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.     

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.     

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.     

A phase-field modeling approach of hydraulic fracture in saturated porous media

Continuum porous media theories, extended by a diffusive phase-field modeling (PFM) approach, introduce a convenient and efficient tool to the simulation of hydraulic fracture in fluid-saturated heterogeneous materials. In this, hydraulic- or tension-induced fracture occurs in the solid phase. This leads to permanent local changes in the permeability, the volume fractions of the constituents as well as the interstitial-fluid flow. In this work, the mechanical behaviors of the multi-field, multi-phase problem of saturated porous media, such as the pore-fluid flow and the solid-skeleton deformation, are described using the macroscopic Theory of Porous Media (TPM). To account for crack nucleation and propagation in the sense of brittle fracture, the energy-minimization-based PFM procedure is applied, which approximates the sharp edges of the crack by a diffusive transition zone using an auxiliary phase-field variable. Furthermore, the PFM can be implemented in usual continuum finite element packages, allowing for a robust solution of initial-boundary-value problems (IBVP). For the purpose of validation and comparison, simulations of a two-dimensional IBVP of hydraulic fracture are introduced at the end of this research paper.     

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．     

Effects of Mineral Dissolution Ratios on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Media

The main purpose of this article is to investigate, both theoretically and computationally, the effects of mineral dissolution ratios on the different respects of chemical-dissolution front instability problems in fluid-saturated porous media. In order to get a better understanding of how the mineral dissolution ratio affects the propagation and evolution of a planar chemical-dissolution front in an infinite space consisting of a fluid-saturated porous medium, the theoretical analysis method is used to derive the generous solution to the propagation speed of the planar chemical-dissolution front, while the computational simulation method is employed to simulate the detailed evolution process when the planar chemical-dissolution front is evolved into complicated morphologies at the supercritical Zhao numbers. The related theoretical results reveal that the mineral dissolution ratio plays an important role in controlling the propagation speed of a planar chemical-dissolution front in the fluid-saturated porous medium. An increase in the value of the mineral dissolution ratio can result in a remarkable decrease in the value of the propagation speed of a planar chemical-dissolution front. On the other hand, the related computational simulation results demonstrate that the mineral dissolution ratio has a considerable influence on the evolution pattern of a planar chemical-dissolution front during its propagation in the fluid-saturated porous medium. An increase in the mineral dissolution ratio can reduce the likelihood for a planar chemical-dissolution front to evolve from the initial planar shape into different morphologies within the fluid-saturated porous medium of finite size.     

A micromechanical analysis of damage propagation in fluid-saturated cracked mediaUne analyse micromécanique de la propagation de l'endommagement d'une fissure sous pression de fluide

We first revisit the well known framework of Linear Elastic Fracture Mechanics (LEFM) in the case of a fluid-saturated crack. We next consider a r.e.v. of cracked medium comprising a family of cracks characterized by the corresponding crack density parameter ε. Generalizing the classical energy approach of LEFM, the proposed damage criterion is written on the thermodynamic force associated with ε, which is estimated by means of standard homogenization schemes. This criterion proves to involve a macroscopic effective strain tensor, or alternatively the Terzaghi effective stress tensor. The stability of damage propagation is discussed for various homogenization schemes. A comparison with experimental results is presented in the case of a uniaxial tensile test on concrete. To cite this article: L. Dormieux et al., C. R. Mecanique 334 (2006).     

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.     

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.     

流体饱和多孔介质的动力学Gurtin型变分原理和有限元模拟

基于多孔介质理论。在两相不可压和小变形的假设下，建立了流体饱和弹性多孔介质的动力学Gurtin型变分原理，并导出了以此变分原理为基础的有限元离散公式，由于Gurtin型变分原理是卷积型的空间积分泛函，空间的有限元离散导致一个关于时间的对称微分—积分方程组，在一般条件下。该积分—微分方程组可转化为对称的微分方程组，这组方程有别于标准Galerkin有限元的非对称离散方程组，作为数值例子，分析了流体饱和弹性多孔介质中一维纵向波的传播和反射，其结果进一步揭示了饱和多孔介质中波的传播特性。     

Theoretical Analyses of the Effects of Solute Dispersion on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Media

This article deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including solute dispersion effects. Since the solute equilibrium concentration is much smaller than the molar density of the dissolvable mineral in a mineral dissolution system, a limit case, in which the ratio of the solute equilibrium concentration (in the pore fluid) to the molar density of the dissolvable mineral (in the solid matrix of the porous medium) approaches zero, is considered in the theoretical analysis. Under this assumption, the critical condition under which a planar chemical-dissolution front becomes unstable has been mathematically derived when solute dispersion effects are considered. The present theoretical results clearly demonstrated that: (1) the propagation speed of a planar chemical-dissolution front in the case of considering solute dispersion effects is the same as that when solute dispersion effects are neglected. This indicates that solute dispersion does not affect the propagation speed of the planar chemical-dissolution front in a fluid-saturated porous medium. (2) The consideration of solute dispersion can cause a significant increase in the critical Zhao number, which is used to judge whether or not a planar chemical-dissolution front may become unstable in the fluid-saturated porous medium. This means that the consideration of solute dispersion can stabilize a planar chemical-dissolution front, because an increase in the critical Zhao number reduces the likelihood of the planar chemical-dissolution front instability in a fluid-saturated porous medium. In addition, the present results can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of chemical dissolution fronts in two-dimensional fluid-saturated porous media.     

川藏公路地质环境与整治改建方案的思考

川藏公路由于地质环境复杂、建设标准低、后遗病害多,抗灾能力差,泥石流、滑坡、山崩、雪害、水毁等自然灾害频繁发生,公路阻车断道严重。国家投入巨资进行整治改建,并取得了明显的效果,但由于自然环境特殊、影响因素复杂,许多特大型、大型工程地质病害问题还没有可行、可靠的解决方案。本文通过分析川藏公路沿线的地质环境和灾害特点,总结历年整治改建和经验的教训,提出川藏公路建设的途径、可能达到的目标和应采用的原则。     

Characteristic analysis for stress wave propagation in transversely isotropic fluid-saturated porous media

According to generalized characteristic theory, a characteristic analysis for stress wave propagation in transversely isotropic fluid-saturated porous media was performed. The characteristic differential equations and compatibility relations along bicharacteristics were deduced and the analytical expressions for wave surfaces were obtained. The characteristic and shapes of the velocity surfaces and wave surfaces in the transversely isotropic fluid-saturated porous media were discussed in detail. The results also show that the characteristic equations for stress waves in pure solids are particular cases of the characteristic equations for fluid-saturated porous media.     

Influence of a rigid skeleton pore structure on wave propagation in a fluid-filling porous medium

This work concerns an analysis of the influence of a rigid skeleton pore structure on wave propagation in a fluid-filling porous medium. The analysis is based on the continuum theory of a deformable porous medium in which the pore structure is described by two macroparameters. Considerations comprise two questions: the influence of the pore structure on wave-propagation velocity analysed for the quasilinear case and the role of structure in the reflection-refraction wave phenomenon in fluid at the contact surface of two porous media. It has been shown that the pore structure reduces the velocity of wave and together with the angle of incidence it defines the reflection-refraction wave phenomenon.     

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.     

A solution to the hydraulic fracture problem in the traveling wave form

Solutions to the system of equations describing the propagation of hydraulic fracture cracks in a porous medium are obtained in the traveling wave form. The only sought solution is the separatrix of integral curves on the “penetration depth-crack width” plane. Some necessary dependencies that should be given at the crack inlet are found for the fluid flow rate and the fluid pressure. The crack width and the fluid penetration depth are related by power laws in the limiting cases when the crack propagation processes or the fluid penetration processes are dominant.     

基于物理界面的双重介质有限裂隙渗流模型

基于连续介质或者离散裂隙假设,含裂隙的多孔介质渗流问题有多种数学力学模型。受物理界面的启发,提出一种新的有限裂隙连续介质力学模型,可以为宏观裂隙-多孔介质内的流体输运问题等提供近似计算方案。该模型属于一类双重介质模型,将曲面上低维度的流场转化为三维空间的流场,并且与连续的多孔介质的流场耦合,在数学上表示为统一的输运控制方程和初始边界条件。这个近似模型为不方便实施高维度-低维度耦合求解的数值计算方法提供新的模拟思路,如光滑粒子流体动力学等无网格粒子类方法。     

Consecutive matrix cracking in contiguous plies of composite laminates

Propagation behaviors of obliquely-crossed microcracks induced by matrix cracks in adjacent plies of composite laminates were numerically analyzed using finite element modeling. Oblique coordinate system along obliquely-crossed cracks was defined and applied to the finite element formulation, which enabled geometrically parametric analysis for arbitrary oblique angles using a single discrete model. Three-dimensional stress analyses of [S/θ_n/90]s laminate with microcracks in θ-ply and fully developed matrix cracks in 90-ply were performed under various conditions of angle θ, θ-ply crack length, θ-ply thickness, etc. Energy release rates associated with θ-ply crack propagation in the θ-ply fiber direction were calculated in order to assess θ-ply cracking conformations. The results suggested that presence of 90-ply cracks affects θ-ply crack propagation, especially mode-I energy release rates, depending on angle θ. Furthermore, effects of angle θ, θ-ply thickness and S layer configuration on the interaction between matrix cracks in θ- and 90-plies were clarified. Finally, crack accumulation behaviors in [0/θ₂/90]s laminates were experimentally investigated and compared with the analytical results.     

DQM for dynamic response of fluid-saturated visco-elastic porous media

Based on the Porous Media Theory (PMT), a mathematical model of space-axisymmetrical problems for incompressible fluid-saturated visco-elastic porous media is presented in the case of small deformation, in which the differential-type constitutive relation is applied to describe the mechanical characteristics of solid skeleton. The differential quadrature method (DQM) and the second-order backward difference scheme are used to discretize the governing equations on the spatial and temporal domains, respectively, and a method is proposed to deal with the singularity conditions at points located on the symmetry axis. As application, the dynamic behavior of a column of fluid-saturated elastic porous media is analyzed firstly. The obtained results are compared with the analytical results in the existing literature, they are comparatively accordant, which means that the model and method presented in this paper are correct, and the obtained results are reliable. Further, the dynamic response of a space-axisymmetrical body of fluid-saturated visco-elastic porous media is analyzed, in which the material characteristic of the solid skeleton is described by Burgers model with four parameters.