Coupled modelling of hydro‐mechanical behaviour of unsaturated compacted expansive soils

The Barcelona basic model cannot predict the mechanical behaviour of unsaturated expansive soils, whereas the Barcelona expansive model (BExM) can only predict the stress–strain behaviour of unsaturated expansive soils without the water‐retention behaviour being incorporated. Moreover, the micro‐parameters and the coupling function between micro‐structural and macro‐structural strains in the BExM are difficult to determine. Experimental data show that the compression curves for non‐expansive soils under constant suctions are shifted towards higher void ratios with increasing suction, whereas the opposite is true for expansive soils. According to the observed water‐retention behaviour of unsaturated expansive soils, the air‐entry value increases with density, and the relationship between the degree of saturation and void ratio is linear at constant suction. According to the above observation, an elastoplastic constitutive model is developed for predicting the hydraulic and mechanical behaviour of unsaturated expansive soils, based on the existing hydro‐mechanical model for non‐expansive unsaturated soil. The model takes into consideration the effect of degree of saturation on the mechanical behaviour and that of void ratio on the water‐retention behaviour. The concept of equivalent void ratio curve is introduced to distinguish the plastic potential curve from the yield curve. The model predictions are compared with the test results of an unsaturated expansive soil, including swelling tests under constant net stress, isotropic compression tests and triaxial shear tests under constant suction. The comparison indicates that the model offers great potential for quantitatively predicting the hydraulic and mechanical behaviour of unsaturated expansive soils. Copyright © 2011 John Wiley & Sons, Ltd.     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part II: Unsaturated soil modeling

The aim of this paper is to extend the generalized plasticity state parameter‐based model presented in part 1 to reproduce the hydro‐mechanical behavior of unsaturated soils. The proposed model is based on two pairs of stress–strain variables and a suitable hardening law taking into account the bonding—debonding effect of suction and degree of saturation. A generalized state parameter for unsaturated state is proposed to reproduce soil behavior using a single set of material parameters. Generalized plasticity gives a suitable framework to reproduce not only monotonic stress path but also cyclic behavior. The hydraulic hysteresis during a drying—wetting cycle and the void ratio effect on the hydraulic behavior is introduced. Comparison between model simulations and a series of experimental data available, both cohesive and granular, are given to illustrate the accuracy of the enhanced generalized plasticity equation. Copyright © 2010 John Wiley & Sons, Ltd.     

A density‐dependent elastoplastic hydro‐mechanical model for unsaturated compacted soils

This paper presents a three‐dimensional elastoplastic constitutive model for predicting the hydraulic and mechanical behaviour of unsaturated soils. It is based on experimental results obtained from a series of controlled‐suction triaxial tests on unsaturated compacted clay with different initial densities. Hydraulic hysteresis in the water‐retention behaviour is modelled as an elastoplastic process, with the elastic part modelled by a series of scanning curves and the elastoplastic part modelled by the main drying and wetting curves. The effect of void ratio on the water‐retention behaviour is studied using data obtained from controlled‐suction wetting–drying cyclic tests on unsaturated compacted clay with different initial densities. The effect of the degree of saturation on the stress–strain‐strength behaviour and the effect of void ratio on the water‐retention behaviour are considered in the model, as is the effect of suction on the hydraulic and mechanical behaviour. The initial density dependency of the compacted soil behaviour is modelled by experimental relationships between the initial density and the corresponding yield stress and, thereby, between the initial density and the normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure and yield surfaces in the deviatoric stress plane are given by the Matsuoka–Nakai criterion. Model predictions of the stress–strain and water‐retention behaviour are compared with those obtained from triaxial tests with different initial densities under isotropic compression, triaxial compression and triaxial extension, with or without variation in suction. The comparisons indicate that the model accurately predicts the hydraulic and mechanical behaviour of unsaturated compacted soils with different initial densities using the same material constant. Copyright © 2006 John Wiley & Sons, Ltd.     

A thermo‐hydro‐mechanical model for unsaturated soils based on the effective stress concept

A simple thermo‐hydro‐mechanical (THM) constitutive model for unsaturated soils is described. The effective stress concept is extended to unsaturated soils with the introduction of a capillary stress. This capillary stress is based on a microstructural model and calculated from attraction forces due to water menisci. The effect of desaturation and the thermal softening phenomenon are modelled with a minimal number of material parameters and based on existing models. THM process is qualitatively and quantitatively modelled by using experimental data and previous work to show the application of the model, including a drying path under mechanical stress with transition between saturated and unsaturated states, a heating path under constant suction and a deviatoric path with imposed suction and temperature. The results show that the present model can simulate the THM behaviour in unsaturated soils in a satisfactory way. Copyright © 2010 John Wiley & Sons, Ltd.     

ACMEG‐TS: A constitutive model for unsaturated soils under non‐isothermal conditions

This paper introduces an unconventional constitutive model for soils, which deals with a unified thermo‐mechanical modelling for unsaturated soils. The relevant temperature and suction effects are studied in light of elasto‐plasticity. A generalized effective stress framework is adopted, which includes a number of intrinsic thermo‐hydro‐mechanical connections, to represent the stress state in the soil. Two coupled constitutive aspects are used to fully describe the non‐isothermal behaviour. The mechanical constitutive part is built on the concepts of bounding surface theory and multi‐mechanism plasticity, whereas water retention characteristics are described using elasto‐plasticity to reproduce the hysteretic response and the effect of temperature and dry density on retention properties. The theoretical formulation is supported by comparisons with experimental results on two compacted clays. Copyright © 2008 John Wiley & Sons, Ltd.     

非饱和土水-力本构模型及其隐式积分算法

在已有工作基础上建立了水力-力学耦合的非饱和土本构模型,在硬化方程中考虑饱和度的影响,同时在土水特征曲线中考虑了塑性体变的影响,从而使模型可以反映非饱和土中的毛细现象与土中弹塑性变形现象的耦合行为。采用隐式积分方法,建立了非饱和土耦合模型的数值模型,并推导了得到了水力-力学耦合的非饱和土的一致切线模量。利用该算法编制了本构模型计算的子程序,使其能向外输出切线刚度矩阵,用于有限元计算。为了验证该算法和程序的正确性,用所编制程序对不同路径下的土体行为进行了预测。通过预测结果与试验结果相对比,表明程序预测结果与试验数据相吻合,模型可以较好地模拟土体的水力-力学耦合行为特性。     

Implicit integration under mixed controls of a breakage model for unsaturated crushable soils

This paper discusses a series of stress point algorithms for a breakage model for unsaturated granular soils. Such model is characterized by highly nonlinear coupling terms introduced by breakage‐dependent hydro‐mechanical energy potentials. To integrate accurately and efficiently its constitutive equations, specific algorithms have been formulated using a backward Euler scheme. In particular, because implementation and verification of unsaturated soil models often require the use of mixed controls, the incorporation of various hydro‐mechanical conditions has been tackled. First, it is shown that the degree of saturation can be replaced with suction in the constitutive equations through a partial Legendre transformation of the energy potentials, thus changing the thermomechanical state variables and enabling a straightforward implementation of a different control mode. Then, to accommodate more complex control scenarios without redefining the energy potentials, a hybrid strategy has been used, combining the return mapping scheme with linearized constraints. It is shown that this linearization strategy guarantees similar levels of accuracy compared with a conventional strain–suction‐controlled implicit integration. In addition, it is shown that the use of linearized constraints offers the possibility to use the same framework to integrate a variety of control conditions (e.g., net stress and/or water‐content control). The convergence profiles indicate that both schemes preserve the advantages of implicit integration, that is, asymptotic quadratic convergence and unconditional stability. Finally, the performance of the two implicit schemes has been compared with that of an explicit algorithm with automatic sub‐stepping and error control, showing that for the selected breakage model, implicit integration leads to a significant reduction of the computational cost. Such features support the use of the proposed hybrid scheme also in other modeling contexts, especially when strongly nonlinear models have to be implemented and/or validated by using non‐standard hydro‐mechanical control conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Discussing the definition of the second‐order work for unsaturated soils

The volumetric compaction due to wetting processes is a phenomenon observed quite often in unsaturated soils. Under certain circumstances, saturation events can result into a sudden and unexpected collapse of the system. These phenomena are usually referred to as wetting‐induced collapses, without providing any detailed theoretical justification for this terminology. In order to predict in a general fashion the occurrence of coupled instabilities induced by saturation processes, a generalization of the theoretical approaches usually employed for saturated geomaterials is here provided. More specifically, this paper addresses the problem of hydro‐mechanical instability in unsaturated soils from an energy standpoint. For this purpose, an extension of the definition of the second‐order work is here suggested for the case of unsaturated porous media. On the basis of some examples of numerical simulations of laboratory tests, coupled hydro‐mechanical instabilities are then interpreted in the light of this second‐order energy measure. Finally, the implications of the theoretical results here presented are commented from a constitutive modelling perspective. Two possible alternative approaches to formulate incremental coupled constitutive relations are indeed discussed, showing how the onset of hydro‐mechanical instabilities can be predicted using an extended form of Hill's stability criterion. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of degree of saturation on mechanical behaviour of unsaturated soils and its elastoplastic simulation

The two stress-state variable approach has been widely used in interpreting unsaturated soil behaviour. However this approach cannot take into account the effect of degree of saturation or water contents on the stress–strain behaviour and strength of unsaturated soils. The triaxial test results presented in this paper show that even if the same path of net stress and suction is followed, the stress–strain relation and strength are different due to different degrees of saturation. When other conditions are the same, the higher the degree of saturation for the soil sample is, the higher the stress ratio corresponding to a given axial strain will be. This effect can be modeled by using an elasto-plastic constitutive model coupling hydraulic and mechanical behaviour of unsaturated soils. Comparisons between the predicted and measured results are presented, which demonstrate that the model can quantitatively simulate the influence of the degree of saturation on stress–strain behaviour and strength of unsaturated soils.     

非饱和土的水力和力学特性及其弹塑性描述

简单回顾了非饱和土本构模型研究的发展历程,总结了近几年非饱和土弹塑性本构模型最新研究成果,重点介绍了能统一模拟非饱和土水力性状和力学性状耦合的弹塑性本构模型。通过对建立模型过程中的几个核心问题讨论,较详细地说明该类模型的结构、性能以及相关问题。非饱和土水力性状的滞回性用假定存在饱和度弹性区间的弹塑性过程来模拟;该类耦合模型不仅考虑了吸力对非饱和土水力性状和力学性状的影响,还考虑了饱和度对应力-应变关系和强度的影响以及土体变形对土-水特征曲线的影响。用同一套模型参数,耦合模型可统一预测在吸力控制或含水率控制下沿各种应力路径下非饱和土的水力-力学特性,并简单介绍了膨胀性非饱和土的弹塑性本构模型以及耦合模型在有限元数值计算中的应用。     

饱和度对非饱和土力学性质的影响

现在被广泛公认的由Fredlund提出的非饱和土力学的双参数理论,即净应力和吸力为非饱和土的应力状态量,不能直接考虑饱和度或含水率对非饱和土的应力-应变关系和强度的影响。在非饱和土三轴试验结果表明,即使在净应力和吸力路径相同的条件下,具有不同饱和度试样的应力-应变关系和强度也是不同的。其他条件相同时,试样饱和度越高,其应力比-应变关系曲线越高,强度越大。最新的水力-力学特性耦合的弹塑性本构模型可以定量地表示上述非饱和土的性质     

基质吸力对非饱和土抗剪强度的影响

在自然界和工程实践中遇到的土大多数是非饱和土,研究吸力对非饱和土抗剪强度的作用,对于工程实践具有重要的意义。通过压力板仪和直剪仪组合试验,探讨了击实土抗剪强度和基质吸力的关系。试验结果表明：凝聚力在饱和度为40%-60%时最大,而内摩擦角则随饱和度增加而有所减少。进一步对比土-水特征曲线与抗剪强度的关系,并整合前人研究成果,指出了非饱和土中吸力对其抗剪强度影响的规律。对于无黏性土,在边界效应区不产生假凝聚力,且内摩擦角不变;在过渡区与非饱和残余区,假凝聚力和基质吸力的关系存在峰值且变化较大,内摩擦角则随吸力增加而增加。对于黏性土,残余体积含水率所对应的最小吸力可能是影响抗剪强度的界限值,小于此吸力值,φb可近似为常数。但在非饱和残余区,凝聚力将随土状态路径的不同而变化。对于重塑土,凝聚力降低;而对于原状土,则凝聚力可能不变或增加。     

On the use of effective stress in three-dimensional hydro-mechanical coupled model

In the last decades, a number of hydro-mechanical elastoplastic constitutive models for unsaturated soils have been proposed. Those models couple the hydraulic and mechanical behaviour of unsaturated soils, and take into account the effects of the degree of saturation on the stress–strain behaviour and the effects of deformation on the soil–water characteristic response with a simple reversible part for the hysteresis. In addition, the influence of the suction on the stress–strain behaviour is considered. However, until now, few models predict the stress–strain and soil–water characteristic responses of unsaturated soils in a fully three-dimensional Finite Element code. This paper presents the predictions of an unsaturated soil model in a Three-dimensional Framework, and develops a study on the effect of partial saturation on the stability of shallow foundation resting on unsaturated silty soil. Qualitative predictions of the constitutive model show that incorporating a special formulation for the effective stress into an elastoplastic coupled hydro-mechanical model opens a full range of possibilities in modelling unsaturated soil behaviour.     

Formulation of a three‐dimensional constitutive model for unsaturated soils incorporating mechanical–water retention couplings

Wheeler, Sharma and Buisson proposed an elasto‐plastic constitutive model for unsaturated soils that couples the mechanical and water retention behaviours. The model was formulated for isotropic stress states and adopts the mean Bishop's stress and modified suction as stress state variables. This paper deals with the extension of this constitutive model to general three‐dimensional stress conditions, proposing the generalized stress–strain relationships required for the numerical integration of the constitutive model. A characteristic of the original model is the consideration of a number of elasto‐plastic mechanisms to describe the complex behaviour of unsaturated soils. This work presents the three‐dimensional formulation of these coupled irreversible mechanisms in a generalized way including anisotropic loading. The paper also compares the results from the model with published experiments performed under different loading conditions. The response of the model is very satisfactory in terms of both mechanical and water retention behaviours. Copyright © 2013 John Wiley & Sons, Ltd.     

Three‐dimensional elasto‐plastic model for unsaturated compacted soils with different initial densities

This paper presents an elasto‐plastic model for unsaturated compacted soils and experimental results obtained from a series of suction‐controlled triaxial tests on unsaturated compacted clay with different initial densities. The initial density dependency of the compacted soil behaviour is modelled by establishing experimental relationships between the initial density and the corresponding yield stress and thereby between the initial density and the location and slope of normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure surface and the yield surface in the deviatoric plane are given by the extended SMP criterion. A considerable number of the isotropic compression, triaxial compression and extension tests on unsaturated compacted clay with different initial densities were performed using a suction‐controllable triaxial apparatus, to measure the stress–strain–volume change in different stress paths and wetting paths. The model has well‐predicting capabilities to reproduce the mechanical behaviour of specimens compacted under different conditions not only in isotropic compression but also in triaxial compression and triaxial extension. Copyright © 2003 John Wiley & Sons, Ltd.     

不饱和土动弹塑性本构模型研究

以饱和度与有效应力为状态变量,通过引入描述不饱和与饱和土孔隙比差的状态变量,将Zhang等提出的饱和土体应力诱导各向异性动弹塑性本构模型推广到不饱和土体中,使其可描述不饱和土在动力循环荷载作用下的力学特性行为。通过对已有不饱和土体在完全不排水条件下的动三轴试验进行理论模拟,验证了所提出不饱和土本构模型的正确性。最后基于所提出本构模型,讨论了在不排水条件下初始饱和度对不饱和土动力特性研究。结果表明,不饱和土在动力荷载作用下,土体的孔隙比将减少,导致饱和度增加;当初始饱和度较高时,不饱和土会转化为饱和土,从而发生液化现象。该研究成果对研究不饱和土在地震等动力荷载作用下的力学特性行为具有重要意义。     

Modelling the mechanical behaviour of unsaturated soils using a genetic algorithm-based neural network

Modelling the mechanical behaviour of unsaturated soils has been the subject of many research works in the past few decades. A number of constitutive models have been developed to describe the complex behaviour of unsaturated soils. Despite the significant advances in the constitutive theories for unsaturated soils, none of the existing models can completely describe the various aspects of the real behaviour of unsaturated soils. In this paper, a new unified approach is presented, based on the integration of a neural network and a genetic algorithm, for the modelling of unsaturated soils. In the proposed approach, a genetic algorithm was used to optimise the weights of the neural network. A three-layer sequential architecture was chosen for the neural network. The network had eight input neurons, five neurons in the hidden layer and three neurons in the output layer. The eight input neurons represented the initial gravimetric water content, initial dry density, degree of saturation, net mean stress with respect to pore-air pressure, axial strain, deviatoric stress, soil suction and volumetric strain, and the three neurons in the output layer represented the deviatoric stress, suction and volumetric strain at the end of each increment. The network was trained and tested using a database that included results from a comprehensive set of triaxial tests on unsaturated soils from the literature. The predictions of the proposed model were compared with the experimental results. The comparison of the results indicates that the proposed approach was accurate and robust in representing the mechanical behaviour of unsaturated soils.     

Theoretical Evaluation of the Mechanical Behavior of Unsaturated Soils

An evaluation method for the mechanical behavior of unsaturated soils is studied in this paper. Although the mechanical behavior of unsaturated soils is complicated, a simple modeling is preferable in practice. This is because the soil properties are not homogeneous and ground data is limited when structures are being designed. In addition, in order to evaluate the reliability of the design, the physical meanings of the parameters applied in the prediction model should be clear. Firstly, the authors study the relationship between compaction curves and compression indexes in the unsaturated state that is used in the proposed constitutive model. Based on the constitutive model, the stress paths for constant volume shear tests are formulated under a constant void ratio condition and the stress paths for undrained shear tests are calculated under a constant water content condition. In the case of unsaturated specimens, the volume of these specimens changes with the shear deformation and the stress paths depend on the initial degree of saturation. The results of the calculation qualitatively describe the test results by considering the changes in effective confining pressure in the undrained condition and the water retention curves.     

A bounding surface plasticity model for unsaturated soil at small strains

Most existing hydromechanical models for unsaturated soils are not able to fully capture the nonlinearity of stress–strain curves at small strains (less than 1%). They cannot therefore, for example, accurately predict ground movements and the performance of many earth structures under working conditions. To tackle this problem, a state‐dependent bounding surface plasticity model has been newly developed. Particularly, the degradation of shear modulus with strain at small strains ranging from 0.001% to 1% is focused. The proposed model is formulated in terms of mean average skeleton stress, deviator stress, suction, specific volume and degree of saturation. Void ratio‐dependent hydraulic hysteresis is coupled with the stress–strain behaviour. Different from other elastoplastic models for unsaturated soils, plastic strains are allowed inside bounding surfaces. In this paper, details of model formulations and calibration procedures of model parameters are presented. To evaluate the capability of the new model, it is applied to simulate a series of triaxial compression tests on compacted unsaturated silt at various suctions. Effects of suction, drying and wetting as well as net stress on unsaturated soil behaviour are well captured. The model shows good predictions of the degradation of shear modulus with strain over a wide range of strains from 0.001% to 1%. Copyright © 2015 John Wiley & Sons, Ltd.     

Finite element formulation and algorithms for unsaturated soils. Part I: Theory

This paper presents a complete finite‐element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress–strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time‐stepping scheme which automatically adjusts the time‐step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non‐linearity caused by suction‐dependent plastic yielding, suction‐dependent degree of saturation, and saturation‐dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress–strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction. Copyright © 2003 John Wiley & Sons, Ltd.