This paper considers the interaction between a penny-shaped crack and a center of dilatation in an elastic half-space. The problem is decomposed into two “Auxiliary Problems”: (I) a half-space containing a center of dilatation and (II) a penny-shaped crack subject to tractions that cancel those induced by the Auxiliary Problem I. The fundamental solutions for penny-shaped crack subject to point forces on the crack surface are first derived, then they are used to generate the solution for Auxiliary Problem II. When the free surface is far from the crack and the center of dilatation, the results by E. Karapetian and M. Kachanov [International Journal of Solids Structure 33 (1996) 3951±3967] is recovered as a special case. If the overburden stress and the friction on crack surface are neglected, all modes I, II, and III stress-intensity factors (K1, K2 and K3) are induced at the crack tips. In general, the maximum value of K2 is observed when the center of dilatation is located in front of the crack tip at an elevation close to that of the penny-shaped crack. However, tensile cracking is likely to be prohibited by the overburden stress and friction on the crack surface, while shear cracking remains possible even when both overburden and friction on the crack surface are included. Generally speaking, the mode II stress intensity factor is larger than those for mode I and III cracking.

This paper examines the interaction between a crack parallel to the free surface of an elastic half-plane and an internal center of dilatation. The problem is decomposed into two auxiliary problems. When the center of dilatation approaches the crack tip, two kinds of singularity are analytically obtained. If the overburden stress and the friction on crack surface are neglected, both modes I and II stress intensity factors (KI and KII ) are induced at the crack tips. The maximum of KI and KII occurs when the center of dilatation is located in front of the crack tips. The tensile cracking is likely to be prohibited by the overburden stress, while shear cracking remains possible even including the effects of both overburden and friction on the crack surface.

A continuum model for the interaction analysis of a fully coupled soil–pile–structure system under seismic excitation is presented in this paper. Only horizontal shaking induced by harmonic SH waves is considered so that the soil–pile–structure system is under anti-plane deformation. The soil mass, pile and superstructure were all considered as elastic with hysteretic damping, while geometrically both pile and structures were simplified as a beam model. Buildings of various heights in Hong Kong designed to resist wind load were analysed using the present model. It was discovered that the acceleration of the piled-structures at ground level can, in general, be larger than that of a free-field shaking of the soil site, depending on the excitation frequency. For typical piled-structures in Hong Kong, the amplification factor of shaking at the ground level does not show simple trends with the number of storeys of the superstructure, the thickness and the stiffness of soil, and the stiffness of the superstructure if number of storeys is fixed. The effect of pile stiffness on the amplification factor of shaking is, however, insignificant. Thus, simply increasing the pile size or the superstructure stiffness does not necessarily improve the seismic resistance of the soil–pile–structure system; on the contrary, it may lead to excessive amplification of shaking for the whole system. Copyright.

Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constitutes of solid and fluid phase. The finite element formulation based on this variational principle is also derived. As functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in time domain. In some situations, the differential-integral equations can be reduced to symmetrical differential equations, and, as an numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results can provide the further understanding of the wave propagation in porous media.

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论，在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下，建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型，利用Laplace变换，求得了原初边值问题在变换空间中的解析解，并利用Laplace逆变换的Crump数值反演方法，得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应，分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明，与不可压流体饱和弹性多孔介质相同，不可压流体饱和粘弹性多孔介质中亦只存在一个纵波，并且固相骨架的粘性对动力行为有显著的影响。