Stress–strain model for clays with anisotropic void ratio distribution

The porosity of soils is considered to be a directional measure and its distribution is characterized by a functional form. This form has been used to extend the critical state soil mechanics framework to include the effects of structure in soils. A new internal plastic energy dissipation formulation has been proposed to account for fabric arrangement. New expressions for the yield locus, and the plastic stress–strain response of structural soils have been derived. The applicability of the concepts to model the plastic stress–strain behaviour of a number of soils is illustrated. The advantage of the new model is very well identified in modelling the stress–strain behaviour of K₀ consolidated and natural clays. © 1998 John Wiley & Sons, Ltd.     

A double hardening thermo-mechanical constitutive model for overconsolidated clays

On the basis of a double hardening model for clays and available experimental results, a new thermo-elasto-plastic constitutive model for saturated clays is proposed to describe the effects of temperature and overconsolidation ratio on the mechanical properties of saturated clays. Two hardening parameters are introduced: s_c^￠ {\sigma}_{{\rm c}}^{\prime} and α. The proposed model is then applied to simulate the relevant important features of saturated clays with different overconsolidation ratios under different temperature and loading conditions. The model predictions are compared with available experimental results to demonstrate its accuracy and usefulness.     

天然沉积饱和有明粘性土的Burland 孔隙指数与归一化含水量的关系

如何评价土结构性对天然沉积饱和土的力学性状的影响是一个非常重要的研究课题。Burland在第30届郎肯讲座论文中导入孔隙指数对各种重塑土的压缩曲线进行归一化，提出固有压缩曲线用于评价天然沉积土的压缩性状。通过对广泛沉积在日本九洲岛的有明粘性土进行试验研究，探讨了灵敏有明粘性土的特征，提出一个比Burland孔隙指数更为简单实用的评价天然沉积土力学性状的指标——归一化含水量，定义为含水量与液限之比。根据大量的试验结果，得出了天然沉积有明粘性土的Burland孔隙指数与归一化含水量的相关关系，提出了对应于归一化含水量的固有压缩曲线。     

A hypoplastic constitutive model for clays

This paper presents a new constitutive model for clays. The model is developed on the basis of generalized hypoplasticity principles, which are combined with traditional critical state soil mechanics. The positions of the isotropic normal compression line and the critical state line correspond to the Modified Cam clay model, the Matsuoka–Nakai failure surface is taken as the limit stress criterion and the non‐linear behaviour of soils with different overconsolidation ratios is governed by the generalized hypoplastic formulation. The model requires five constitutive parameters, which correspond to the parameters of the Modified Cam clay model and are simple to calibrate on the basis of standard laboratory experiments. This makes the model particularly suitable for practical applications. The basic model may be simply enhanced by the intergranular strain concept, which allows reproducing the behaviour at very small strains. The model is evaluated on the basis of high quality laboratory experiments on reconstituted London clay. Contrary to a reference hypoplastic relation, the proposed model may be applied to highly overconsolidated clays. Improvement of predictions in the small strain range at different stress levels is also demonstrated. Copyright © 2005 John Wiley & Sons, Ltd.     

结构性粘土的堆砌体模型

天然粘土一般都具有结构性, 其变形过程必然伴随着结构的破坏。 提出了一种新型的堆砌体模型, 用以描述这种结构破坏现象。 这一模型把变形过程中的结构性土看作不同大小土块的集合体, 总的变形将由土块的弹性变形、土块之间滑动引起的塑性变形和土块破碎引起的损伤变形三部分组成。 塑性变形常用屈服函数描述, 损伤变形则可以引入一种类似的损伤函数加以描述。推导了相应的应力应变关系式并提出了模型参数的测定方法。     

A constitutive thermomechanical model for saturated clays

The structural deformation in clays results from microscopic phenomena involving the mechanical contact-stress change, the physico-chemical variation of repulsive forces in expansive clays, and thermal dilatancy of macropores. These textural strains are associated to three plastic mechanisms represented by respectively the yield surfacesf_Tm, f_R-A andf_T. Under a thermal cycle, the sizes of interlamellar spaces between clay platelets are not modified, hence the temperature cycle is expected to have no effect on repulsive forces and thus the second mechanism is not affected by temperature changes.

This paper suggests a formulation of a model of thermo-elasto-plastic behaviour of non-expansive saturated clays characterised by two plastic mechanisms. The mechanical yield surfacef_Tm of the contact-stress mechanism is based on a modified cam-clay model; the thermal softening yield surfacef_T is a plane separating two thermal domains. In normally consolidated conditions, the resulting response to an increase of temperature is compressive. However, in highly overconsolidated conditions, a small irreversible dilative volumetric strain is observed when the temperature is above a threshold value. In intermediate conditions, the material starts with an expansion and tends to a compression.

The constitutive model combines thermo-mechanical hardening, predominant in normally consolidated states (NCS) and absent in overconsolidated states (OCS) where the thermal softening occurs. The characterisation of the model requires information about rheological parameters obtained from oedometric and triaxial paths. Lastly, some numerical simulations of thermo-mechanical tests onremoulded Boom, ‘Bassin Parisien’ andPontida clays are presented, which show satisfactory agreement between experiments and model predictions.     

A novel finite element double porosity model for multiphase flow through deformable fractured porous media

Based on the theory of double-porosity, a novel mathematical model for multiphase fluid flow in a deforming fractured reservoir is developed. The present formulation, consisting of both the equilibrium and continuity equations, accounts for the significant influence of coupling between fluid flow and solid deformation, usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretize the governing equations both in the space and time domain. Throughout the derived set of equations the solid displacements as well as the fluid pressure values are considered as the primary unknowns and may be used to determine other reservoir parameters such as stresses, saturations, etc. The final set of equations represents a highly non-linear system as the elements of the coefficient matrices are updated during each iteration in terms of the independent variables. The model is employed to solve a field scale example where the results are compared to those of ten other uncoupled models. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered. © 1997 by John Wiley & Sons, Ltd.     

A new and simple stress-dependent water retention model for unsaturated soil

The water retention curve (WRC) is an important hydraulic property of unsaturated soil needed for seepage analysis. Experimental evidence shows that the WRC is affected by various factors such as net stress and soil type. Many attempts have been made to describe the effects of net stress by including the void ratio in a water retention model. But the void ratio (i.e., soil density) is not the only parameter altered by the application of net stress. The pore structure, including the pore size distribution, pore shape and pore orientation, is also changed. Thus the influence of net stress on the WRC should not be treated as equivalent to density effects. In this study, it is verified that the inclusion of the void ratio cannot adequately capture the effects of net stress on the water retention behaviour. A new and simple water retention model is thus developed by considering the stress effects on the void ratio as well as the pore structure. The model is then applied to simulate the WRCs of three different soils tested over a wide range of stress conditions, including isotropic and anisotropic stress conditions. The results show that better predictions of experimental data can be made by incorporating the effects of net stress on both the void ratio and the pore structure.     

考虑颗粒破碎对特征孔隙比影响的堆石体亚塑性本构模型

颗粒破碎是影响堆石体强度和变形特性的主要问题之一。相比于砂土,堆石料在较低的应力水平下就会发生严重的颗粒破碎,因此,在进行堆石体力学特性及本构模型研究时必须考虑颗粒破碎的影响。同时,堆石体在受力过程中孔隙比是变化的,而传统本构模型不能使用一组参数模拟不同孔隙比的同种材料。因此,以能够考虑应力水平和土体孔隙比影响的Gudehus-Bauer亚塑性本构模型为基础,考虑堆石体有别于砂土的孔隙比变化特征,提出了考虑堆石破碎的亚塑性本构模型。亚塑性理论是目前可最大限度地减少人为假定的一种本构理论,颗粒材料在不同特征应力路径下,破碎造成的过度变形量不同;但相同应力水平、不同特征应力路径下孔隙比已不满足Gudehus-Bauer亚塑性本构模型中提出的等比例变化规律。据此,结合考虑颗粒破碎的临界状态理论和堆石体常规三轴试验和循环加载试验结果,提出了考虑颗粒破碎堆石体特征孔隙比的表达式,并将其引入到Gudehus-Bauer亚塑性本构模型中,建立了考虑颗粒破碎的堆石体亚塑性本构模型,提出了模型参数的确定方法。与堆石体试验结果对比表明,该本构模型可以较好地模拟其力学与变形特性。     

A critical state model for overconsolidated structured clays

This paper presents a generalised critical state model with the bounding surface theory for simulating the stress–strain behaviour of overconsolidated structured clays. The model is formulated based on the framework of the Structured Cam Clay (SCC) model and is designated as the Modified Structured Cam Clay with Bounding Surface Theory (MSCC-B) model. The hardening and destructuring processes for structured clays in the overconsolidated state can be described by the proposed model. The image stress point defined by the radial mapping rule is used to determine the plastic hardening modulus, which varies along loading paths. A new proposed parameter h, which depends on the material characteristics, is introduced into the plastic hardening modulus equation to take the soil behaviour into account in the overconsolidated state. The MSCC-B model is finally evaluated in light of the model performance by comparisons with the measured data of both naturally and artificially structured clays under compression and shearing tests. From the comparisons, it is found that the MSCC-B model gives reasonable good simulations of mechanical response of structured clays in both drained and undrained conditions. With its simplicity and performance, the MSCC-B model is regarded as a practical geotechnical model for implementation in numerical analysis.     

结构性粘土的边界面砌块体模型

把天然粘土的变形看作是由结构的破坏引起的。总的变形由结构性粘土的弹性变形、结构面的滑移塑性变形和结构体破损引起的的损伤塑性变形组成。把滑移屈服面看作可以扩大、旋转的运动硬化面,并作为边界面,通过内插塑性模量来描述滑移塑性变形。采用损伤边界面,通过规定加荷或反向加荷产生损伤变形,卸荷不产生损伤变形来描述损伤塑性变形。建立了结构性粘土的边界面砌块体模型,并用试验进行了验证。     

A multi-gene genetic programming model for estimating stress-dependent soil water retention curves

Soil water retention curve (SWRC) is an important parameter required for seepage modelling in unsaturated soil and is used for analysing rainfall-induced slope failures, design of waste contaminant liners and cover, etc. The influence of stress, which is one of constitutive variables that governs unsaturated soil behaviour on the SWRC, has been well recognised by researchers. Stress is essential for study as it drastically alters the soil fabric which includes macropores, minipores and micropores and thus affects the ability of soil to retain water. Various computational modelling techniques that formulate models based on existing databases such as UNSODA, ISRIC and HYPRES for the estimation of SWRC do not take into account the stress influence on soil behaviour. In the present work, three artificial intelligence (AI) methods of support vector regression, artificial neural network and multi-gene genetic programming (MGGP) have been applied to formulate the mathematical relationship between the water content and input variables such as stress and suction (i.e. stress-dependent soil water characteristic curves (SDSWRCs)). The results indicate that the MGGP model outperforms the other two models and is able to extrapolate the water content values satisfactorily along the stress value of 800 kPa. This MGGP model can then be deployed by experts for the estimation of SDSWRCs, thus eliminating the need for conducting costly and time-consuming experiments.     

A coupled model for heating and hydratation in unsaturated clays

Knowledge of transport processes of heat and moisture in soils of arid zones is vital to understanding the environmental and economic impacts of many activities: agriculture, waste disposal, geoenvironmental practices and earth sciences. Through extensive review and study on the different aspects of coupled transfer processes in swelling porous media, a general mathematical model for coupled heat, moisture, air flow and deformation problems in clayey soils is proposed in a consistent and unified manner. The model is characterized by the presence of a deformable solid matrix filled with two fluid phases (liquid water and air). In the proposed model, both pore water and air transfers are assumed to be governed by the generalized Darcy’s law. Fully coupled, non-linear partial differential equations are established and then solved by using a Galerkin weighted residual approach in space domain and an implicit integrating scheme in time domain. The obtained model has been finally validated by means of some case tests for the prediction of the thermo-hydro-mechanical behaviour of unsaturated swelling soils. The calculated relative errors between experimental and numerical results are 3% for temperature and 7% for stresses. Consequently, the developed numerical model predicts satisfactory results, compared to experimental test measures. The model is applicable to two-dimensional problems with various initial and boundary conditions; non-linear soil parameters can be easily included in this model.     

A dual-porosity model for ionic solute transport in expansive clays

A microstructure model of dual-porosity type is proposed to describe contaminant transport in fully-saturated swelling clays. The swelling medium is characterized by three separate-length scales (nano, micro, and macro) and two levels of porosity (nano- and micropores). At the nanoscale, the medium is composed of charged clay particles saturated by a binary monovalent aqueous electrolyte solution. At the intermediate (micro) scale, the two-phase homogenized system is represented by swollen clay clusters (or aggregates) with the nanoscale electrohydrodynamics, local charge distribution, and disjoining pressure effects incorporated in the averaged constitutive laws of the electro-chemo-mechanical coefficients and the swelling pressure, which appear in Onsager’s reciprocity relations and in a modified form of Terzaghi’s effective principle, respectively. The microscopic coupling between aggregates and a bulk solution lying in the micropores is ruled by a slip boundary condition on the tangential velocity of the fluid, which captures the effects of the thin electrical double layers surrounding each clay cluster. At the macroscale, the system of clay clusters is homogenized with the bulk fluid. The resultant macroscopic picture is governed by a dual-porosity model wherein macroscopic flow and ion transport take place in the bulk solution and the clay clusters act as sources/sinks of mass of water and solutes to the bulk fluid. The homogenization procedure yields a three-scale model of the swelling medium by providing new nano and micro closure problems, which are solved numerically to construct constitutive laws for the effective electro-chemo-hydro-mechanical coefficients. Considering local instantaneous equilibrium between the clay aggregates and micropores, a quasisteady version of the dual-porosity model is proposed. When combined with the three-scale portrait of the swelling medium, the quasisteady model allows us to build-up numerically the constitutive law of the equilibrium adsorption isotherm, which governs the instantaneous immobilization of the solutes in the clay clusters. Moreover, the constitutive behavior of the retardation coefficient is also constructed by exploring its representation in terms of the local profile of the electrical double layer potential of the electrolyte solution, which satisfies the Poisson–Boltzmann problem at the nanoscale.     

超固结粘土的二元介质模型

为了分析超固结粘土边坡的变形和稳定的需要,在岩土破损力学的框架内建议了一个适用于这类土的二元介质模型。该模型考虑了土体内在的不均一性,把它看作由结构块和结构带组成的复合体,两者共同分担外荷载,模型包含10参数,并拟定了这些参数的测定方法。通过模拟三轴试验的计算表明,该模型可以反映London粘土的应力-应变特征。     

Analysis of soil consolidation by vertical drains with double porosity model

The soil around a drain well is traditionally divided into smeared zone and undisturbed zone with constant hydraulic conductivity. In reality, hydraulic conductivity of the soil changes continuously and it may not be always appropriate to approximate its distribution with two zones. In this study, the horizontal hydraulic conductivity of the soil is described by an arbitrary function of radial distance. The horizontal flow under equal strain condition is analysed for a soil–drain system with a circular or regular polygonal boundary. It is found that the horizontal flow can be generally characterized with a linear equation in which the flow rate of water through soil–drain interface is proportional to the difference between the average excess pore pressure in the soil and the excess pore pressure in the drain well. The water exchange between the drain and the soil is analogous to that between fractures and matrix in a double porosity system, a popular conceptual model of fracture rocks. On the basis of this characterization, a simplified approach to analyse soil–drain systems is developed with one‐dimensional double porosity model (DPM). Analytical solutions for both fully and partially penetrating drains are derived. The solution for partially penetrating drains is compared with both numerical and approximate analytical results in literature. Copyright © 2004 John Wiley & Sons, Ltd.     

A monotonic bounding surface critical state model for clays

This study investigates a simple constitutive model based on the critical state framework and bounding surface (BS) plasticity that is suitable for reconstituted clays over a wide range of overconsolidation ratios under monotonic loading. For heavily overconsolidated (OC) clays, rather than using the conventional Hvorslev line, an empirical surface is introduced into the model formulation based on two image points on the BS. The peak strength and the dilatancy of heavily OC clays can thus be predicted satisfactorily. Comparisons with triaxial test data show that the model well captures the peak strength and the dilatancy of heavily OC clays under monotonic loading.