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。

Based on the porous media theory and by taking into account the effects of the pore fluid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fluid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fluid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de-formation of the solid phase, small velocity of the fluid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fluid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dynamic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fluid-saturated elastic porous media, which have been discussed previously.

研究了流体饱和不可压标准线性粘弹性多孔介质中平面波的传播和反射问题．在固相骨架小变形的流体饱和粘弹性多孔介质；平面波；弥散关系;衰减率；反射系数假定下，得到了粘弹性多孔介质中波动方程的一般解，讨论了弥散关系和波的衰减特性．结果表明：在流体饱和不可压粘弹性多孔介质中，仅存在一个耦合纵波和一个耦合横波，纵波和横波的波速、衰减率等取决于孔隙流体与固相骨架间的相互作用以及固相骨架本身的粘性．同时，研究了半空间自由边界上入射波（纵波、横波）的反射问题，得到了非均匀反射波的波速、反射系数、衰减率等的表达式及其相关的数值结果．

研究了流体饱和不可压黏弹性多孔介质中的非均匀平面波及其能量流和能量耗散规律．在流相和固相物质微观不可压、固相骨架宏观服从积分型本构关系和小变形的假定下，利用Helmholtz分解，得到了饱和黏弹性多孔介质中非均匀平面波的一般解以及纵波、横波相速度和衰减率等的解析表达式，分析了平面波传播矢量和衰减矢量之间的关系，数值结果表明孔隙流体与固相骨架间的相互作用以及固相骨架的黏性对波的相速度、衰减率等有着显著的影响．同时，得到了饱和黏弹性多孔介质的能量方程，给出了能量流矢量和能量耗散率．对非均匀平面纵波和横波，推导了平均能量流矢量和平均能量耗散率的解析表达式．

This paper presents a new model for analyzing a nonlinear soil–pile interaction subject to horizontal shaking of a vertical circular pile embedded in a soil layer of finite thickness. The pile rests on bedrock with either a pinned or a clamped support. The soil mass is assumed composing of a “semi-nonlinear” inner soil zone around the pile and a linear viscoelastic soil zone outside the inner zone. When the inner soil behaves linearly, the present solutions are identical to those obtained by Nogami and Novak in 1977. Numerical results show that soil resistance of less slender piles developed against the vibration is larger than that of more slender piles. Soil resistance depends more strongly on the size of the nonlinear inner zone when the pile is vibrating at a frequency higher than the natural frequency of the soil. Soil nonlinearity, in general, results in a smaller damping and stiffness of the soil–pile system, except at high frequency. At higher vibration frequency, the situation can be very complicated. The exact value of the dynamic stiffness of the soil–pile system depends on elastic shear wave speed, soil nonlinearity, vibration frequency, slenderness ratio of the pile, magnitude of vibration, and tip conditions of the pile. Generally speaking, the dynamic stiffness is smaller than the static stiffness. The normalized dynamic stiffness for pile with a pinned tip is, in general, larger than that with a clamped tip, while the reverse is true for the damping.

基于多孔介质理论，首先建立了饱和多孔弹性杆件弯曲与轴向变形时动力响应的数学模型．其次，基于多孔弹性梁弯曲变形的数学模型，利用Laplace变换，分析了两端可渗透的饱和多孔弹性悬臂梁在自由端受阶梯载荷作用下的动静力响应，给出了梁弯曲时挠度、弯矩以及孔隙流体压力等效力偶等物理量随时间的响应曲线．发现不可压多孔弹性梁的拟静态响应亦存在Mandel-Cryer现象，多孔弹性梁的挠度具有与粘弹性梁挠度类似的蠕变特征，然而，其应力响应不同于粘弹性梁，随着时间的增加，梁拟静态响应的弯矩逐渐增加，并达到一个稳态值．这些结果有助于揭示植物根茎等力学行为的机理.