A fully coupled non-linear dynamic analysis procedure and its verification using centrifuge test results

The equations governing the dynamic behavior of saturated porous media as well as a finite element spatial discretization of these equations are summarized. A three-parameter time integration scheme called the Hilber–Hughes–Taylor α-method is used together with a predictor/multi-corrector algorithm, instead of the widely used Newmark's method, to integrate the spatially discrete finite element equations. The new time integration scheme possess quadratic accuracy and desirable numerical damping characteristics. The proposed numerical solution and bounding surface plasticity theory to describe the constitutive behaviour of soil have been implemented as the computer code DYSAC2. Predictions made by DYSAC2 code are verified using dynamic centrifuge test results for a clay embankment. Importance of initial state of a soil on its dynamic behaviour is demonstrated.     

不同土壤类型与含水率对水平埋管换热性能影响数值分析

为揭示地源热泵系统水平埋管换热器在不同土壤类型中的换热性能,基于土壤毛管水理论知识,结合数值模拟的研究手段,探讨了蓄能不同类型土体内(砂土、壤土、黏土)三相组成的差异对水平埋管换热器换热特性的影响规律。结果表明,在通入308.15 K制冷工况下,水平管在壤土中的出水温度降低至303.3 K,进出口水温差为4.9 K,埋管单位延米换热量37.1 W/m,水平管在壤土中的制冷换热效益显著;不同土壤(砂土、壤土、黏土)在经历相同制冷周期下,水平管的换热过程对壤土的温度场分布影响最小,管体在壤土中运行时热堆积风险系数最低。研究表明,水平管与土壤的换热性能同时受土壤比热容与土壤导热系数的影响,提高土壤导热系数比提高土壤比热容获得的效益更加显著。可以通过压实回填、减少土壤孔隙率、提高固相回填材料导热系数、加大布管深度以提高回填材料含水率等方法来强化埋管的换热性能。      

Development of a technique for modelling clay liner desiccation

This paper presents a model for the analysis of clay liner desiccation in a landfill barrier system due to temperature effects. The model incorporates consideration of fully coupled heat‐moisture‐air flow, a non‐linear constitutive relationship, the dependence of void ratio and volumetric water content on stress, capillary pressure and temperature, and the effect of mechanical deformation on all governing equations. Mass conservative numerical schemes are proposed to improve the accuracy of the finite element solution to the governing equations. The application of the model is then demonstrated by examining three test problems, including isothermal infiltration, heat conduction and non‐isothermal water and heat transport. Comparisons are made with results from literature, and good agreement is observed. Copyright © 2003 John Wiley & Sons, Ltd.     

Arbitrary Lagrangian Eulerian based finite element analysis of cone penetration in soft clay

This paper presents a numerical model for the analysis of cone penetration in soft clay based on the finite element method. The constitutive behaviour of the soil is modelled by modifying an elastic, perfectly-plastic soil model obeying Von-Mises yield criterion to take into account the strain-softening, rate dependent behaviour of soft clay. Since this is a problem involving large soil deformations, the analysis is carried out using an Arbitrary Lagrangian Eulerian method where the quality of the mesh is preserved during penetration. The variation of cone resistance is examined with various parameters such as rigidity index of the soil, in situ stress anisotropy and roughness at the cone–soil interface, which influence the penetration resistance of the cone. A theoretical correlation has been developed incorporating these parameters and the results have been compared with previous correlations based on the cavity expansion theory, finite element method and strain path method. With the increase in strain-softening, relative brittleness of the soil increases and the penetration resistance is significantly reduced. With the rising strain-rate dependency, penetration resistance increases but this increase is independent of the degree of brittleness of the soil.     

Viscosity effect on consolidation of poroelastic soil due to groundwater table depression

In this study, the viscosity effect on consolidation of poroelastic soil due to groundwater table depression is examined. A viscoelastic consolidation numerical model is developed to conduct this examination. By nondimensionalizing the governing equations the viscosity number that depends on hydraulic conductivity, viscous moduli, and thickness of soil is obtained to represent the viscosity effect on consolidation of poroelastic soil. The case of clay stratum sandwiched between sandy strata subjected to sudden and gradual groundwater table depressions is used to investigate the importance of viscosity effect to poroelastic consolidation. The results show that the displacement and pore water pressure of clay stratum are strongly related to the viscosity effect. The overestimation of soil displacement will occur if the viscosity effect is neglected. Hence, the viscosity effect needs to be considered in modeling consolidation of poroelastic soil under groundwater table depression.     

高岭土电渗固结特性及数值模拟研究

电渗固结是促进低渗透性软土排水固结的有效方法。为了揭示不同电势梯度影响高岭土电渗固结的基本规律,在自制电渗试验装置上对高岭土进行电渗试验。试验过程中测量电流、排水量、沉降量以及有效电压随时间的变化,并进行单位排水能耗分析。基于电渗固结多场耦合控制方程,实现土体电渗固结全耦合分析的有限元数值方法,计算结果与解析解吻合良好,验证了程序的有效性。为预测不同电势梯度下土体沉降量随时间的变化关系,分别对0.5,1.0,1.5 V/cm 3种电势梯度电渗固结试验进行数值模拟分析,获得模型表面沉降量分布、阳极超静孔隙水压力时空发展规律、阳极位置固结度等曲线,计算结果和试验结果吻合良好,可为实际电渗试验提供理论指导。     

A comparison of field-monitored and numerically predicted moisture movement in unsaturated soil

This paper presents the results of the application of a numerical model of flow of water in unsaturated soil to simulate real field behaviour. Numerical predictions are compared with field-monitored results as part of an assessment of the approach adopted. The numerical approach is based on a finite element solution of Richards' theoretical formulation, adopting a finite difference recurrence relationship to model the transient nature of the problem. The field results have been collected by British Gas in Kimmeridge clay at a site in Swindon. The simulation addressed the autumn wetting of the soil during 1983. Comparisons of volumetric moisture content readings from the field and numerical predictions give good correlation. It is concluded that the numerical model has adequately represented field behaviour over the depth of interest. Taken in conjunction with previous results, it is claimed that the model should now be capable of use in a predictive mode.     

地埋点热源作用下层状半空间的热-力耦合响应

采用解析层元法对存在地下点热源的岩土工程问题进行解答。首先从热弹性力学三维问题的基本控制方程出发,利用拉普拉斯-傅里叶积分变换推导出其在变换域内单层介质及下卧半空间的解析层元;然后结合有限单元法原理组装得到总刚度矩阵,结合边界条件,得到其在变换域内的解答,最后应用拉普拉斯-傅里叶积分逆变换技术,得到物理域内的解。编制了相应的计算程序,算例分析表明：该结果与已有文献吻合较好,该方法求解层状半空间的热-力耦合响应问题具有较好的适用性和较高的精度;层状岩土介质体系中,热扩散系数对温度及地表隆起的变化过程影响显著,但对其初始值和最终稳定值影响不明显;分层特性对岩土介质温度分布及地表位移变化过程均有显著影响。     

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.     

A STUDY ON A NEW MECHANICAL MODEL FOR FOUNDATIONS AND ITS ELASTIC SETTLEMENT RESPONSE

In the present paper, a new foundation model has been proposed by introducing a stretched rough elastic membrane in the Pasternak shear layer sandwiched between two spring layers which is an extension of Kerr model. Considering the equilibrium of different elements, the equations governing the elastic settlement response of the model are derived. Finite difference scheme has been employed to solve the governing equations. The parametric studies carried out show the effect of several parameters on the elastic settlement response of the model. The proposed model is well suited for idealizing the behavior of geosynthetic-reinforced granular fill—soft soil system besides other applications.     

Incrementalization of a single hardening constitutive model for frictional materials

The governing equations for an elasto‐plastic constitutive model for frictional materials such as soil, rock, and concrete are presented, and the incremental form is indicated in preparation for implementation of the model in a user‐defined module for finite element calculations. This isotropic, work‐hardening and ‐softening model employs a single yield surface, it incorporates non‐associated plastic flow, and its capability of capturing the behaviour of different types of frictional materials under various three‐dimensional conditions has been demonstrated by comparison with measured behaviour, as presented in the literature. The incrementalization procedure is indicated and the resulting equations for the single hardening model are presented together with parameters for a dense sand. Following the implementation of the model, these parameters are used for evaluation of different integration schemes as presented in a companion paper by Jakobsen and Lade (Int. J. Numer. Anal. Meth. Geomech. 2002; 26 :661). Copyright © 2002 John Wiley & Sons, Ltd.     

Modelling coupled heat and contaminant transport in groundwater

This paper presents the results of a research programme conducted on the geotechnical centrifuge at The University of Western Australia to investigate coupled heat and contaminant transport in the soil surrounding a buried waste source. The phenomena which govern heat and contaminant transport through porous media are discussed, the principles of geotechnical centrifuge modelling are outlined, and relevant scaling laws that govern the relationship between a centrifuge model and the prototype, with respect to the problem of coupled waste transport, are presented. A model test, simulating two-dimensional migration from a buried heat and contaminant source, is described, and the results from four model tests are presented. The experimental data show that hydraulic instability is responsible for the transport of contaminant in the soil around the source and that the mode of instability is determined by the magnitude of the effective Rayleigh number.     

Suction-controlled experiments on Boom clay

The understanding of the thermo-hydro-mechanical behaviour of a clay barrier is needed for the prediction of its final in situ properties after the hydration and thermal transient in a radioactive waste repository.

As part of the CEC 1990–1994 R&D programme on radioactive waste management and storage, the CEA (Fr), CIEMAT (Sp), ENRESA (Sp), SCK · CEN (B), UPC (Sp) and UWCC (UK) have carried out a joint project on unsaturated clay behaviour (Volckaert et al., 1996). The aim of the study is to analyse and model the behaviour of a clay-based engineered barrier during its hydration phase under real repository conditions. The hydro-mechanical and thermo-hydraulic models developed in this project have been coupled to describe stress/strain behaviour, moisture migration and heat transfer. A thermo-hydraulic model has also been coupled to a geochemical code to describe the migration and formation of chemical species.

In this project, suction-controlled experiments have been performed on Boom clay (B), FoCa clay (Fr) and Almeria bentonite (Sp). The aim of these experiments is to test the validity of the interpretive model developed by Alonso and Gens (Alonso et al., 1990), and to build a database of unsaturated clay thermo-hydro-mechanical parameters. Such a database can then be used for validation exercises in which in situ experiments are simulated.

The Boom clay is a moderately swelling clay of Rupellian age. It is studied at the SCK · CEN in Belgium as a potential host rock for a radioactive waste repository. In this paper, suction-controlled experiments carried out on Boom clay by SCK · CEN are described. SCK · CEN has performed experiments to measure the relation between suction, water content and temperature and the relation between suction, stress and deformation. The applied suction-control techniques and experimental setups are detailed. The results of these experiments are discussed in the perspective of the model of Alonso and Gens. The influence of temperature on water uptake was rather small. The measured swelling-collapse behaviour can be explained by the Alonso and Gens model.     

Finite element modelling of transport of organic chemicals through soils

Aquifer contamination by organic chemicals in subsurface flow through soils due to leaking underground storage tanks filled with organic fluids is an important groundwater pollution problem. The problem involves transport of a chemical pollutant through soils via flow of three immiscible fluid phases: namely air, water and an organic fluid. In this paper, assuming the air phase is under constant atmospheric pressure, the flow field is described by two coupled equations for the water and the organic fluid flow taking interphase mass transfer into account. The transport equations for the contaminant in all the three phases are derived and assuming partition equilibrium coefficients, a single convective – dispersive mass transport equation is obtained. A finite element formulation corresponding to the coupled differential equations governing flow and mass transport in the three fluid phase porous medium system with constant air phase pressure is presented. Relevant constitutive relationships for fluid conductivities and saturations as function of fluid pressures lead to non-linear material coefficients in the formulation. A general time-integration scheme and iteration by a modified Picard method to handle the non-linear properties are used to solve the resulting finite element equations. Laboratory tests were conducted on a soil column initially saturated with water and displaced by p-cymene (a benzene-derivative hydrocarbon) under constant pressure. The same experimental procedure is simulated by the finite element programme to observe the numerical model behaviour and compare the results with those obtained in the tests. The numerical data agreed well with the observed outflow data, and thus validating the formulation. A hypothetical field case involving leakage of organic fluid in a buried underground storage tank and the subsequent transport of an organic compound (benzene) is analysed and the nature of the plume spread is discussed.     

Rocking vibration of a rigid strip footing on saturated soil

The dynamic response of a rigid strip footing lying on saturated soil is greatly affected by the pore pressure induced by a rocking moment. To consider the complex behavior of the soil under the rocking load, an analytical solution for a rigid strip foundation on saturated soil under a rocking moment is developed under the framework of Biot’s coupling theory. The boundary-value problem for the governing coupling equations for saturated soil is solved using a Fourier transform to yield a pair of dual integral equations. These dual integral equations are transformed into a set of linear equations using an infinite series of orthogonal Jacobi polynomials to yield the compliance functions. In addition, a parametric study has been carried out to examine the influence of: (1) the dimensionless frequency, (2) the dynamic permeability and (3) the Poisson’s ratio on saturated soil under a rocking rigid strip footing.     

On the black cotton soils of North Cameroon

During detailed geotechnical prospecting in North Cameroon, extensive black cotton soil deposits were encountered. Based on classification tests, three samples were selected for mineralogical analysis. The results indicated that the predominant clay mineral was the halloysite governing the geotechnical properties and behaviour of the cotton soils. New correlations were established between clay mineral content and Atterberg limits of the investigated materials.     

Time‐dependent behaviour of a rigid foundation on a transversely isotropic soil layer

An analytical solution is presented in this paper to study the time‐dependent settlement behaviour of a rigid foundation resting on a transversely isotropic saturated soil layer. The governing equations for a transversely isotropic saturated soil, within Biot's poroelasticity framework, are solved by means of Laplace and Hankel transforms. The problem is subsequently formulated in the Laplace transform domain in terms of a set of dual integral equations that are further reduced to a Fredholm integral equation of the second kind and solved numerically. The developed analytical solution is validated via comparison with the existing analytical solution for an isotropic saturated soil case, and adopted as a benchmark to examine the sensitivities of the mesh refinement and the locations of truncation boundaries in the finite element simulations using ABAQUS. Particular attention is paid to the influences of the degree of soil anisotropy, boundary drainage condition, and the soil layer thickness on the consolidation settlement and contact stress of the rigid foundation. Copyright © 2009 John Wiley & Sons, Ltd.     

A study on how to couple thermo-hydro-mechanical behaviour of unsaturated soils: Physical equations,numerical implementation and examples

This paper describes a thermo-hydro-mechanical framework suitable for modelling the behaviour of unsaturated soils. In particular, this paper focuses on bentonite clay subjected to a thermo-hydro-mechanical load, as in the case of nuclear waste engineering barriers. The paper gives a theoretical derivation of the full set of coupled balance equations governing the material behaviour as well as an extended physical interpretation. Finally, a finite element discretisation of the equations and number of simulations verifying their implementation into a custom finite element code is provided. Some aspects of the formulation are also validated against experimental data.     

Consolidation around a point heat source

When a heat source such as a canister of radioactive waste is buried in a saturated soil the temperature changes that occur will cause the pore water to expand a greater amount than the voids of the soil. The temperature change will thus usually be accompanied by an increase in pore pressure. If the soil is sufficiently permeable these pore pressures will dissipate. This paper develops an analytic solution for the fundamental problem of a point heat source buried deep in a saturated soil.