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.     

One-Dimensional Consolidation of Layered and Visco-Elastic Soils under Arbitrary Loading

ＩｎｔｒｏｄｕｃｔｉｏｎＡｆｔｅｒＴｅｒｚａｇｈｉ,ａｌｏｔｏｆｓｃｈｏｌａｒｓｈａｖｅｄｏｎｅｏｕｔｓｔａｎｄｉｎｇｒｅｓｅａｒｃｈｏｎｔｈｅｐｒｏｂｌｅｍｓｏｆｏｎｅ＿ｄｉｍｅｎｓｉｏｎａｌｃｏｎｓｏｌｉｄａｔｉｏｎ .Ｗｉｌｓｏｎ ( 1974) [1] ａｎｄＢａｌｉｇｈ( 1978) [2 ] ｅｔａｌ.ｈａｖｅｓｔｕｄｉｅｄｔｈｅｃｏｎｓｏｌｉｄａｔｉｏｎｕｎｄｅｒｔｈｅｒｅｃｔａｎｇｕｌａｒｌｏａｄｉｎｇ .Ｉｎ 1988,ＷＵｅｔａｌ.[3] ｗｏｒｋｅｄｏｕｔｔｈｅｇｅｎｅｒａｌｓｏｌｕｔｉｏｎｓｏｆｏｎｅ＿ｄｉｍｅｎ…     

循环载荷下淤泥轻量土的细观变形机理研究1)

基于新型室内固结试验及有限元数值模拟分析方法,研究了淤泥轻量土在循环载荷作用下的细观多相变形机理及其宏、细观变形特性之间的相互关系。结果表明,EPS(expanded polystyrene)颗粒掺量及其粒径大小对淤泥轻量土的细观变形特性有显著的影响。试验发现,在所选用的配合比中EPS掺量相差2.0%时,而淤泥轻量土最大体积变形量却相差了4.1%。在相同循环次数下,试样中上、中、下三个点位的EPS颗粒变形量及其应力应变大小关系并不相同,上点位的EPS颗粒变形量最大。通过对不同循环周期下淤泥轻量土各相细观变形关系定量计算分析发现,EPS颗粒变形量在其整个变形过程中占主导地位,平均占到约60%$\sim$80%。该研究可为后续有关EPS淤泥轻量土的微细观结构之间多相耦合作用的研究及其在软土路基填土工程中的应用提供一定的理论支持。     

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.      

On the relative magnitudes of viscous,elastic and texture stresses in liquid crystalline PBG solutions

The relative contributions of the viscous, elastic, and texture stresses in flows of modestly concentrated liquid crystalline solutions of poly(-benzyl glutamate) or PBG, at low shear rates are assessed by comparing published experimental rheological and light-scattering data to theoretical predictions. The data considered include ratios of Leslie-Ericksen viscosities, the shear viscosity jump at the transition from the isotropic to the liquid-crystalline state, the dependence of the shear viscosity on concentration, and the fraction of slowly relaxing stress after cessation of shearing flow. We quantify the relative contributions of viscous and elastic stresses by estimating from these data a value for the parameter ß^* _{V str} D ^* _r /kT, where _str , is the solvent-polymer friction coefficient and D _r ^* is the rotary diffusivity in the isotropic phase at the concentration where the isotropic phase becomes unstable to liquid crystalline order. The experimental evidence suggests a value \^* _v 0.03, five times lower than the value, 0.15, for dilute solutions. The relative contributions of elastic and texture stresses can be quantified by a parameter in the mesoscopic theory for polydomain nematics; a value of 0.03 gives reasonable agreement with transient shearing experiments, and predicts that the shear viscosity will show an upturn at high polymer concentrations, in agreement with experiments.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

Semi-analytical solution to one-dimensional consolidation in unsaturated soils

In this paper, a series of semi-analytical solutions to one-dimensional consolidation in unsaturated soils are obtained. The air governing equation by Fredlund for unsaturated soils consolidation is simplified. By applying the Laplace transform and the Cayley-Hamilton theorem to the simplified governing equations of water and air, Darcy＇s law, and Fick＇s law, the transfer function between the state vectors at top and at any depth is then constructed. Finally, by the boundary conditions, the excess pore-water pressure, the excess pore-air pressure, and the soil settlement are obtained under several kinds of boundary conditions with the large-area uniform instantaneous loading. By the Crump method, the inverse Laplace transform is performed, and the semi-analytical solutions to the excess pore-water pressure, the excess pore-air pressure, and the soils settlement are obtained in the time domain. In the case of one surface which is permeable to air and water, comparisons between the semi-analytical solutions and the analytical solutions indicate that the semi-analytical solutions are correct. In the case of one surface which is permeable to air but impermeable to water, comparisons between the semi-analytical solutions and the results of the finite difference method are made, indicating that the semi-analytical solution is also correct.     

Mesophase formation in high molecular-weight xanthan solutions

After a short review of theoretical background on mesophase formation in polymer solutions, this paper describes the liquid crystal phase transition and the corresponding rheological properties for aqueous solutions of a high-molecularweight xanthan sample (M _w 1.8 10⁶). The formation of mesophases has been studied using polarizing microscopy and viscometry. The effects of the presence of salts, bacteria cells and proteins have been investigated. The variations in the viscosity, due to mesophase formation, are in qualitative agreement with the predictions of Matheson's theory, but the onset of the ordered phase occurs at very low polymer concentrations and the diphasic domain is much broader than predicted by thermodynamic models. These characteristics of the phase transition are related to the very high molecular weight of the sample studied and can be explained mainly by the effects of cooperative interactions between xanthan chains and of chain flexibility reducing translational entropy.     

现代土力学的基本问题

现代土力学可望在今后３０年内建成基本框架，其主要内容将包括新一代的本构模型及一个变形理论和两个破坏理论．本文介绍了作者对这些问题的今后研究重点及发展方向的一些看法．     

A generalization of wieghardt soil for two - dimensional foundation structures

Summary On the basis of a mechanical interpretation (see Reference[1]) the problem of generalization of Wieghardt soils for two-dimensional foundation structures is tackled. The results of experiments agree well with the schematization arrived at. The problem of the rigid circular plate on the thus schematized elastic soil is solved.

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Sommario Premesse alcune considerazioni di carattere generale sulla schematizzazione proposta dal Wieghardt per la legge carichi-spostamenti di un letto elastico di fondazione di un solido monodimensionale si affronta, al lume di un'interpretazione meccanica proposta dall'A. in un articolo precedente[1], il problema della generalizzazione di tale legge per i problemi di fondazione bidimensionali. Si perviene così in forma semplice alla formulazione della legge carichi-spostamenti per un generico piano di fondazione e si dimostra l'ottima rispondenza di tale schematizzazione con i risultati dedotti da prove sperimentali reali. Viene risolto in via completa il problema della piastra circolare rigida sul suolo elastico così schematizzato.

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First published in Italian in La ricerca scientifica, 35 (II-A), 1290–1304, Roma, 1965.     

Probing the nature of the contact between fine particles by using ultrasound propagation

The propagation velocity (vs) of an ultrasonic signal through a granular material depends on the type of interparticle contact. For noncohesive glass beads, a power law behavior for consolidation stresses applied (σc) above 1 MPa has been measured in previous work. This equation is compatible with Hertz's interaction law between elastic solids. In the present work, we have tested the propagation velocity of ultrasound signals through a sample of fine powder. The tensile strength and compactivity of the powder were previously measured by means of the Seville powder tester (SPT), indicating plastic deformation of the surface asperities in contact for small to moderate consolidation stresses. However, the measurements of ultrasound propagation at high consolidations presented here are compatible with Hertz's law. This finding suggests that for high consolidation stresses, surface asperities are flattened, and it is therefore the elastic deformation of the bulk of the particles that determines the transmission of ultrasonic pulses.     

Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with semi-permeable drainage boundary

The semi-analytical solutions to Fredlund and Hasan's one-dimensional(1 D)consolidation for unsaturated soils with a semi-permeable drainage boundary are presented. Two variables are introduced to transform the two coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations(PDFs), which are easily solved by the Laplace transform method. Then, the pore-water pressure, pore-air pressure, and soil settlement are obtained in the Laplace domain. The Crump method is adopted to perform the inverse Laplace transform in order to obtain the semi-analytical solutions in the time domain. It is shown that the proposed solutions are more applicable to various types of boundary conditions and agree well with the existing solutions from the literature. Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with single, double, mixed, and semi-permeable drainage boundaries. The changes in the pore-air and pore-water pressures and the soil settlement with the time factor at different values of the semi-permeable drainage boundary parameters are illustrated. In addition, parametric studies are conducted on the pore-air and pore-water pressures at different ratios(the air permeability coefficient to the water permeability coefficient) and depths.     

Analytical solution to one-dimensional consolidation in unsaturated soils

This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. The analytical solution is for Fredlund＇s one-dimensional consolidation equation in unsaturated soils. The transfer relationship between the state vectors at top surface and any depth is obtained by using the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy＇s law and Fick＇s law. Excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and boundary conditions. By performing inverse Laplace transforms, the analytical solutions are obtained in the time domain. A typical example illustrates the consolidation characteristics of unsaturated soil from an- alytical results. Finally, comparisons between the analytical solutions and results of the finite difference method indicate that the analytical solution is correct.     

沥青混合料蠕变柔量的一种实用模型及其应用

通过分析沥青混合料加载时的"固结效应"和卸载时的"永久变形"等流变学特征,提出了一个较为实用的流变学模型,并给出了模型参数的确定方法,该模型参数数目可多可少,且能满足Blotzmann叠加原理,可应用于应力随时间变化以及其它各种复杂应力状态的情况.     

Effects of electric fields and volume fraction on the rheology of hematite/silicone oil suspensions

Electrorheological (ER) fluids composed of iron(III) oxide (hematite) particles suspended in silicone oil are studied in this work. The rheological response has been characterized as a function of field strength, shear rate and volume fraction. The dielectric properties of the suspensions were first studied in order to get information about the conductivity of the solid. Rheological tests under a.c. electric fields elucidated the influence of the electric field strength and volume fraction on the field-dependent yield stress. It was found that this quantity scales as a square power law in both cases. The viscosities of electrified suspensions were found to increase by several orders of magnitude as compared to the unelectrified suspension at low shear rates, although at high shear rates hydrodynamic effects become dominant and no effects of the electric field on the viscosity are observed. The ER behaviour of the suspensions was analysed by considering the fundamental forces (of hydrodynamic and electrostatic origin) acting on the particles and it is found that, at a given volume fraction, all the dependencies of relative viscosity on shear rate and field strength can be described by a single function of the Mason number, Mn. Finally, two different chain models were used to explain the shear-thinning behaviour observed: rheological measurements showed a power-law dependence of relative viscosity decrease on the Mason number, _F~Mn, with –0.95.     

确定地基固结过程中材料参数的反分析法

结合有限单元法和数学规划法提出一确定地基固结过程中材料参数的反分析法。该法可以根据固结过程中的位移值和孔隙水压力值反算地基土的弹性系数、泊松比以及渗透系数。文中通过一些算例对该法进行了验证。     

A generalized equation for rheology of emulsions and suspensions of deformable particles subjected to simple shear at low Reynolds number

We present analyses to provide a generalized rheological equation for suspensions and emulsions of non-Brownian particles. These multiparticle systems are subjected to a steady straining flow at low Reynolds number. We first consider the effect of a single deformable fluid particle on the ambient velocity and stress fields to constrain the rheological behavior of dilute mixtures. In the homogenization process, we introduce a first volume correction by considering a finite domain for the incompressible matrix. We then extend the solution for the rheology of concentrated system using an incremental differential method operating in a fixed and finite volume, where we account for the effective volume of particles through a crowding factor. This approach provides a self-consistent method to approximate hydrodynamic interactions between bubbles, droplets, or solid particles in concentrated systems. The resultant non-linear model predicts the relative viscosity over particle volume fractions ranging from dilute to the the random close packing in the limit of small deformation (capillary or Weissenberg numbers) for any viscosity ratio between the dispersed and continuous phases. The predictions from our model are tested against published datasets and other constitutive equations over different ranges of viscosity ratio, volume fraction, and shear rate. These comparisons show that our model, is in excellent agreement with published datasets. Moreover, comparisons with experimental data show that the model performs very well when extrapolated to high capillary numbers (C a?1). We also predict the existence of two dimensionless numbers; a critical viscosity ratio and critical capillary numbers that characterize transitions in the macroscopic rheological behavior of emulsions. Finally, we present a regime diagram in terms of the viscosity ratio and capillary number that constrains conditions where emulsions behave like Newtonian or Non-Newtonian fluids.     

强夯加固机理的非线性动态冲击显式有限元数值分析

根据强夯的特点,采用同时考虑几何非线性、材料非线性、状态非线性,并且考虑瞬态大变形的非线性动态显式有限元,分析了强夯对地基土的冲击碰撞过程。该方法克服了以往有限元计算强夯动力问题时需再引入其他的简化假定的已知量,能较实际地反映强夯加固的动力特性。通过对工程实例计算研究,取得了令人满意的效果。     

K+ uptake by root systems grown in soil under salinity: II. Sensitivity analysis

A numerical algorithm for the solution of multicomponent transport of Ca²⁺, Mg²⁺, Na⁺, K⁺, Cl^– in soil and their uptake by plant roots has been developed. The model emphasizes adsorptiondesorption due to cation exchange mechanism, dissolution-precipitation of CaCO₃, and pH changes at the root surface controlled by the anion-cation influx balance. A fully implicit finite difference scheme is used for numerical implementation. Sensitivity analysis was conducted to evaluate the effect of each parameter on nutrient uptake. Each parameter (independent of all others) was varied between 0.25 to 4 times its speculated average level. Predicted K⁺ uptake was found to be more sensitive to changes of root radius and the parameter indicating maximal influx of K⁺. Effective diffusion coefficient and soil moisture are less influential. The influence of C_aCO₃ dissolution and different kinds of boundary conditions were also considered.Nomenclature A, B, E matrices of coefficients for finite difference scheme - b _i coefficients of equation for H⁺ concentration - C ^I concentration of theI-component in water - C ₀ ^I initial concentration of theI-component - _I ^r0 concentration of theI-component at the inner side of the root surface - C _I ^r1 concentration of theI-component at the external boundary - C _Na ^cr critical concentration for Na⁺ influx into root - CEC cation exchange capacity - D ^*I effective diffusion coefficient of theI-component in soil - F ^I concentration of theI-component on the exchange complex - G vector of coefficients in finite difference scheme - h Hill's cooperativity index for K⁺ influx - h ⁰ value ofh whenC ^Na=0 - J ^I uptake of theI-component by a root length unit - J _I ^r0 influx at the root surface of theI-component - J _max maximal influx of K⁺ - J _max ⁰ value ofJ ^max whenC ^Na=0 - K _a apparent Michaelis-Menten coefficient for K⁺ influx - K _a ⁰ value ofK _a whenC ^Na=0 - K _i selectivity coefficient of the exchange reaction - P _m ^I permeability of root surface for theI-component - P_CO2 partial pressure of CO₂ - r radial distance - r ₀ root radius - r ₁ half the distance between adjacent root (external boundary) - R ^I retardation factor of the-component in mass balance equation for theI-component - t time - t ₀ initial time - T simulation time - v ₀ water radial velocity at the root surface - x _i coordinate of nodes of finite difference mesh Greek coefficient of linear change of K⁺ influx - coefficient of linear change of Na⁺ influx - _s mass density of soil solid phase - soil porosity - volumetric content of liquid in soil - _i coefficients in formulae for parameters of K⁺ influx - parameter of perturbation in finite difference scheme - gg ^I activity coefficient of theI-component - accuracy of iteration convergence - time step for finite difference scheme - steps of finite difference mesh Special Symbols [...] activity symbol     

二维有限区域饱和软土Biot固结的数值模拟

针对二维有限矩形区域饱和软土固结问题,选取四种不同边界条件组合,利用数值模拟方法研究了在上表面剪切载荷作用下土体沉降变形的特征和规律。结果表明:在剪切载荷单独作用下,土体位移以水平位移为主,同时竖向位移也客观存在。这反映了土体固结过程中流固耦合的物理现象。土层最终变形量(沉降和水平位移)由剪切载荷与土体物性决定,与边界透水性无关;边界条件对土体的变形模式有着决定性影响。剪切载荷作用、法向载荷作用及二者联合作用的计算结果对比表明:虽然软土Biot固结是复杂的流固耦合过程,但在这个过程中载荷叠加原理依然成立。     

The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: finite shear rates

The purpose of this paper is to extend the rheological predictions of the Doi-Hess kinetic theory for sheared nematic polymers from the anomalous weak shear regime (Forest et al. 2004a) to arbitrary shear rates, and to associate salient rheological and optical properties with the solution space of kinetic theory. Using numerical bifurcation software (AUTO), we provide the phase diagram of all stable monodomain orientational probability distribution functions (PDFs) and their phase transitions (bifurcations) vs nematic concentration (N) and normalized shear rate (Peclet number, Pe) for Pe1. Shear stresses, normal stress differences, the peak direction of the orientational distribution, and birefringence order parameters are calculated and illustrated for each type of PDF attractor: steady flow-aligning, both in and out of the flow deformation plane and along the vorticity axis; unsteady limit cycles, where the peak orientation direction rotates in-plane or around the vorticity axis or in bi-stable orbits tilted between them; and chaotic attractors first observed in kinetic simulations by Grosso et al. (2001). We pay particular attention to correlations between rheological features and the variety of monodomain phase transitions. Together with the weak flow regime, these results provide a nearly complete picture of the rheological consequences of the Doi-Hess kinetic theory for sheared monodomains of rigid, extreme aspect ratio, nematic rods or platelets.