非均匀饱和半空间的Lamb问题

基于Biot多孔介质波动理论,建立孔隙率、密度、剪切模量和渗透系数相互耦合且同时沿深度变化的非均匀饱和半空间模型,引入量化的非均匀梯度表征地基非均匀程度。在柱坐标系下构建以土骨架位移和孔隙压力为基本未知量的三维动力控制方程,采用算子运算和Hankel积分变换求解控制方程,推导出简谐集中力作用下半空间地基振动响应的积分解。将所得结果分别退化到均匀饱和半空间和弹性半空间与经典Lamb解做了对比,验证了结果的正确性。利用已有研究结论,给出孔隙率、密度、剪切模量和渗透系数之间的耦合关系式,代入推导结果进行数值计算。分别对水饱和地基和气饱和（干土）地基的动力响应进行分析,给出两类地基在动力作用下的振动位移和孔隙压力分布,并对非均匀性的影响作出分析。结果表明：4参数沿地基深度耦连变化对地基的动力响应产生一定程度影响,振动位移和孔隙压力在地层中的衰减速度由此加快。由于水的黏滞性远大于气体,所以水饱和地基中的振动衰减更快。非均匀程度越高,耦合效应的影响越明显。     

移动荷载作用下非均匀地基的动力响应分析

基于线弹性动力学理论,结合坐标变换,建立了移动荷载作用下非均匀弹性半平面地基的动力控制方程,利用半解析法研究了移动荷载作用下二维非均匀地基的动力响应问题。采用傅里叶（Fourier）级数展开,假设了响应函数的级数形式,通过理论推导获得了剪切模量随深度任意变化的非均匀地基在移动荷载作用下各物理量的解析表达式。考虑土体的剪切模量沿厚度方向按幂函数梯度变化,通过数值算例分析并讨论了地基非均匀参数、荷载移动速度以及地基表面的剪切模量等对地基力学响应的影响规律,并与均质地基的计算结果进行了比较。数值结果表明：地基中各点的竖向位移随着土体表面剪切模量和表征土体非均匀性的梯度因子的增大而减小,随着荷载移动速度的增大而增大。在移动荷载作用下,非均匀地基与均匀地基的动力响应有着显著的区别。     

层状地基中瑞利波随深度的衰减特性

层状地基中瑞利波（Rayleigh wave）的传播规律以及随深度的衰减规律是工程环境微振动分析与控制研究的关键问题之一。采用解析法（矩阵传递法）分析了层状地基中瑞利波弥散曲线,并在此基础上研究了各种频率下不同类型土层（上软下硬、软夹层、硬夹层）中瑞利波位移随深度衰减规律,通过与弹性半空间解的对比发现,瑞利波位移随深度的衰减规律与频率、土层分布密切相关：频率越高,传播深度越浅;特殊土层（软夹层、硬夹层）的存在会局部显著地改变其衰减规律,并且位移峰值的分布受到频率和土层分布的共同影响。最后,将该方法用于分析上海光源工程地基条件下瑞利波随深度的衰减规律,并与现场深孔微振动测试数据进行了比较。结果证明,与弹性半空间解相比,层状地基中瑞利波随深度的衰减规律可以更为准确地反映真实条件下瑞利波随深度的衰减规律。     

地基土中道路交通振动的衰减特性测试分析

通过对道路交通荷载下50m和80m深孔的现场振动测试,在时域和频域上分析了有车工况与无车工况下场地孔中位移随深度的衰减规律.结果表明:峰值频率随深度增大而逐步减小,在40m左右深度,峰值衰减因子接近0.2,振动衰减已很明显;与弹性半空间瑞利波的衰减规律对比发现,水平向位移衰减较弹性半空间瑞利波衰减慢,但随着深度增大,衰减因子逐渐接近弹性半空间的瑞利波衰减曲线;垂直向位移衰减因子随着深度逐步减小,且比弹性半空间瑞利波衰减得快.     

饱和冻土中弹性波的传播特性

用混合物连续介质理论,考虑了土颗粒骨架、冰、水三相介质,选取土颗粒位移、孔隙水位移、孔隙水压和孔隙冰压为基本变量,采用Bishop有效应力原理,建立了饱和冻土多孔介质的弹性波弥散方程。经理论推导,给出了饱和冻土中弹性波的传播速度及衰减的解析表达式。通过数值算例,探讨了饱和冻土中两种压缩波（Pl波和P2波）及剪切波（S波）的波速和衰减与频率和孔隙率、含冰量等土参数的关系。通过参数分析研究了饱和冻土中3种体波的传播特性。     

条形荷载作用下梯度饱和土的动力响应分析

根据Biot波动理论,研究了条形均布荷载作用下非均匀饱和土地基的动力响应问题。利用Fourier积分变换,通过Helmholtz矢量分解原理,建立了饱和土层在动荷载作用下的回传射线矩阵法计算列式,考虑饱和土的物理力学性质沿深度方向按幂函数连续变化,采用数值Fourier逆变换获得了饱和土地基的位移、应力和孔隙压力等物理量的数值解。分析讨论了材料非均匀性对饱和土介质动力特性的影响。结果表明,非均匀饱和土的动力行为与均匀饱和土有着明显的不同,当土体的非均匀程度越高,条形荷载中点下流体压力和应力幅值越大,而位移、流体压力以及应力等物理量在水平方向的振动频率均随着土体非均匀变化程度的增强而增大。     

饱和多孔介质表面透水性对表面波传播特性影响薄层分析法

饱和半无限体表面透水性会影响表面波（瑞利波和斯通利波）存在及其传播特性。在表面透水情况下,只有瑞利波存在,而在不透水情况,不仅有瑞利波而且还有斯通利波。表面波在工程勘探及声波测试中扮演很重要角色,因此,有必要研究表面透水性对表面波传播特性的影响。采用薄层法,将表面波频率方程根的搜索问题转换成求特征值问题。根据表面波沿深度衰减特性,从一组计算的特征值及特征向量中筛选出与表面波对应特征值、特征向量,由特征值得到表面波频率特性（频散和衰减特性）,由特征向量得到孔隙压力、骨架位移随深度变化,进而分析在表面不透水情况下瑞利波和斯通利波影响深度及程度。     

饱和多孔热弹性介质中Rayleigh波传播特性分析

基于多孔介质理论和广义的热弹性模型,研究了饱和多孔热弹性介质中Rayleigh波(R波)的传播特性。以考虑流-固耦合的饱和多孔介质波动方程和连续性方程及考虑热-弹耦合的广义热弹性基本方程出发,建立了饱和多孔介质的热-流-固耦合弹性波动模型。通过引入势函数并结合自由透水及绝热的边界条件,经过理论推导最终给出了饱和多孔热弹性介质中R波的弥散特征方程。利用数值算例分析了孔隙率、渗透系数、热膨胀系数、初始温度和松弛时间等热物理参数对R波的波速和特征衰减的影响。结果表明:孔隙率的增加将引起R波的波速下降,但使得R波的特征衰减反而增大;R波的波速随着渗透系数的增大先不变,再急剧增大,最后趋于稳定,其特征衰减随着渗透系数的增加先增大后减小,最后趋于稳定;热膨胀系数的增大将引起R波波速的增大,但对其特征衰减的影响较小;初始温度的增加导致R波波速的小幅上升,而对其特征衰减影响不大;松弛时间对R波波速和特征衰减几乎无影响。     

非均匀地基与均匀地基解答之间的相似关系：弹性波速

考虑物理力学特性沿深度连续变化的非均匀地基,研究了非均匀弹性体波相速度和群速度与相应均匀弹性地基解答之间的转换关系。首先,基于弹性动力学基本方程,获得了任意非均匀变化的地基中平面弹性体波相速度以及群速度的解析表达式;与均匀地基弹性波相速度的经典解答进行了比较,发现可将非均匀地基的解答用均匀地基解答线性表示,从而获得了两种解答之间的相似转换关系;最后,作为数值算例,考虑材料特性沿厚度按幂律连续变化的非均匀地基,分析了地基非均匀程度、泊松比以及相位角等对相似转换系数的影响。研究表明,借助于均匀地基中弹性波速的经典解答,可将非均匀地基中波速的求解转化为对相似转换系数的计算,从而使得求解过程得以简化。     

竖向简谐荷载下二维层状饱和地基的解析层元解

基于Biot固结理论,运用解析层元方法求解竖向简谐荷载作用下二维层状饱和地基的动力响应问题。从直角坐标平面应变问题控制方程出发,通过Fourier-Laplace变换将偏微分方程组转化为常微分方程组,求解得到单层饱和地基的解析层元。结合层间连续条件和边界条件,组装得到多层饱和地基的总刚度矩阵方程,进而求得变换域内的解。借助Fourier-Laplace逆变换的数值积分方法,获得平面应变动力问题在物理域内的解,编制了相应的计算程序,其计算结果与已有文献结果吻合较好。通过算例分析了荷载圆频率、荷载作用深度及地基成层性对地基竖向位移的影响。计算结果表明：随荷载圆频率的增大,地基竖向位移先增加后减小;地基竖向位移在荷载作用点处呈现波峰,且受表层土性的影响较大。     

Propagation of Rayleigh waves in fluid‐saturated non‐homogeneous soils with the graded solid skeleton distribution

The propagation characteristic of Rayleigh waves in a fluid‐saturated non‐homogeneous poroelastic half‐plane is addressed. Based on Biot's theory for fluid‐saturated media, which takes the inertia, fluid viscosity, mechanical coupling, compressibility of solid grains, and fluid into account, the dispersion equations of Rayleigh waves in fluid‐saturated non‐homogeneous soils/rocks are established. By considering the shear modulus of solid skeleton variation with depth exponentially, a small parameter, which reflects the relative change of shear modulus, is introduced. The asymptotic solution of the dispersion equation expressing the relationship between the phase velocity and wave number is obtained by using the perturbation method. In order to analyze the effects of non‐homogeneity on the propagation characteristic of Rayleigh waves, the variation of the phase velocity with the wave number is presented graphically and discussed through numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

饱和冻土中弹性体波传播特性影响参数研究

基于Leclaire对饱和双相孔隙弹性介质Biot模型的扩展,研究含有两种不同固相组分的三相多孔弹性介质中体波的传播特性。以饱和冻土为例,分析了各相体积分数、颗粒形状,接触参数等因素对波动方程中惯性参数、黏性参数、刚度参数的影响;对该三相介质模型进行了退化,分析了孔隙中只含液态水或固态冰时体波的特性;以饱和冻土为例,通过数值计算,探讨了饱和冻土中体波的相速度和衰减系数与胶结参数、接触参数、频率、饱和度、孔隙率等参数的关系。结果表明：与一般的饱和土不同,饱和冻土中存在5种体波,即3种纵波和2种横波;5种体波均具有弥散性和衰减性,且P1波、S1波弥散性和衰减性远小于P2、P3、S2波;胶结参数、饱和度、孔隙率对5种体波的传播特性影响显著,接触参数对传播特性影响较小。     

非饱和土中Rayleigh波的传播特性分析

基于对非饱和多孔介质的研究成果,考虑孔隙中液相和气相的相互影响,研究了非饱和土地基中Rayleigh波的传播特性。通过非饱和土中固相、液相和气相的质量平衡方程、动量平衡方程和非饱和土有效应力原理,建立了问题的弹性波动方程。通过引入势函数及考虑自由透水（透气）的边界条件,经过理论推导给出了非饱和土中Rayleigh波的弥散特征方程。通过数值算例分析了Rayleigh波的波速和衰减系数随饱和度、频率和固有渗透系数等因素的变化规律。结果表明：不同饱和度下波速随频率和固有渗透系数的变化均是先不变,然后小幅下降,再急剧增加,最后趋于一致;衰减系数在不同饱和度下随频率的增大而增大,随固有渗透系数的增大而先增大后减小。     

THE SETTLEMENT OF A RIGID CIRCULAR FOUNDATION RESTING ON A HALF-SPACE EXHIBITING A NEAR SURFACE ELASTIC NON-HOMOGENEITY

The present paper examines the elastostatic problem pertaining to the axisymmetric loading of a rigid circular foundation resting on the surface of a non-homogeneous elastic half-space. The non-homogeneity corresponds to a depth variation in the linear elastic shear modulus according to the exponential form G(z)=G₁+G₂e^-ζz. The equations of elasticity governing this type of non-homogeneity are solved by employing a Hankel transform technique. The mixed boundary value problem associated with the indentation of the half-space by the rigid circular foundation is reduced to a Fredholm integral equation which is solved via a numerical technique. The numerical results presented in the paper illustrate the influence of the near-surface elastic non-homogeneity on the settlement of the foundation.     

Rayleigh waves in liquid layer resting over an initially stressed orthotropic half-space under self-weight

The study of surface waves (Rayleigh wave) finds their virtuous applications in a numerous geological and geophysical fields including water, oil, gas, and other subsurface geological probing and exploration. The present paper efforts to investigate the influence of initial stress, Earth magnetism, and gravity on propagation of Rayleigh waves. Considered model is consist of a liquid layer lying over a magnetoelastic orthotropic half-space under self-weight and initial stress. Method of separation of variable is used to solve the equation of motion. Solutions of governing equations are obtained in terms of displacement. Frequency relation for Rayleigh wave has been obtained and matched with classical Rayleigh wave equation. In addition to classical case, some existing results have been deduced as particular case of the present study. Obtained results have been shown through numerical illustrations. It is found that the considered parameters (initial stress, Earth magnetism, and gravity) have prominent effect on phase velocity of Rayleigh wave. Graphical representations have been made to exhibit the velocity profile of Rayleigh waves for different cases with the help of MATHEMATICA. The present study may be useful for seismologists and engineers who are concern with applications of wave propagation in magnetoelastic orthotropic medium.     

Pore Structure Parameters Influence on Various Types of Seismic Wave Propagation

For the case of seismic waves in a more complex architecture porous medium wave field occurs slightly changed with changes in the structure, several parameters characteristics of the structure of the media which influence on various types of seismic wave propagation were studied. Firstly, the article establishes the isotropic elastic porous medium model, derive the corresponding elastic wave equation, and uses high-order staggered-grid finite difference method for forward modeling, the article also analyze the pore structure parameters such as porosity, viscosity and penetration influence on the wave field characteristics were also analyzed. At the same time, the study analyze the influence of porosity, permeability and viscosity on phase velocity and attenuation coefficient was analyzed in the stady. The results showed that the influence on attenuation coefficient was more sensitive than that on phase velocity. This study helps to deepen the understanding of seismic wave propagation in the practical system of complex medium.     

Elastic waves along a cylindrical borehole in a poroelastic medium saturated by two immiscible fluids

The propagation of elastic waves along a cylindrical borehole filled with/without liquid and embedded in an infinite porous medium saturated by two immiscible fluids has been studied. The theory of porous media saturated by two immiscible fluids developed by Tuncay and Corapcioglu (1997) is employed. Frequency equations determining the phase velocity of axial symmetric waves are obtained. It is found that the surface waves along cylindrical borehole are dispersive. The dispersion equation of Rayleigh-type surface waves along the boundary of a poroelastic solid half-space saturated by two immiscible fluids is also obtained. Some special cases have been deduced and the dispersion curves are obtained numerically for a peculiar model. It is found that the density of fluids affects the Rayleigh mode.     

Response of circular footings and anchor plates in non-homogeneous elastic soils

The axisymmetric elastic response of circular footings and anchor plates in a linearly non-homogeneous elastic soil is analysed. It is assumed that footings/anchors are flexible and subjected to axisymmetric vertical loads. The response of the footing/anchor is modelled by using the classical Poisson–Kirchhoff thin plate theory. A variational technique is used to analyse the interaction problem. A representation for the contact stress is established by using a fundamental solution corresponding to a unit vertical pressure acting over an annular region in the interior of the non-homogeneous soil. The fundamental solution can be derived by using rigorous analytical procedures. The influence of the footing flexibility and the degree of soil non-homogeneity on the displacements, bending moments and contact stresses of a surface footing is examined over a wide range of governing parameters. In the case of anchor plates the influence of depth of embedment, degree of soil non-homogeneity and anchor flexibility on the anchor displacement is investigated.