衰变热源作用下饱和多孔介质热固结问题的扩展精细积分法

热源作用下饱和多孔介质热固结效应是土木及能源工程领域的一个重要课题.由于问题的复杂性,已有的研究大多将介质假定为均匀各向同性,且将热源假定为恒定强度.实际工程中,天然饱和多孔介质常表现出明显的分层特性,热源强度也存在衰变性,为此本工作采用扩展精细积分法对衰变热源作用下层状饱和多孔介质的热固结问题进行研究.借助于积分变换,将饱和多孔介质热固结问题的偏微分方程转化为变换域内的常微分方程;然后对饱和多孔介质微层元进行合并消元,并结合边界条件,推导出衰变热源作用下层状饱和多孔介质热固结问题在积分变换域内的扩展精细积分解;对所得解答进行相应的数值积分逆变换,可获得所求温度、超静孔压及竖向位移在物理域内的解答.基于上述求解过程,编制相应的计算程序进行数值计算,通过与已有文献对比,验证本文扩展精细积分法在求解层状饱和多孔介质热固结问题中的适应性和正确性;最后通过几组算例,分析热源衰变周期、热源埋深及介质的成层性对热固结效应的影响.结果表明:热源衰变周期对温度和超静孔压的峰值、以及达到峰值的时间均有明显影响,衰变周期越长,二者峰值均越大,且达到峰值所需时间越长;热源埋深对超静孔压及竖向位移变化影响显著,深埋热源作用时热源两侧竖向位移呈对称分布,而浅埋热源两侧则无此现象;饱和多孔介质的分层特性对热固结效应影响明显.     

成层饱和介质平面波斜入射问题的一维化时域方法

地震波斜入射下自由场的输入是大型结构抗震分析中亟待解决的问题之一,尤其是成层饱和多孔介质自由场问题,由于问题的复杂性,目前研究甚少. 本文基于Biot提出的饱和多孔介质动力方程,建立了一种新的求解平面波斜入射下基岩上覆饱和多孔介质成层场地自由场分析的一维化时域计算方法. 该方法首先根据Snell定律将饱和多孔介质二维空间问题转化为一维时域问题,通过对深度方向的有限元离散,得到饱和多孔介质波动问题的一维化有限元方程,然后采用单相弹性介质精确人工边界条件模拟基岩半空间的波动辐射和输入特征,通过考虑基岩与饱和多孔介质间透水或不透水边界条件以及不同饱和多孔介质交界面边界条件,形成基岩上覆成层饱和介质系统的整体有限元方程,最后采用中心差分法与Newmark平均加速度近似格式相结合的方法对时间进行离散,得到节点的动力时程的显式表达. 典型场地的地震反应分析表明,本文方法的计算结果与传递矩阵法结合傅里叶变换的计算结果完全吻合,证明了其有效性.      

A new integral equation formulation of two-dimensional inclusion–crack problems

A new integral equation formulation of two-dimensional infinite isotropic medium (matrix) with various inclusions and cracks is presented in this paper. The proposed integral formulation only contains the unknown displacements on the inclusion–matrix interfaces and the discontinuous displacements over the cracks. In order to solve the inclusion–crack problems, the displacement integral equation is used when the source points are acting on the inclusion–matrix interfaces, whilst the stress integral equation is adopted when the source points are being on the crack surfaces. Thus, the resulting system of equations can be formulated so that the displacements on the inclusion–matrix interfaces and the discontinuous displacements over the cracks can be obtained. Based on one point formulation, the stress intensity factors at the crack tips can be achieved. Numerical results from the present method are in excellent agreement with those from the conventional boundary element method.     

覆水饱和双相介质圆弧场地P波激励下散射问题的理论解

采用波函数展开法对平面P波入射复杂水域地形的空间变异性地震动场进行研究,该水域地形具有覆水层、饱和双相介质、场地非平坦以及第二类分层(场地跨越分层界面)等属性.首先,依据地震波反射和透射特性推导直角坐标系下的自由波场分布;然后,根据场地属性并引入大圆弧法分析极坐标系下的含有待定系数的散射波场;进而,结合土-水分界面和饱和土层分界面边界条件,求解散射波场中的待定系数;最后,通过自由波场和散射波场得到覆水饱和双相介质圆弧场地波函数理论解.基于理论解,通过算例验证了理论推导的合理性及可靠性,分析了地表位移在不同入射条件下的差异性.结果 表明,相对于均匀介质,饱和双相介质会显著影响地表位移分布.此外,入射波频率和角度对地震地面运动特性也有较大的影响.     

饱和土埋置力源的三维动力Lamb问题解答

基于一组弹性土波动方程，应用Fourier级数展开和Hankel积分变换，得到了三维问题饱和土骨架与孔隙水的应力及位移分量在变换域内的积分形式通解．考虑地基表面透水情形，由边界条件导出了半空间饱和土体在埋置力源作用下的三维动力Lamb问题的解答．给出了埋置水平力作用下地基表面竖向位移、径向位移及周向位移的数值解．该研究为运用边界元法求解饱和地基的动力响应课题奠定了理论基础．     

Three-dimensional steady-state closed form solution for multilayered fluid-saturated anisotropic finite media due to surface/internal point source

A three-dimensional(3 D)steady-state solution of fluid saturated anisotropic finite media is presented.The eigenequation method and the pseudo-Stroh formalism are used to obtain the exact solution for homogeneous saturated finite media.The propagator matrix method is introduced to deal with the corresponding multilayered poroelastic media.The poroelastic solutions due to surface or internal point fluid source are obtained.The comparison of the results of the saturated isotropic media in a half space and those obtained by the finite element method is given to illustrate the accuracy of the solution in a finite domain.Numerical solutions of a sandwich poroelastic medium are presented to analyze its hydromechanical behaviors.Two ratios of the horizontal permeability to vertical permeability and different source positions are investigated.The results show that the fluid parameters and source positions have great influence on the hydromechanical behaviors of the layered media.     

波数-频率域内地基土表面位移Green函数的理论分析

建立了柱面坐标系下分层弹性半空间地基土模型。利用钟阳刚度矩阵法和Haskell-Thomson传递矩阵法推导出所有分层土体之间的振动传递关系;根据Helmholtz定理将土体的位移向量分解成势函数的形式,推导出弹性半空间表面应力与位移之间的关系;再将分层土体和半空间地基土通过位移与应力之间的关系进行耦合,得到分层弹性半空间地基土模型表面位移与应力之间的关系。结合单位脉冲荷载作用下地基土表面的边界条件,推导出波数-频率域内地基土表面位移Green函数的解析解,用Matlab程序语言对理论进行实现并通过算例对地基土表面位移Green函数的特征进行了分析和总结。     

Stress analysis of a layered elastic solid in contact with a rough surface exhibiting fractal behavior

A contact stress analysis is presented for a layered elastic half-space in contact with a rough surface exhibiting self-affine (fractal) behavior. Relationships for the mean contact pressure versus representative strain and the real half-contact width versus elastic properties of the layer and the substrate, asperity radius, layer thickness, and truncated half-contact width were derived from finite element simulations of a layered medium compressed elastically by a rigid cylindrical asperity. These relationships were incorporated in a numerical algorithm that was used to obtain the contact pressure distributions and stresses generated by the asperity contacts formed at the interface of the layered medium and the fractal surface. Analytical solutions illustrate the significance of the elastic material properties, layer thickness, and surface topography (roughness) on global parameters such as normal load and real contact area. Results for the contact pressure distribution and the surface and subsurface stresses provide insight into the initiation of yielding and the tendency for cracking in the layered medium. It is shown that cracking at the surface and the layer/substrate interface is more likely to occur in the case of a stiff layer, whereas surface cracking is more prominent for a relatively compliant layer.     

Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground

The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground was studied.First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soils were transformed into a group of governing differential equations with 1-order by the technique of Fourier ex- panding with respect to azimuth,and the state equation is established by Hankel integral transform method,furthermore the transfer matrixes within layered media are derived based on the solutions of the state equation.Secondly,by the transfer matrixes,the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions, drainage conditions on the surface of.ground as well as the contact conditions.Thirdly, the problem was led to a pair of dual integral equations describing the mixed boundary- value problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily.At the end of this paper,a numerical result concerning vertical and radical displacements both the surface of saturated ground and plate is evaluated.     

饱和土–隧道动力响应的2.5维有限元–边界元耦合模型

针对饱和土中异形隧道的三维动力响应问题,建立了2.5维有限元与边界元耦合模型.将隧道结构视为弹性体,采用2.5维有限元建立隧道模型;将地基土视为饱和多孔介质,采用2.5维边界元建立饱和土体模型.借助组合辅助问题基本解消除了边界积分方程的奇异性.利用饱和土与隧道接触面的位移、面力连续和完全透水或完全不透水边界条件,实现2.5维有限元和边界元模型的耦合求解.模型具有计算效率高、适用范围广的优点.通过与完全透水和完全不透水边界条件下轴对称问题的半解析解以及单相介质的2.5维有限元与边界元耦合模型对比,验证了本文模型的正确性.最后利用该模型计算了饱和土体中类矩形隧道在移动载荷作用下的三维动力响应,分析了不同土体渗透性下位移及孔隙水压力沿隧道轴向、环向和深度的分布规律.结果表明:(1)孔隙水压力随土体渗透性增大而显著减小,位移受土体渗透性影响小;(2)位移及孔隙水压力在隧道环向主要分布在距载荷作用点两侧约2 m的范围内;(3)孔隙水压力沿深度的衰减比土体位移快,且孔隙水压力和轴向位移沿深度的分布受土体渗透性影响大.     

3-D DYNAMIC RESPONSE OF TRANSVERSELY ISOTROPIC SATURATED SOILS

Introduction Thedynamicanalysisofsaturatedporoelasticmediaisofbroadmeaninginmanyaspectssuchasseismology,earthquakeengineering,soilmechanicsandgeophysics,etc.Thetransverselyisotropicsaturatedsoilsissolid fluidcoupledtwophasemediainwhichthe soilskeletondisp…     

A thermodynamical gradient theory for deformation and strain localization of porous media

In this work, a thermodynamically consistent gradient formulation for partially saturated cohesive-frictional porous media is proposed. The constitutive model includes a classical or local hardening law and a softening formulation with state parameters of non-local character based on gradient theory. Internal characteristic length in softening regime accounts for the strong shear band width sensitivity of partially saturated porous media regarding both governing stress state and hydraulic conditions. In this way the variation of the transition point (TP) of brittle-ductile failure mode can be realistically described depending on current confinement condition and saturation level. After describing the thermodynamically consistent gradient theory the paper focuses on its extension to the case of partially saturated porous media and, moreover, on the formulation of the gradient-based characteristic length in terms of stress and hydraulic conditions. Then the localization indicator for discontinuous bifurcation is formulated for both drained and undrained conditions.     

Theoretical analysis of generalized loadings and image forces in a planar magnetoelectroelastic layered half-plane

The problem of a planar transversely isotropic magnetoelectroelastic layered half-plane subjected to generalized line forces and edge dislocations is analyzed. The complete solutions consist only of the simplest solutions for an infinite magnetoelectroelastic medium with applied loadings. The physical meaning of this solution is the image method. It is shown that the explicit solutions include Green's function for originally applied singularities in an infinite medium and the other image singularities are induced to satisfy free surface and interface continuity conditions. The mathematical method used in this study provides an automatic determination for the locations and magnitudes of all image singularities. The locations and magnitudes of image singularities are dependent on the roots of the characteristic equation which is related to the material constants of the layered half-plane. With the aid of the generalized Peach-Koehler formula, the explicit expressions of image forces acting on dislocations are easily derived from the full-field solutions of the generalized stresses. Numerical results for the full-field distributions of stresses, electric fields, and magnetic fields in the layered half-plane medium are presented based on the analytical solutions. The image forces and equilibrium positions of one dislocation, two dislocations, and an array of dislocations are presented by numerical calculations and are discussed in detail.     

加层半空间硬币形(Penny—Shaped)交界裂纹的弹性波散射——远场散射波导分析

本文研究了加层半空间硬币形交界裂纹的弹性波散射。文中采用Hankel积分变换,将散射问题转化为求解对偶积分方程,进而变换为奇异积分方程组.应用积分变换,围道积分技术和渐近分析方法,得到了弹性层中散射位移场的远场模式,理论分析表明弹性层中的散射位移场主要由RayLeigh-Like-Mode波组成,该波是弹性层中的散射波导.最后,给出两组弹性常数组合情形下的数值结果及讨论.     

Features of deformation of poroelastic media with low structural strength

Many natural and technological processes are associated with deformation and fracture of saturated or being saturated poroelastic media. Among such processes one can mention fluid soaking through a dam, fluid inflow to the cracks of hydraulic fracture, polishing using porous materials and special fluids, flow in catalytic pellets. All these processes are accompanied by deformation and fracture of a matrix with fluid flow. The effects at the interface porous body–fluid are essential for the processes.The specific features of deformation of poroelastic media with low structural strength are considered in this paper. The compressibility of the matrix skeleton is larger as compared to the compressibility of the saturating fluid in such media.It is shown that the oozing of the fluid at the surface of the poroelastic medium occurs in the consolidated flow regime under the action of `fluid piston' like loads if the structural strength of the medium is low. This result is obtained for both plane (deformation of a layer or halfinfinite medium) and centrally symmetric (deformation of a sphere) problems.     

层状横观各向同性饱和土的非轴对称动力响应

通过方位角的Fourier变换,将圆柱坐标系下横观各向同性饱和土的Biot非轴对称波动方 程转化为一组一阶常微分方程组. 然后基于径向Hankel变换,建立问题的状态方程;求解状态方程后,得到传递矩阵. 进而利用传递矩阵,结合饱和层状地基的边界条件、排水条件及层间接触和连续条件,求解 了任意震源力作用下层状横观各向同性饱和地基频域动力响应问题. 时域解可通过频率的Fourier积分得到.     

多孔饱和半空间上弹性圆板垂直振动的积分方程

应用新的方法求解多孔饱和固体的动力基本方程－Ｂｉｏｔ波动方程,首先把Ｂｉｏｔ波动方程化为仅有土骨架位移和孔隙水压力的偏微分方程组,并且逐次解耦方法（不引入位移势函数）求解此偏微分方程组,然后按混合边值条件建立多孔饱和半空间上弹性圆板垂直振动的对偶积分方程,用Ａｂｅｌ变换化对偶积分方程为第二类Ｆｒｅｄｈｏｌｍ积分方程。文中考虑两种孔隙流体的表面边界条件：（ａ）半空间表面（包括圆板与半空间的接触面）是     

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids.The propagation of three longitudinal waves is represented through three scalar potential functions.The lone transverse wave is presented by a vector potential function.The displacements of particles in different phases of the aggregate are defined in terms of these potential functions.It is shown that there exist three longitudinal waves and one transverse wave.The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated.For the presence of viscosity in pore-fluids,the waves refracted to the porous medium attenuate in the direction normal to the interface.The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations.These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave.The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model.The conservation of the energy across the interface is verified.The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.     

层状饱和土Biot固结问题状态空间法

针对饱和多孔介质空间非轴对Biot固结问题，引入状态变量，构造了两组相比独立的状态变量方程，利用Fourier级数和Laplace-Hankel变换，将状态变量方程转换为两组一阶常微分方程组，提出了均质饱和多孔介质空间非轴对称Biot固结问题的传递矩阵，得到以状态变量和传递矩阵乘积的形式表示的均质饱和多孔介质空间非轴对称Biot固结问题的解，利用层间完全接触的条件，可得到N层饱和多孔介质空间非轴对称Biot固结问题的一般解析表达式，文中考虑几种不同的边界条件，分析了两个算例，数值结果表明该方法具有较高的计算精度和良好的计算稳定性。