考虑桩周土竖向作用大直径楔形桩纵向振动特性

将桩土系统划分为数量足够多的微元段,相邻微元桩段接触面处的环形凸面与土的相互作用采用单个Voigt体模拟,求得Voigt体的弹簧和黏壶系数。结合相邻微元桩段接触面上的应力平衡条件和位移连续条件,得到修正的阻抗函数递推法,桩身采用Rayleigh杆考虑桩身的横向惯性效应。结合桩底的边界条件,运用拉普拉斯变换和修正的阻抗函数递推法求得了平面应变条件下成层土中考虑桩周土竖向作用时大直径楔形桩桩顶复阻抗的解析解。通过与已有解对比,研究了桩周土竖向作用对桩顶复刚度和桩顶在瞬态激振下的速度响应的影响,并在低频域内详细分析了桩周土的竖向作用与桩土系统参数对桩顶复刚度的影响的耦合作用。     

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.     

Torsional dynamic response of a pile embedded in layered soil based on the fictitious soil pile model

The torsional dynamic response of a pile embedded in layered soil is investigated while considering the influence of the pile end soil. The finite soil layers under the end of the pile are modeled as a fictitious soil pile that has the same cross-sectional area as the pile and is in perfect contact with the pile end. To allow for variations of the modulus or cross-sectional area of the pile and soil, the soil surrounding and below the pile is vertically decomposed into finite layers. Using the Laplace transform and impedance function transfer method, the analytical solution for the dynamic response of the pile head in the frequency domain is then obtained, and the relevant semi-analytical solution in the time domain is derived using the inverse Fourier transform and convolution theorem. The rationality and accuracy of the solution is verified by comparing the torsional dynamic behavior of the pile calculated with the fictitious soil pile with those based on a rigid support model and a viscoelastic support model. Finally, a parametric study is conducted to investigate the influence of the properties and thickness of the pile end soil on the torsional dynamic response of the pile.     

刚性承台下变截面柔性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对单桩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,推出了刚性承台下变截面柔性单桩与地基相互作用的系列近似解析算式,并通过算例,将承台下变截面柔性桩的情况与同体积的等截面柔性桩的情况进行了对比。对比表明：改变桩型能提高柔性单桩及单桩承台的承载力。将模型试验结果与计算结果进行了比较,验证了解析算式的可行性。     

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。     

A new analytical model to study the influence of weld on the vertical dynamic response of prestressed pipe pile

This investigation is concerned with the mathematical analysis of a viscoelastic prestressed pipe pile embedded in multilayered soil under vertical dynamic excitation. The pile surrounding soil is governed by the plane strain model, and the soil plug is assumed to be an additional mass connected to the pipe pile shaft by applying the distributed Voigt model. Meanwhile, the prestressed pipe pile is assumed to be a vertical, viscoelastic, and hollow cylinder governed by the one‐dimensional wave equation. Then, analytical solutions of the dynamic response of the pipe pile in the frequency domain are derived by means of the Laplace transform and impedance function transfer method. Subsequently, the corresponding quasi‐analytical solution in the time domain for the case of the prestressed pipe pile undergoing a vertical semi‐sinusoidal exciting force applied at the pile top is obtained by employing the inverse Fourier transform. Utilizing these solutions, selected results for the velocity admittance curve and the reflected wave curve are presented for different heights of the soil plug to examine the influence of weld properties on the vertical dynamic response of prestressed pipe pile. The reasonableness of the theoretical model is verified by comparing the calculated results based on the presented solutions with measured results. Copyright © 2017 John Wiley & Sons, Ltd.     

Development of a three-dimensional soil model for the dynamic analysis of end-bearing pile groups subjected to vertical loads

This paper presents a new analytical model for calculating the steady-state impedance of pile groups subjected to vertical dynamic loads. The derived solution allows considering effects of radially but also vertically propagating soil waves on the soil attenuation function, pile interaction factor, and pile group impedance. The proposed model provides accurate estimates of the soil stress field and of the response of the pile group in the low as well as in the high-frequency range, unlike earlier solutions based on the plane-strain model to describe the soil surrounding the piles, which ignores the vertical soil stress gradient. The latter assumption results in underestimating pile group impedance and overestimating radiation damping for frequencies lower than the cutoff frequencies of the system, which are explicitly captured with the proposed solution.     

轴对称径向非均质土中单桩纵向振动特性研究

为了分析径向非均质土中单桩纵向振动特性,基于复刚度传递径向多圈层并采用黏性阻尼模型描述桩周土材料阻尼,建立了三维轴对称径向成层非均质土体中桩基纵向振动简化分析模型。采用Laplace变换和复刚度传递方法,递推得出桩周土体与桩体界面处复刚度,进而利用桩-土完全耦合条件推导得出桩顶动力阻抗解析解,并将所得解退化到均质土情况,与已有解答进行比较验证其合理性。在此基础上对桩基纵向振动特性进行参数化分析,计算结果表明：桩周土体阻尼系数、桩底土阻尼因子仅对桩顶动力阻抗曲线振幅有较明显的影响,而桩底土刚度因子对桩顶动力阻抗曲线振幅及共振频率均有显著影响;桩周土软（硬）化程度越高（低）,桩顶动力阻抗曲线振幅越大（小）;桩周土软（硬）化范围越大,桩顶动力阻抗曲线振幅水平越高（低）;但桩周土软（硬）化程度、软（硬）化范围对桩顶动力阻抗曲线共振频率影响则可忽略。     

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。     

Vertical impedance of an end‐bearing pile in viscoelastic soil

This paper presents a new method to derive the analytical solution for the vertical impedance of an end‐bearing pile in viscoelastic soil. The soil is assumed as a homogeneous and isotropic layer, and the pile is considered as a one‐dimensional Euler rod. Considering both the vertical and radial displacements of soil and soil–pile coupled vibration, the governing equations of the soil and pile are established. The volumetric strain of soil is obtained by transformation on the equations of soil and variable separation method. Then the vertical and radial displacements of soil are obtained accordingly. The displacement response and impedance function of pile are derived based on the continuity assumption of the displacement and stress between the pile and soil. The solution is verified by being compared with an existing solution obtained by introducing potential functions. Furthermore, a comparison with two other simplified solutions is conducted. Numerical examples are presented to analyze the vibration characteristics of the pile. Copyright © 2014 John Wiley & Sons, Ltd.     

按桩的割线刚度确定深厚覆盖土层中普通桩有效桩长

在提出的基桩有效桩长定义基础上,提出了桩的割线刚度控制法来确定有效桩长,并采用线弹塑性荷载传递函数,将其应用于确定深厚覆盖土层中普通桩有效桩长。分析了桩土刚度比K,桩径D,桩顶沉降量So,桩侧土极限位移Um,桩端土弹性模量与桩周土弹性模量比值Ko及土层泊松比μ对普通桩有效桩长的影响,其结果表明,除Ko和μ外,其余均有一定或较大地影响。为了将理论分析应用到工程桩中,对参数的取值进行了分析。     

Dynamic characteristics of a large‐diameter pile in saturated soil and its application

This study theoretically investigates the dynamic response of an end‐bearing pile embedded in saturated soil considering the transverse inertial effect of the pile. The saturated soil surrounding the pile is described by Biot poroelastic theory, and the pile is represented by a Rayleigh‐Love rod because both the vertical and radial displacements at the soil‐pile interface are considered. The potential function decomposition method and variable separation method are introduced to solve the governing equations of the soil, in which the vertical and radial displacement components are coupled. The governing equation of the pile is solved using the continuity conditions at the pile‐soil interface. Next, the velocity admittance in the frequency domain and the velocity response in the time domain at the pile top are presented based on the Laplace transform and inverse Fourier transform, respectively. Subsequently, the reduced solution is compared with a 1‐dimensional model solution to verify the validity, and the influences of the slenderness ratio of the pile on the transverse inertial effect of the pile are analyzed. Moreover, Poisson ratio, the slenderness ratio of the pile, and the pile‐soil modulus ratio are studied. Finally, the theoretical and measured curves in the engineering project are compared, and the results demonstrate the good application prospects of the solution presented in this article.     

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.     

群桩与筏板的竖向动力相互作用研究

对沿深度离散形成一系列均质的土层,应用传递矩阵法推导出单桩的动力阻抗。借助推求的桩-桩动力相互作用因子,研究承台板与群桩的竖向动力相互作用,通常假设承台板是刚性的,并充分考虑了承台板具有一定的刚度、可以变形的柔性承台板,提出承台板-群桩动力相互作用模型,然后推出其动力相互作用方程。通过算例说明了承台板的刚度对承台板的动力作用是有影响的。研究结果表明,振动频率越低,柔性承台板的振幅与刚性承台板的振幅相差越大;随着频率的增大,二者差别也减小,并逐渐趋于相等。     

Vertical vibration of a large-diameter pipe pile considering the radial inhomogeneity of soil caused by the construction disturbance effect

This paper presents an analytical solution for the vertical vibration of a large-diameter pipe pile considering the radial inhomogeneity of both the outer and inner soil caused by the construction disturbance effect. The radial inhomogeneity of the soil is simulated by gradually varying the soil parameters in the radial direction. The complex impedance at the pile head is obtained by introducing the variable separation method and impedance function transfer method. The proposed solution is compared with existing solutions to verify its reliability. Parametric studies are conducted to investigate the vertical vibration characteristics of the pile.     

横观各向同性地基中管桩扭转振动响应解析解

考虑地基沉积过程中产生的竖向和水平向力学性质的差异,对横观各向同性地基中管桩扭转振动频域响应进行了理论研究。基于横观各向同性材料的本构关系以及桩-土耦合扭转振动,建立了桩土系统定解问题,通过Laplace变换和分离变量法求得了桩周土和桩芯土扭转振动位移形式解。通过桩-土接触面的连续条件,求得了管桩扭转频域响应解析解,并得到了桩顶复动刚度和速度导纳的表达式。将所得解退化到横观各向同性地基中实心桩解以及均匀地基中管桩解,并与已有文献进行了对比,验证了解的合理性。通过数值算例,分析了桩周土和桩芯土的横观各向同性力学参数对桩顶扭转复刚度及速度导纳的影响。     

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.     

Influence of pile installation on adjacent structures

Pile installation leads to significant changes in the main state variables of the surrounding soil. In addition, the installation process may have an influence on adjacent or intersecting structures such as pile grillages. In this paper, three‐dimensional numerical analyses are presented to investigate the effects of pile driving with open or closed cross‐sections on the surrounding soil and on adjacent structures. Two different installation methods are used: quasi‐static pile jacking and vibratory pile driving. The numerical models are evaluated and verified using data from field tests performed in situ during the construction of the quay wall at the container terminal CT4 in Bremerhaven. Two case studies are presented to characterize the main influence factors for additional loading on adjacent structures due to pile installation. Finally, a parametric study is conducted showing the influence of the installation method, pile cross‐section and distance of a pile from an existing structure on the additional loading for this structure. Copyright © 2009 John Wiley & Sons, Ltd.     

刚性桩复合地基的主动土压力分析

桩足够长、桩间距不大于6倍桩径的刚性桩复合地基中,在桩间土内部的剪切力和桩土间摩擦力共同作用下,桩顶段桩间土压力仅在一定深度范围内有所增加,且随深度迅速衰减,而桩顶段桩身轴力随深度增加。基于刚性桩复合地基的这一特点,紧邻刚性桩复合地基开挖基坑且基坑底高于刚性桩桩底时,得出刚性桩复合地基上的附加荷载作用在支护结构上的主动土压力可以简化为倒三角形,最大主动土压力作用在刚性桩桩顶平面与支护结构相交处,随深度增加,主动土压力迅速衰减至0。实践表明该计算方法比较符合工程实际。     

上海软土地区打入桩基长期沉降性状研究

通过对上海25栋高层建筑打入桩基长期沉降观测资料的对比分析,研究压缩层的组成与桩周土特性对打入桩基长期沉降性状的影响,指出桩周浅部厚砂土层对打入桩基长期沉降性状的影响同压缩层有密切的关系。当压缩层以准砂土为主（准砂土比 ? > 75 %）时,桩周厚砂土层对降低桩基沉降及改善沉降性状有明显作用;当准砂土比? < 50 %（或可塑性黏土比?3 > 50 %）时,桩周厚砂土层的上述作用将消失。即使在桩周存在厚砂土层时,压缩层组成对桩基沉降性状的基本特征起主导作用仍然是具有普遍意义的概念。在浅部厚砂土层中得到的上述研究结果,实际上同挤土桩施工的复杂作用有关。