Longitudinal vibration of a pile embedded in layered soil considering the transverse inertia effect of pile

The dynamic response of a viscoelastic bearing pile embedded in multilayered soil is theoretically investigated considering the transverse inertia effect of the pile. The soil layers surrounding the pile are modeled as a set of viscoelastic continuous media in three-dimensional axisymmetric space, and a simplified model, i.e., the distributed Voigt model, is proposed to simulate the dynamic interactions of the adjacent soil layers. Meanwhile, the pile is assumed to be a Rayleigh–Love rod with material damping and can be divided into several pile segments allowing for soil layers and pile defects. Both the vertical and radial displacement continuity conditions at the soil–pile interface are taken into account. The potential function decomposition method and the variable separation method are introduced to solve the governing equations of soil vibration in which the vertical and radial displacement components are coupled. On this basis, the impedance function at the top of the pile segment is derived by invoking the force and displacement continuity conditions at the soil–pile interface as well as the bottom of pile segment. The impedance function at the pile head is then obtained by means of the impedance function transfer method. By means of the inverse Fourier transform and convolution theorem, the velocity response in the time domain can also be obtained. The reasonableness of the assumptions of the soil-layer interactions have been verified by comparing the present solutions with two published solutions and a set of well-documented measured pile test data. A parametric analysis is then conducted using the present solutions to investigate the influence of the transverse inertia effect on the dynamic response of an intact pile and a defective pile for different design parameters of the soil–pile system.     

On the mechanics of dynamic penetration tests

This paper describes a numerical model developed to simulate the wave propagation in an elastic media that is applied to in situ dynamic penetration test devices currently used for site characterization. In the model, dynamic equilibrium equations are solved by finite difference analysis in the time domain to produce the discretization of a penetration system – including hammer, rod, penetrometer (or sampler) and soil. In standard penetration tests numerical simulations are shown to agree well with energy measurements derived from force and acceleration signals produced by the impact of a hammer. A parametric study allowed the identification of the relevant factors affecting penetration by demonstrating that the energy effectively delivered to the soil is a function of hammer height of fall and weight of both hammer and rods, as well as the permanent penetration of the penetrometer into the ground produced by a single stroke. Based on these evidences, an approach is suggested to compare results from different dynamic penetration tests without the need to rely on empirical correlations, which is achieved by demonstrating that different equipments should yield the same normalized energy once the influence of both the hammer and rod potential energies are properly considered.     

Improving dynamic soil parameters and advancing the pile signal matching technique

The pile signal matching technique widely used for estimating vertical resistances of piles during construction is highly influenced by the assumed dynamic soil parameters. Due to the lack of understanding and supporting data, constant soil parameters for the entire pile length have been routinely used. This practice is unrealistic and compromises the signal match quality. Using recently completed field tests, this paper develops empirical equations for dynamic soil parameters in terms of measureable soil properties and proposes an improved signal matching technique, thereby allowing for better match quality.     

饱和黏弹性地基土中管桩纵向振动研究

用解析方法在频率域内研究考虑质量耦合效应的饱和黏弹性地基土中管桩的纵向振动特性。基于Biot理论,采用薄层法,推导得到饱和黏弹性地基土的位移、应力等的表达式。将管桩等效为一维弹性杆件处理。根据界面连续性条件,给出饱和黏弹性地基土中管桩的纵向振动一般分析方法和桩顶动力复刚度的表达式。在该基础上,对比分析饱和地基土中实心桩和管桩纵向振动特性。通过算例分析,考察桩周土和桩芯土的力学参数对桩顶刚度因子和等效阻尼的影响。研究表明,饱和黏弹性地基土中实心桩和管桩的纵向振动有明显的差异。     

Numerical analysis of the interface shear transfer mechanism of a single pile to tunnelling in weathered residual soil

Three-dimensional (3D) numerical analyses have been carried out to study the behaviour of a single pile to adjacent tunnelling in the lateral direction of the pile. The numerical analyses have included comparisons between the current study, previous elastic solutions and advanced 3D elasto-plastic analyses. In the numerical analyses, the interaction between the tunnel, the pile and the soil next to the pile has been analysed. The study includes the axial force distributions on the pile, the relative shear displacement between the pile and the soil, the shear stresses at the soil next to the pile and the pile settlement. In particular, the shear stress transfer mechanism along the pile related to tunnel advancement has been analysed by using interface elements allowing soil slip. It has been found that existing solutions may not accurately estimate the pile behaviour since several key issues are not included. Due to changes in the relative shear displacement between the pile and the soil next to the pile with tunnel advancement, the shear stresses and axial force distributions along the pile change drastically. Downward shear stress develops at the upper part of the pile, while upward shear stress is mobilised at the lower part of the pile, resulting in a compressive force on the pile. A maximum compressive force of about 0.25–0.52P_a was developed on the pile, solely due to tunnelling, depending on the pile tip locations relative to the tunnel position, where P_a is the service pile loading prior to tunnelling. The majority of the axial force on the pile developed within ±2D in the transverse direction (behind and ahead of piles) relative to the pile position, where D is the tunnel diameter. In addition, mobilisation of shear strength at the pile–soil interface was found to be a key factor governing pile–soil–tunnelling interaction. The reduction of apparent allowable pile capacity due to tunnelling was dependent on the pile location relative to the tunnel position. Some insights into the pile behaviour in tunnelling obtained from the numerical analyses will be reported and discussed.     

Vertical dynamic response of an inhomogeneous viscoelastic pile

The vertical dynamic response of an inhomogeneous viscoelastic pile embedded in layered soil subjected to axial loading has been investigated. The interaction between pile and soil is simulated by a general Voigt model, one that has been demonstrated by earlier investigators to be capable of representing the plane strain case of soil adequately. The analytical solutions of pile responses in the frequency domain are obtained by using the (two-sided) Laplace transform. The corresponding semi-analytical solutions in the time domain for the case of a pile subjected to an instantaneous half-sine exciting force applied at the pile top are obtained via Fourier transform inversion. Using these solutions, a parametric study of the influence of the pile and soil properties on the vertical dynamic responses has been undertaken. It is shown that an abrupt variation of the soil properties with depth cannot yield evident reflection signal that may lead geotechnical engineers to assess the pile integrity wrongly from the velocity curve of the pile top, and the influence of viscosity of the pile material on the response is different from that of the damping of the soil surrounding the pile. The theoretical model developed in the present paper has also been validated in field studies, where it is shown by means of three examples that the solution developed in this study has been adequately verified by comparison of the theoretical pile model and field measurements of the dynamic responses.     

PHC管桩荷载传递的试验研究和数值分析

通过在预应力高强混凝土管桩(PHC桩)的桩顶、桩端及桩周各主要土层的分界面埋设应变计的静荷载试验，研究了PHC管桩的荷载传递机理，分析了轴力和桩侧摩阻力的变化规律。并以工程中PHC管桩的竖向抗压静载试验为基础，运用有限单元法对软土地区的PHC管桩桩-土相互作用进行模拟，在分析中采用弹塑性模型，引入了非线性接触面单元，并且考虑了土体的材料非线性。分析结果表明，计算值和实测值有一定的差别，但是变化趋势基本一致。     

桩-桩水平振动动力相互作用研究

在采用动力Winkler地基模型并考虑了被动桩与桩周土体相互作用的基础上,运用传递矩阵法求解出层状地基中的群桩水平振动桩-桩动力相互作用因子。与严格解（Kaynia和Kausel,1982年）进行对比,验证了方法的有效性。研究了各因素如桩长、桩底约束、桩间角度以及地基土对桩-桩动力相互作用因子的影响,并提出了＂影响桩长＂的概念。     

土体参数对大直径空心桩承载性状影响的仿真分析

借助MARC软件,系统分析了桩周土体c、值及土体模量E值对大直径空心桩承载力的影响,分析表明E值是影响 大直径桩承载力的主要因素。文章进一步分析了桩端土体模量E对Se值(桩端沉降与桩顶沉降之比)及对桩身轴力曲线的影 响。通过与实测结果比较,证明所建模型合理。     

门架式双排抗滑桩的弹塑性模型与计算分析

门架式双排抗滑桩的计算模型大部分将桩排间岩土体视为弹性材料,而岩土体为弹塑性材料,使得抗滑桩内力、位移计算结果与实际情况相差较大。假设桩排间岩土体为弹塑性材料,提出一种弹塑性计算模型,该模型将桩排间岩土体看作线弹性单元和塑性单元的组合,根据结构力学知识、土的本构关系和数值分析方法建立一种计算前后排抗滑桩内力的计算方法。首先,由已知的桩顶位移,并结合结构力学位移法求出桩间土总应力。根据Lade-Duncan模型导出这两个单元的基本参数,然后,结合数值分析方法计算出抗滑桩的内力,最后,结合工程实例,运用ANSYS有限元软件进行计算分析,得出门架式双排抗滑桩的内力图。对比监测数据和弹性模型计算结果表明,弹塑性模型的计算结果比弹性模型更加接近监测值。     

Three‐dimensional finite element analysis of lined tunnels

This paper describes finite element procedures that have been developed to model the ground movements that occur when a shallow tunnel is installed in a clay soil. This study is part of a wider project concerned with the development of new methods to predict the likely extent of damage to surface structures caused by nearby shallow tunnelling. This particular paper, however, is concerned only with the numerical model of tunnel installation. The structural liner is an important component of this tunnel installation model; two different ways of modelling the liner (based on continuum elements and shell elements) are discussed in the paper. A test problem consisting of the installation of a lined tunnel in an elastic continuum is used to investigate the merits of these different approaches. When continuum elements are used to model the liner, the numerical results agree well with an analytical solution to the problem. When shell elements are used to model the liner, however, the results were found to be significantly influenced by the particular formulation adopted for the shell elements. Example analyses, involving incremental tunnel construction in a clay soil where the soil is modelled using a kinematic hardening plasticity model, are described. These analyses confirm that a thin layer of continuum elements may be used, satisfactorily, to model tunnel linings in a soil–structure interaction analysis of this sort. Copyright © 2001 John Wiley & Sons, Ltd.     

非饱和土中端承桩水平振动特性研究

针对非饱和土中桩的水平稳态振动问题,采用三相多孔介质波动方程,考虑固、液、气三相材料间的惯性和黏性耦合效应以及基质吸力的影响,通过Helmholtz矢量分解及分离变量法解耦波动方程,并将基桩等效为能描述其剪切变形和转动惯性效应的铁摩辛柯（Timoshenko）梁模型,采用Novak三维连续介质模型对非饱和土中端承桩的稳态水平振动进行了理论推导,获得了桩顶水平频域响应解析解,讨论了饱和度对土层和桩顶阻抗的影响以及桩身位移、内力沿深度的分布规律。结果表明,随着土体饱和度的升高,土层复阻抗和桩顶动力阻抗增大,桩身位移和内力则相应地减小;饱和度,包括渗透系数在内的影响仅在土体接近准饱和时才得以发挥;频率较低时,短桩拥有较大的刚度因子。桩长越长,阻抗因子越大,而共振频率越低。当长径比超过10时,桩顶阻抗不再随长径比的增加而改变。     

桩承式路堤承载特性的颗粒流模拟

现有的土拱效应计算方法中,由于采用的计算模型不同,计算结果差异很大。文中克服传统连续介质力学模型的宏观连续性假设,采用二维颗粒流程序（PFC）建立基于模型试验的细观数值分析模型,对桩承式路堤中土体接触力、应力分布、主应力方向、竖向位移进行分析,并比较计算和实测结果,研究土拱效应的荷载传递机制。同时,对不同桩帽、桩间距、填土高度、颗粒大小、摩擦角的情况进行PFC方法的参数敏感性分析。研究结果表明,桩承式路堤桩顶处局部范围可按弹性核考虑;土拱的分布型式受桩帽型式、桩净距、格栅的影响;实际土拱作用的影响范围主要集中在路堤底面以上约1倍桩净距的区域;土拱内部的竖向应力和水平应力均随深度非线性改变,桩土应力比随着荷载水平、土体内摩擦角、颗粒大小的增大而增加。     

Numerical analysis of a pile–slab-supported railway embankment

This paper presents a numerical analysis of a well-monitored pile–slab-supported embankment for the Beijing–Tianjin high-speed railway in China. Cement–fly ash–gravel piles were used in this project. A coupled two-dimensional mechanical and hydraulic numerical model was used for this analysis and the results are compared with the field measurements including settlement, load distribution between soil and pile, and excess pore pressure. The numerical model calculated the settlement profile close to that measured in the field. The proportion of the load carried by the soil was small thus significantly reducing the settlement. The stress transfer from the soil to the piles reduced the excess pore pressure effectively. A parametric study was conducted to investigate the influence of three key factors on the performance of the embankment. The parametric study indicated that the existence of a cushion reduced the shear force in the slab. The increase in slab thickness and pile stiffness increased the shear force and bending moment in the slab. An increase in pile stiffness reduced the settlement and lateral displacement of the embankment.     

地震作用下饱和土-桩-上部结构动力相互作用研究

将土体视为液固两相多孔介质,利用连续介质力学得到了饱和土层的水平动力阻抗,将上部结构视为梁单元,桩-饱和土-桩之间的动力相互作用借助于等效的Winkler动力弹簧和波的干涉来模拟,并通过承台处力的平衡将群桩和上部结构耦合起来,研究了简谐SH地震波作用下饱和土-桩-上部结构的动力相互作用问题。以2×2群桩为例,对饱和土-桩-上部结构体系进行了数值分析,讨论有关参数对结构体系动力特性特别是抗震性能的影响。数值分析表明,桩间距、桩-土弹性模量比、长径比等对结构体系的抗震性能有较大影响。桩间距对地震放大系数的影响与外界激励的频率有关,桩土模量比较小、结构和桩基的阻尼较大时结构体系的抗震效果较好,长径比越大地震作用下产生的结构变形越大     

Interaction of a cylindrical thin‐walled pile with an inhomogeneous isotropic elastic medium

This paper presents a rigorous analysis for the static interaction of a cylindrical thin‐walled pile with an inhomogeneous isotropic elastic half‐space under vertical, horizontal, and torsional forces individually applied at the top of pile. The inhomogeneity is specified with the exponential variation of shear modulus along depth of the embedding medium, and the Poisson's ratio is assumed to be constant. By means of a set of Green's functions for pile and soil medium and satisfying the compatibility conditions between the 2 interacting media, the formulation is reduced to coupled Fredholm integral equations. Using the adaptive‐gradient elements, capable of capturing the singular stress transfer at both ends of the pile, a numerical procedure is developed and utilized for evaluating the relevant integral equations and studying the inhomogeneity effect on the soil‐pile interaction responses. The analysis results have been validated for different soil‐pile modulus ratios under axial load and for a Poisson's ratio of 0.3 under lateral load. The procedure does not consider the nonlinear behavior of the soil medium or plastic yielding in the pile section, and the impact of the unreliable results for the case of high Poisson's ratio is not examined.     

基桩缺陷逐步能量恢复递推定量分析

通过大量正演计算,对不同桩周土条件下缺陷程度与时域速度响应波形中入射波波幅与反射波波幅的比值进行了相关性分析,拟合出桩侧土为粘土、砂土、粉土条件下桩径变化程度与波幅比之间的关系式。通过理论分析,在基桩存在多缺陷时,导出了缩颈与扩颈对下一个缺陷引起的反射波幅值的影响系数,进而,提出了逐步能量恢复递推缺陷程度的理论与方法,在时间域中,实现了基桩存在多缺陷时的低应变动测缺陷量化分析。模型桩试验分析结果表明,缺陷量化分析方法可取得显著效果。     

成层饱和土中考虑横向惯性的单桩纵向振动

基于饱和多孔介质理论,研究了成层饱和黏弹性土层中端承桩的纵向振动特性。首先利用Novak薄层法,得到了土层对纵向振动桩的动力阻抗。其次,将桩等效为Rayleigh-Love杆,给出了成层饱和黏弹性土中端承桩纵向振动的一般分析方法和桩头动力复刚度的解析表达式。具体分析了两层饱和黏弹性土中端承桩的纵向振动特性,得到了桩头动刚度因子和等效阻尼随频率的响应特征,讨论了物理和几何等参数对动刚度因子和等效阻尼的影响。结果表明：桩长径比、土层模量比以及桩土模量比等对桩头动刚度因子和等效阻尼有显著的影响。相比于均质土层中的桩,上层土越硬或下层为软弱土层,桩的动刚度因子和等效阻尼振动幅值增大,其周期随长径比显著变化,且对于大直径桩,动刚度因子和等效阻尼随频率呈振动变化。同时,土体与孔隙水相互作用系数和桩泊松比等的影响相对较小。其结果可作为桩基动力基础设计和动力检测等基础数据。     

可液化场地微型桩地震响应特性研究

可液化场地微型桩的地震响应分析是确保工程安全和优化抗震设计的前提。应用动态离心机试验和三维有效应力数值分析方法,研究了微型单桩桩台的侧向变形和加速度、不同埋深桩身弯矩、可液化场地的加速度及超孔隙水压力等响应特征。首先开展了相对密实度为57%饱和土层、输入波是频率为1 Hz和峰值加速度为1.516 m/s2正弦波的微型桩40 g动态地震响应离心机试验,进而应用基于多重剪切机构塑性模型和液化前缘状态面概念的三维有效应力分析方法,反演了试验结果,并进行了对比分析,结果表明,数值模拟与离心机试验结果吻合,液化场地特性控制着建于其中微型桩的地震响应特征,微型桩桩台的水平变形和残余变形可达78、30 mm,桩身最大弯矩和最大残余弯矩呈现向桩身底部迁移特点,同时表明,基于动态土工离心机试验和数值分析相结合的研究方法,分析可液化场地微型桩地震响应特性是有效可行的,研究结论为可液化场地微型桩的抗震设计提供了可靠的依据和参考。     

Soil‐pile interaction in the pile vertical vibration considering true three‐dimensional wave effect of soil

The dynamic response of an end bearing pile embedded in a linear visco‐elastic soil layer with hysteretic type damping is theoretically investigated when the pile is subjected to a time‐harmonic vertical loading at the pile top. The soil is modeled as a three‐dimensional axisymmetric continuum in which both its radial and vertical displacements are taken into account. The pile is assumed to be vertical, elastic and of uniform circular cross section. By using two potential functions to decompose the displacements of the soil layer and utilizing the separation of variables technique, the dynamic equilibrium equation is uncoupled and solved. At the interface of soil‐pile system, the boundary conditions of displacement continuity and force equilibrium are invoked to derive a closed‐form solution of the vertical dynamic response of the pile in frequency domain. The corresponding inverted solutions in time domain for the velocity response of a pile subjected to a semi‐sine excitation force applied at the pile top are obtained by means of inverse Fourier transform and the convolution theorem. A comparison with two other simplified solutions has been performed to verify the more rigorous solutions presented in this paper. Using the developed solutions, a parametric study has also been conducted to investigate the influence of the major parameters of the soil‐pile system on the vertical vibration characteristics of the pile. Copyright © 2013 John Wiley & Sons, Ltd.