层状半空间中单桩对任意入射地震波的响应

本文以任意入射地震波作为初始运动输入，采用层状半空间中显式表达形式的动力Ｇｒｅｅｎ函数形成桩－土相互作用分析所需的土介质柔度矩阵，用梁单元模拟桩的运动，在文献〔５〕的基础上，建立了层状半空间中单桩对任意入射地震波响应的实用计算模型，研究了层状半空间中单桩对不同角度入射ＳＨ波、ＳＶ波和Ｐ波的动力响应，得到了一些新的结果。     

分析层状半空间对入射地震波响应的改进模型

采用层内位移线性近似的薄层元及基岩半空间刚度的Ｔａｙｌｏｒ级数展开技术，利用基岩地震动三分量反算入射波振幅，建立了层状半空间场地地震波响应分析的一种改进模型，分析了层状半空间对倾斜入射ＳＨ，ＳＶ和Ｐ波的动力响应．结果表明，本文模型不仅具有较高精度，而且非常便于数值处理和计算机编程     

横观各向同性层状场地对入射SH波的响应分析

本文采用横观各向同性层状弹性模型模拟半空间之上的层状了，推导了在ＳＨ波入射时这种场地土的动力刚度矩阵及基岩输入运动时场地呼应的计算公式，算例表明，横观各向同性层状场地与各向同性层状了频谱特性有明显的区别，应当引起重视。     

层状地基中单桩扭转振动特性分析

采用积分变换和Muki的方法求解了层状地基中单桩的扭转振动问题.在分析过程中,首先对基本控制方程进行Hankel变换,建立了单层地基的初参数解答和刚度矩阵,得到层状地基的递推矩阵;然后利用递推矩阵、边界条件和桩-土变形协调条件建立了层状地基中单桩扭转振动问题的基本积分方程并进行数值求解.文末数值算例给出了退化的层状地基中刚性单桩的扭转变形,其结果与已有经典解答吻合良好.同时,并研究了两层地基中单桩的扭转动力响应,分析了桩-土参数对动力响应的影响,所得结论对工程实践和桩基扭转波检测有一定的指导意义.     

单桩横向非线性惯性响应简化分析计算方法

根据已建立的地基土-单桩系统横向非线性动力相互作用的简化分析模型,在动力Winkler模型的基础上,研究单桩横向非线性惯性响应。简化模型中．地基土对桩轴的横向非线性作用力．由非线性迟滞退化弹簧模拟,地基土在运动过程中的能量耗散,由与弹簧并联的粘壶模拟。利用有限元空间离散技术和Newmark-β法,讨论了横向惯性荷载作用下．单桩运动方程在时域中的求解方法。计算结果表明,该模型能够反映单桩非线性惯性响应的主要特征。能够揭示各种非线性因素,如：桩周土的迟滞效应、退化、屈服,以及土-桩界面的分离等,对单桩惯性响应的影响。计算结果与试验结果相当吻合。     

垂直受荷群桩在半空间饱和土中的稳态反应

研究了均质半空间饱和土中群桩在垂直稳态荷载作用下的动力反应问题。半空间饱和土采用Biot提出的三维波动原理。将桩看作是一维的弹性杆单元。利用圆形简谐载荷作用下的Biot固结方程的基本解和桩土之间的变形协调条件得到饱和土中群桩的第二类Fredholm积分方程,群桩的动力阻抗采用动力相互作用因子的方法。分析桩距等参数对群桩阻抗、轴力和孔压等的影响。本文的方法可以用于计算层状饱和土中群桩的动力反应问题。     

任意圈层径向非均质土中桩的纵向振动特性

研究三维轴对称条件下径向非均质土中桩的纵向振动. 首先将桩周土体沿径向分为任意圈层来考虑土体的径向非均质性,每个圈层土体均质; 然后结合边界条件和相邻圈层土体之间接触面上位移和应力连续条件,对任意圈层土体动力平衡方程由外而内逐层求解,进而利用桩-土完全耦合条件求解桩动力平衡方程,得到桩顶的频域响应解析解和时域响应半解析解; 最后通过对土体主要控制参数的研究,得出了土体径向非均匀性对桩-土动力响应的影响.      

层状土中群桩沉降分析

本文提出一个半解析的方法分析单桩和群桩基础的沉降，地基土可以是任意层状的，并且可以是有限深的，单桩沉降采用荷载传递法计算。群桩中桩－桩相互作用采用近解析法计算。通过与其它数值分析方法结果的对比，表明本文提出的方法与更严密的计算方法有很好的一致性，能大大减少计算量，可分析桩数较多的群桩基础。     

层状饱和土中管桩瞬态扭转振动研究

对瞬态扭转激振荷载作用下层状饱和土中端承管桩的动力响应问题进行了研究。首先借助Laplace变换和分离变量法解耦Biot波动方程,土层层间动力相互作用简化为分布式线弹簧,并结合桩-土交界面上的应力和位移连续边界条件,导出了各节段管桩在Laplace变换域内扭转动力响应的解析表达式;然后,根据阻抗函数传递原理,并对得到的解进行Laplace数值逆变换,最终获得了瞬态扭转荷载作用下层状饱和土中管桩动力响应的时域解答。研究表明：桩顶作用三角形或半正弦荷载情况下,最大桩顶扭转角产生时刻落后于最大荷载对应时刻;且当桩周土渗透系数处于相对较高和较低范围内,桩顶转角几乎保持不变,在中间范围内则随渗透系数增大而增大;硬夹层的存在将使桩身上部扭矩增大,下部扭矩减小,软夹层下规律相反。     

各向异性对半圆形河谷散射影响的数值分析

半圆形河谷场地可构造为包含河谷的广义子结构和具有规则边界的开挖场地两部分，基于土-结构相互作用SSI原理，建立子结构控制方程。利用比例边界有限元SBFEM求解开挖场地动刚度，解析求解各向异性介质自由场qP波波动，将两者代入控制方程，可求得广义结构的动力响应。与文献中各向同性半空间中半圆形河谷在P波入射下的位移结果对比，验证了方法的精度和有效性。进一步分析了椭圆各向异性和非椭圆各向异性对半圆形河谷在qP波入射下位移分布的影响。数值算例显示，介质的各向异性改变了半圆形河谷散射位移的空间分布，增大了水平向位移的峰值；同时，介质的各向异性加剧了入射角对散射波场位移分布的影响。     

层状弹性半空间轴对称动力问题的奇异解

本文利用Laplace-Hankel联合变换及传播矩阵技术导出了任意层数的层状弹性半空间轴对称动力问题时域奇异解的一般解析表达式,并给出了奇异解数值化实施的计算方法。文末的实例计算表明了本文给出解答的正确性以及数值化实施的可靠性,从而为进一步用边界元法直接解决由于层状介质而引起的非匀质动力问题开拓了一条潜在的途径。     

横观各向同性层状场地中的单桩横向动力阻抗函数

本文采用横观各向同性层状弹性模型，模拟半空间上的层状场地，用阻尼器模拟透射边界代替半空间以吸收能量。利用薄层元素法和于结构法，并利用在这种边界下受水平简谐荷载作用下的格林函数，推导了这种场地中竖直单桩在水平—摇摆简谐荷载作用下的横向动力阻抗函数，并用实例计算了不同横观各向同性性质场地下的动力阻抗函数，并由此分析了场地的横观各向同性性质的强弱对单桩的横向动力阻抗函数所将产生的影响。计算表明：弱横观各向同性场地对阻抗函数的影响很小，以至可以忽略这种影响；而强横观各向同性场地对阻抗函数的影响较大，必须考虑其影响。另外，桩头约束的存在与否，对单桩的横向阻抗函数值也有较大的影响，桩头有约束的阻抗函数值要明显大于无约束的阻抗函数值。     

Analysis of scattering waves in an elastic layered medium by means of the complete eigenfunction expansion form of the Green’s function

A scattering problem due to an object and a plane incident wave in an elastic layered half space is presented in this paper. The complete eigenfunction expansion form of the Green’s function developed by the author and the boundary integral equation method are introduced into the analysis. First, the complete eigenfunction expansion form of the Green’s function is investigated for its application to the scattering problem. A comprehensive explanation is also given for the fact that the complex Rayleigh wave modes exhibit standing waves. Next, a method for the analysis of scattering waves by means of the Green’s function is presented. The advantage of the present method is that the formulation itself is independent of the number of layers and the scattering waves can be decomposed into the modes for the spectra defined for the layered medium. Several numerical calculations are performed to examine the efficiency of the present method as well as the properties of the scattering waves. According to the numerical results, the complete eigenfunction expansion form of the Green’s function provides accurate values for application to a boundary element analysis. The spectral structure and radiation patterns of the scattering wave are presented and investigated. The differences in directionality can be found from the radiation patterns of the scattering waves decomposed into the modes for the spectra.     

Scattering of elastic waves by three-dimensional surface topographies

Diffraction of plane harmonic waves by three-dimensional surface irregularities is investigated through the use of an indirect boundary integral equation method. The irregularity of an arbitrary shape is embedded in an elastic half-space and subjected to incident P, SV, SH, and Rayleigh waves. The material of the half-space is assumed to be linear, weakly anelastic, homogeneous and isotropic.

The accuracy of the method is demonstrated through comparison of the results with existing axisymmetric solutions. Several numerical examples for non-axisymmetric canyons are presented. The resulting amplification patterns exhibit strong sensitivity on type and angle of the incident waves and on the location of the observation point. Systematic comparisons of three-dimensional and corresponding two-dimensional models demonstrate similarity of the amplification pattern. The amplification is larger in some three-dimensional models than in two-dimensional ones. Strong coupling between SH and P-SV modes is observed for off-azimuthal incident waves. This phenomenon is specially pronounced for incident SH waves and it is intrinsic to three-dimensional scattering.     

Application of the theory of generalized rays to diffractions of transient waves by a cylinder

The theory of generalized rays was developed to analyze transient waves in layered media where incident circular or spherical waves are reflected and refracted by plane boundaries. The theory has been recently extended to analyze the diffraction of transient waves by a spherical or a cylindrical boundary. In this paper, the generalized ray integrals, which represent the fourier transformed diffracted waves, are formulated for the diffraction of an incident spherical pulse by a circular cylinder. The ray integral involves a double integration with respect to two variables of wave slowness. Through a simultaneous transformation of variables, the inverse Fourier transform of these double integrals are completed by applying the Cagniard method.     

Diffraction of Love waves by a stress-free crack of finite width in the plane interface of a layered composite

A rigorous theory of the diffraction of Love waves by a stress-free crack of finite width in the interface of a layered composite is presented. The incident wave is taken to be either a bulk wave or a Love-wave mode. The resulting boundary-value problem for the unknown jump in the particle displacement across the crack is solved by employing the integral equation method. The unknown quantity is expanded in terms of a complete sequence of expansion functions in which each separate term satisfies the edge condition. This leads to an infinite system of linear, algebraic equations for the coefficients of the expansion functions. This system is solved numerically. The scattering matrix of the crack, which relates the amplitudes of the outgoing waves to the amplitudes of the incident waves, is computed. Several reciprocity and power-flow relations are obtained. Numerical results are presented for a range of material constants and geometrical parameters.     

流固耦合地震波动问题的显式谱元模拟方法

流固耦合地震波动问题主要研究由流体和固体构成的复杂系统中地震波传播特性及其规律. 传统模拟方法中一般以声波方程、弹性波方程的数值解分别描述理想流体和弹性固体中的波动, 并实时地处理两种不同性质介质之间的相互耦合作用, 数值格式复杂且限制数值模拟精度与计算效率. 本文采用谱元法结合多次透射公式人工边界条件实现了一种流固耦合地震波动问题的高阶显式数值计算方法. 该方法利用了流固耦合问题统一计算框架,可将饱和多孔介质的Biot波动方程分别退化为理想流体的声波方程和弹性固体的弹性波方程. 通过P波垂直入射的水平成层理想流体-饱和多孔介质-弹性固体场地模型、P波斜入射的不规则层状界面以及任意形状界面的理想流体-饱和多孔介质-弹性固体场地模型等三个算例, 与传递函数法解析解以及集中质量有限元法计算结果进行对比分析, 证明了本文方法的正确性与有效性. 数值模拟结果表明, 本文方法相较传统有限元法可以少得多的节点数量获得更高的数值精度, 并且在较宽的频率范围内都能可靠地模拟出流固耦合系统的动力响应, 充分体现出本文方法兼顾高精度、计算效率和复杂场地建模灵活的特点.      

Numerical analysis of the isolation of the vibration due to Rayleigh waves by using pile rows in the poroelastic medium

The isolation of the vibration due to harmonic Rayleigh waves using pile rows embedded in a saturated poroelastic half-space is investigated in this study. Based on Biot’s theory and the potential function method, the free field solution for Rayleigh waves along the surface of the poroelastic half-space is derived first. The fundamental solution for a harmonic circular patch load applied in the poroelastic half-space are obtained in terms of Biot’s theory and the integral transform method. Using Muki’s method and the fundamental solution for the circular patch load as well as the Rayleigh waves solution for the poroelastic half-space, the second kind of Fredholm integral equations in the frequency domain for pile rows are derived. Numerical solution of the integral equations yields the dynamic response of the pile–soil system to incident Rayleigh waves. Influences of various parameters on the vibration isolation effect of piles rows are investigated numerically. Numerical results suggest that for the same vibration source, the same pile rows will produce a better vibration isolation effect for the poroelastic medium than for a single phase elastic medium. Also, stiffer piles tend to have better vibration isolation effect than flexible piles. Moreover, the pile length and the spacing between neighboring piles in each pile row have significant influence on the vibration isolation effect of pile rows.     

Scattering of monochromatic elastic waves on a planar crack of arbitrary shape

Scattering of monochromatic elastic waves on an isolated planar crack of arbitrary shape is considered. The 2D-integral equation for the crack opening vector is discretized by Gaussian approximating functions. For such functions, the elements of the matrix of the discretized problem have forms of standard one-dimensional integrals that can be tabulated. For regular grids of approximating nodes, the matrix of the discretized problem has the Toeplitz structure, and the corresponding matrix–vector products can be calculated by the fast Fourier transform technique. The latter strongly accelerates the process of iterative solution of the discretized problem. Examples of calculations of crack opening vectors, dynamic stress-intensity factors, and differential cross-sections of circular (penny-shaped) and non-circular cracks for various incident wave fields are presented. For a penny-shaped crack and longitudinal incident waves normal to the crack plane, an efficient semi-analytical method of the solution of the scattering problem is developed. The results of both methods are compared in a wide frequency region of the incident field.