考虑横向惯性效应时黏弹性支承桩纵向振动特性研究EI北大核心CSCD

考虑土体三维波动效应及桩身横向惯性效应,建立了均质滞回阻尼土中黏弹性支承桩受稳态或瞬态纵向激振时的定解问题,并获得了严格桩土耦合条件下的解析解。首先,将桩底土层对桩及桩侧土层的作用简化为均布Vogit体,桩视为Rayleigh-Love杆,利用土体三维轴对称振动方程,土层边界条件,以及桩与桩侧土接触面上的纵向和径向位移连续条件,求解得到桩侧土作用在桩身的剪切复刚度。然后,结合桩底黏弹性支承条件,推导得到桩顶复阻抗函数的解析解。最后,采用参数分析方法,研究了横向惯性效应对单桩桩顶动力响应的影响规律及其与桩及土层参数的关系。结果表明:相对于不考虑横向惯性效应,计及横向惯性效应时单桩纵向振动特性的差异受桩及土共同的影响。     

考虑横向惯性效应时黏弹性支承桩纵向振动特性研究

考虑土体三维波动效应及桩身横向惯性效应,建立了均质滞回阻尼土中黏弹性支承桩受稳态或瞬态纵向激振时的定解问题,并获得了严格桩土耦合条件下的解析解。首先,将桩底土层对桩及桩侧土层的作用简化为均布Vogit体,桩视为Rayleigh-Love杆,利用土体三维轴对称振动方程,土层边界条件,以及桩与桩侧土接触面上的纵向和径向位移连续条件,求解得到桩侧土作用在桩身的剪切复刚度。然后,结合桩底黏弹性支承条件,推导得到桩顶复阻抗函数的解析解。最后,采用参数分析方法,研究了横向惯性效应对单桩桩顶动力响应的影响规律及其与桩及土层参数的关系。结果表明:相对于不考虑横向惯性效应,计及横向惯性效应时单桩纵向振动特性的差异受桩及土共同的影响。     

考虑土体径向位移时桩土耦合纵向振动特性及其应用

从三维轴对称土体模型出发,同时考虑土体竖向和径向位移,对完整端承桩在垂直谐和激振力作用下与土的耦合纵向振动特性进行了分析。假定桩为竖直弹性等截面体,土为线性粘弹性体,其材料阻尼为滞回阻尼。首先通过引入势函数对土体位移进行分解,从而将土体动力平衡方程解耦,求解得到了土体的振动模态形式,然后利用该解,以小应变条件下桩土接触面上力平衡和位移连续条件来考虑桩土耦合作用,求解桩的动力平衡方程,得到了桩的频域响应解析解、桩顶复刚度和速度导纳。利用所得解对土体动力反应特性和桩的纵向振动特性进行了无量纲参数分析,得到了许多新的结论。     

土与结构接触面弹塑性损伤模型用于单桩与地基相互作用分析

基于粗粒土与结构接触面弹塑性损伤静动力统一模型(称作EPDI模型)建立了可用于有限元分析的弹塑性损伤接触面单元。对接触面试验进行了模拟,采用不同的接触面本构模型及参数对单调和循环荷载作用下的单桩基础的侧摩阻力和桩顶位移进行了有限元分析。结果表明:包括剪应力应变关系和剪胀特性在内的接触面力学特性对桩土相互作用分析有重要影响,需要合理地加以描述。基于试验结果建立的弹塑性损伤接触面单元能够有效地用于土体与结构物相互作用分析,并能够合理地反映土与结构接触面的包括体应变及其与剪应变耦合特性在内的接触面主要静动力学特性。     

轴对称横观各向同性土体中桩的扭转振动响应研究

基于单相弹性土体的运动方程以及横观各向同性材料的本构关系,研究了轴对称条件下端承桩在横观各向同性土体中的耦合扭转振动响应问题.在柱坐标下推导得到横观各向同性土体受谐和扭转荷载作用的动力控制方程,并采用分离变量法求得了土体扭转振动位移形式解.依据桩土接触面上的衔接条件,求解了桩身的动力平衡方程,并在频域内得到了桩身转角、扭矩和桩顶复刚度的解析解.最后分析了横观各向同性土体的力学参数对动力响应的影响.结果表明,横观各向同性土体的力学参数对桩顶复刚度、桩身转角和扭矩沿深度方向的变化均有着显著影响.     

非饱和土中端承桩纵向振动问题简化解

基于单相流固结理论与Bishop有效应力原理,研究了单相流条件下非饱和土中端承桩的耦合纵向振动问题。建立了简化条件下非饱和土体的动力平衡方程,通过引入拉普拉斯变换和势函数对此方程进行解耦,并采用算子分解理论及分离变量法求得土体纵向振动位移形式解。依据桩土系统的边界和衔接条件,进而得到了桩顶动力响应的闭合形式解,并研究了主要参数对桩顶速度导纳和速度时域响应的影响。结果表明,桩长径比和桩土模量比对桩顶动力响应有着显著的影响,而吸力折减系数对其基本上没有影响。     

基于传递矩阵法的分层饱和土中单桩扭转动力阻抗

以分层饱和土中单桩扭转振动为研究对象,将桩周土体视为分数阶黏弹性饱和土,借助分数阶黏弹性本构模型和土体运动平衡方程、应力位移关系建立分层分数阶黏弹性饱和土层扭转振动微分方程。以两层分数阶黏弹性饱和土为例,讨论主要桩土力学参数对扭转动力阻抗影响。结果表明：下上层土体本构模型阶数比对扭转动力阻抗随频率变化曲线峰值影响较大,下上层土体剪切波速比、土层厚度比和桩土模量比对扭转动力阻抗的影响与频率有关,下上层土体液固耦合系数较小时,其对扭转动力阻抗的影响很小。     

考虑桩土非完全粘结及桩底土波动效应的浮承桩纵向振动特性研究

为合理考虑浮承桩纵向振动问题中桩端土作用及桩-土界面相对位移条件,同时引入动力Winkler模型和虚土桩模型,建立了一种适用性更广的浮承桩纵向振动特性研究方法。引入分离变量法对三维土体位移控制方程进行求解,结合土体表面及基岩处边界条件得到三维土体位移基本解;通过将动力Winkler模型相关参数考虑为桩-土界面边界条件在频域内解析求解了桩纵向振动特性,并将所得频域解析解拓展到时域,采用离散傅里叶逆变换方法（IFT）求解了桩顶速度时域响应;开展参数化分析探讨了桩-土界面非完全粘结条件及虚土桩参数对浮承桩动力响应的影响,计算结果表明：桩-土界面完全耦合假定会过高估计桩侧土对桩的约束作用,无法合理评估桩基的抗振性能,并会对桩基抗振防振设计及桩底反射信号识别产生不利影响;另外,针对浮承桩纵向振动问题,采用虚土桩模型描述其桩底土作用具有合理性和必要性。     

基于矩阵位移法的桩锚结构分析方法

采用将桩锚结构视为荷载作用-侧向弹簧支承的连续梁模型,支护桩为直立的弹性地基梁,主动土体转换为土压力,锚杆简化成为可逐步施加的弹簧支承,而被动土体则用侧向支承的土体弹簧替代.土体弹簧的刚度K是通过半无限大弹性空间内部水平荷载作用下的Mindlin 解来确定,这种方法降低了因深度加深而带来弹簧刚度的增长率,更加符合实际情况.针对这种弹性地基梁模型,提出了以矩阵分析为手段的计算方法,该法优点在于将桩锚视为桩-锚-土三者协同作用的支护结构,同时在计算过程中充分考虑了基坑分步开挖的施工过程对支护桩、锚杆以及被动土体的变形影响.通过实例分析表明:矩阵位移法为桩锚结构设计提供了一种合理、有效的计算方法.     

双向非均质黏性阻尼土中桩基扭转振动频域阻抗解答与分析

基于三维连续黏性阻尼介质理论和径向多圈层复刚度传递模型,综合考虑桩周土径向非均质效应和纵向成层性,建立双向非均质土体中桩基扭转振动简化分析模型。采用拉普拉斯变换和复刚度传递法求解得出土体位移形式解,进而利用桩-土耦合条件将该形式解耦合进桩身动力平衡方程中,并通过扭转阻抗传递法推导得出桩顶扭转阻抗解析解答。将该解退化并分别与均质土及径向非均质土中的解答进行对比验证其合理性。在此基础上,通过参数化分析探讨了桩周土施工扰动程度和扰动范围、扩颈及缩颈缺陷对桩顶扭转阻抗的影响规律,可为具体工程实践提供理论指导和参考作用。     

轴向荷载作用下非均匀地基中单桩及群桩分析

该文发展了一种非均匀地基中单桩及群桩分析方法。该方法将桩身离散成若干圆柱形和圆形单元,相应地也将与桩接触的土体界面离散成同样类型和数量的单元,分别建立桩单元和土体界面单元的应力与位移方程。建立桩身单元的位移应力方程时,采用压缩杆理论;建立土体界面单元方程时,采用层状材料基本解。然后,采用桩和土体界面上位移相容条件建立整体方程,计算垂直荷载作用下单桩及群桩的荷载和位移,并且给出桩-基础滑移的计算方法。最后进行了算例分析。由于采用了层状材料的基本解,该数值方法能处理力学参数沿深度方向任意变化的地基。     

A boundary element method for the static analysis of raft foundations on piles

This paper presents a Boundary Element Method formulation for the static analysis of piled rafts in which all the interactions between the plate, the pile and the soil are simultaneously considered. In this approach the soil is treated as an elastic linear homogeneous half space, the plate is assumed to be thin and both are represented by integral equations. Each pile is represented by a single element and the shear force along it is approximated by a second-degree polynomial. The pile-tip stress is assumed to be constant over the cross-section. The cap–soil interface is divided into triangular elements and the contact pressure is assumed to vary linearly across each element. The vertical displacement of each node in the plate and in the piles is represented by an integral equation so that a set of linear equations is obtained involving the tractions and displacements at all nodal points on all the interfaces. From these equations the nodal displacements and the overall stiffness of the system can be calculated. Numerical results are presented and they correspond closely to those obtained by other authors.     

考虑桩、土、垫层协同作用的刚性桩复合地基沉降计算方法

提出计算刚性桩复合地基沉降的一种新方法,该方法充分考虑桩、土、垫层协同作用。通过假定桩土界面摩阻力与相对位移为理想弹塑性关系;同一水平面上的桩间土沉降相同;桩端土符合Winkler地基模型,结合桩、土、垫层工作机理分析,建立了协同作用基本微分方程,进而得到了大面积群桩复合地基桩、桩间土沉降解析解。对两个9桩复合地基的分析显示,该方法和现场实测及有限元分析吻合较好。     

轮对运动状态对轮轨滚动接触应力的影响

分析计算了锥型踏面轮对沿轨道滚动接触时轮轨接触几何参数和不同运动状态下的轮轨之间的刚性蠕滑率。根据确定的轮轨接触几何参数和轮轨接触界面之间的蠕滑率,利用非Hertz滚动接触理论分析计算了锥型轮对和钢轨滚动接触斑作用力的分布。再利用弹性力学中Bossinesq-Cerruti力/位移计算公式并借助Gauss数值积分方法,确定了轮轨滚动接触时体内的弹性位移、应变和应力随轮对运动状态变化情况。数据结果为轮轨强度设计提供了重要的参考依据。     

循环温度作用下饱和黏土中摩擦型桩变形特性研究

能量桩兼具支承上部荷载与能量交换的双重功能,循环温度作用下端承型桩的承载性能、摩擦型桩的变形问题是两大主要问题;目前针对长期循环温度作用下饱和黏土中摩擦型桩变形特性与机理的研究仍相对较少。该文针对饱和黏土中的摩擦型桩,开展了长期循环温度作用下桩基热响应特性模型试验研究,实测了桩/土温度分布、温度引起的桩周土体孔隙水压力以及桩顶变形等发展规律,初步探讨了桩顶累积沉降的产生机理与变化规律。研究结果表明:单次温度循环过程中,桩顶位移变化率在制热时略小于制冷时,桩顶位移变化率的差值随着循环次数的增加而逐渐减小,从而累积沉降也逐渐趋于稳定;该文试验条件下,经过长期（20次）温度循环,摩擦型桩的桩顶累积沉降逐渐稳定在2%D（D为桩径）。     

Free vibration of semi-rigid connected Reddy-Bickford piles embedded in elastic soil

The literature on free vibration analysis of Bernoulli-Euler and Timoshenko piles embedded in elastic soil is plenty, but that of Reddy-Bickford piles partially embedded in elastic soil with/without axial force effect is fewer. The soil that the pile partially embedded in is idealized by Winkler model and is assumed to be two-layered. The pile part above the soil is called the first region and the parts embedded in the soil are called the second and the third region, respectively. It is assumed that the behaviour of the material is linear-elastic, that axial force along the pile length to be constant and the upper end of the pile that is semi-rigid supported against rotation is modelled by an elastic spring. The governing differential equations of motion of the rectangular pile in free vibration are derived using Hamilton’s principle and Winkler hypothesis. The terms are found directly from the solutions of the differential equations that describe the deformations of the cross-section according to the high-order theory. The models have six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments. Natural frequencies of the pile are calculated using transfer matrix and the secant method for non-trivial solution of linear homogeneous system of equations obtained due to values of axial forces acting on the pile, total and embedded lengths of the pile, the linear-elastic rotational restraining stiffness at the upper end of the pile and to the boundary conditions of the pile. Two different boundary conditions are considered in the study. For the first boundary condition, the pile’s end at the first region is semi-rigid connected and not restricted for horizontal displacement and the end at the third region is free and for the second boundary condition, the pile’s end at the first region is semi-rigid connected and restricted for horizontal displacement and the end at the third region is fixed supported. The calculated natural frequencies of semi-rigid connected Reddy-Bickford pile embedded in elastic soil are given in tables and compared with results of Timoshenko pile model.     

An elastostatic FEM/BEM analysis of vertically loaded raft and piled raft foundation

In this paper, a static analysis of vertically loaded raft and piled raft foundations in smooth and continuous contact with the supporting soil is presented. In this approach the finite element method (FEM) and the boundary element method (BEM) are coupled: the bending plate is assumed to have linear elastic properties and is modelled by FEM while the soil is considered as an elastic half-space in the BEM. The pile is represented by a single element and the shear force along the shaft is interpolated by a quadratic function. The plate–soil interface is divided into triangular boundary elements (soil) also called cells and finite elements (plate) and the subgrade reaction is linearly interpolated across each cell. The subgrade tractions are eliminated from the FEM and BEM algebraic systems of equations, resulting in the governing system of equations for plate–pile–soil interaction problems. Numerical results are presented and they are close to those resulting from much more elaborate analyses.     

考虑位移的土压力理论在支护桩受力分析中的应用

针对支护桩所受土反力与土体位移呈非线性关系的问题,通过引入梅国雄提出的考虑位移的土压力计算方法,将计算方法中的土压力代换单桩挠曲四阶微分方程中的土反力,得到一个四阶变系数非齐次非线性常微分方程;然后根据支护桩位于基坑底面上、下所处受力状态的差异和桩顶的初值条件,采用泰勒级数解法求出支护桩任意深度处的挠度解析解;再根据桩体的挠度计算出桩周土体的位移量,并得到桩周土反力的计算式;由此便可计算桩身任意深度以及该深度截面上任意点处的受力情况,使得问题的求解更简捷。最后还给出了计算实例来验证所采用的方法以及所推导出的公式的正确性。     

Finite–infinite element for dynamic analysis of axisymmetrically saturated composite foundations

The formulations of axisymmetrically infinite elements for dynamic analysis of vertical vibration problems in unbounded saturated composite foundations are presented. The theoretical basis as well as the implementation of the elements is discussed, and the element decay functions are derived using the analytical solutions of axially symmetric configurations. Using the proposed finite–infinite element method, the surface vertical displacements of air‐saturated soil (‘dry’ soil) and of water‐saturated soil with extremely low permeability subjected to a surface point excitation (called as the Lamb's problem) are calculated and the results agree very well with the existing theoretical solutions of single‐phase elastic media. As an application, the velocity admittances of a concrete block resting on cement mixing‐pile or gravel‐pile saturated composite foundations are calculated. The influence of soil permeability and pile rigidity on the dynamic response of the composite foundations is investigated. The method proposed by this paper is a simple and reliable numerical one that could be used to study axisymmetrically dynamic problems of layered saturated media and to get the mechanism of dynamic testing on single‐pile saturated composite foundations. Copyright © 2006 John Wiley & Sons, Ltd.     

饱和地基上含刚核弹性圆板的摇摆振动分析

基于饱和土弹性波动方程,研究了饱和地基上含刚核弹性圆板在摇摆谐和力矩作用下的振动特性。首先应用Hankel积分变换求解该饱和土波动方程,然后按混合边值条件建立起一组描述含刚核弹性圆板振动的对偶积分方程,并将其化为第二类Fredholm积分方程进行数值求解。此外,给出了含刚核弹性圆板在饱和地基上振动的阻抗函数随无量纲频率的变化曲线,并考察了土的渗透系数、弹性板含刚域的大小以及板的柔度等参数对阻抗函数的影响,得出了一些有意义的结论。