BIOT’S CONSOLIDATION ANALYSIS FOR CYLINDRICAL SOIL-SAMPLE BASED ON HANSBO’S FLOW1)

诸多黏性土渗流试验表明,在低水力梯度下渗流会出现明显偏离Darcy定律的现象. 为了分析渗流的非Darcy特性对固结过程 的影响,引入Hansbo渗流方程描述圆柱土样内的渗流,重新推导轴对称条件下的Biot固结方程,并给出方程的Crank--Nicolson有限 差分格式. 通过与Darcy渗流条件下轴对称Biot固结方程解析解的对比,验证计算方法的有效性. 然后分析Hansbo模型参数对圆柱 土样固结过程的影响. 计算结果表明：与Darcy渗流相比,Hansbo渗流会延缓圆柱土样的固结过程. 随着Hansbo渗流参数m或I¹的增大,在固结前期,Mandel--Cryer效应会更加显著,即孔隙水压力峰值将提高,且达到该峰值的时间 会延迟;在固结中后期,孔压消散滞后的现象也更加明显. 不过,Hansbo渗流对位移的影响很小.     

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．     

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.     

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。     

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 multi-scale theory of swelling porous media: I. Application to one-dimensional consolidation

A theory is developed which describes flow in multi-scale, saturated swelling media. To upscale information, both the hybrid theory of mixtures and the homogenization technique are employed. In particular, a model is formulated in which vicinal water (water adsorbed to the solid phase) is treated as a separate phase from bulk (non-vicinal) water. A new form of Darcy's law governing the flow of both vicinal and bulk water is derived which involves an interaction potential to account for the swelling nature of the system. The theory is applied to the classical one-dimensional consolidation problem of Terzaghi and to verify Low's empirical, exponential, swelling result for clay at the macroscale.     

软粘土深基坑开挖时间效应的有限元分析

目前对开挖工程一般只作总应力法分析,本文将Ｂｉｏｔ固结有限元用法饱和软粘土地基深基坑性状的研究,通过典型算例分析土体超散负孔压的分布及分步开挖工程的固结效应,阐述了开挖速率的影响。最后对某深开挖工程实例进行了分析,旨在为基坑工程的设计和施工提供参考。     

Analytical Investigation of the Effect of Viscous Dissipation on Couette Flow in a Channel Partially Filled with a Porous Medium

An analytical study of viscous dissipation effect on the fully developed forced convection Couette flow through a parallel plate channel partially filled with porous medium is presented. A uniform heat flux is imposed at the moving plate while the fixed plate is insulated. In the fluid-only region the flow field is governed by Navier–Stokes equation while the Brinkman-extended Darcy law relationship is considered in the fully saturated porous medium. The interface conditions are formulated with an empirical constant β due to the stress jump boundary condition. Fluid properties are assumed to be constant and the longitudinal heat conduction is neglected. A closed-form solution for the velocity and temperature distributions and also the Nusselt number in the channel are obtained and the viscous dissipation effect on these profiles is briefly investigated.     

Analytical Solution of Compression,Free Swelling and Electrical Loading of Saturated Charged Porous Media

Analytical solutions are derived for one-dimensional consolidation, free swelling and electrical loading of a saturated charged porous medium. The governing equations describe infinitesimal deformations of linear elastic isotropic charged porous media saturated with a mono-valent ionic solution. From the governing equations a coupled diffusion equation in state space notation is derived for the electro-chemical potentials, which is decoupled introducing a set of normal parameters, being a linear combination of the eigenvectors of the diffusivity matrix. The magnitude of the eigenvalues of the diffusivity matrix correspond to the time scales for Darcy flow, diffusion of ionic constituents and diffusion of electrical potential.     

考虑桩体内径向渗流的复合地基固结解

考虑了桩体内径竖向组合渗流和涂抹区土体水平渗透系数的两种变化模式,得到了此类固结问题的控制方程.采用新的初始条件,得到了控制方程的解答,给出了桩周土体和桩体内的平均孔压.在此基础上,把桩体的固结压缩引人对复合地基总平均固结度的定义中,分别给出了复合地基按应力和按应变定义的总平均固结度.结果表明:按应力和按应变定义的复合地基的总平均固结度相等;考虑桩体内径向渗流比不考虑桩体内径向渗流的复合地基固结度要小,而且随着桩间距的增大,两者之间的差值逐渐减小;考虑涂抹区水平渗透系数逐渐变化比假定涂抹区水平渗透系数保持不变的复合地基的总平均固结度大.     

Boundary conditions at the interface between fluid layer and fibrous medium

The flow through a channel partially filled with fibrous porous medium was analyzed to investigate the interfacial boundary conditions. The fibrous medium was modeled as a periodic array of circular cylinders, in a hexagonal arrangement, using the boundary element method. The area and volume average methods were applied to relate the pore scale to the representative elementary volume scale. The permeability of the modeled fibrous medium was calculated from the Darcy's law with the volume‐averaged Darcy velocity. The slip coefficient, interfacial velocity, effective viscosity and shear jump coefficients at the interface were obtained with the averaged velocities at various permeabilities or Darcy numbers. Copyright © 2008 John Wiley & Sons, Ltd.     

Electro-chemo-mechanical couplings in saturated porous media: elastic–plastic behaviour of heteroionic expansive clays

Chemically active saturated clays containing several cations are considered in a two-phase framework. The solid phase contains the negatively charged clay particles, absorbed water and ions. The fluid phase, or pore water, contains free water and ions. Electroneutrality is ensured in both phases, which gives rise to electrical fields. Water and ions can transfer between the two phases. In addition, a part of free water diffuses through the porous medium. A global understanding of all phenomena, deformation, transfer, diffusion and electroneutrality, is provided. Emphasis is laid on the electro-chemo-mechanical constitutive equations in an elastic–plastic setting. Elastic chemo-mechanical coupling is introduced through a potential, in such a way that the tangent elastic stiffness is symmetric. Material parameters needed to estimate the coupling are calibrated from specific experiments available in the recent literature. The elastic–plastic behaviour aims at reproducing qualitatively and quantitatively typical experimental phenomena observed on natural clays during chemical and mixed chemo-mechanical loadings, including chemical consolidation and swelling already described in Int. J. Solids Structures (39 (10), 2773–2806) in the simpler context of Na-Montmorillonite clays. Crucially, the successive exposure of a clay to pore solutions with chemical content dominated by a cation already present in the clay or quasi-absent leads to dramatically different volume changes, in agreement with experimental data.     

Finite Deformation Models and Field Performance

This paper reports about the derivation of a fully nonlinear model characterized by finite deformations without smallness assumptions. The soil is assumed to be saturated, and no restrictions are introduced on the constitutive laws. Initial boundary value problems are formulated with reference to geotechnical problems, such as consolidation under own weight or sedimentation of solid particles in a quiescent fluid, and back-analyses of field performance of an embankment resting on a soft clay deposit.     

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.     

Sharp approximation to a filtration problem by maximum principle

Consider an incompressible fluid, filtrating through a saturated cylindrical porous layer with rectangular cross-section. A steady pressure gradient, parallel to the axis of the layer, drives a one-directional stationary non recirculating flow when the Darcy law has to include inertial and viscous corrections. This is the case, for instance, when the porosity of the medium or the seeping flow rate are not very small. The resulting nonlinear problem belongs to a class of equations which was proved to have positive solutions. It also satisfies a comparison principle from which approximations from above and from below are derived for the steady flow. The estimate from above is the flat profile which solves the Darcy-Forchheimer equation, which does not take account of viscous effects, and the approximation is excellent when the modified Darcy number is small, under the additional condition that the Forchheimer coefficient be small also. The flow still solves the problem when gradient forces, orthogonal to the axis of the layer, are also present.     

Low Pressure Gas Percolation Characteristic in Ultra-low Permeability Porous Media

Low pressure gas percolation characteristic in ultra-low permeability porous media is investigated in this article through core flow experiments. The results show that the wall-slip layer covers more than 10% of the average porous channel radius on account of minimum pore size when the permeability is below 0.1 × 10^?3μ m ² order, and seepage behavior is contrasted to that in mid-high permeability pore media. When the gas pressure is not high enough, the flow regime turns into transitional flow instead of slip flow, and nonlinear relationship between the measured gas permeability and the reciprocal of average pressure exists. The gas measuring permeability experiment would be influenced by the non-linear relationship. If Klinkenberg-corrected method is applied to speculate the equivalent liquid permeability, the extrapolated value will become less or minus. Simultaneously, actual gas flow velocity at the outlet is beyond the calculated value with Klinkenberg formula. A new gas seepage model based on the general slip boundary condition is derived from the homogenization technique in this article. At last the flow model is examined to be suitable for representing the gas flow behavior in ultra-low permeability media and estimating the absolute permeability from single-point, steady-states measurements.     

Mixed Convection in a Darcy–Brinkman Porous Medium with a Constant Convective Thermal Boundary Condition

The characteristics of the boundary layer flow past a plane surface adjacent to a saturated Darcy–Brinkman porous medium are investigated in this paper. The flow is driven by an external free stream moving with constant velocity. The surface is heated with a convective boundary condition with constant heat transfer coefficient. The problem is non-similar and is investigated numerically by a finite difference method. The problem is governed by four non-dimensional parameters, that is, the convective Darcy number, the convective Grashof number, the Prandtl number, and the axial distance along the plate. The influence of these parameters on the results is investigated, and the results are presented in tables and figures. The Darcy term and the Grashof term in the momentum equation contradict each other and this contradiction makes the problem complicated. However, the wall shear stress and the wall temperature increase continuously along the plate and the wall temperature always tends to 1.     

Analysis of a benchmark solution for non-Newtonian radial displacement in porous media

We present an analytical formulation useful to interpret the key phenomena involved in non-Newtonian displacement in porous media and an analysis of the results obtained by considering the uncertainty associated with relevant problem parameters. To derive a benchmark solution, we consider the radial dynamics of a moving stable interface in a porous domain saturated by two fluids, displacing and displaced, both non-Newtonian of shear-thinning power-law behavior, assuming the pressure and velocity to be continuous at the interface, and constant initial pressure. The flow law for both fluids is a modified Darcy’s law. Coupling the nonlinear flow law with the continuity equation, and taking into account compressibility effects, yields a set of nonlinear second-order partial differential equations. Considering two fluids with the same flow behavior index n allows transformation of the latter equations via a self-similar variable; further transformation of the equations incorporating the conditions at the interface shows for n<1 the existence of a compression front ahead of the moving interface. Solving the resulting set of nonlinear equations yields the positions of the moving interface and compression front, and the pressure distributions; the latter are derived in closed form for any value of n. A sensitivity analysis of the model responses is conducted both in a deterministic and a stochastic framework. In the latter case, Global Sensitivity Analysis (GSA) of the benchmark analytical model is adopted to study how the effects of uncertainty affecting selected parameters: (a) the fluids flow behavior index, (b) the relative total compressibility and mobility in the displaced and displacing fluid domains, and (c) the domain permeability and porosity, propagate to state variables. The relative influence of input parameters on model outputs is evaluated by means of associated Sobol indices, calculated via the Polynomial Chaos Expansion (PCE) technique. The goodness of the results obtained by the PCE is assessed by comparison against a traditional Monte Carlo (MC) approach.     

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。