流体饱和多孔弹性柱体动力响应的微分求积法

基于多孔介质混合物理论,在小变形的假设下,建立了两相不可压流体饱和多孔介质弹性空间轴对称问题的控制方程。在空间域和时间域内分别采用微分求积方法和二阶向后差分格式来离散控制方程,给出了处理对称轴处奇异性条件的方法,并在空间离散后采用消元法来缩减未知量,提高计算速度。作为应用,分析了流体饱和弹性多孔介质圆柱体的动力响应,考察了所布节点数对数值结果的影响。     

不可压饱和粘弹性多孔介质的变分原理及其无网格模拟

基于饱和多孔介质理论,在固相和液相微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,建立了流体饱和粘弹性多孔介质动力响应的若干Gurtin型变分原理,包括Hu-Washizu变分原理.利用所建立的变分原理,导出了流体饱和粘弹性多孔介质动力响应无网格数值模拟的离散控制方程,此方程是一个关于时间的对称微分方程组,便于分析计算.作为数值例子,研究了流体饱和粘弹性多孔柱体的一维动力响应,数值结果揭示了流体饱和粘弹性多孔柱体中波的传播特性以及固相粘性的影响.     

液饱和多孔介质中三维应力波的传播

为了深入研究液饱和多孔介质中应力波的传播，提出了三维两相细观计算模型．基于此模型。应用Galerkin余量法并计及流-固耦合界面的耦合效应，利用直接耦合的技术，开发了三维流-固混合显式动力有限元计算程序．在此基础上对冲击载荷作用下液饱和多孔介质中三维应力波的传播现象进行了数值模拟，并详细讨论了孔隙率，孔隙形状等因素对应力波传播主导波形的影响．     

基于显式有限元方法的两相介质弹塑性动力反应计算分析

针对增量形式的流体饱和两相多孔介质弹塑性波动方程组,运用基于显式逐步积分格式的时域显式有限元方法对该波动方程组进行求解,并应用基于SMP破坏准则的弹塑性动力本构模型描述两相介质的动力反应性质,对两相介质在输入地震波作用下的弹塑性动力反应进行计算和分析,将计算结果与相应的弹性动力反应的计算结果进行对比;对本文应用的弹塑性...     

不可压饱和粘弹性多孔介质固结问题的Gurtin型变分原理

基于多孔介质理论,在固相骨架和孔隙流体微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,利用卷积积分的性质,本文首先建立了以固相骨架位移、孔隙流体相对速度和孔隙流体压力为宗量的流体饱和粘弹性多孔介质固结问题的一个Gurtin型变分原理.其次,利用Lagrange乘子法解除相关的变分约束条件,建立了流体饱和粘弹性多孔介质固结问题的若干广义Gurtin型变分原理,包括第三类的Hu-Washizu型变分原理.最后,简单讨论了等价初边值问题的相应变分原理.这些Gurtin型变分原理的建立不仅丰富了饱和粘弹性多孔介质的相关理论,而且为相关数值模拟方法,如有限元法、无网格法等的建立奠定了理论基础.     

Homogenization of acoustic waves in strongly heterogeneous porous structures

We consider acoustic waves in fluid-saturated periodic media with dual porosity. At the mesoscopic level, the fluid motion is governed by the Darcy flow model extended by inertia terms and by the mass conservation equation. In this study, assuming the porous skeleton is rigid, the aim is to distinguish the effects of the strong heterogeneity in the permeability coefficients. Using the asymptotic homogenization method we derive macroscopic equations and obtain the dispersion relationship for harmonic waves. The double porosity gives rise to an extra homogenized coefficient of dynamic compressibility which is not obtained in the upscaled single porosity model. Both the single and double porosity models are compared using an example illustrating wave propagation in layered media.     

Singularities on wave fronts of slow waves in anisotropic fluid-saturated porous media

Energy focusing is found on the wave fronts of slow waves, which is a new propagation characteristic for slow waves in fluid-saturated porous materials. The material parameters, as well as the propagation directions, are chosen as the control parameters. Combined with the two axial variables, the influence of the anisotropy of the solid skeleton and pore fluid parameters on the propagation characteristic of slow waves in anisotropic fluid-saturated porous materials is discussed. The correspondence between the focusing on the wave fronts and the contours of zero Gaussian curvature on the slowness surface is explored. The development of the focusing patterns is investigated and the distinct trends in the energy flux focusing structures are revealed. This is helpful in further understanding the roles of the pore fluid in the damage of the fluid-saturated porous media.     

饱和土地基在简谐荷载作用下的解析分析

基于多孔介质混合物理论,用解析的方法研究了不可压饱和土地基受到简谐荷载作用下的动力响应问题。利用Fourier积分变换求解耦合方程组,得到了二维饱和土介质在简谐荷载作用下的通解。针对表面透水的具有下卧基岩的饱和土层以及半无限饱和土地基的边界条件,获得了固体骨架位移、孔隙流体位移、固体骨架有效应力以及孔隙流体压力的积分形式解答,并通过数值算例分析了饱和土地基在简谐荷载作用下的响应。     

流体饱和多孔介质动力问题的显式时域解法

为了简化分析,Zienkiewicz等基于Biot理论,在忽略流体相对于土骨架运动的加速度条件下,建立了以土骨架位移u和孔隙流体压力p为基本变量的u-p格式饱和两相介质动力方程。针对该u-p方程,在空间上,采用伽辽金法有限元离散,并结合对角化形式的质量矩阵和流体压缩矩阵,忽略相邻结点间的惯性和流体压缩量间的耦合作用。在时域内,基于杜修力等提出的显式算法和Euler预估-校正法,建立了一种具有二阶精度的全显式时域积分法。采用一维饱和土模型,对比提出算法的数值解与Simon方法的解析解,发现两者吻合良好,验证了本文方法的正确性。并分析了饱和土二维动力问题,以及渗透系数和排水条件对饱和土动力响应的影响。     

基于显式有限元方法的两相多孔介质地震反应研究

基于流体饱和两相多孔介质的弹性波动方程组,运用显式逐步积分格式与局部透射人工边界相结合的时域显式有限元方法对该波动方程组进行求解,对两相多孔介质在输入地震波作用下的弹性动力反应进行了计算和分析,以揭示两相多孔介质弹性地震反应的规律和性质.计算结果表明:两相介质弹性地震反应时程的波形与入射地震波的波形相同,且弹性地震反应的峰值出现的时刻对应于入射地震波的峰值出现的时刻.本文的数值计算同时表明了时域显式有限元方法在进行两相多孔介质地震反应计算分析时的有效性.     

一维流体饱和粘弹性多孔介质层的动力响应

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。     

Material instabilities of anisotropic saturated multiphase porous media

This paper analyses the material instability of fully saturated multiphase porous media. On account of the fact that anisotropic mechanical behaviours are widely observed in saturated and partially saturated geomaterials, the anisotropic constitutive model developed by Rudnicki for geomaterials is used to model the anisotropic mechanical behaviour of the solid skeleton of saturated porous geomaterials in axisymmetric compression test. The inertial coupling effect between solid skeleton and pore fluid is also taken into account in dynamic cases. Conditions for static instability (strain localisation) and dynamic instability (stationary discontinuity and flutter instability) of fully saturated porous media are derived. The critical modulus, shear band angle for strain localisation, and the bound within which flutter instability may occur are given in explicit forms. The effects of material parameters on material instability are investigated in detail by numerical computations.     

流固耦合地震波动问题的显式谱元模拟方法

流固耦合地震波动问题主要研究由流体和固体构成的复杂系统中地震波传播特性及其规律. 传统模拟方法中一般以声波方程、弹性波方程的数值解分别描述理想流体和弹性固体中的波动, 并实时地处理两种不同性质介质之间的相互耦合作用, 数值格式复杂且限制数值模拟精度与计算效率. 本文采用谱元法结合多次透射公式人工边界条件实现了一种流固耦合地震波动问题的高阶显式数值计算方法. 该方法利用了流固耦合问题统一计算框架,可将饱和多孔介质的Biot波动方程分别退化为理想流体的声波方程和弹性固体的弹性波方程. 通过P波垂直入射的水平成层理想流体-饱和多孔介质-弹性固体场地模型、P波斜入射的不规则层状界面以及任意形状界面的理想流体-饱和多孔介质-弹性固体场地模型等三个算例, 与传递函数法解析解以及集中质量有限元法计算结果进行对比分析, 证明了本文方法的正确性与有效性. 数值模拟结果表明, 本文方法相较传统有限元法可以少得多的节点数量获得更高的数值精度, 并且在较宽的频率范围内都能可靠地模拟出流固耦合系统的动力响应, 充分体现出本文方法兼顾高精度、计算效率和复杂场地建模灵活的特点.      

On well-posedness of the dynamic problem for an anisotropic fluid-saturated solid

It is known that a high degree of anisotropy in the constitutive behaviour of a solid may result in the loss of hyperbolicity of the dynamic equations in the form of either complex-conjugate or purely imaginary characteristic wave speeds (flutter ill-posedness and shear band formation, respectively). In the present paper we investigate the characteristic wave speeds in the dynamic problem for a transversely isotropic fluid-saturated porous solid. Three cases are considered: a dry solid and a saturated solid under locally undrained and drained conditions. It is shown that, for given constitutive parameters of the solid skeleton, the dynamic problem for a drained solid may become ill-posed due to the flutter-type loss of hyperbolicity, while the dynamic equations for a dry and an undrained solids remain hyperbolic. For a given solid skeleton, the characteristic wave speeds are strongly influenced by the pore fluid compressibility which, in turn, is extremely sensitive to the presence of a small amount of free gas.     

3-D DYNAMIC RESPONSE OF TRANSVERSELY ISOTROPIC SATURATED SOILS

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

Gradient-dependent plasticity model and dynamic strain localisation analysis of saturated and partially saturated porous media: one dimensional model

Dynamic strain localisation in saturated and partially saturated porous media is investigated with a one-dimensional model in this paper. The porous medium is treated as a multiphase continuum, with the pores filled by water and air, this last one at atmospheric pressure. A gradient-dependent plasticity model is introduced to describe the plastic behaviour of the solid skeleton. Material instability due to the softening behaviour of the solid skeleton and the well-posedness of the initial value problem are studied. The advantages of the enhanced model are that the governing equations remain hyperbolic even in the softening regime and convergent solutions with mesh refinements are obtained. Moreover, the influence of permeability in the seepage process for the development of the localised zones is discussed. We find that the permeability plays an important part in the compressive wave propagation, but not in the shear wave cases. For numerical implementation of the present method, a parametric variational principle is introduced by which the original problem is reduced to a standard linear complementary problem in mathematical programming. The results of a one dimensional example are given to illustrate the efficiency of the techniques presented here.     

GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

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

Nonlinear and semilinear dynamic poroelasticity with microstructure

Nonlinear equations for wave propagation through dry or fluid-saturated porous elastic media are derived using a variational formulation. The method presented is very similar to the approach of Bedford and Drumheller, including microinertia terms for local density fluctuations of fluid and solid. One major difference is the choice of a Lagrangian (rather than Eulerian) reference frame locked to the solid constituent. This choice of reference frame is preferable for porous solids and also allows direct comparison to Biot's theories of nonlinear and semilinear rheology of porous solids.     

Parameters inversion of fluid-saturated porous media based on neural networks

The multi-layers feedforward neural network is used for inversion of material constants of fluid-saturated porous media. The direct analysis of fluid-saturated porous media is carried out with the boundary element method. The dynamic displacement responses obtained from direct analysis for prescribed material parameters constitute the sample sets training neural network. By virtue of the effective L-M training algorithm and the Tikhonov regularization method as well as the GCV method for an appropriate selection of regularization parameter, the inverse mapping from dynamic displacement responses to material constants is performed. Numerical examples demonstrate the validity of the neural network method. Project supported by the National Natural Science Foundation of China (Nos. 19872002 and 10272003) and Climbing Foundation of Northern Jiaotong University.     

Hydraulic fracture in poro-hydro-elastic media

The prediction of fluid-driven crack propagation in deforming porous media has achieved increasing interest in recent years, in particular with regard to the modeling of hydraulic fracturing, the so-called “fracking”. Here, the challenge is to link at least three modeling ingredients for (i) the behavior of the solid skeleton and fluid bulk phases and their interaction, (ii) the crack propagation on not a priori known paths and (iii) the extra fluid flow within developing cracks. To this end, a macroscopic framework is proposed for a continuum phase field modeling of fracture in porous media that provides a rigorous approach to a diffusive crack modeling based on the introduction of a regularized crack surface. The approach overcomes difficulties associated with the computational realization of sharp crack discontinuities, in particular when it comes to complex crack topologies including branching. It shows that the quasi-static problem of elastically deforming, fluid-saturated porous media at fracture is related to a minimization principle for the evolution problem. The existence of this minimization principle for the coupled problem is advantageous with regard to a new unconstrained stable finite element design, while previous space discretizations of the saddle point principles are constrained by the LBB condition. This proposed formulation includes a generalization of crack driving forces from energetic definitions towards threshold-based criteria in terms of the effective stress related to the solid skeleton of a fluid-saturated porous medium. Furthermore, a Poiseuille-type constitutive continuum modeling of the extra fluid flow in developed cracks is suggested based on a deformation-dependent permeability, that is scaled by a characteristic length.