A linear constitutive model for unsaturated poroelasticity by micromechanical analysis

This paper extends the Biot theory of poroelasticity from the saturated to unsaturated case. The Biot phenomenological model uses parameters that are easily observable, such as the deformation of porous frame, total stress, pore pressure, and fluid specific discharge. Such model is preferred for engineering applications. At this macroscopic level, the extension of Biot theory from saturated to unsaturated is straightforward. The constitutive constants, however, are combined properties of solid, pore space, and fluids. In the unsaturated case, the constants are functions of the degree of saturation. Their measurements and tabulation over a range of saturation is generally not feasible for practical applications. In this work, a Biot-Willis type analysis is performed for the unsaturated case to provide a theory that the bulk material constants can be evaluated using laboratory measurable micromechanical constants under saturated condition, plus a capillary pressure curve (saturation versus suction pressure) typically available for unsaturated porous medium, without the need of measurement at each state of saturation. In particular, it is demonstrated that the surface energy contained in the meniscus interface manifests as a “capillary modulus,” given by the negative inverse slope of the capillary pressure curve. A rigorous analysis based on the thermodynamic variational energy approach is also conducted to lend theoretical support to the phenomenological approach. The presented model can bring a closure to the practical engineering modeling of the deformation of partially saturated porous medium that lacks the information of material constants over the range of saturation.     

Three-dimensional finite element modelling for consolidation due to groundwater withdrawal in a desaturating anisotropic aquifer system

A poroelastic numerical model is presented to evaluate three-dimensional consolidation due to groundwater withdrawal from desaturating anisotropic porous media. This numerical model is developed based on the fully coupled governing equations for groundwater flow in deforming variably saturated porous media and the Galerkin finite element method. Two different cases of unsaturated aquifers are simulated for the purpose of comparison: a cross-anisotropic soil aquifer, and a corresponding isotropic soil aquifer composed of a geometrically averaged equivalent material. The numerical simulation results show that the anisotropy has a significant effect on the shapes of three-dimensional hydraulic head distribution and displacement vector fields. Such an effect of anisotropy is caused by the uneven partitioning of the hydraulic pumping stress between the vertical and horizontal directions in both groundwater flow field and solid skeleton deformation field. Copyright © 1999 John Wiley & Sons, Ltd.     

Vertical vibrations of a rigid disk embedded in a poroelastic medium

This paper considers the steady-state vertical vibrations of a rigid circular disk embedded at a finite depth below the free surface of a poroelastic medium. Biot's elastodynamic theory for porous media is used in the analysis. General solutions for axisymmetric poroelastic fields are obtained by using Hankel integral transforms. Analytical solutions for influence functions corresponding to four types of buried axisymmetric excitations are derived. The embedded disk problem is fomulated in terms of a set of coupled integral equations for unknown traction and pore pressure jumps across the disk. The kernel functions of the integral equations are the influence functions corresponding to buried vertical, radial and pore pressure ring loads. The system of integral equations is solved numerically by discretizing the disk into several concentric annular rings. Selected numerical solutions for displacements, vertical stress and pore pressure due to a buried fully flexible disk (uniform pressure) are also presented. The vertical compliances of a rigid disk are examined for different depths of embedment, poroelastic materials and hydraulic boundary conditions. Solutions for traction and pore pressure jumps are also examined. The present results are useful in the study of dynamic response of embedded foundations and anchors in poroelastic soils. Copyright © 1999 John Wiley & Sons, Ltd.     

基于多孔介质弹性理论的碳酸盐岩地层超压预测

碳酸盐岩地层超压预测目前仍然是国内外研究的难点问题。碎屑岩超压预测方法均是建立在明显的超压测井、地震宏观响应规律基础上的经验关系,这些经验性方法不适用于因岩性致密使得超压地球物理响应微弱的碳酸盐岩地层。通过碳酸盐岩样品超压岩石物理模拟实验,分析了在应力-孔隙压力共同作用下岩石中声波速度、弹性参数的变化规律;基于多孔介质弹性理论和广义胡克定律推导并建立了表征孔隙压力与岩石弹性参数定量关系的理论模型,即多孔介质弹性理论的超压预测量化模型。以川东北地区典型碳酸盐岩超压钻井为例,开展了碳酸盐岩地层超压预测应用研究:针对碳酸盐岩地层选择油气水测井综合解释模型获取岩石物性参数;利用Voigt-Reuss-Hill平均模量模型计算岩石基质体积模量,利用Wood模型和Patchy模型计算孔隙流体体积模量,利用BISQ模型计算岩石骨架体积模量,然后通过多孔介质弹性理论量化模型预测超压。预测结果显示预测压力与钻杆实测压力(DST)吻合较好,与泥浆密度换算压力和随钻监测压力变化趋势相近,表明这种基于多孔介质弹性理论的超压预测量化模型是一种解决碳酸盐岩地层超压预测的新途径。     

Cracking risk of partially saturated porous media—Part II: Application to drying shrinkage

Drying of deformable porous media results in their shrinkage, and it may cause cracking provided that shrinkage deformations are hindered by kinematic constraints. Herein, we focus on slow drying of an initially water‐saturated sample of a microheterogeneous poroelastic material damaged by parallel mesocracks. The cracking risk is analyzed by means of the thermodynamics‐based microporoelasticity model described in the companion paper (Part I), which is extended toward consideration of the hierarchical organization of cracked argillite. Drying of a material sample is studied in a framework where macrodisplacements in direction of the crack normal are blocked, while elsewise macrostress‐free boundary conditions prevail. The model implies that the opening/closure behavior of the cracks is governed by an effective pressure, in which the average crack (under)pressure, making the crack opening smaller, competes with the average micropore (under)pressure that makes the crack opening larger. The driving force for crack propagation is a quadratic function of this effective pressure. The model proposes that if drying shrinkage deformations are hindered by kinematic constraints, onset of cracking becomes possible once air entry into the cracks is observed. Copyright © 2009 John Wiley & Sons, Ltd.     

Drained and undrained pullout capacity of a stiff inclusion in a saturated poroelastic matrix

Shear‐lag analysis is used to obtain closed‐form solutions for the problem of a stiff inclusion embedded in a poroelastic soil matrix. The following assumptions are made: the soil matrix and the inclusion are elastic; plane strain conditions apply; and shear stresses at the soil‐inclusion interface follow Coulomb's friction law. Two solutions are obtained, the first one for drained conditions where no excess pore pressures are generated, and the second one for undrained conditions where excess pore pressures are produced and the soil does not change volume during pullout. The solutions are verified by comparing analytical predictions with numerical results obtained using a finite element method. Predictions from the analytical solutions are also compared with results from experiments conducted in a large‐scale pullout box. Both comparisons show good agreement. The analytical solution shows that the pullout capacity in drained and undrained conditions is overall independent of the relative stiffness of the soil and the inclusion. The most important factor controlling the pullout capacity is the coefficient of friction between the soil and the inclusion. Both drained and undrained pullout capacities increase with the coefficient of friction; although the drained capacity shows a proportional increase, it is not so for the undrained capacity. The ratio of undrained to drained pullout capacity is about 0.9 for friction coefficients smaller than 0.2, but can be as small as 0.6 for a coefficient of friction of 1.0. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimating the crust permeability from fluid-injection-induced seismic emission at the KTB site

During the hydraulic-fracturing experiment in the German Continental Deep Drilling Borehole (KTB) in December 1994, microseismic activity was induced. Here we develop a technique for estimating permeability using the spatio-temporal distribution of the fluid-injection-induced seismic emission. The values we have obtained for the KTB experiment (0.25times10^-16 to 1.0times10^-16 1.0times10^-16 m²) are in a very good agreement with the previous hydraulic-type permeability estimates from KTB deep-observatory studies. In addition, our estimates of the hydraulic diffusivity support the previously calculated value for the upper crust, which is of the order of 1 m² s^-1. However, this estimate now relates to the depth range 7.5-9 km.     

Transient solution for multilayered poroviscoelastic media obtained by an exact stiffness matrix formulation

The authors propose a semi‐analytical approach to studying wave propagation in multilayered poroviscoelastic grounds due to transient loads. The theoretical development is based on the exact stiffness matrix method for the Biot theory coupled with a matrix conditioning technique. It is developed in the wavenumber frequency domain after a Fourier transform on the surface space variables and the time variable. The usual methods yield a poorly conditioned numerical system. This is due in particular to the presence of mismatched exponential terms. In this article, increasing exponential terms are eliminated and only decreasing exponential terms remain. Consequently, the method can be applied to a large field of configurations without restriction concerning high frequencies, large Fourier transform parameters or large layer thicknesses. Validation and efficiency of the method are discussed. Effects of layering show that the layer impedance influence on solid and fluid displacements. Moreover, this approach can be of interest for the validation of numerical tools. Copyright © 2009 John Wiley & Sons, Ltd.