different but more convenient means of estimating the interaction factor between piles that have dissimilar diameters, lengths and pile tip conditions, and the settlement of dissimilar piles in pile groups. Copyright © 2010 John Wiley & Sons, Ltd.     

柔性群桩承台下变截面角桩与地基相互作用的线性分析

对桩侧土及桩端土均采用线性荷载传递函数,同时考虑桩周土所分担的荷载及桩型对桩基荷载传递规律的影响,利用力学理论及微分方程的近似解法—子域法,推导出了柔性群桩承台下变截面角桩与地基相互作用的近似的解析算式,并通过算例将等截面桩桩侧摩阻力和桩身轴力与变截面桩桩侧摩阻力和桩身轴力作了对比,表明改变桩型能提高桩侧摩阻力。为验证本文方法的可行性,将模型试验结果与本文计算结果进行了比较,表明本文方法有较好的精度。     

饱和土半解析边界元法及在双排桩被动隔振中的应用

针对均质饱和地基中双排桩远场被动隔振问题,首先,基于饱和多孔介质的边界元法,建立了以薄层法（TLM）基本解作为动力Green函数的饱和土半解析边界元法,该方法可有效地分析饱和半空间的土-结构动力相互作用问题。在此基础上,根据双排桩与周围土体的邻接条件,推导了双排桩对Rayleigh波散射的三维边界元方程;运用上述边界元方程,对双排桩的远场被动隔振问题进行了研究。结果表明：双排桩能够有效地降低屏障后的位移振幅,其隔振效果要优于单排桩;排间净距对隔振效果影响不大,而桩间净距则对双排桩隔振效果起控制作用。     

饱和土中刚性排桩对平面SV波的隔离分析

在Biot波动理论的基础上,用单排刚性排桩作为屏障,对全空间饱和土中入射平面SV波进行了隔离分析。采用波函数展开法,将散射波的势函数展开成Fourier-Bessel级数的形式,利用一组可以求解多散射问题的圆柱坐标系统和桩土界面处位移连续的条件,以及刚性桩的动力平衡条件,得到问题的理论解。对影响排桩隔离效果的桩间距和饱和土的渗透系数等参数进行了分析,结果表明,桩间距对饱和土中排桩的隔离效果有较明显影响;与弹性土体中排桩的隔离效果相比,饱和土中排桩的隔离效果有所不同,随着饱和土渗透系数的减小,排桩的隔离效果越好。     

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.     

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.     

边坡桩-土相互作用的土拱力学模型与桩间距问题

桩-土相互作用机制是边坡抗滑桩设计需要考虑的重要因素之一。基于抗滑桩在侧向荷载作用下的受力条件,通过土力学和弹性力学的基本理论,导出了桩-土作用下桩后土体任意点的应力解析解,建立了土拱的力学模型;获得了土拱应力的等值线分布,得出了双曲拱、扩肩拱、马鞍拱和圆弧拱4种土拱形态,分析了不同桩间距、桩宽、桩后距离及土体力学特性对土拱效应的影响及其变化规律,阐明了土拱的作用机制。以拱体内土体破坏时的极限平衡状态为依据,基于Mohr-Coulomb抗剪强度理论建立了最大桩间距控制方程,并给出了具体的工程实例,对桩-土相互作用机制和抗滑桩设计理论研究具有一定的参考价值。     

A general viscous‐spring transmitting boundary for dynamic analysis of saturated poroelastic media

A time‐domain viscous‐spring transmitting boundary is presented for transient dynamic analysis of saturated poroelastic media with linear elastic and isotropic properties. The u–U formulation of Biot equation in cylindrical coordinate is adopted in the derivation. By this general viscous‐spring boundary, the effective stress and pore fluid pressure on the truncated boundary of the computational area are replaced by a set of continuously distributed spring and dashpot elements, of which the parameters are defined assuming an infinite permeability and considering the two dilatational waves. Numerical examples demonstrate good absorption of both the two cylindrical dilatational waves by the proposed ‘drained’ boundary. For general two‐dimensional wave propagation problems, acceptable accuracy can still be achieved by setting the proposed boundary relatively far away from the scatter. Numerical comparison shows that the results obtained by using this boundary are more accurate for all permeability values than those by the traditional viscous‐spring or viscous boundaries established for u–U formulation. Copyright © 2015 John Wiley & Sons, Ltd.     

饱和粘性土地基振击锤击碎石桩加固处理效果的应用对比

本文针对饱和粘性土地基,分别采用振击、锤击两种技术方法、工艺对其进行加固处理。结果表明:在相同布桩方案和用料条件下,振动(φ550)沉管桩较锤击(φ377)沉管桩加固效果更好。同原天然地基土相比,二者处理后的复合地基承载力和变形模量提高幅度分别为94.0%5、2.9%和65.0%、21.5%。主要因为前者有利于地基土颗粒之间的剪切与重组及其土的三维结构改变,有利于桩间土排水固结和挤密作用的发挥,且置换因素亦有较大作用;而后者不利于地基土颗粒之间的剪切与重组及其土的三维结构改变,虽然成桩密度较大,但该致密桩体却不利于超孔隙水压力的消散与桩间土排水固结作用的发挥,且由于所成桩径较小,桩体置换作用和径向挤密作用相对均较弱。     

考虑桩间土体抗滑作用的单排抗滑桩受力计算方法

为了充分考虑桩间距范围内滑体对抗滑桩受力的影响,从单排抗滑桩加固边坡的整体稳定角度出发,在采用传递系数法分析指定设计安全系数情况下抗滑桩的内力时,提出对一个桩间距范围内的加固坡体进行整体分析,将抗滑桩所在部位单独划分条块,该条块包括桩体受荷段及其两侧桩间距范围内的滑体。推导了与此分析模型相应的桩体受荷段底端内力计算公式,并给出了在滑坡推力线性分布条件下作用于受荷段的净滑坡推力计算表达式。分析结果显示,在不考虑与完全考虑受荷段两侧桩间距范围内滑体抗力作用时,得到是桩体内力及位移的上、下边界值。实例分析进一步表明,理论分析与数值模拟结果具有良好的一致性。所提出的方法比传统方法更有利于抗滑桩设计的经济性。     

非均质地基中群桩竖向荷载沉降关系分析

运用剪切位移法计算了桩轴向荷载传递因子。对于桩端采用线性的荷载传递函数,推导了基于弹塑性模型的单桩竖向荷载沉降的解析解。分析过程中考虑了土体强度沿深度线性变化的特性和桩土间的滑移现象,因此更符合大部分土体的实际性状。在此基础上,建立了考虑桩土滑移的桩-桩相互作用系数的计算公式,并将上述方法应用于群桩的分析,获得了群桩的荷载沉降特性。该分析方法克服了目前应用较多的弹性理论方法夸大桩土相互作用的缺点,单桩和群桩的荷载沉降曲线的分析结果和实测数据吻合,证明了该方法的合理性。     

Elastic analysis of laterally loaded pile in multi-layered soil

An analysis is developed to determine the response of laterally loaded piles in layered elastic media. The differential equations governing pile deflections in different layers due to a concentrated static force and/or moment acting at the pile head are obtained using the principle of minimum potential energy and calculus of variations. The differential equations are solved analytically using the method of initial parameters. Pile deflection, slope of the deformed axis of the pile, bending moment and shear force can be reliably 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. It is observed that soil layering has a definite impact on pile response and must be taken into account for proper analysis and design. The analysis forms the basis for future formulations that can consider stress–strain nonlinearity.     

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。     

Method of initial parameters for laterally loaded piles embedded in layered soils

The method of initial parameters (MIP) was originally developed to solve the problem of a beam on an elastic foundation with applied concentrated forces along the span, which introduce discontinuities in the mathematical formulation of the problem. MIP is modified in this paper so that it can be used for solving the problem of a laterally loaded pile with discontinuities due to soil layering along the length of the pile. In this paper, the basis of MIP is outlined, and its use to find the deflection, slope, bending moment and shear force of laterally loaded piles is illustrated. Example problems of laterally loaded piles embedded in multi-layered soil media are provided.     

A hybrid element method for dynamics of piles and pile groups in transversely isotropic media

A hybrid analytical-numerical method is proposed for the dynamic analysis of single piles and pile groups embedded in semi-infinite transversely isotropic media. In the method proposed, the soil-pile system is modeled using finite elements combined with massless rigid radiation discs representing pile-soil-pile interaction. The elasto-dynamic response of the radiation discs buried at different depths in a transversely isotropic half-space is analytically derived in a transform domain using a set of complete potential functions. A Boussinesq-type loading distribution is introduced to act on the disc region to achieve the proper mode of deformation at the cross sections of piles. Numerical results and comparisons with known analytical/numerical solutions are presented, demonstrating the application of the method.     

上海深厚饱和覆盖土层的动力耦合地震反应分析

上海的第四纪沉积土层呈水平层状分布，市区的土层厚度约为270－290m，年平均地下水位0.5-0.7m。上海地区上覆深厚、饱和的沉积土层，对土层的地震反应特性具有重要的影响。基于动力耦合理论，将上海深厚饱和覆盖土层视为由固相和液相组成的两相饱和多孔介质，建立了能够反映上海土层深厚、饱和特点的地震反应计算模型。然后应用该模型，以El Centro,Taft，苏南和唐山地震波作为基岩输入加速度，对深度280m的上海深厚覆盖土层进行了动力耦合地震反应计算，并对加速度、振动孔隙水压力和地基震陷结果进行了分析。