Analysis of a point sink embedded in a porous elastic half space

Closed-form solutions are presented for the steady-state distributions of displacement, pore pressure and stress around a point sink embedded in a homogeneous, isotropic elastic half space. These solutions have been evaluated for a typical case of a sink (pump) buried in sand and the magnitude of the settlement of the ground surface has been estimated.     

Consolidation of a poroelastic half-space with anisotropic permeability and compressible constituents by axisymmetric surface loading

The fully coupled Biot quasi-static theory of linear poroelasticity is used to study the consolidation of a poroelastic half-space caused by axisymmetric surface loads. The fluid and solid constituents of the poroelastic medium are compressible and its permeability in the vertical direction is different from its permeability in the horizontal direction. An analytical solution of the governing equations is obtained by taking the displacements and the pore pressure as the basic state variables and using a combination of the Laplace and Hankel transforms. The problem of an axisymmetric normal load is discussed in detail. An explicit analytical solution is obtained for normal disc loading. Detailed numerical computations reveal that the anisotropy in permeability as well as the compressibilities of the fluid and solid constituents of the poroelastic medium have significant effects on the consolidation of the half-space. The anisotropy in permeability may accelerate the consolidation process and may lead to a dilution in the theoretical prediction of the Mandel-Cryer effect. The compressibility of the solid constituents may also accelerate the consolidation process.     

Analysis of subsidence due to a point sink in an anisotropic porous elastic half space

Analytical solutions of the long-term consolidation deformation and excess pore water pressure due to fluid withdrawal from a saturated anisotropic porous elastic half space are presented. In the analysis, both the permeability and the elastic properties are considered cross-anisotropic. Cases of pervious and impervious half-space boundary are studied. The consolidation settlements as effected by the anisotropy and boundary conditions for pore water are illustrated and discussed.     

Quasi-static deformation due to two-dimensional seismic sources embedded in an elastic half-space in welded contact with a poroelastic half-space

The Biot linearized theory of fluid saturated porous materials is used to study the plane strain deformation of a two-phase medium consisting of a homogeneous, isotropic, poroelastic half-space in welded contact with a homogeneous, isotropic, perfectly elastic half-space caused by a two-dimensional source in the elastic half-space. The integral expressions for the displacements and stresses in the two half-spaces in welded contact are obtained from the corresponding expressions for an unbounded elastic medium by applying suitable boundary conditions at the interface. The case of a long dip-slip fault is discussed in detail. The integrals for this source are solved analytically for two limiting cases: (i) undrained conditions in the high frequency limit, and (ii) steady state drained conditions as the frequency approaches zero. It has been verified that the solution for the drained case (ω → 0) coincides with the known elastic solution. The drained and undrained displacements and stresses are compared graphically. Diffusion of the pore pressure with time is also studied.     

Rayleigh波在饱和半空间中圆形洞室周围的散射

基于Biot的两相介质理论,采用间接边界积分方程法,求解了Rayleigh波在饱和半空间中圆形洞室周围的二维散射问题,分析了入射波频率、孔隙率、边界渗透条件和洞室埋深等参数对地表位移幅值、洞室表面和地表孔隙水压力的影响。研究结果表明,由于圆形洞室的存在,饱和半空间地表位移幅值和地表孔隙水压被明显放大:在透水条件下,水平和竖向位移最大值分别比自由场放大了10.1倍和11.2倍;在不透水条件下,水平和竖向位移最大值分别比自由场放大了12.0倍和9.6倍,地表孔隙水压力放大了2.1~3.0倍。地表位移和孔隙水压力最大值均出现在入射波近端洞室边界附近。随着Rayleigh波入射频率的增大和洞室埋深的增加,地表位移幅值的放大作用有所减小。在相同孔隙率条件下,当入射频率为1.0时,洞室表面孔隙水压力最大;当入射频率为2.0时,洞室表面孔隙水压力最小,洞室表面最大孔隙水压力出现在洞室顶部。     

Consolidation around a point heat source

When a heat source such as a canister of radioactive waste is buried in a saturated soil the temperature changes that occur will cause the pore water to expand a greater amount than the voids of the soil. The temperature change will thus usually be accompanied by an increase in pore pressure. If the soil is sufficiently permeable these pore pressures will dissipate. This paper develops an analytic solution for the fundamental problem of a point heat source buried deep in a saturated soil.     

The axial loading of a rigid circular anchor plate embedded in an elastic half-space

The present paper examines the axisymmetric problem related to the loading of a rigid circular anchor plate which is embedded in bonded contact with an isotropic elastic half-space. A Hankel transform development of the governing equations is used to reduce the associated mixed boundary value problem to a set of coupled Fredholm integral equations of the second kind. These equatons are solved in a numerical fashion to generate results of engineering interest. In particular, the results indicate the influence of the depth of embedment on the axial stiffness of the rigid anchor plate.     

An analytical solution for the consolidation around a driven pile

Field studies have shown that the driving of a displacement pile into cohesive soil generates large excess pore pressures in the vicinity of the pile. These pore pressures are often larger than the effective overburden pressure and facilitate the installation of the pile. The subsequent increase in bearing capacity of the pile is largely controlled by the dissipation of the excess pore pressures and a consequent increase in the effective stresses acting on the pile. The paper presents a closed formanalytical solution for the radial consolidation of the soil around a driven pile, assuming that the soil skeleton deforms elastically. This assumption is examined in the light of the predicted effective stress changes in the soil and is shown to lead to, a realistic model for the decay of pore pressure near the pile with time after driving. Although the solution may be applied to any initial distribution of excess pore pressure, attention is focussed on that due to the expansion of a cylindrical cavity in an ideal elastic, perfectly plastic soil. The resulting logarithmic variation of excess pore pressure with radius is considered to be close to that generated around a pile as a result of driving. In addition to giving estimates of the time needed for a driven pile to achieve its maximum strength, the solution may also be used in the analysis of pressuremeter tests to provide in-situ measurements of the coefficient of consolidation of the soil.     

Consolidation around a heat source buried deep in a porous thermoelastic medium with anisotropic flow properties

A solution is derived for the heat flow and consolidation which occur when a heat source is buried deep in a porous thermoelastic soil having anisotropic flow properties. This solution is used to examine the pore pressure generation and dissipation near both point and cylindrical heat sources. An increase in temperature will tend to generate an increase in excess pore pressure. However, the pore water will tend to flow from regions of high excess pore pressure to regions of low excess pore pressure, and so consolidation will occur, and temperature-generated excess pore pressures will tend to dissipate. Many natural soils exhibit horizontal layering and so have a higher horizontal than vertical permeability. It is shown that in soils the excess pore pressure generated by a heat source is significantly less than that in an isotropic soil having an equal vertical permeability.     

条形埋置基础固结分析计算图表

基于比奥固结理论,用有限元方法研究了有限饱和土层中条形埋置基础的固结沉降特性。仔细分析了影响固结度的3个参数：基础埋深与土层厚度的比值;土层厚度与基础宽度的比值;土骨架的泊松比。根据分析结果,提出了归一化无量纲时间,并给出了计算条形埋置基础固结度的计算图表。这些图表为基础设计提供了便捷准确的计算方法。运用文中图表计算固结度的最大误差不超过3 %。     

Determination of permeability in anisotropic rock-masses from integral samples

Summary Determination of Permeability in Anisotropic Rock-Masses From Integral SamplesA method is presented which makes it possible to characterize the permeability of a rock mass as an anisotropic magnitude — i. e. to determine its permeability tensor — from a characterization of its fracturing by means of integral samples.For the purpose, a theory is developed by means of which the permeability tensor can be calculated from the attitudes and openings of the fractures and — if infillings are present — also from their coefficient of permeability. All these magnitudes are determined in integral samples, it being assumed that the sampled fractures are continuous and plane, and have the same characteristics as the section of the fractures present in the samples. Possible deviations with respect to this assumption are taken into account by means of correcting factors derived from the results of pressure tests in situ. The permeability tensor of a rock mass at a point can be determined from a single integral sample, provided this is representative of the fracturing.Results of the application of the method are presented, which show it to look very promising.With 16 Figures     

Land subsidence due to gas/oil production in inhomogeneous transversally anisotropic half-space by a boundary element method

In a previous paper¹ the authors have developed and implemented a new boundary element (BE) model to simulate and predict land subsidence occurring over three-dimensional gas/oil fields in a homogeneous and isotropic half-space. The approach relies on Betti's reciprocal theorem and makes use of the classical fundamental solution of Boussinesq in the framework of the theory of linear poroelasticity. The BE method is here extended to inhomogeneous, transversally anisotropic soils by the aid of a two-dimensional finite element (FE) model which provides a fundamental numerical solution for the actual multi-layer setting of the subsurface system. The new FE–BE approach is then used to simulate the subsidence caused by gas production over the deep reservoir of Campo Ravenna Terra, Ravenna (Italy) from 1950 to 1980. The results compare very favourably with the outcome from a full more expensive three-dimensional FE model of the same occurrence.     

含橡胶纤维钙质砂的渗透和固结特性试验研究

珊瑚岛礁常年处于复杂的海洋动力环境中,岛上堤坝围堰、基坑等构筑物的地基渗透变形甚至破坏会导致地基承载力失效的可能性变高。为探究橡胶纤维固化钙质砂的渗透特性和固结特性,采用常水头渗透试验和固结试验研究不同纤维含量下钙质砂的渗透规律和固结变形规律,并设置含纤维玻璃珠对照组。钙质砂具有颗粒形状极不规则、多棱角、内孔隙多等特点,为进一步研究颗粒形状的影响,采用高速动态图像粒度分析仪对钙质砂和玻璃珠的颗粒形状和粒径进行分析。试验结果表明,纤维含量对钙质砂试样渗透特性几乎无影响,但是含纤维玻璃珠试样中,随着纤维含量的增加,渗透系数先增加后减小。由于形状不规则橡胶纤维的加入,一定程度上填补了钙质砂之间的孔隙;钙质砂试样存在 800 kPa 的压力阈值,当压力超过800 kPa后,其压缩模量增幅变缓;不同纤维含量试样的e-lg p曲线可以用Harris模型表示,钙质砂组的材料系数 C= 5,玻璃珠组材料系数C= 3,此外,材料参数a、b与纤维含量有较好的线性关系。提出了合理的预测模型指导地基加固,具有十分重要的理论价值与工程实际意义。     

Coupling between anisotropic damage and permeability variation in brittle rocks

In this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second‐order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro–macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data. Copyright © 2005 John Wiley & Sons, Ltd.     

SH波作用下各向异性弹性半空间中浅埋圆孔附近的动应力集中研究

研究了稳态水平剪切（SH）波作用下含有圆柱形孔洞的各向异性弹性半空间的动力响应问题,探讨介质的各向异性对孔附近动应力的影响规律。运用复变函数和多极坐标方法在变换空间中构造出各向异性弹性半空间中圆孔的散射波函数,所构造的散射波函数能够自动满足半空间水平表面上应力自由的边界条件和无穷远处的Sommerfeld辐射条件。根据圆孔表面应力自由的边界条件,采用最小二乘法求解所构造的散射波函数的系数。分析了SH波以不同角度自弹性半空间内入射时,不同介质特性、入射波数和埋深对圆孔附近动应力集中系数的影响。数值结果表明,各向异性弹性半空间中孔附近的动应力比各向同性情况有明显增高。     

考虑自愈合效应的泥岩巷道开挖扰动区渗透性反演分析

泥岩自愈合特性是核废料库选址评价及储库安全稳定性分析的一项重要研究内容。以某泥岩高放废物处置库为研究背景,在室内和现场试验的基础上,采用指数模型建立了巷道围岩渗透性分布模型和裂隙渗透性自愈合模型;结合巷道围岩孔隙水压力的多年观测资料,通过建立能够反映实际施工过程的水-力耦合计算模型,采用精确罚函数法以及Nelder-Mead算法相结合的有限元优化反分析程序,对巷道围岩渗透性参数进行反演研究。结果表明：反演所得的围岩渗透系数量级与试验值量级均为10-12 m/s,反演孔隙水压力值与实测值比较接近;围岩垂向渗透系数的扰动程度和范围明显大于水平向渗透系数,垂向渗透系数提高了2个数量级,扰动范围约为25 m,渗透性恢复到初始水平时间约需5 a。     

Prediction of stresses and strains around model tunnels with adjacent embedded walls in overconsolidated clay

This paper presents the results of finite element analyses carried out using different constitutive models for overconsolidated clay: the Modified Cam clay model and the Three-Surface Kinematic Hardening (3-SKH) model. These analyses are evaluated against data from an extensive series of physical model tests examining the influence of an embedded wall placed near a tunnel on ground movements and tunnel stability. It is shown that for heavily overconsolidated soils reasonable predictions of both deformations and failure can be obtained from kinematic hardening models such as the 3-SKH model, which allow plastic deformation inside a Modified Cam clay state boundary surface.     

Consequences of crystal shape and fabric on anisotropic permeability in magmatic mush

Crystals that form an interconnected porous network can become preferentially oriented both prior to and during compaction of magmatic mush. This introduces anisotropy in the melt pore-space that can reduce permeability in the direction of compaction and in turn decrease melt flux and compaction rate. Using a number of grain-scale numerical models, the consequences of end-member magmatic fabrics on the directional dependence of permeability are tested over a range in melt fraction from 22 to 77%. As the crystal aspect ratio (i.e. ratio of long to short axis length) increases from 2 to 10, isotropic permeability decreases by a factor of 2 and 5 for randomly oriented prolate and oblate-shaped crystals, respectively, at a melt fraction of 22%. With a flattening fabric, permeability is reduced in the compaction direction no more than approximately a factor of 2 relative to the isotropic permeability at the same melt fraction and crystal shape for both oblate and triaxial prisms. However, permeability is enhanced in directions orthogonal to the compaction direction. For example, permeability is enhanced up to a factor of 11 relative to the isotropic permeability at a melt fraction of 22% for oblate prisms with a ratio of the long to short axis length of 10. Anisotropy in permeability increases as the melt fraction decreases and the crystal aspect ratio increases. Ratios of the principal permeabilities are sufficiently large based on the realistic crystal shapes tested here to warrant including anisotropic permeability into macroscale melt segregation models including those for compaction.     

Negative skin friction on single piles in a layered half-space

Settlement of the surrounding soil due to surcharge placement may give rise to negative skin friction developed in piles. In this paper, a simple discrete element approach using subgrade reaction method is proposed to analyse negative skin friction on single piles. The pile is embedded in a two-layer soil where the upper soil layer undergoes consolidation while the lower soil layer acts as a stiffer bearing stratum. Two different and uncoupled deformation modes, one at the pile shaft and the other at the pile toe have been assumed in the determination of the soil stiffness. The effects of a compressible bearing stratum and embedment length of the pile in the bearing stratum are considered in the analysis. This simple approach is verified by comparison with rigorous methods of modelling the soil as an elastic continuum. Three reported case histories are analysed and the computed results are shown to be in reasonable agreement with the field measurements.     

Dispersion law of rayleigh-type waves in a compressible gibson half-space

An analytical-numerical examination has been made of the behavior of harmonic Rayleigh-type waves in a compressible elastic half-space of constant density and whose shear modulus increases linearly with depth. The dispersion law is presented for values of Poisson's ratio of 1/2, 1/3 and 1/4 for wide ranges of degree of inhomogeneity.