A constitutive model based on modified mixture theory for unsaturated rocks

Non-equilibrium thermodynamics and Biot poro-elasticity have been combined to give a coupled hydro-mechanical formulation for unsaturated rock. Darcy’s law for unsaturated flow has been derived from the dissipation process by using standard arguments of non-equilibrium thermodynamics, whereas Helmholtz free energy has been used to derive the relationship between stress and pore pressure changes. The resulting general framework accommodates both large and small deformation theories. When small deformations are assumed, the formulation is comparable with coupled equations derived using an alternative approach. For illustrative purposes, the formulation has been used to analyse a seasonally affected tunnel model. Numerical results for the desaturation in winter and resaturation in summer, of the zone near the tunnel wall, have been evaluated and compared with the findings of other researchers.     

A constitutive model for unsaturated soils with consideration of inter-particle bonding

The paper presents a physically-based constitutive model for unsaturated soils that considers the bonding effect of water menisci at inter-particle contacts. A bonding factor has been used to represent the magnitude of the equivalent bonding stress, defined as the bonding force per unit cross-sectional area. The average skeleton stress is employed to represent the effect of average fluid pressures within soil pores. Based on an empirical relationship between the bonding factor ζ and the ratio e/e_s (where e and e_s are void ratios at unsaturated and saturated states, respectively, at the same average skeleton stress), we propose an elasto-plastic constitutive model for isotropic stress states, and then extend this model to triaxial stress states within the framework of critical state soil mechanics. Because only one yield surface is needed in the proposed model, a relatively small number of parameters are required. Comparisons between experimental data and model results show that, in most cases, the proposed model can reasonably capture the important features of unsaturated soil behavior.     

An advanced hydro-mechanical constitutive model for unsaturated soils with different initial densities

This paper presents an advanced constitutive model for unsaturated soils, using Bishop’s effective stress (σ′) and the effective degree of saturation (S_e) as two fundamental constitutive variables in the proposed constitutive model. A sub-loading surface and a unified hardening parameter (H) are introduced into the σ′–S_e modelling framework to interpret the effects of initial density on coupled hydro-mechanical behaviour of compacted soils. Compared with existing models in the literature, the main advantage of the proposed model that it is capable of modelling hydro-mechanical behaviour of unsaturated soils compacted to different initial densities, such as the dependence of loading–collapse volume on initial void ratio and density effect on the shearing-induced saturation change. The proposed model requires 13 material parameters, all of which can be calibrated through conventional laboratory tests. Numerical studies are conducted to assess the performance of the model for a hypothetical soil under two typical hydro-mechanical loading scenarios. The proposed advanced unsaturated soil model is then validated against a number of experimental results for both isotropic and triaxial conditions reported in the literature.     

列车运行时由轨道不平顺引起的地基振动研究

采用半解析法研究了列车荷载作用下列车-轨道-饱和地基系统的耦合振动问题。研究模型共分为3部分：车体简化为一个多刚体系统,在车轮与钢轨之间引入线性Hertizian弹簧接触模型模拟轮轨动力相互作用、采用离散轨枕支撑的弹性Euler梁来模拟轨道系统、下卧土体采用多孔饱和半空间模型。列车荷载分为轴重和由轨道不平顺引起的轮轨动力相互作用力。采用Fourier变换分别求解各子系统的控制方程,并通过动力子结构法对各子系统进行耦合。土体在时域内的动力响应通过快速Fourier变换求得。在分析了轮轨动力相互作用力的基础上,研究了轮轨动力作用力和列车轴重作用下饱和地基的动力响应,并分析了轨枕间距和土体渗透系数对饱和地基振动响应的影响。研究表明,轮轨动力作用力对地基远场振动有重要贡献,同时枕木间距对轨道与地基振动响应有较大影响。     

考虑Hansbo渗流的二维Biot固结有限元分析

为进一步深入研究弹性饱和黏性土地基的二维固结机制,引入Hansbo渗流方程描述固结过程中的非达西渗流,修正Biot二维固结方程。基于加权残数法,给出相应的有限元数值求解格式。通过和饱和黏性土一维非达西渗流固结理论有限体积法数值结果的对比,证明数值计算方法的有效性。在此基础上,探讨Hansbo渗流参数对二维地基固结进程的影响。计算结果表明,在固结初期,Hansbo渗流将增强Mandel-Cryer效应,增大孔压的峰值,并延长孔隙水压力达到峰值的时间;在固结中后期,整个土层存在孔隙水压力滞后现象。同时,Hansbo渗流将阻碍地基沉降的发展。而且,上述影响会随着Hansbo渗流参数的增大而更加明显。     

Consolidation analysis of non-homogeneous soil by the weak form quadrature element method

A weak form quadrature element formulation for consolidation analysis of non-homogeneous saturated soil is established based on Biot’s theory. Numerical examples are given, and the results are compared with the analytical solutions available or those from the commercial finite element software ABAQUS, demonstrating accuracy and rapid convergence of quadrature element solutions. The disparity between various treatments of non-homogenous soil is discussed, and the effectiveness and advantages of the quadrature element formulation in consolidation analysis of non-homogeneous soil are demonstrated.     

The influence of coupled physical swelling and chemical reactions on deformable geomaterials

Coupled thermo‐hydro‐mechanical‐chemical modelling has attracted attention in past decades due to many contemporary geotechnical engineering applications (e.g., waste disposal, carbon capture and storage). However, molecular‐scale interactions within geomaterials (e.g., swelling and dissolution/precipitation) have a significant influence on the mechanical behaviour, yet are rarely incorporated into existing Thermal‐Hydro‐Mechanical‐Chemical (THMC) frameworks. This paper presents a new coupled hydro‐mechanical‐chemical constitutive model to bridge molecular‐scale interactions with macro‐physical deformation by combining the swelling and dissolution/precipitation through an extension of the new mixture‐coupling theory. Entropy analysis of the geomaterial system provides dissipation energy, and Helmholtz free energy gives the relationship between solids and fluids. Numerical simulation is used to compare with the selected recognized models, which demonstrates that the swelling and dissolution/precipitation processes may have a significant influence on the mechanical deformation of the geomaterials.     

基于黏弹塑性本构模型的泥石流数值模拟

泥石流是一个世界范围的地质灾害问题,多年来受到广泛而深入的研究。大多数工作致力于分离地研究岩土材料破坏前的失稳机制和失稳后的快速流动扩展。尝试以一种连续方法模拟完整的泥石流过程,仅用一个本构模型描述泥石流的起始、扩展和停滞。首先讨论了重力增大和基质吸力降低诱发泥石流的力学机制,描述了泥石流过程中岩土材料力学性质的弹塑性–黏性转变现象,对泥石流进行了黏弹塑性的全程模拟,并对挡土墙的冲击效应进行了启发性研究,证明了研究中所使用的本构模型可以准确地描述岩土材料的固流转化现象,数值方法可以很好地对均质连续介质进行大位移模拟。     

空沟对列车运行引起的地基振动隔振效果研究

为研究空沟对高速列车引起地基振动的隔振效果,在已有研究基础上改进出一种新的解析研究模型。模型中首次运用了饱和半空间模型来研究地基上隔振沟对高速列车的隔振效果;隔振沟则通过在饱和半空间土体上设置3个合适宽度、截面为矩形的弹性层来模拟;中间矩形弹性层为路堤,路堤上方放置了枕木与轨道。枕木与轨道分别通过纵向异性Kirchhoff薄板与Euler梁来模拟,饱和土地基采用Biot多孔饱和介质理论来描述。控制方程通过傅立叶变换与傅立叶级数展开,在变换域中进行求解。研究表明,随着列车运行速度的提高,空沟的隔振效果明显提高;饱和土体固-液相的耦合作用对隔振沟的隔振效果的影响明显,尤其当列车运行速度超过土体表面Rayleigh波速时,随着土体渗透系数的增加,空沟隔振效果显著降低。此外,列车运行速度超过土体表面波速时,饱和土地基上空沟的隔振效果明显优于相应单相弹性地基上空沟的隔振效果。     

考虑损伤阈值影响的岩石脆-延性转化统计损伤本构模型研究

普通岩石在三向受力状态下随着围压由低到高,会表现出由脆性向延性转化的特征.首先,在深入探讨岩石压缩变形机理与变形过程特征的基础上,并针对Lemaitre应变等价性理论的不足之处,基于能量理论建立了更符合实际情况的损伤模型;其次,从岩石并非一受力就会产生损伤这一客观事实出发,建立了能反映损伤阈值影响的岩石单元强度度量方法与损伤演化模型.最后,在上述模型基础之上,建立了可体现岩石在三轴试验中脆-延性转化特征的统计损伤本构模型及模型参数确定方法.     

多孔隙岩石加卸载力学特性及本构模型研究

为了研究岩石在加载-卸载过程中的应力-应变关系,以砂岩为例,对其进行常规三轴加卸载试验。分析了峰后卸载阶段岩石的非线性特性,对岩石的损伤变量进行定义,给出了峰后卸载过程中用于描述应力-应变关系的弹性模量模型。通过分析加载-卸载过程中的轴向应变与径向应变的关系,得到了卸载过程中泊松比模型。引入D-P塑性模型,针对砂岩的塑性硬化特性,对硬化函数进行修正,建立了与等效塑性应变相关联的损伤模型。将计算模型矩阵化后进行数值计算。在此过程中得到如下结论:多孔隙岩石在加载过程中表现出明显的非线性特征,随着体应力的增大,岩石的弹性模量逐渐增大。岩石峰后卸载过程中,当轴向应力大于围压时,应力-应变可以利用峰前弹性阶段的弹性模量模型乘以连续性因子进行描述。随着等效塑性应变的增大,泊松比先增大后减小,最终趋于稳定。峰后卸载过程中,等效塑性应变不发生变化,此时泊松比保持不变。利用提出的本构模型进行了数值计算,数值计算结果与试验结果进行对比,结果表明,提出的模型能够反映出岩石在峰后卸载过程中的应力-应变规律。     

止水帷幕对基坑环境效应影响的有限元分析

采用Biot固结理论分析了止水帷幕对基坑工程环境效应的影响,包括止水帷幕不同打设深度的效果,以及两种封闭式止水帷幕发生漏水意外时对地下水位和坑外土体位移的影响等。在有限元编程中,将开挖土体置为空气单元可以简化处理过程。算例分析结果表明,深厚透水地基中增加竖向止水帷幕的深度并不能有效减小对周围环境的影响;漏水部位周围土体的渗流等势线较为密集,渗流速度较大,容易诱发扩大破坏;竖向封闭式止水帷幕漏水引起的坑边土体的沉降和地表土体的侧移相对较大,水位下降迅速等。其结果可供基坑工程漏水事故环境效应的评价和对策研究时参考。     

Thermomechanical model of hydration swelling in smectitic clays: I two-scale mixture-theory approach

A thermomechanical theory of hydration swelling in smectitic clays is proposed. The clay is treated as a three-scale swelling system wherein macroscopic governing equations are derived by upscaling the microstructure. At the microscale the model has two phases, the disjoint clay platelets and adsorbed water (water between the platelets). At the intermediate (meso) scale (the homogenized microscale) the model consists of clay particles (adsorbed water plus clay platelets) and bulk water. At the macroscale the medium is treated as an homogenized swelling mixture of clay particles and bulk-phase water with thermodynamic properties defined everywhere within the macroscopic body. In Part I, the mesoscopic model governing the swelling of the clay particles is derived using a mixture-theoretic approach and the Coleman and Noll method of exploitation of the entropy inequality. Application of this procedure leads to two-scale governing equations which generalize the classical thermoelastic consolidation model of non-swelling media, as they exhibit additional physico-chemical and viscous-type terms accounting for hydration stresses between the adsorbed fluid and the clay minerals. In Part II the two-scale model is applied to a bentonitic clay used for engineered barrier of nuclear waste repository. The clay buffer is assumed to have monomodal character with most of the water essentially adsorbed. Further, partial results toward a three-scale thermomechanical macroscopic model including the bulk phase next to the swelling particles are derived by homogenizing the two-scale model with the bulk water. A notable consequence of this three-scale approach is that it provides a rational basis for the appearance of a generalized inter-phase mass transfer between adsorbed and bulk water. Copyright © 1999 John Wiley & Sons, Ltd.     

水位流速耦合演算模型研究

河道防洪,水位和流速是重要的预报特征量.目前对于缺乏流量观测资料和没有稳定水位流量关系线的河道,几乎还没有实用、有效和具有通用性的水位与流速双变量预报模型.以水流质量和力的平衡方程为基础,根据因次分析方法,提出摩阻的导数表达结构,并差分形成水位流速双变量耦合演算模型.通过钱塘江、赣江和桂江3个流域中4个河段的模拟检验,取得了较好的结果,率定期和检验期的确定性系数都大于0.7.初步证明了双变量耦合演算模型结构的合理性和模拟实际河道水流的有效性.     

基于HBP本构模型的泥石流动力过程SPH数值模拟

本构模型是描述泥石流流变特性的关键,也是决定其动力过程数值模拟准确性的核心问题之一。泥石流流体属多相混合物,现有的研究已证实其存在剪切增稠或剪切变稀的现象,传统基于Bingham及Cross线性本构关系的数值模型难以准确描述泥石流流变特性。文中探讨了Bingham模型在低剪应变率下的数值发散问题,在光滑粒子流体动力学（SPH）方法框架上建立了整合Herschel-Bulkley-Papanastasiou(HBP）本构关系的稀性泥石流动力过程三维数值模型。相比传统基于浅水波假设的二维数值模型,所述方法从三维尺度建立SPH形式下的泥石流浆体纳维?斯托克斯方程并进行数值求解,可获取泥石流速度场时空分布及堆积形态,同时采用HBP本构关系描述泥石流流变特性,能在确保数值收敛的前提下反映泥石流流体在塑性屈服过渡段及大变形状态下应力?应变的非线性变化。为验证提出方法的合理性,结合小型模型槽实验观测进行了对比,结果表明数值模拟与实测结果基本吻合。     

统一弹塑性本构模型在FLAC3D中的计算格式

统一强度理论是一个有着坚实理论基础、可表达各种岩土材料强度特性且被广泛应用的新的强度理论。FLAC3D是一个具有强大的计算分析功能且专门针对岩土工程问题开发并被广泛应用的数值分析软件。若能将二者结合起来,无疑会大大促进岩土工程领域相关问题的解决。针对这一问题,研究了统一弹塑性本构模型在有限差分方法中应用的基本理论格式。根据FLAC3D软件中UDM接口计算格式的要求,将统一强度理论引入其中,详细推导了统一弹塑性本构模型在FLAC3D软件中应用的计算公式。由于统一屈服面在应力空间内由12个面组成,在应力角为[0,π/3]的范围内,统一屈服面由两个相交面组成,为计算塑性因子及处理计算中应力超出屈服面的应力调整问题,利用应力角分析了应力空间的分区,推导了区域分界面的公式。最后,编制了相应的UDM接口程序对一圆形隧洞进行了弹塑性分析,对比了计算结果与解析解,结果很好地验证了此计算格式及相应接口程序的正确性。统一强度理论和FLAC3D软件的结合,将使二者的优点得以充分发挥,以解决更多的岩土工程问题。     

A coupled model for prediction of settlement and gas flow in MSW landfills

Prediction of long‐term settlement and control of gas pollution to the environment are two principle concerns during the management of municipal solid waste (MSW) landfills. The behavior of settlement and gas flow in MSW landfills is complicated due to the combined effect of mechanical deformation of the solid skeleton and continuous biodegradation of the waste. A one‐dimensional settlement and gas flow model is presented in this paper, which is capable of predicting time evolution of settlement as well as temporal and spatial distribution of gas pressure within multi‐layered landfills under a variety of operating scenarios. The analytical solution to the novel model is evaluated with numerical simulation and field measurements. The resulting efficiency and accuracy highlight the capability of the proposed model to reproduce the settlement behavior and gas flow in MSW landfills. The influences of operating conditions and waste properties on settlement and gas pressure are examined for typical MSW landfills. Copyright © 2009 John Wiley & Sons, Ltd.     

Development of a sharp interface model that simulates coastal aquifer flow with the coupled use of GIS

A simulation program, which works seamlessly with GIS and simulates flows in coastal aquifers, is presented in the present paper. The model is based on the Galerkin finite element discretization scheme and it simulates both steady and transient freshwater and saltwater flow, assuming that the two fluids are separated by a sharp interface. The model has been verified in simple cases where analytical solutions exist. The simulation program works as a tool of the GIS program, which is the main database that stores and manages all the necessary data. The combined use of the simulation and the GIS program forms an integrated management tool offering a simpler way of simulating and studying saline intrusion in coastal aquifers. Application of the model to the Yermasogia aquifer illustrates the coupled use of modeling and GIS techniques for the examination of regional coastal aquifer systems.

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Resumen Se ha desarrollado un modelo casi tridimensional de elementos finitos para simular el flujo de agua dulce y salada, tanto en régimen estacionario como en transitorio, en sistemas acuíferos costeros, bajo la hipótesis de separación por medio de una interfaz abrupta. Las ecuaciones del modelo han sido discretizadas mediante un esquema de Galerkin de discretización en elementos finitos. El modelo ha sido verificado en casos sencillos para los que existe solución analítica. Todos los datos necesarios se introducen y gestionan con un Sistema de Información Geográfica [SIG] por ordenador. El programa de simulación forma parte del programa de SIG, constituyendo una herramienta integrada de gestión para estudiar la intrusión salina en acuíferos costeros. La aplicación del modelo al acuífero de Yermasogia ilustra el uso acoplado de las técnicas de modelación y de SIG con el fin de examinar sistemas acuíferos costeros a escala regional.

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Résumé Pour étudier un système aquifère côtier, nous avons développé un modèle aux éléments finis en quasi 3-D qui simule les écoulements deau douce et deau salée en régime aussi bien permanent que transitoire. Les équations qui les régissent sont discrétisées par un schéma de discrétisation de Garlekin aux éléments finis. Le modèle a été vérifié dans des cas simples où il existe des solutions analytiques. Toutes les données nécessaires sont introduites et gérées grâce à un logiciel de gestion de SIG. Le programme de simulation est utilisé comme un outil du logiciel de SIG, constituant ainsi un outil de gestion intégrée dont le but est de simuler et détudier lintrusion saline dans les aquifères côtiers. Lapplication du modèle à laquifère de Yermasogia illustre lutilisation couplée de la modélisation et des techniques de SIG pour létude des systèmes aquifères côtiers régionaux.

     

筒型基础负压沉贯流固耦合渗流分析模型

分析筒型基础沉贯作用的土层,利用 流动理论各项同性硬化原理,研究海积软土颗粒本构关系,结合离散元方法计算土体体应变,并将其引入海积软土的物性参数动态计算模型。根据筒型基础沉贯特征,结合体应变以及物性参数动态模型,由有效应力原理和瞬时质量守恒原理分别确定应力和渗流方程,并给出上述模型的定解条件。建立了新的流固耦合渗流的数学模型,求解筒型基础沉贯渗流场分布。     

渗流-化学溶解耦合作用下岩石单裂隙渗透特性研究

为揭示在渗流-化学溶解耦合作用下单裂隙渗透特性的变化规律,建立了描述二维渗流-化学溶解耦合作用的偏微分方程组,并利用COMSOL Multiphysics软件成功地求解该方程组。首先,模拟了文献[1]中的盐岩渗流-溶解耦合渗流试验结果,数值模拟结果与试验结果较为吻合,验证了数学模型的正确性和有效性。然后,利用分形理论生成了一个粗糙的裂隙面数字模型,着重分析了二维石灰岩粗糙裂隙面在水流、矿物溶解和输运过程中其渗透特性的变化规律。数值分析显示,（1）溶质浓度对裂隙面的溶解具有非常重要的作用,从而水流进口端的溶解厚度比出口端大得多。（2）裂隙的整体渗透性在初始时刻增加较慢,随着裂隙开度的增大和贯通,溶解速度会逐渐增大,是一个加速的过程。