Influence of a point sink on a pile group in saturated multilayered soils with anisotropic permeability

The behavior of a pile group is solved using the finite element method, and the fundamental solution of saturated multilayered soils with anisotropic permeability is obtained by the analytical layer element method. Based on the supposition of no slip occurring at the pile‐soil interface, the governing equations of the interaction between the pile group and the soils due to a point sink are established in the Laplace‐Hankel transformed domain by considering the pile‐soil compatibility condition. Numerical results are presented to study the effect of point sink pumping, the properties of soils, and the geometries of piles on the behavior of the pile group.     

Consolidation analysis of saturated multi‐layered soils with anisotropic permeability caused by a point sink

This paper presents the analytical layer‐element method to analyze the consolidation of saturated multi‐layered soils caused by a point sink by considering the anisotropy of permeability. Starting from the governing equations of the problem, the solutions of displacements and stresses for a single soil layer are obtained in the Laplace–Hankel transformed domain. Then, the analytical layer‐element method is utilized to further derive the solutions for the saturated multi‐layered soils in the transformed domain by combining with the boundary conditions of the soil system and continuity conditions between adjacent layers. The actual solutions in the physical domain can be acquired by the inversion of Laplace–Hankel transform. Numerical results are carried out to show the accuracy and stability of the proposed method and evaluate the influence of sink depth and anisotropic permeability on excess pore pressure and surface settlement. Copyright © 2011 John Wiley & Sons, Ltd.     

轴对称多层可压缩渗透各向异性岩基固结分析

从轴对称固结基本方程出发,通过对时间t、坐标r的Laplace-Hankel变换,再对坐标z的Laplace变换,得到三元一次方程组,解此方程组,并进行Laplace逆变换,得到了单层可压缩渗透各向异性岩基轴对称固结问题的传递矩阵,然后利用传递矩阵法,结合层间连续性条件和边界条件,得到了多层可压缩渗透各向异性岩基轴对称固结问题在积分变换域内的解。最后应用Laplace-Hankel逆变换技术得到轴对称固结问题在物理域内的理论解。编制了相应的计算程序,并进行了数值计算与分析,讨论了可压缩性和渗透各向异性对岩基固结的影响,结果表明：可压缩性越大,岩基瞬时沉降越大;渗透各向异性对固结过程影响明显,但对初始和最终沉降的影响很小。     

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.     

Elastic solutions for a transversely isotropic half-space subjected to a point load

We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the effect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite different for the displacement and stress calculated from isotropic solutions. © 1998 John Wiley & Sons, Ltd.     

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.     

Axisymmetric consolidation of saturated multi-layered soils with anisotropic permeability due to well pumping

Axisymmetric consolidation of multi-layered soils induced by groundwater extraction from a dewatering well is studied with consideration of the anisotropic permeability and the well length. Laplace-Hankel transforms are utilized to solve the governing equations. The analytical layer-element method is used to build relationships between displacements, stresses, excess pore pressure and seepage velocity in the transformed domain. The real solutions can be obtained by the inversion of Laplace-Hankel transforms. A series of parametric studies, especially the length of a dewatering well and the combined effect of pumping and recharging, are conducted to analyze the consolidation behaviors of layered soils.     

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.     

二维饱和多孔介质因点汇诱发比奥固结的解析解

给出了有限二维饱和多孔介质因点汇诱发的Biot固结的一个解析解。其中假设多孔介质为均匀各向同性和线弹性,假设孔隙压力场符合第1类边界条件,数学模型采用可压缩多孔介质模型。利用傅里叶和拉普拉斯变换及相应反演获得了双重无穷项级数和形式的精确解。然后特别探讨了定流量点汇诱发的稳态解析解,并用文献现有解析解进行了验证。所提出的解析解适合于验证数值解,并可用于深入分析有限二维多孔介质的流-固耦合行为。     

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.     

地埋点热源作用下层状半空间的热-力耦合响应

采用解析层元法对存在地下点热源的岩土工程问题进行解答。首先从热弹性力学三维问题的基本控制方程出发,利用拉普拉斯-傅里叶积分变换推导出其在变换域内单层介质及下卧半空间的解析层元;然后结合有限单元法原理组装得到总刚度矩阵,结合边界条件,得到其在变换域内的解答,最后应用拉普拉斯-傅里叶积分逆变换技术,得到物理域内的解。编制了相应的计算程序,算例分析表明：该结果与已有文献吻合较好,该方法求解层状半空间的热-力耦合响应问题具有较好的适用性和较高的精度;层状岩土介质体系中,热扩散系数对温度及地表隆起的变化过程影响显著,但对其初始值和最终稳定值影响不明显;分层特性对岩土介质温度分布及地表位移变化过程均有显著影响。     

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。     

Elastic solutions for a transversely isotropic half-space subjected to buried asymmetric-loads

Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to various buried loading types are presented. The loading types include finite line loads and asymmetric loads (such as uniform and linearly varying rectangular loads, or trapezoidal loads). The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are directly obtained from integrating the point load solutions in a transversely isotropic half-space, which were derived using the principle of superposition, Fourier and Hankel transformation techniques. The solutions for the displacements and stresses in transversely isotropic half-spaces subjected to linearly variable loads on a rectangular region are never mentioned in literature. These exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, and the degree and type of rock anisotropy. Two illustrative examples, a vertical uniform and a vertical linearly varying rectangular load acting on the surface of transversely isotropic rock masses, are presented to show the effect of various parameters on the vertical surface displacement and vertical stress. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Copyright © 1999 John Wiley & Sons, Ltd.     

半空间饱和土中圆形衬砌对弹性压缩波的散射

借助于Biot 波动理论和弹性波的传播理论,采用复变函数和多级坐标法,对半空间饱和土中圆形衬砌结构对弹性稳态压缩波的散射问题进行求解和分析。利用一个半径很大的圆弧来逼近半空间直边界,将待解问题转化为稳态弹性压缩波在一个大圆孔和一个弹性衬砌结构的散射问题。通过引入势函数,将饱和土的Biot波动方程和衬砌的弹性波动方程解耦成Helmholtz 方程,借助复变函数级数展开便可以预先写出该组Helmholtz方程的通解。然后,通过引用复变量,把饱和土和衬砌结构中的应力、位移及孔压用设定的势函数表示出来,再利用半空间饱和土和衬砌结构的连续性条件和近似直边界的圆弧边界和衬砌内边界的边界条件求解出该组势函数的特解。最后,利用势函数的特解,得到饱和土中的位移,应力和孔压及衬砌结构的位移和应力;变换不同的参数求解衬砌结构内外边界的动应力和孔压的集中系数,通过对算例结果的分析得出一系列有益的结论。     

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.     

Radial consolidation with variable compressibility and permeability following pile installation

The excess pore pressure generated by pile installation gradually dissipates following installation, which mainly dominates the increase of pile capacity with time. The dissipation of the excess pore pressure following pile installation has been widely investigated by experimental and theoretical studies. However, in most research, the consolidation coefficients were assumed to be constant for simplification, which may lead to errors. In the present study, the dissipation of the excess pore pressure is analyzed by radial consolidation theory with a variable consolidation coefficient based on the linear responses of e − ln(p^′) and e − log(k). The governing equation of the radial consolidation considering variable compressibility and permeability are solved by the variable separation method. Bessel functions are used to solve the differential functions for the time independent part. The excess pore pressure immediately after pile installation is obtained from cavity expansion theory and is used as the initial condition of the consolidation process. Moreover, the influences of variable compressibility and permeability on the variation of consolidation coefficient and excess pore pressure dissipation are analyzed.     

考虑渗透系数变化的非饱和土固结性状分析

基于Fredlund非饱和土一维固结理论,研究了有限厚度的表面透水透气、底面不透水不透气的线弹性和黏弹性非饱和土地基在加荷随时间指数性变化时的一维固结特性。分别得到了两类地基在固结过程中同时考虑液相、气相渗透系数非线性变化和仅考虑液相渗透系数变化两种情况下的半解析解答。利用典型算例进行计算,分析了不同情况下两类地基中超孔隙水、气压力消散以及地基固结度随时间的变化规律,并与不考虑渗透系数变化时的半解析解计算结果进行了对比。结果发现：固结过程中渗透系数呈非线性变化;只考虑液相渗透系数变化时,超孔隙气压力的消散变化不大,超孔隙水压力的消散加快;气相渗透系数变化对超孔隙气的消散产生明显影响,对超孔隙水压力消散影响不大。同时考虑液相和气相渗透系数变化时,土体中超孔隙水、气压力的消散均有明显变化,土体固结速度也相应加快;分析结果对非饱和土固结的进一步研究具有重要意义。     

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.