饱和两相介质动力基础半空间理论地表波场基本解

本文以饱和两相介质复模的Ｂｉｏｔ波动方程为基础,根据弹性动力学半空间理论,严格推导出了饱和两个介质动力基础半空间理论地表面波场基本解。     

横观各向同性饱和两相介质动力反应计算分析

针对横观各向同性饱和两相介质的弹性波动方程组,应用基于显式逐步积分计算格式的时域显式有限元方法对其在输入地震波作用下的动力反应进行计算和分析,并将计算结果与完全各向同性饱和两相介质的计算结果进行对比研究。结果显示横观各向同性饱和两相介质与完全各向同性饱和两相介质的动力反应具有较为显著的差异。同时表明时域显式有限元方法是进行横观各向同性饱和两相介质动力反应计算分析的一种有效方法。     

层状饱水软土地基三维非轴对称动力响应分析方法

将饱水软土地基视为两相介质、考虑水的渗流和土骨架9变形的耦合作用，用Fourier展开和Hankel积分变换分析三维非称对称饱和弹性土层波动方程，用刚度矩阵方法，建立了层状饱和软土地基三维非轴对称动力响应的解析分析方法。以数值算例对比分析了单相土介质与两相饱和土介质三维非轴对称稳态动力响应，结果表明：在饱水软土地基动力响应分析中应该考虑土体中孔隙流体的影响。     

三维层状孔隙介质中弹性波的一种积分表达式II：正确性检验和数值模拟实验

基于前一篇文章中得到的关于三维层状孔隙介质中弹性波场的积分形式半解析解,本文通过离散波数法开展了数值模拟.将全空间均匀孔隙介质中单力点源和爆炸点源作用下弹性波场的解析解和我们的数值模拟结果进行对比,发现两者是完全一致的.而在一个两层半空间模型下的数值模拟,验证了固相位移Green函数的9组空间互易性情况.通过以上两种对比检验,验证了半解析解理论公式、数值模拟方法以及相应程序代码的正确性和可靠性.随后利用敏感度分析研究了不同的介质参数变化对爆炸点源在界面上会产生的反射波场的影响.通过垂直地震剖面模型的数值模拟,发现弹性波场能很好地反映孔隙介质物理性质的变化,同时也讨论了动力协调这一孔隙介质中的特殊现象.我们发展的基于半解析解的数值模拟方法可以为三维层状孔隙介质中弹性波传播特征的研究提供一种可供选择的有效工具和手段.     

横观各向同性场地中埋置衬砌隧道对qP波的散射

采用间接边界元法(IBEM)结合"分区契合"技术,研究qP波入射下横观各向同性(TI)场地中衬砌隧道的动力响应问题。方法充分利用半空间和全空间动力格林函数在分别构造含孔半无限空间域和闭合域内散射波场方面的优势,将含有衬砌隧道的层状弹性半空间分解为含孔半无限空间域和一个环形衬砌闭合域来分别进行波场构造,有效地降低了求解时间和存储量。文中验证方法的正确性,并以均匀TI半空间和基岩上单一TI土层为例,计算分析弹性半空间场地中隧道衬砌内表面动应力放大问题。结果表明qP波入射下,TI介质与各向同性介质场地中埋置衬砌隧道的动力响应差异显著,TI介质参数的变化导致场地动力特性的改变,进而改变场地与衬砌隧道的动力相互作用机制,显著影响着衬砌内表面动应力的大小及其空间分布。     

两相介质波动问题显式有限元方法稳定性研究

基于动力反应递推计算格式传递矩阵的性质,进行了饱和两相介质波动问题时域显式有限元方法稳定性问题的研究。定义了综合考虑各种影响因素的稳定性判别指标——传递因子;研究了稳定性影响因素,包括时间步长、空间步距和渗透系数取值的作用规律;给出了方法稳定性的实用判别准则。研究结果表明:时间步长、空间步距和渗透系数取值都对饱和两相介质波动问题的时域显式有限元方法的稳定性有较为显著的影响。随着时间步长的增大,方法的稳定性降低;随着空间步距的增大,方法的稳定性增加;当渗透系数取值增大时,方法的稳定性增加。     

具有饱和土沉积层的充水河谷对平面波的散射

把波函数展开方法用于地震波散射问题的研究中,首次在频域内给出了具有饱和土沉积层的圆弧形充水河谷对平面P波和SV散射问题的解析解答. 其中半空间场地用单相介质弹性动力理论模拟,河谷中的饱和土沉积层用饱和多孔介质的Biot动力学理论模拟,河谷中的水用无黏性流体(理想流体)介质模拟. 文中还给出算例,计算了不同高宽比的河谷谷底的位移幅值,分析表明河谷地形的存在使得半空间介质表面的位移幅值随着观察点位置的变化变化较大.     

横观各向同性饱和地基中埋置荷载的非轴对称瞬态响应

基于孔隙介质的Biot理论,首先利用Laplace变换,给出圆柱坐标系下横观各向同性饱和弹性多孔介质在变换域上的波动方程;将波动方程解耦后,根据方位角的Fourier展开和径向Hankel变换,求解了Biot波动方程,得到以土骨架位移、孔隙水压力和土介质总应力分量的积分形式的一般解;借助一般解,建立了有限厚度饱和土层和饱和半空间的精确动力刚度矩阵,并由土层的层间界面连续条件建立三维非轴对称层状饱和地基的总刚度方程;在此基础上,系统研究了横观各向同性饱和半空间体在内部集中荷载激励下的动力响应,并给出了问题的瞬态解答.该研究为运用边界元法求解饱和地基动力响应奠定了理论基础.     

水库区应力－孔压耦联分析

基于Ｂｉｏｔ耦联固结理论［１］，推导出二维饱水弹性岩石介质的应力－孔压耦联微分方程，并用有限元法和有限差分法分别对其进行了空间和时间的离散化。     

致密砂岩波速各向异性及弹性参数随围压变化规律的实验研究

为研究致密砂岩储层弹性波速度各向异性及弹性参数随围压的变化规律,应用地质力学研究所从美国New England Reaearch Inc引进的Autolab2000岩石物性实验设备,对采自长庆油田延长组储层的3组典型致密砂岩,对其X、Y、Z三个方向分别取样,进行了不同孔隙介质(干燥、饱水及饱油)条件下弹性波速度随围压(5~180 MPa)变化规律的实验研究工作,得到了X、Y、Z三个方向分别在干燥、饱水及饱油时的弹性波速度,并对X、Y、Z三个方向的各向异性进行计算和对比分析.同时根据测得的弹性波平均速度得到样品的弹性参数随围压的变化规律,对实验曲线进行拟合,获得不同孔隙介质条件下弹性波速度、各向异性、弹性参数随围压的变化规律及其拟合公式.结果表明,垂直方向速度值最低,横波各向异性指数小于纵波各向异性指数;随着围压的增加,致密砂岩波速增大,其各向异性以幂函数形式减小,体模量、弹性模量、剪切模量和拉梅常数以对数函数形式有不同程度的增加,泊松比因所含介质不同而有不同的变化趋势,除个别线外,拟合系数皆在0.956以上.在围压高于140 MPa时,干燥、饱水和饱油状态下的泊松比皆在0.24左右.     

Combined paraxial-consistent boundary conditions finite element model for simulating wave propagation in elastic half-space media

In this paper, a finite element model of a soil island is coupled to both a consistent transmitting boundary and a paraxial boundary, which are then used to model the propagation of waves in semi-infinite elastic layered media. The formulation is carried out in the frequency domain while assuming plane strain conditions. It is known that a discrete model of this type, while providing excellent results for a wide range of physical parameters in the context of a half-space problem, may deteriorate rapidly at low frequencies of excitation. This is so because at low frequencies the various waves in the model eventually attain characteristic wavelengths which exceed the distance of the bottom boundary, which then causes that boundary to fail. Also, the paraxial boundaries themselves break down at very low frequencies. In this paper, this difficulty is overcome and the model׳s performance is improved upon dramatically by incorporating an artificial buffer layer sandwiched between the bottom of the soil medium and the underlying elastic half-space. Applications dealing with rigid foundations resting on homogenous or layered half-space media are shown to exhibit significant improvement. Following extensive simulations, clear guidelines are provided on the performance of the coupled model and an interpretation is given on the engineering significance of the findings. Finally, clear recommendations are provided for the practical use of the proposed modelling strategy.     

Harmonic wave response of two 3-D rigid surface foundations

A boundary element methodology is developed for studying the response of a system of two rigid, massless or massive, surface foundations of arbitrary plan-forms to various harmonic waves under three-dimensional conditions. The method employs the frequency domain Green's function for the surface of the elastic half-space, thereby restricting the discretization only to the soil-foundation interfaces, and isoparametric quadratic quadrilateral boundary elements for increased accuracy. Extensive comparison studies with other known numerical solutions confirm the high accuracy of the proposed method. Detailed parametric studies are conducted in order to study the harmonic wave response of two square foundations as a function of the kind of incident wave, the angles of wave incidence, the wave frequency, the separation distance between the foundations and the amount of mass in each foundation and compare it against that of a single foundation for assessing the through the soil coupling effect.     

Elastic wave propagation in an irregularly layered medium

The indirect boundary element method (IBEM) is used to simulate wave propagation in two-dimensional irregularly layered elastic media for internal line sources. The method is based on the integral representation for scattered elastic waves using single layer boundary sources. Fulfillment of the boundary conditions leads to a system of integral equations. Results are obtained in the frequency domain and seismograins are computed through Fourier synthesis. In order to test and validate the method we present various comparisons between our results and the time series obtained analytically for a buried line source in a half-space and by using the recently developed spectral element method (SEM).     

饱和层状场地中任意凹陷地形对入射SV波的散射

利用饱和土层的精确动力刚度矩阵和动力格林(Green)函数,采用间接边界元法,在频域内求解了层状饱和场地中任意凹陷地形对入射SV波的散射问题.通过自由场反应分析,求得凹陷地形表面各点的位移和各单元的应力响应;同样计算了虚拟分布荷载的格林影响函数,求得相应的位移和应力响应;根据边界条件确定虚拟分布荷载,将自由场位移响应和...     

平面S波在饱和多孔热弹性介质边界的反射问题研究

针对饱和多孔介质中热弹性波的传播特性问题,基于多孔介质理论和广义的热弹性模型,研究平面S波在饱和多孔热弹性介质边界上的反射问题。以考虑流-固耦合的饱和多孔介质波动方程和热-弹耦合的广义热弹性基本方程出发,建立饱和多孔介质的热-流-固耦合弹性波动模型。通过引入势函数并考虑自由透水和绝热的边界条件,经过理论推导最终给出在饱和多孔热弹性介质边界上的四种反射波的振幅反射率的理论表达式。在此基础上进行数值计算,分别讨论平面S波的入射频率、入射角和热膨胀系数等参数对四种反射波的振幅反射率的影响情况。结果表明:各反射波的振幅反射率分别随频率和热膨胀系数的增大而增大,同时也受到平面S波入射角变化的影响。该结论对于土动力学的理论研究及其相关的工程勘探具有一定的指导意义。     

Scattering of plane P waves by circular-arc alluvial valleys with saturated soil deposits

This paper presents an analytical solution for two-dimensional scattering and diffraction of plane P waves by circular-arc alluvial valleys with shallow saturated soil deposits. The solution is based on Biot's dynamic theory for saturated porous media, and derived by employing Fourier–Bessel series expansion technique. In this analysis, soil deposits in the circular-arc valley are modeled as saturated porous media based on Biot's dynamic theory, and the circular-arc valley is assumed to be imbedded in an infinite half-space, filled with elastic single-phase media. Numerical results from this solution show that the amplitudes of displacement at the surface of an alluvial valley are mainly relative to the angle of incidence, the dimensionless frequency of incident P wave, the degree of saturation and porosity of soil deposits, and the stiffness and Poisson's ratio of the solid skeleton of the soil deposits. Furthermore, the proposed solution is compared with the previous solution, in which the soil deposit was modeled as an elastic single-phase solid.     

Dynamic analysis of large 3-D underground structures by the bem

An up to date literature survey on the dynamics of underground structures is presented briefly. The dynamic response of large three-dimensional underground structures to external or internal dynamic forces or to seismic waves is numerically determined by the frequency domain boundary element method. This method is used to model both the structure and the soil medium, which are assumed to behave as linear elastic or viscoelastic bodies. The full-space dynamic fundamental solution is employed in the formulation and this requires a free soil surface discretization, confined to a finite portion around the area of interest, in addition to soil—structure interface and free structural surface discretizations. The dynamic disturbances can have a harmonic or a transient time variation. The transient case is treated with the aid of numerical Laplace transforms with respect to time. Various numerical examples involving lined cavities and long lined tunnels buried in the full- or the half-space subjected to harmonic or transient external forces or seismic waves are presented to illustrate the method and demonstrate its advantages.     

The Green￠s function of the harmonic horizontal force applied at the interior of the saturated half-space soil

By using integral transform methods, the Green's functions ofhorizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous con-ditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green's functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.     

饱和土中深埋圆柱形衬砌洞室对瞬态平面波的散射

基于Biot饱和多孔介质动力学理论,运用Laplace变换和波函数展开法,根据饱和土体与衬砌结构交界面的连续条件和衬砌结构内边界上的应力自由条件,得到饱和土中深埋圆柱形衬砌洞室对瞬态平面P波和SV波散射问题的解答,该解答可以退化成为饱和土中深埋圆柱形空穴或弹性夹塞物的情形,并很容易转换成为对稳态波散射的解.通过与已有的相关问题的解析解答进行对比,验证了该解答的正确性.同时利用Laplace逆变换的数值方法,给出了饱和土和衬砌中应力和位移场在时域内的数值解,通过算例,分析了衬砌厚度、刚度对衬砌内边界处应力集中因子的影响.     

2D dynamic response of unlined and lined tunnels in poroelastic soil to harmonic body waves

The problem of harmonic wave diffraction by tunnels in an infinite poroelastic saturated soil obeying Biot's theory is studied numerically under conditions of plane strain and the effect of poroelasticity on the response is assessed through some parametric studies. The method is based on the theory of Mei and Foda, which considers the total field to be approximated by the superposition of an elastodynamic problem with modified elastic constants and mass density for the whole domain and a diffusion problem for the pore fluid pressure confined to a boundary layer at the free boundaries. Both problems are solved numerically by the boundary element method in the frequency domain. Results dealing with the response of a circular tunnel with and without an elastic concrete liner in an infinite poroelastic medium to incident harmonic P and SV plane waves are provided and compared against analytical ones as well as to those corresponding to linear elastic soil behaviour. Copyright © 2002 John Wiley & Sons, Ltd.