两相饱和介质半无限空间位错位移场

弹性位错理论是研究地震震源正演和反演的重要工具之一. 单相介质位错理论求得的地面变形场是稳定的、不变的，而实际地震后的地面变形场是变化的. 本文利用集中力作用下无限空间中两相饱和介质Green函数的柱函数表达式，通过弹性运动方程积分解的Helmholtz方程的Hansen矢量变换，再叠加自由表面影响场的方法求得两相饱和介质半无限空间位错位移场. 本文结果结合Nur的DD模式，在进水排水的假说下能解释地震后地面变形场的变化.     

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。     

关于两相饱和介质中流相Green函数的解析解

自然界中许多动力学问题需要用两相饱和介质Green函数求得解答,本文在两相饱和介质位移场Green函数解答的基础上,求得的有关饱和流体孔隙压力,进、排流体流量等三个Green函数.从而使两相饱和介质涉及流体问题的Lamb方程能完整地使用.论文在推导过程中详细地阐述了流体三个Green函数的物理意义,并将所得结果与Chen（1994）的纯数学的结果作了对比.最后文章讨论了解析解的稳定性.     

非混溶饱和两相渗流与孔隙介质耦合作用的理论研究Ⅱ——方程解耦与有 …

通过对上文（１）所推证数学模型方程的进一步处理与简化，得到解耦的流场系统压力方程，以Ｇａｌｅｒｋｉｎ弱积分解的形式，给出模型方程数值分析的有限元分式，并进行了初步验证。     

两相介质动力学问题的研究进展

本回顾了两相多孔介质研究的历史，包括基本运动微分方程，两相介质中弹性波的传播性质，两相介质动力问题的解析方法及数值方法，以及数值方法中涉及的人工边界条件，并指出其中存在的问题和今后值得研究的方向。     

两相饱和介质中的集中力点源位移场解与应用

通过两相饱和介质Ｂｉｏｔ方程变换,利用势场分解较好地解决了饱和两相介质中Ｐ１和Ｐ２波的耦合问题．再由Ｐｏｉｓｓｏｎ方程和Ｈｅｌｍｈｏｔｚ方程的特性,求解得到两相饱和介质在集中力点源作用下的位移场Ｇｒｅｅｎ函数,进而通过阶跃函数和Ｆｏｕｒｉｅｒ逆变换,求得两相介质在集中力．作用下的波场．由上述结果,根据扩容进水模型,合理地解释了孕震前各主要阶段在地震记录中垂直向振幅与振幅比统计值的变化．最后结合工作实例,利用两相介质波场理论求得由一般弹性介质理论不易求得的骨架固体力学参数．     

两相饱和介质中的集中力点源位移场解与应用

通过两相饱和介质Ｂｉｏｔ方程变换,利用势场分解较好地解决了饱和两相介质中Ｐ１和Ｐ２波的耦合问题．再由Ｐｏｉｓｓｏｎ方程和Ｈｅｌｍｈｏｔｚ方程的特性,求解得到两相饱和介质在集中力点源作用下的位移场Ｇｒｅｅｎ函数,进而通过阶跃函数和Ｆｏｕｒｉｅｒ逆变换,求得两相介质在集中力．作用下的波场．由上述结果,根据扩容进水模型,合理地解释了孕震前各主要阶段在地震记录中垂直向振幅与振幅比统计值的变化．最后结合工作实例,利用两相介质波场理论求得由一般弹性介质理论不易求得的骨架固体力学参数．     

两相饱和介质中的集中力点源Green函数

通过对两相饱和介质 Ｂｉｏｔ 方程的变换,利用 Ｐｏｉｓｓｏｎ 方程和 Ｈｅｌｍ ｈｏｌｔｚ 方程性质,求解得到两相饱和介质在集中力点源作用下的位移场 Ｇｒｅｅｎ 函数     

二维土坝的两相动力分析

提出了一种分析饱和土坝动力反应的方法,考虑了土坝的两相介质特性,在固液耦联动力方程的基础上,选取固相位移,液相位移、孔隙水压作为场变量,采用伽辽金加权残数法进行有限元空间离散化,然后在时域上采用Ｗｉｌｓｏｎ－θ法进行逐步积分。该方法不仅能计算出固相位移和液相位移,而且能直接得到孔隙水压的反应过程。文中以一饱和土坝模型进行算例分析,并与将其作为单相介质时的结果进行了比较。该法可用于分析饱和介质的地震     

半空间饱和介质内圆形洞室对平面P1波的散射

考虑土颗粒和孔隙流体的压缩性以及孔隙流体与土骨架之间的粘性耦合作用,采用修正的Biot模型,假定半空间表面不透水,得到了平面P1波(快压缩波)在半空间表面的反射P1波、P2波(慢压缩波)和SV波(剪切波)的幅值.采用大圆弧假定将半空间内圆形洞室的散射问题转化为大圆弧和圆形洞室的多重散射问题,运用波函数展开法将入射波、反射波以及半空间表面和洞室的散射波的势函数展开成Fourier-Bessel函数的无穷级数形式,由Graf加法定理得到同一坐标系下的势函数的表达式,根据半空间表面和洞室完全自由的边界条件得到了待定复系数的理论解.通过数值计算,着重分析了平面P1波垂直向上入射时无量纲入射频率和洞室埋藏深度等对洞室的动应力集中因子和半空间表面的归一化水平和竖向位移的影响.     

Transient foundation solution of saturated soil to impulsive concentrated loading

The transient dynamic response of saturated soil under suddenly applied normal and horizontal concentrated loading is studied in this paper. The behavior of saturated soil is governed by Biot's consolidation theory. The general solutions for Biot equations of equilibrium are derived in terms of displacements and variations of fluid volume, using Laplace–Hankel integral transforms. The solutions in the time domain can be evaluated by numerical inverse Laplace–Hankel transforms. Selected numerical results for displacements, stresses, and pore pressures are presented. Comparisons with existing closed-form solutions for the elastic half-space are made to confirm the accuracy of the present solutions. The solutions can be used to study a variety of transient wave propagation problems and dynamical interactions between saturated soil and structures.     

The source vector and static displacement field by elastic dislocation on the two-phase saturated medium

IntroductionSince Steketee introduced the elastic dislocation theory into geophysics in 1958, it has become an important part of seismology. Because the fracture of fault can be treated as a displacement bound, the elastic displacement field (forward problem) can be studied by the static elastic dislocation theory under some given condition. Vice versa, if the static displacement field is known, the cause (inverse problem) can be inferred by the dislocation theory. In the last 40 years, many …     

Three‐dimensional dynamic response of underground openings in saturated rock masses

In this paper a three‐dimensional dynamic analysis program for saturated porous rocks and soils is presented. The theoretical formulations incorporated in the proposed computer program are the extension of Biot's two‐phase theory to non‐linear region. Numerical study using the program is carried out to demonstrate the three‐dimensional features of the program and to show the effects of pore water on the dynamic response of underground openings in saturated rock masses. It is shown that underground openings in saturated porous media could be significantly more vulnerable to the potential damages associated with high motions and shear failure than those in dry media. Copyright © 2001 John Wiley & Sons, Ltd.     

饱和土体动力本构模型研究进展

饱和土体的动力本构模型对于土体的动力反应计算分析和岩土工程初边值问题的求解发挥着重要的作用。本文对饱和砂土干口饱和粘土动力本构模型的研究进展情况进行了较为详细的综述，并对其未来发展的一些方向和有待进一步研究的问题作了介绍。     

Analytical layer-element solution to axisymmetric dynamic response of transversely isotropic multilayered half-space

Starting with the governing equations of motion and the constitutive equations of transversely isotropic elastic body, and based on the corresponding algebraic operations and the Hankel transform, the analytical layer-elements of a finite layer and a half-space are obtained in the transformed domain. According to the continuity conditions between adjacent layers, the global stiffness matrix equation is obtained by assembling the analytical layer-element of each single layer. The solutions in the transformed domain are acquired by introducing the boundary conditions into the global stiffness matrix equation, and thus, the corresponding solutions in frequency domain are achieved by taking the inversion of Hankel transform. Finally, some numerical examples are given to illustrate the accuracy of the proposed method, and to study the influence of properties and the frequency of excitation on the dynamic response of the medium.     

关于两相介质动力学问题建模的注记

本以清楚的物理概念、依据经典力学原理建立了两相介质完整的动力学非线性方程组。然后，阐明了将此方程组线性化的条件：孔隙率、密度随空间的变化远小于它们在该处随时间的变化；孔隙率、密度的变化所引起的位移和孔压等量的变化可以忽略不计。在此条件下，位移、孔压等变量与孔隙率和密度变量解耦，可独立地进行求解，澄清了Biot等模型中隐含的矛盾，即孔隙率和密度不变与孔隙流体可压缩和骨架可变形之间的矛盾。最后，通过比较几种常用的模型，指出它们之间的主要匹配在于本构关系和连续性方程，且土力学模型是Biot模型和Zienkiewicz模型的特例。     

Torsional response of a rigid circular foundation on a saturated half-space to SH waves

An analytical approach is used to study the torsional vibrations of a rigid circular foundation resting on saturated soil to obliquely incident SH waves. Biot’s poroelastic dynamic theory is considered to characterize the saturated soil below the foundation, which is solved by Hankel transform later. In order to consider the scattering phenomena caused by the existence of the foundation, the total wave field in soil is classified into free-field, rigid-body scattering field and radiation scattering field. According to the classification of wave field and the mixed boundary-value conditions between the soil and the foundation, torsional vibrations of the foundation are formulated in two sets of dual integral equations. Then, the dual integral equations are reduced to Fredholm integral equation of the second kind to be solved. Combining with the dynamic equilibrium equations of the foundation, the expressions for the torsional vibrations of the foundation are obtained. Numerical results are presented to demonstrate the influence of excitation frequency, incident angle, the torsional inertia moment of the foundation and permeability of the saturated half-space on the torsional vibrations of the foundation.     

软件ABAQUS在饱和土体动力响应分析中的应用

研究表明:地震作用下土体的动力特性及变形特性与超静孔隙水压力的发展变化密切相关,因此,在土体动力分析过程中考虑孔隙水压的影响是非常必要的。本文通过对基本方程的推导,借助于大型有限元软件ABAQUS,进行了饱和土体在动力作用下孔隙水压变化的数值模拟。计算结果表明,ABAQUS完全适用于此类问题的数值模拟,并且稳定性和收敛性较好。     

基础动力刚度的精确数值解及集中参数模型

土－结构相互作用分析的关键是建立以土－结构界面定义的无限半空间的动力刚度矩阵。本文介绍了一种求解半无限地基动力刚度的新方法，通过两个算例验证了该方法的精度，并给出了一种利用频域刚性基础动力刚度计算基础时域荷载响应的实用方法，该研究为刚性基础设计提供了一种新的，可靠的理论方法。