饱和土一维简谐响应解析解的求解和应用：II 应用

将相关论文[1]中得到的饱和土一维简谐响应解析解，应用到饱和土中两类压缩波的独立作用、饱和土中波的传播速度、u-p方程的适用范围等研究中。在两类压缩波的独立作用研究中，克服了以前文献中的数学不严密性。研究了饱和土各参数对三种体波波速的影响。通过比较u-w和u-p方程的解答，定量地说明了u-p方程的适用范围。     

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。     

饱和土动力反应中两类压缩波的独立作用分析

饱和土动力反应中存在2种类型的压缩波，它们有不同的特性，第1类压缩波类似于单相体中的压缩波；第2类压缩波由于有粘滞阻尼而衰减很快，由于数学分析和实验观测的复杂性，这两类压缩波在饱和土动力反应中的独立作用并不为人熟知，沿有J.Yang提出的方法求解基岩上的饱和土层在地表受到竖向均布简谐荷载作用下的稳态反应，通过分离变量得到解析解，定量比较了两类压缩波对土骨架位移、土体总应力、孔隙水压的独立作用。还讨论他粘性和荷载频率对两类压缩波的影响。     

非饱和土中热弹性波的传播特性分析

基于非饱和多孔介质的研究成果,考虑热效应和孔隙流体迂曲度的影响,研究了非饱和土中热弹性波的传播特性。利用非饱和土中耦合热的固-液-气三相介质的质量平衡方程、渗流连续方程、动量平衡方程和广义非Fourier热传导定律,建立了问题的热弹性波动方程。通过引入势函数,经过理论推导给出了非饱和土中热弹性波的弥散特征方程。结合数值算例,分析了几类热弹性波的波速和衰减系数随迂曲度、热膨胀系数和介质温度等热物理参数的变化规律。结果表明：孔隙水迂曲度的增大将引起P1波、P3波和S波的波速增大,而孔隙气体迂曲度的增大仅使得P2波的波速增大;热膨胀系数的增大将造成P1波波速的增大和热（T）波波速的减小;介质温度的升高将引起各类热弹性波波速的增大;频率、热膨胀系数和介质温度的变化对各类热弹性波的衰减系数均有较大影响,不可忽视。     

群桩基础引发饱和地基振动的近似解析解

建立了饱和半空间-群桩基础耦合动力近似解析模型,其中基桩考虑为欧拉梁,饱和地基采用Biot两相介质动力控制方程,二者在频率-波数域中利用桩-土相互作用点处的饱和地基柔度矩阵进行耦合,并采用快速傅里叶逆变换获得频域解答。分析了饱和地基中群桩基础的动力阻抗及刚性承台上施加简谐振动荷载时群桩基础引起的饱和地基振动响应。研究结果表明,荷载类型、激振频率以及地基渗透系数对饱和地基位移和孔压响应有明显影响。特别的,群桩基础动力阻抗峰值频率会随着地基渗透系数的增加而增大。     

非饱和土中热弹性波的传播特性分析

基于非饱和多孔介质的研究成果,考虑热效应和孔隙流体迂曲度的影响,研究了非饱和土中热弹性波的传播特性。利用非饱和土中耦合热的固-液-气三相介质的质量平衡方程、渗流连续方程、动量平衡方程和广义非Fourier热传导定律,建立了问题的热弹性波动方程。通过引入势函数,经过理论推导给出了非饱和土中热弹性波的弥散特征方程。结合数值算例分析了几类热弹性波的波速和衰减系数随迂曲度、热膨胀系数和介质温度等热物理参数的变化规律。结果表明：孔隙水迂曲度的增大将引起P_(1)波、P_(3)波和S波的波速增大,而孔隙气体迂曲度的增大仅使得P_(2)波的波速增大;热膨胀系数的增大将造成P_(1)波波速的增大和热（T）波波速的减小;介质温度的升高将引起各类热弹性波波速的增大;频率、热膨胀系数和介质温度的变化对各类热弹性波的衰减系数均有较大影响,不可忽视。     

饱和土中管桩的水平动阻抗研究

为了考察桩、土主要参数对饱和土中管桩水平振动的影响,将土体分为桩周饱和土和桩芯饱和土两部分,利用多孔介质理论的饱和土控制方程建立了饱和土-管桩的耦合振动模型。在考虑桩周饱和土和桩芯饱和土边界条件的情况下,运用势函数解耦的方法对桩周饱和土和桩芯饱和土的水平振动进行了求解。在考虑桩周饱和土和桩芯饱和土对管桩作用的情况下对饱和土中管桩的水平振动进行了求解,得到了管桩桩顶的水平动力阻抗,并分析了主要桩、土参数对管桩水平动力阻抗的影响。研究表明：管桩内外半径、桩周土和桩芯土剪切模量比、泊松比之比对管桩水平动力阻抗的影响较大,低频时液-固耦合系数比对管桩水平动力阻抗有一定的影响,而阻尼比之比对管桩水平动力阻抗阻尼因子有一定的影响。     

群桩基础引发饱和地基振动近似解析研究

建立了饱和半空间-群桩基础耦合动力近似解析模型,其中基桩考虑为欧拉梁,饱和地基采用Biot两相介质动力控制方程。求解了饱和地基中群桩基础的动力阻抗,分析了刚性承台上施加简谐振动荷载时,群桩基础引起的饱和地基振动响应。研究结果表明荷载类型、激振频率以及地基渗透系数对饱和地基位移和孔压响应有明显影响。     

群桩基础引发饱和地基振动近似解析研究

建立了饱和半空间-群桩基础耦合动力近似解析模型,其中基桩考虑为欧拉梁,饱和地基采用Biot两相介质动力控制方程。求解了饱和地基中群桩基础的动力阻抗,分析了刚性承台上施加简谐振动荷载时,群桩基础引起的饱和地基振动响应。研究结果表明荷载类型、激振频率以及地基渗透系数对饱和地基位移和孔压响应有明显影响。     

群桩基础引发饱和地基振动近似解析研究

建立了饱和半空间-群桩基础耦合动力近似解析模型,其中基桩考虑为欧拉梁,饱和地基采用Biot两相介质动力控制方程。求解了饱和地基中群桩基础的动力阻抗,分析了刚性承台上施加简谐振动荷载时,群桩基础引起的饱和地基振动响应。研究结果表明荷载类型、激振频率以及地基渗透系数对饱和地基位移和孔压响应有明显影响。     

Numerical and analytical investigation of compressional wave propagation in saturated soils

In geotechnical earthquake engineering, wave propagation plays a fundamental role in engineering applications related to the dynamic response of geotechnical structures and to site response analysis. However, current engineering practice is primarily concentrated on the investigation of shear wave propagation and the corresponding site response only to the horizontal components of the ground motion. Due to the repeated recent observations of strong vertical ground motions and compressional damage of engineering structures, there is an increasing need to carry out a comprehensive investigation of vertical site response and the associated compressional wave propagation, particularly when performing the seismic design for critical structures (e.g. nuclear power plants and high dams). Therefore, in this paper, the compressional wave propagation mechanism in saturated soils is investigated by employing hydro-mechanically (HM) coupled analytical and numerical methods. A HM analytical solution for compressional wave propagation is first studied based on Biot’s theory, which shows the existence of two types of compressional waves (fast and slow waves) and indicates that their characteristics (i.e. wave dispersion and attenuation) are highly dependent on some key geotechnical and seismic parameters (i.e. the permeability, soil stiffness and loading frequency). The subsequent HM Finite Element (FE) study reproduces the duality of compressional waves and identifies the dominant permeability ranges for the existence of the two waves. In particular the existence of the slow compression wave is observed for a range of permeability and loading frequency that is relevant for geotechnical earthquake engineering applications. In order to account for the effects of soil permeability on compressional dynamic soil behaviour and soil properties (i.e. P-wave velocities and damping ratios), the coupled consolidation analysis is therefore recommended as the only tool capable of accurately simulating the dynamic response of geotechnical structures to vertical ground motion at intermediate transient states between undrained and drained conditions.     

不同饱和度土层分界面上剪切波的反射与透射

基于多相孔隙介质弹性理论,给出了非饱和土中不同弹性波的传播方程。根据分界面上的边界条件,建立了各势函数波幅值之间的关系式,讨论了入射剪切波在不同饱和度土层分界面上的反射与透射问题。在无限空间非饱和土体中存在3种压缩波和1种剪切波,因此,当剪切波传播到不同饱和度的非饱和土层分界面上将分别在上、下土层激发产生4种反射波和4种透射波。推导出不同反射波和透射波的振幅比例系数和能量比例系数的理论表达式,并且在此基础上进行数值分析。在数值算例中分别研究了各反射波与透射波的能量比例系数（即能量反射率和能量透射率）受入射频率、入射角度以及上、下土层土体饱和度变化的影响情况。计算结果表明：各能量反射率和能量透射率不仅与入射角和入射频率有关,而且其受上、下土层饱和度变化的影响也同样不能忽视。     

半空间饱和土中圆形衬砌对弹性压缩波的散射

借助于Biot 波动理论和弹性波的传播理论,采用复变函数和多级坐标法,对半空间饱和土中圆形衬砌结构对弹性稳态压缩波的散射问题进行求解和分析。利用一个半径很大的圆弧来逼近半空间直边界,将待解问题转化为稳态弹性压缩波在一个大圆孔和一个弹性衬砌结构的散射问题。通过引入势函数,将饱和土的Biot波动方程和衬砌的弹性波动方程解耦成Helmholtz 方程,借助复变函数级数展开便可以预先写出该组Helmholtz方程的通解。然后,通过引用复变量,把饱和土和衬砌结构中的应力、位移及孔压用设定的势函数表示出来,再利用半空间饱和土和衬砌结构的连续性条件和近似直边界的圆弧边界和衬砌内边界的边界条件求解出该组势函数的特解。最后,利用势函数的特解,得到饱和土中的位移,应力和孔压及衬砌结构的位移和应力;变换不同的参数求解衬砌结构内外边界的动应力和孔压的集中系数,通过对算例结果的分析得出一系列有益的结论。     

层状非饱和土地基的轴对称稳态动力响应

考虑土颗粒、孔隙流体的压缩性及各相物质间的黏性、惯性耦合作用,采用理论上更加严谨的饱和度本构关系式,建立了非饱和土的动力控制方程。该组方程与饱和土的经典Biot波动方程完全兼容,因此,具有更广泛的适用性。通过引入一组状态向量,在圆柱坐标系下将非饱和土满足的波动方程转化为状态方程组,利用Hankel变换,求解状态方程组,得到了传递矩阵。结合边界条件及层间接触连续条件,求解了层状非饱和地基的稳态动力响应问题。数值算例表明：土层对地表动位移的影响主要集中在临界深度范围内;软硬土层的相对次序对地表动位移幅值有显著影响;饱和度增大会引起土的物理参数发生相应的改变,尤其是动剪切模量通常降幅较大,而动剪切模量是决定位移幅值的关键因素,最终的结果是导致地表动位移幅值明显增大。     

Wave propagation in a general anisotropic poroelastic medium: Biot’s theories and homogenisation theory

Anisotropic wave propagation is studied in a fluid-saturated porous medium, using two different approaches. One is the dynamic approach of Biot’s theories. The other approach known as homogenisation theory, is based on the averaging process to derive macroscopic equations from the microscopic equations of motion. The medium considered is a general anisotropic poroelastic (APE) solid with a viscous fluid saturating its pores of anisotropic permeability. The wave propagation phenomenon in a saturated porous medium is explained through two relations. One defines modified Christoffel equations for the propagation of plane harmonic waves in the medium. The other defines a matrix to relate the relative displacement of fluid particles to the displacement of solid particles. The modified Christoffel equations are solved further to get a quartic equation whose roots represent complex velocities of the four attenuating quasi-waves in the medium. These complex velocities define the phase velocities of propagation and quality factors for attenuation of all the quasi-waves propagating along a given phase direction in three-dimensional space. The derivations in the mathematical models from different theories are compared in order to work out the equivalence between them. The variations of phase velocities and attenuation factors with the direction of phase propagation are computed, for a realistic numerical model. Differences between the velocities and attenuations of quasi-waves from the two approaches are exhibited numerically.     

Hydro-micromechanical modeling of wave propagation in saturated granular crystals

Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro-micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two-way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore-scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one-dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face-centered-cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.     

The influence of petrophysical properties on the salt weathering of porous building rocks

The influence of pore structure, water transport properties and rock strength on salt weathering is evaluated by means of a thorough rock characterisation and a statistical analysis. The pore structure was described in terms of its porosity, pore size distribution (quantified by mean pore radius) and specific surface area, density and water transport was characterised by means of water permeability (saturated flow) and capillary imbibition (unsaturated flow); whilst the rock strength test was carried out using uniaxial compressive strength, compressional and shear wave velocities, dynamic elastic constants and waveform energy and attenuation were obtained from the digital analysis of the transmitted signal. A principal component analysis and a stepwise multiple regression model was carried out in order to examine the direct relationships between salt weathering and petrophysical properties. From the principal component analysis, two main components were obtained and assigned a petrophysical meaning. The first component is mostly linked to mechanical properties, porosity and density whereas the second component is associated with the water transport and pore structure. Salt weathering, quantified by the percentage of weight loss after salt crystallisation, was included in both principal components, showing its dependence on their petrophysical properties. The stepwise multiple regression analysis found that rock strength has a predominant statistical weight in the prediction of salt weathering, with a minor contribution of water transport and pore structure parameters.     

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。     

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。     

非饱和土中圆柱形衬砌隧道的瞬态动力响应

在以往关于圆柱形衬砌隧道的瞬态动力响应中,衬砌周围土体大多假定为弹性介质或饱和介质。然而,自然界中的土体大多为非饱和介质。考虑土体与衬砌结构的动力相互作用及动荷载引起的附加质量密度的影响,研究了瞬态荷载作用下非饱和土中无限长深埋圆柱形衬砌隧道的动力响应。基于多孔介质混合物理论和连续介质力学理论,建立了非饱和土中圆柱形衬砌隧道受到瞬态荷载作用时衬砌及周围土体的控制方程,利用Durbin数值反演法得到了衬砌及土体在时间域的动力响应。数值分析了饱和度对瞬态荷载下径向位移、径向应力、环向应力和孔隙水压力的影响。结果表明：饱和度对衬砌及周围土体的瞬态响应影响显著;饱和度对径向位移沿径向的衰减影响较小,对环向应力和孔隙压力沿径向的衰减影响较大。