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。     

基于非保守体力的大变形固结有限元法

考虑土体固结过程中体力的非保守特点,完善了T.L.描述的大变形固结平衡方程,并以伴生体力代替非保守体力,提出了相应的大变形固结增量有限元列式. 当忽略土体体积应变的影响时,改进的大变形固结平衡方程及其有限元法均可退化为基于保守体力的传统形式. 采用自主开发的程序对大变形自重固结算例进行分析,结果初步表明:传统方法低估了地基固结度,但高估了地基沉降量和超静孔隙水压力. 基于非保守体力的大变形固结分析在理论上能够更合理地预测地基的固结性状.      

理论力学研究性教学新探索:刚体运动基点法公式与连续介质速度场分解

基础力学课程体系是现代工程教育的重要基础。理论力学作为力学课程体系的起点,提供了力学基本概念和原理。一方面,以离散体系(质点/刚体)为研究对象的理论力学与以连续体系(介质/变形微元体)为对象的连续介质力学,它们之间既存在密切联系又差异明显;另一方面,源于理论/经典力学的动力系统理论和非线性科学研究对应用力学学科产生了广泛影响。围绕这两个侧面,作者将在《理论力学研究性教学新探索》系列教研论文中阐释它们之间的联系。本篇探讨刚体运动基点法公式和连续介质速度场分解之间的关系,它们分别给出刚体模型和连续介质模型的速度分布规律,前者依赖刚体转动角速度矢量,而后者由速度梯度张量所刻画。本文将说明,两者存在对应理论关系,且刚体基点法公式是连续介质速度场分解的退化形式,即忽略变形效应。     

刚-柔耦合动力学系统的建模理论研究

刚－柔耦合动力学系统的传统的混合坐标方法是零次近似方法,在建模过程中,直接套用的结构动力学的小变形假设,忽略了变形位移的高次耦合变形量．本文对柔性梁建立较零次近似更精确的高次耦合动力学模型,从连续介质力学理论出发,在变形位移中,计及横向位移引起的轴向缩短,导出变形位移的二次耦合量．用一致质量有限元方法对梁进行离散,基于Jourdain速度变分原理导出大范围运动为自由的柔性梁的刚－柔耦合动力学方程．计算了柔性重力摆的角速度和摆端点的横向变形,揭示零次近似模型和耦合模型的刚－柔耦合动力学性质的根本差异．     

饱和砂土中泥浆渗透的变形-渗流-扩散耦合计算模型

传统的泥浆渗透计算中没有考虑土体变形和浆液流速的影响.根据泥浆颗粒的质量守恒定律推导了耦合流速的浓度扩散方程,并通过在浓度方程中引入沉积系数进一步计算得到沉积颗粒的质量;同时,以沉积量作为耦合项对毕奥固结方程中的水量连续方程进行了修正,在此基础上建立了变形-渗流-扩散耦合的控制方程及其变分原理. 采用有限单元法求解基本方程,运用了时间增量法与直接迭代法,并利用一维试验验证计算方法的可靠性,并与赫齐格的经典模型的计算结果进行了比较,结果表明,本文建立的模型的计算结果可以较好地预测各组试验中颗粒的沉积规律,且吻合程度优于仅考虑颗粒对流和扩散的传统计算方法. 最后,将泥浆在槽壁中的渗透简化为二维问题并进行了计算,计算结果与工程认识相符合,泥浆的沉积填充效应随深度的增加而增大,施工时需要严格控制浅层作业段的机械垂直度;成槽机的下斗抓挖时机可以根据地层填充的致密程度进行计算,对现场施工具有一定的指导意义.      

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。     

一种化学-力学耦合连续介质理论与数值格式

对化学驱动的连续介质化学-力学耦合系统进行研究,从热力学定律和化学势角度出发,推导了等温过程的化学-力学耦合本构关系和控制方程,利用变分方法建立了化学-力学耦合系统的能量泛函,得到化学-力学耦合控制方程的等效积分形式和相应的有限元列式. 结合算例,对连续介质的化学-力学耦合行为进行了数值计算,数值结果反映了化学与力学系统的相互耦合作用,即浓度变化能引起介质的变形,同样力学作用也能引起浓度重分布. 从全新的角度建立了描述连续介质的化学-力学耦合行为的基本理论和数值方法,能够较好地反映一类连续介质的化学-力学耦合行为.      

考虑Hansbo渗流的砂井地基大变形固结问题

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I1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I1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。     

钢管桩固结过程的分析

本文用连续介质力学的基本理论分析了钢管桩的固结过程。采用径向固结模型进行了描述并给出了它的解析解。指出了固结过程提高了钢管桩的承载能力。     

采空区流场非达西渗流一种新的迭代算法

对Bachmat非线性渗流方程求解问题，结合采空区问题的力学特点，提出基于变渗透率达西 (Darcy)渗流求解非线性渗流的迭代算法. 建立了冒落采空区非线性漏风流态的有限元数 值模型，通过对复杂边界采空区的漏风渗流的计算，得到与实际流态更接近的流动规律(风 压等值线和流函数线)和采空区漏风强度分布(速度场). 结果表明，迭代算法是振荡性收 敛的，收敛速度快；与Darcy渗流相比，采空区非线性渗流速度场趋向于平缓，在工作面附 近30\,m范围内最大风速降低到原来的0.61倍，其余大部分区域速度略有增加. 迭代方法满 足工程要求.     

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 theory of finite elastic consolidation

Presented in this paper is a general theory describing the consolidation of a porous elastic soil. The formulation allows for the occurrence of finite geometry changes and finite elastic strains during the consolidation process. The governing equations have been cast in a rate form and the laws which determine deformation and pore fluid flow, i.e. Hooke's law and Darcy's law, are presented in a frame indifferent manner. A numerical technique is described that provides an approximate solution to the governing equations. The theory and the solution technique are illustrated by several examples of practical interest.     

Plane strain consolidation of soil layer with anisotropic permeability

This paper presents an alternative analytical technique to study a plane strain consolidation of a poroelastic soil by taking into account the anisotropy of permeability. From the governing equations of a saturated poroelastic soil, the relationship of basic variables for a point of a soil layer is established between the ground surface （z=0） and the depth z in the Laplace-Fourier transform domain. Combined with the boundary conditions, an exact solution is derived for plane strain Biot＇s consolidation of a finite soil layer with anisotropic permeability in the transform domain. Numerical inversions of the Laplace transform and the Fourier transform are adopted to obtain the actual solution in the physical domain. Numerical results of plane strain Biot＇s consolidation for a single soil layer show that the anisotropic of permeability has a great influence on the consolidation behavior of the soils.     

平面应变 Biot 固结的解析层元

提出用解析层元法有效地解决任意深度单层土的平面应变 Biot 固结问题. 从 Biot 固结问题的控制方程出发, 采用特征值法在 Laplace-Fourier 变换域内推导出一个精确对称的解析层元刚度矩阵. 通过表示单层土广义力和广义位移之间关系的解析层元, 并结合土层的边界条件, 推导出土层任意点的解答; 物理域内的真实解可以通过 Laplace-Fourier 数值逆变换进一步获得. 通过数值计算验证理论的正确性, 研究了土层性质及时间因素对固结的影响.}      

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.     

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

A new analytical method is presented to study the axisymmetric Blot'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.     

Non-linear theories of beams and plates accounting for moderate rotations and material length scales

The primary objective of this paper is to formulate the governing equations of shear deformable beams and plates that account for moderate rotations and microstructural material length scales. This is done using two different approaches: (1) a modified von Kármán non-linear theory with modified couple stress model and (2) a gradient elasticity theory of fully constrained finitely deforming hyperelastic cosserat continuum where the directors are constrained to rotate with the body rotation. Such theories would be useful in determining the response of elastic continua, for example, consisting of embedded stiff short fibers or inclusions and that accounts for certain longer range interactions. Unlike a conventional approach based on postulating additional balance laws or ad hoc addition of terms to the strain energy functional, the approaches presented here extend existing ideas to thermodynamically consistent models. Two major ideas introduced are: (1) inclusion of the same order terms in the strain–displacement relations as those in the conventional von Kármán non-linear strains and (2) the use of the polar decomposition theorem as a constraint and a representation for finite rotations in terms of displacement gradients for large deformation beam and plate theories. Classical couple stress theory is recovered for small strains from the ideas expressed in (1) and (2). As a part of this development, an overview of Eringen׳s non-local, Mindlin׳s modified couple stress theory, and the gradient elasticity theory of Srinivasa–Reddy is presented.     

一维渗透力与浮力

为简化分析,针对一维渗流问题,研究提出了土力学中渗透力和浮力的两种推导方法,作为传统的宏观尺度孔隙水隔离体法的有益补充.弹性力学平衡微分方程、土力学Terzaghi有效应力方程和流体力学简化Bernoulli方程构成本文分析渗透力和浮力的3个基本方程.在基本方程基础上,容易推导出相应的骨架和孔隙水两种隔离体的平衡微分方程,从而在静力平衡范畴内揭示渗透力和浮力的内涵.单位体积饱和土体的渗透力,源于总水头压力的梯度,而浮力则源于位置水头压力在竖向的梯度,这两者统一于骨架或孔隙水的平衡微分方程.实际工程关注的有效应力计算问题,一般可以直接应用3个基本方程来确定;只有在简化条件下可按渗透力和浮力计算土体中有效应力分布规律.还讨论了若干研究热点问题,重点探讨了当前一种渗透力新定义j=nγ_wi在形式上的合理性以及在实际应用中可能存在的风险,并验证了一维渗透力的一种经典精细化表述结果中考虑渗流速度时间导数的严谨性.在土力学渗透力和浮力问题研究中应重视和正确应用Terzaghi有效应力方程.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain, water and gas. In this paper, the consolidation problem of unsaturated soil is investigated based on the theory of mixture. A theoretical formula of effective stress on anisotropic porous media and unsaturated soil is derived. The principle of effective stress and the principle of Curie symmetry are taken as two fundamental constitutive principles of unsaturated soil. A mathematical model of consolidation of unsaturated soil is proposed, which consists of 25 partial differenfial equations with 25 unknowns. With the help of increament linearizing method, the model is reduced to 5 governing equations with 5 unknowns, i.e., the three displacement components of solid phase, the pore water pressure and the pore gas pressure. 7 material parameters are involved in the model and all of them can he measured using soil tests. It is convenient to use the model to engineering practice. The well known Biot’s theory is a special case of the model.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain,water andgas.In this paper,the consolidation problem of unsaturated soil is investigated basedon the theory of mixture.A theoretical formula of effective stress on anisotropicporous media and unsaturated soil is derived.The principle of effective stress and theprinciple of Curie symmetry are taken as two fundamental constitutive principles ofunsaturated soil.A mathematical model of consolidation of unsaturated soil isproposed,which consists of25 partial differenfial equations with25 unknowns.Withthe help of increament linearizing method,the model is reduced to5 governingequations with5 unknowns,i.e.,the three displacement components of solid phase,thepore water pressure and the pore gas pressure.7 material parameters are involved inthe model and all of them can be measured using soil tests.It is convenient to use themodel to engineering practice.The well known Biot’s theory is a special case of themodel.