考虑热渗效应的有限长圆柱热固结解

在作者已建立的饱和多孔介质耦合非线性热弹性理论基础上,考虑热渗效应,建立了饱和多孔介质耦合热弹性固结方程,并推导了有限长圆柱热固结问题的解析解,进而以温控三轴试验的试样为例进行了算例分析,同时利用COMSOL软件进行了数值模拟,并将解析结果和数值结果进行对比．结果表明：在不排水条件下,影响试样最终孔压大小的参数是：土的泊松比>弹性模量>水的体膨胀系数,渗透系数对孔压变化影响不大,考虑与不考虑水土压缩性不影响孔压的计算;相对线弹性情况,考虑非线弹性膨胀系数随温度变化时的孔压有所下降,轴向应变变化很小．     

ANALYTICAL SOLUTION OF THERMAL CONSOLIDATION OF SATURATED SOILS WITH TWO PARALLEL CYLINDRICAL HEAT SOURCES1）

基于应力平衡条件、渗流连续方程、能量守恒方程,考虑土颗粒和孔隙水热膨胀系数的不同,建立考虑热水力耦合的饱和土体三维热固结控制方程。利用傅里叶变换和拉普拉斯变换导出变换域上的控制方程,解得点热源在变换域和实数域上的解析解,再利用区域积分给出两平行圆柱形热源热固结土体温度、孔压、位移的解析解,并对其进行分析,发现径距比增大会导致两热源温度相互影响程度减弱,热固结系数减小会导致孔压和位移的峰值增大。     

LARGE-STRAIN CONSOLIDATION OF FOUNDATION WITH SAND DRAINS BASED ON HANSBO'S FLOW 1)

基于Gibson大变形固结理论,通过引入Hansbo渗流模型和软黏土非线性变形特性,同时考虑土层的沉积效应,分别建立了以孔隙比$e$和超孔压$u$表示的砂井地基大变形固结方程。通过与已有研究成果的对比,验证了本文方法的可靠性和砂井地基大变形固结方程两种描述方式的等效性。通过FlexPDE得到方程的数值解,在此基础上,研究了砂井地基大、小应变固结理论与Barron固结解的差异性,探讨了Hansbo渗流参数$m$和$I_1$对砂井地基固结的影响,最后对比分析了砂井地基轴对称固结、径向固结和竖向一维固结的关系。研究结果表明：考虑Hansbo渗流的砂井地基非线性大变形固结模型的固结速率最慢,且在固结后期,Hansbo渗流时大、小应变固结与Barron固结的平均固结度基本趋近;随着Hansbo渗流参数$m$和$I_1$的逐渐增大,砂井地基的固结速率逐渐降低;随着砂井影响半径的增大,砂井地基轴对称固结与径向固结的差异性也越来越大,且在固结早期会出现一维竖向固结速率高于轴对称固结和径向固结的现象。     

Law of nonlinear flow in saturated clays and radial consolidation

It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media.There is good agreement between the derived results and test ones.Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow.Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius.The interaction is an important reason why nonlinear flow in saturated clays occurs.An exact mathematical model was presented for nonlinear flow in micro-scaie pore of saturated clays.Dimension and physical meanings of parameters of it are definite.A new law of nonlinear flow in saturated clays was established.It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one.Darcy law is a special case of the new law.A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow.Equations of average mass conservation and moving boundary,and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer,a method of steady state in stead of transient state and a method of integral of an equation.Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained.Re- suits show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay.The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases.Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.     

循环荷载作用下考虑Hansbo渗流的饱和黏土固结分析

针对传统一维Terzaghi固结理论的局限性,本文引入了考虑时间效应的UH (unified hardening)本构模型,将Hansbo渗流模型耦合到UH本构模型固结方程中,建立了几种典型循环荷载作用下基于UH模型和考虑Hansbo渗流模型的固结方程。采用FlexPDE软件进行了数值分析,将计算结果与已有文献结果对比,验证了该算法的可靠性。在此基础上,研究了饱和黏土在几种典型循环荷载作用下的渗流固结特性,分析了各模型参数对饱和黏土固结特性的影响。结果表明:在循环荷载作用下,地基的平均固结度、沉降量等始终处于循环状态;Hansbo渗流模型参数对平均固结度的影响相对于Darcy渗流参数影响程度较大,其中UH模型中次固结系数对固结过程影响程度较大。另外,Hansbo渗流参数及土的回弹指数和渗透指数等对固结过程的影响主要体现在中期,固结过程后期将处于稳定循环状态。     

A RHEOLOGICAL CONSOLIDATION MODEL FOR SOFT CLAY WITH CONSIDERATION OF TEMPERATURE AND THE ANALYTICAL

基于四元件流变模型,考虑温度影响,建立了宁波软黏土流变固结模型,并利用拉普拉斯变换得到瞬时加载条件下的考虑温度 影响的饱和软黏土流变固结解析解;利用不同温度下软黏土的流变固结试验结果,拟合获得了四元件流变模型参数,进行编程得到理论值, 并与试验值进行对比. 结果表明：该模型能较好反映宁波软黏土流变固结特性,计算结果与试验结果较为吻合.温度的升高导致渗透系数增大,在相同的时间内孔压消散 越快, 固结 越快.     

ONE-DIMENSIONAL NONLINEAR CONSOLIDATION THEORY FOR SOFT GROUND WITH CONSIDERATION OF SECONDARY CONSOLIDATION1)

将软黏土变形分为有效应力变化引起的变形和次固结引起的变形,推导了软土新型应力应变关系。然后结合Davis固结理论,建立了考虑次固结的一维非线性固结控制方程,并对其进行解析求解。通过与数值方法对比,验证了解析解的可靠性。在此基础上,分析了次固结对软土地基固结沉降的影响。结果表明：考虑次固结的孔压消散速度与固结速度较不考虑次固结的慢;忽略次固结将低估软黏土地基的工后沉降。     

饱和土地基的非轴对称固结

固结问题是土力学的基础课题之一，现有的研究主要针对饱和土的平面固结和轴对称固结问题。本文应用Fourier展开、Laplace变换和Hankel变换求解了各向同性饱和土的Blot固结方程；讨论了半空间各向同性饱和土的非轴对称固结。借助数值计算，本文的方法可以用于分析各向同性饱和土的非轴对称固结问题。     

Chemo-Mechanical Consolidation of Clays: Analytical Solutions for a Linearized One-Dimensional Problem

Consolidation (and swelling) of clayey soils caused by change in chemistry of pore fluid is addressed. Such phenomena are caused by changes in the concentration of various species in the solution and result primarily from a stress-independent deformation of individual clusters, and from a mechanical weakening or strengthening of the clay solid matrix in the presence of stress. Second, transport of chemicals that involves concentration gradients induces additional driving forces of osmotic consolidation due to semipermeable membrane nature of clay. In this paper an extension of Terzaghi's model of the mechanical consolidation to incorporate chemical loading of soil is proposed. A linearized model is used to solve analytically two one-dimensional problems of consolidation of a homogeneous layer simulating a landfill liner with drained or undrained boundaries. The numerical results show a strong dependence of distribution of pore pressure on the chemical load and chemically induced settlements of soil to be comparable to the mechanical ones.     

Semi-Analytic Axisymmetric Pressure Distribution in a Consolidating Porous Medium

A semi-analytic solution of the consolidation problem in a finite hollow axisymmetric elastic porous medium is given. According to Biot's theory, we have rigorously derived the consolidation equations and demonstrated that in the axisymmetric problems, the pore pressure diffusion equation can be uncoupled. In the problem of infinite domain, the uncoupled pressure diffusion equation is homogeneous and only the diffusion coefficient is changed. In the problem of finite domain, the uncoupled pressure diffusion equation is nonhomogeneous. In fact, it is a linear differential-integral equation. We solve it by the variables separation method in the time domain.     

Constitutive unsaturated hydro-mechanical model based on modified mixture theory with consideration of hydration swelling

This paper has extended modified mixture theory with consideration of hydration swelling in unsaturated rock. By using non-equilibrium thermodynamics and Biot elasticity, a fully coupled formulation including hydration swelling term is derived. Standard arguments of non-equilibrium thermodynamics are used to derive the Darcy’s law for unsaturated flow. Helmholtz free energy has been used to give the relationship between the stress and pore pressure. The chemical potential of water in pore space and clay platelets has been included in the analysis of water sensitive materials such as shale. Finally, a simple numerical example has been presented for illustrative purpose, the results show that the swelling parameter has a strong influence on stress and strain.     

动力排水固结法加固吹填黏性土的模型试验研究

为了研究动力排水固结法加固吹填土地基的效果,研发了大比例尺的室内模拟试验装置并开展了试验。重点对夯沉量、土体内孔隙水压力的瞬时和长期变化进行了监测和分析,得到如下结论:夯击产生的能量以波的形式向土体内部传播,由于波的作用造成土体拉伸形成裂隙,这些裂隙成为初期的排水通道; 孔隙水压力的动态变化具有明显的脉动特性,夯击瞬间出现负增长,然后再累积增长; 不同深度土体的孔隙水压力增幅不一样; 土体表面铺设的砂垫层不仅可以用做排水,还可以作为静力荷载,有助于土体的排水固结。     

A CONSOLIDATION MODEL OF GROUP WELLS ON COMPOSITE FOUNDATION1)

针对复合地基固结问题,考虑井阻和土体径竖向渗流的影响,建立 以"桩-土-桩"为单元的复合地基群井计算模型,采用解析解法,推导出瞬时载荷作用下复合地基群井固结解析解,讨论了复合地基固结特点和孔压等的变化规律。研究表明,复合地基群井固结模型为复合地基固结理论的研究提供了一种新思路,在井径比大于5 时,基于中心桩、边桩流量相等假设,复合地基群井固结理论所求固结度和传统固结理论所求固结度相差很小,可忽略不计;桩体渗透系数、内外扰动区土体径向渗透系数、土体竖向渗透系数越大,复合地基固结速率越快;堆载越大,最终达到稳定时的沉降量和竖向应变越大;地基表层土体的孔压消散速率和竖向应变速率大于地基深部土体。     

一种考虑液相惯性的一维准静力固结模型

经典Terzaghi一维固结理论不考虑孔隙流体惯性影响,且该理论在不同时期模型推导和表述结果差别较大,导致当前仍存在诸多困惑甚至认识混乱的现象. 在笔者前期研究大变形动力固结理论框架内,忽略固相惯性而重点考虑液相惯性影响,经过合理简化建立反映孔隙流体惯性的一维小变形固结波动模型. 该固结波模型具有频散和耗散特性. 采用分离变量法,可得到单面排水和瞬时加载条件下无量纲形式固结波解析解答. 算例分析结果表明:固结波发展规律受无量纲数D_{\mathrm{c}}变化影响而呈现不同性态;D_{\mathrm{c}}数值较大时固结波响应会出现阶跃和正负波动现象;当D_{\mathrm{c}}值较小时,可能出现Mandel-Cryer效应等特殊现象. 通过对早期和后期Terzaghi固结模型的分析和对比,初步探明Terzaghi固结理论模型内部的矛盾性,在普通土体坐标和固相体积坐标两种不同解读条件下,早期Terzaghi (1923,1925)模型可以分别诠释为具有小变形和大变形属性的不同固结模型. 在经典一维固结理论模型的不同诠释背景下,固结波模型也可以据此作出相应拓展和表述. 固结波理论揭示缩尺固结试验中土体物理力学参数与固结波响应两种因素之间存在一种不确定性矛盾,据此建议微观土力学研究重视尺度效应. 固结波模型的意义还在于,可为Terzaghi经典固结模型理论精度分析提供新的依据.      

CONSOLIDATION THEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅱ)

The present paper uses the mathematics model for consolidation of unsaturatedsoil developed in ref.[1]to solve boundary value problems.The analytical solutionsfor one-dimensional consolidation problem are gained by making use of Laplacetransform and finite Fourier transform.The displacement and the pore water pressureas well as the pore gas pressure are found from governing equations simultaneously.The theoretical formulae of coefficient and degree of consolidation are also given inthe paper.With the help of the method of Galerkin Weighted Residuals,the finiteelement equations for two-dimensional consolidation problem are derived.A FORTRANprogram named CSU8 using8-node isoparameter element is designed.A plane strainconsolidation problem is solved using the program,and some distinguishing features onconsolidation of unsaturated soil and certain peculiarities on numerical analysis arerevealed.These achievements make it convenient to apply the theory proposed by theauthor in engineering practice.     

A new method for solving Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system

A new method is developed to solve Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot＇s consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface （z = 0） and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.     

衰变热源作用下饱和多孔介质热固结问题的扩展精细积分法

热源作用下饱和多孔介质热固结效应是土木及能源工程领域的一个重要课题.由于问题的复杂性,已有的研究大多将介质假定为均匀各向同性,且将热源假定为恒定强度.实际工程中,天然饱和多孔介质常表现出明显的分层特性,热源强度也存在衰变性,为此本工作采用扩展精细积分法对衰变热源作用下层状饱和多孔介质的热固结问题进行研究.借助于积分变换,将饱和多孔介质热固结问题的偏微分方程转化为变换域内的常微分方程;然后对饱和多孔介质微层元进行合并消元,并结合边界条件,推导出衰变热源作用下层状饱和多孔介质热固结问题在积分变换域内的扩展精细积分解;对所得解答进行相应的数值积分逆变换,可获得所求温度、超静孔压及竖向位移在物理域内的解答.基于上述求解过程,编制相应的计算程序进行数值计算,通过与已有文献对比,验证本文扩展精细积分法在求解层状饱和多孔介质热固结问题中的适应性和正确性;最后通过几组算例,分析热源衰变周期、热源埋深及介质的成层性对热固结效应的影响.结果表明:热源衰变周期对温度和超静孔压的峰值、以及达到峰值的时间均有明显影响,衰变周期越长,二者峰值均越大,且达到峰值所需时间越长;热源埋深对超静孔压及竖向位移变化影响显著,深埋热源作用时热源两侧竖向位移呈对称分布,而浅埋热源两侧则无此现象;饱和多孔介质的分层特性对热固结效应影响明显.     

含离子类溶质黏土的 C-H-M 本构模型简

在水力-力学本构模型基础上,采用化学软化公式引入孔隙水中含盐、碱类等离子类溶质对土体前期固结压力的影响,得到土体的化学-水力-力学耦合本构模型（C-H-M 模型）. 根据试验结果对化学软化公式的参数进行数值拟合,通过算例验证了C-H-M 本构模型的有效性     

Thermal Responses of Saturated Silty Clay During Repeated Heating–Cooling Processes

The thermal responses of the saturated silty clay to repeated heating–cooling are studied in laboratory. Results show that the pore pressure induced by undrained heating increases with increasing temperature, but the peak pore pressure appears a degradation trend with increasing temperature cycles. During the consolidation process at an elevated temperature, the specimen contracts due to the dissipation of the pore pressure; however, the thermally induced pore pressure is under no conditions fully dissipated to zero, therefore, there always exists a residual pore pressure in the specimens once a thermal loading higher than the ambient temperature is applied. During the undrained cooling, pore pressure continues to decline and eventually falls below zero. During the isothermal consolidation at the original temperature, the specimen begins to expand due to water absorption caused by the negative pore pressure, and eventually reaches a steady value. In addition, the consolidation volumetric strain generated during the drainage process at 50°C is greater than that during the water absorption process at 25°C, the difference seems to be most obvious for the first three cycles, and begins to diminish gradually thereafter.     

A new analytical solution to axisymmetric Biot＇s consolidation of a finite soil layer

A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface （z= 0） and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.