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.     

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。     

A plasticity constitutive model for unsaturated,anisotropic, nonexpansive soils

The paper describes and evaluates an incremental plasticity constitutive model for unsaturated, anisotropic, nonexpansive soils (CMUA). It is based on the modified Cam-Clay (MCC) model for saturated soils and enhances it by introducing anisotropy (via rotation of the MCC yield surface) and an unsaturated compressibility framework describing a double dependence of compressibility on suction and on the degree of saturation of macroporosity. As the anisotropic and unsaturated features can be activated independently, the model is downwards compatible with the MCC model. The CMUA model can simulate effectively: the dependence of compressibility on the level of developed anisotropy, uniqueness of critical state independent of the initial anisotropy, an evolving compressibility during constant suction compression, and a maximum of collapse. The model uses Bishop's average skeleton stress as its first constitutive variable, favouring its numerical implementation in commercial numerical analysis codes (eg, finite element codes) and a unified treatment of saturated and unsaturated material states.     

一个高饱和度非饱和土的本构模型

高饱和度的非饱和土中由于气体处于封闭状态,其内部气压的变化必将对土体的行为产生影响。首先,对高饱和度非饱和土特性进行探讨和研究,随后,在已有非饱和土模型框架基础上,采用广义有效应力原理,建立一个适用于高饱和度条件下的非饱和土的弹塑性本构模型。模型中引入气相耗散的影响,在硬化方程中考虑封闭气体压力改变的影响。最后,利用已有的试验结果来对模型进行验证,并将模型预测结果与前人模型进行对比,表明模型预测可以很好地预测土体的行为,尤其是在高饱和度条件下其结果比其他模型更加接近实际情况。     

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.     

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‐mechanical model for variably saturated soils based on hypoplasticity

The paper presents a mechanical model for non‐isothermal behaviour of unsaturated soils. The model is based on an incrementally non‐linear hypoplastic model for saturated clays and can therefore tackle the non‐linear behaviour of overconsolidated soils. A hypoplastic model for non‐isothermal behaviour of saturated soils was developed and combined with the existing hypoplastic model for unsaturated soils based on the effective stress principle. Features of the soil behaviour that are included into the model, and those that are not, are clearly distinguished. The number of model parameters is kept to a minimum, and they all have a clear physical interpretation, to facilitate the model usefulness for practical applications. The step‐by‐step procedure used for the parameter calibration is described. The model is finally evaluated using a comprehensive set of experimental data for the thermo‐mechanical behaviour of an unsaturated compacted silt. Copyright © 2011 John Wiley & Sons, Ltd.     

考虑残余含气量的非饱和土的水力耦合本构模型

大量的非饱和土干湿循环试验表明,当土体处于吸湿过程直至吸力降低为0 kPa时,土体并不能达到完全饱和状态,还存在一定的残余气体。在高饱和度时,由于残余气体以封闭气泡的形式分布在土体中,土体呈现较大的压缩性,使其与饱和土的性质不同。在这种状态下,现有的非饱和土本构模型预测到的土饱和度为100%,与试验结果存在一定的偏差。为了使本构模型在高饱和度状态时具有较高的精度,对非饱和土的毛细滞回和塑性变形耦合本构模型进行了修正,使其能够考虑残余含气量的影响。通过预测与实测结果比较,证明了新模型能够有效地模拟残余含气量对非饱和土力学特性的影响。     

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.     

Explicit integration of a porosity‐dependent hydro‐mechanical model for unsaturated soils

An adaptive substepping explicit integration scheme is developed for a porosity‐dependent hydro‐mechanical model for unsaturated soils. The model is referred to as the modified σ –Θ model in this paper, which features the employment of the subloading surface plasticity and the stress–saturation approach. On numerical aspects, convex/nonconvex subloading surfaces in the σ –Θ space may result in incorrect loading–unloading decisions during the integration. A new loading–unloading decision method is developed here to solve the problem and then embedded into the explicit integration scheme for the modified σ –Θ model. In addition, to enhance the accuracy of the explicit integration, local errors from both hydraulic and mechanical components are included in the error control for each substep. A drift correction method is also developed to ensure the state point lies on the subloading surface in the σ –Θ space within a set error level. The performance of the loading–unloading decision method for the modified σ –Θ model is discussed through comparing it with the conventional loading–unloading decision method. The importance of involving the hydraulic component in the error control is also demonstrated. The accuracy and efficiency of the proposed adaptive substepping explicit integration scheme for the modified p–Θ model are also studied via several numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

A kinematic hardening based model for unsaturated soils considering different hydraulic conditions

At present, several of the existing elastoplastic constitutive models are adapted for describing the stress–strain behavior of unsaturated soils. However, most of them present certain limitations in this field. These limitations can be related to the basic model and/or added unsaturated state variables and formulations. In this regard, inability to model the hydro‐mechanical behavior in constant water (CW) conditions is an example of these limitations. In this paper, an advanced version of CJS model is selected for adaptation to the unsaturated states. Adaptation to unsaturated states is achieved in the framework of effective stress approach. Effective stress equation and unsaturated state variables are selected based on the recent research existing in the literature. The developed model is capable of describing the complex behavior of unsaturated soil in the CW condition in addition to predicting the behavior at failure and post–failure, nonlinear elastoplastic behavior at low levels of stress and strain (by selecting a very small elastic domain), as well as wetting and collapse behaviors. In order to validate the model, results of triaxial tests in CD and CW conditions are used. The validation results indicate the good capability of the proposed model. Behavior of the unsaturated soils during wetting is an important issue. For this reason, the model is also evaluated based on the results of wetting and collapse triaxial tests. A comparison between the tests and simulation results shows that the model is able to predict the soil behavior under the wetting path. Copyright © 2016 John Wiley & Sons, Ltd.     

非饱和土的本构模型研究

引用平均土骨架应力的概念,研究推导出非饱和土的刚度参数随吸力变化而变化的关系式,进而推导得到用平均土骨架应力表述的非饱和土LC屈服面函数以及硬化规律。从土力学原理推导,得到土样由于在净应力和吸力作用下产生体积变形引起土样饱和度变化的关系式。由平均土骨架应力推广,得到三轴应力状态的椭圆屈服函数,这一非饱和土本构模型的优点在于考虑了应力作用后土样饱和度的变化,通过对已有试验数据的初步验证,表明提出的非饱和土本构模型的合理性和适用性。     

非饱和土弹塑性模型参数的试验确定及有限元法

简要介绍广泛应用的非饱和土Alonso模型的原理与发展,并通过3组共7个试样的非饱和土三轴试验,得到模型的11个参数。在饱和土Cam本构关系的基础上,推导出一个基于非饱和土Alonso模型的应力-应变增量方程的计算公式,该方程与饱和土的本构方程形式相同。编制了能够考虑净应力和吸力二者对土体硬化规律影响的有限元程序,从而为非饱和土弹塑性计算提供一条途径,便于进一步应用于实际工程。     

A constitutive model for unsaturated soil interfaces

A constitutive model based on the disturbed state concept is presented to describe the behavior of interfaces in unsaturated soil. The model is an extension of an existing model developed for a sand–steel interface. As opposed to the original model, the modified model incorporates two independent stress variables, which are the net normal stress and matric suction. The saturated and dry state of the interface can be modeled as a special case using the constitutive model presented in this paper. The modified model is capable of capturing the main features of unsaturated interfaces observed during laboratory testing, including increasing shear strength and strain softening with increasing suction and net normal stress and increasing dilatancy with increasing suction. Laboratory tests were carried out on unsaturated interfaces in a modified direct shear test apparatus. The observed behavior of interfaces between unsaturated soil and steel plates (rough and smooth) is presented in comparison with model predictions. Copyright © 2008 John Wiley & Sons, Ltd.     

A constitutive model for unsaturated soil–structure interfaces

A constitutive model for simulation of the behavior of unsaturated interfaces is presented here. The model is an extension of an existing critical state compatible interface model for dry and saturated interfaces that was already proposed by one of the authors [Lashkari, A. 2013. Int. J. Numer. Anal. Meth. Geomech. 37 (8): 904–931]. For a proper simulation of the behavior of partially saturated interfaces, the extended model is formulated in terms of two pairs of work conjugate stress–strain‐like variables. The modified model simulations are compared with the existing data of dry, unsaturated, and saturated interfaces. For each interface type, it is shown that the proposed model can capture the essential elements of the behavior using a unique set of parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

A three‐phase model for unsaturated soils

A comprehensive framework to define the constitutive behaviour of unsaturated soils is developed within the theory of mixtures applied to three‐phase porous media. Each of the three phases is endowed with its own strain and stress. Elastic and elastic–plastic constitutive equations are developed. Particular emphasis is laid on the interactions between the phases both in the elastic and plastic regimes. Nevertheless, the clear structure of the constitutive equations requires a minimal number of material parameters. Their identification is provided: in particular, it incorporates directly the soil–water characteristic curve. Crucial to the formulation is an appropriate definition of the effective stress. The coupled influence of this effective stress and of suction makes it possible to describe qualitatively many of the characteristic features observed in experiments, e.g. for normally consolidated soils, a plastic behaviour up to air entry followed by an elastic behaviour at increasing suctions, and, on the way back, an elastic behaviour, unless compression is applied in which case plastic collapse occurs. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

Three‐dimensional transient thermo‐hydro‐mechanical fundamental solutions of unsaturated soils

The governing differential equations of unsaturated soils considering the thermo‐poro‐mechanical behaviour consist of equilibrium, moisture air and heat transfer equations. In this paper at first, following some necessary simplifications, the thermal three‐dimensional fundamental solution for an unsaturated deformable porous medium with linear elastic behaviour in Laplace transform domain is presented. Subsequently, the closed‐form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Then a set of numerical results are presented, which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Finally, the closed‐form time domain fundamental solution will be verified mathematically by comparison with the previously introduced corresponding fundamental solution. Copyright © 2009 John Wiley & Sons, Ltd.     

考虑基质吸力变化时非饱和土的一维本构模型

当地下水位上升或地面遇水浸润时,土的饱和度将因毛细作用而变化,以此使土体产生变形。其中由于含水量增加而使土的重度增大,从而引起压缩变形;同时含水量的增加而使基质吸力下降,从而引起土的回弹变形,因此最终变形取决于上述两种变形趋势的综合效应。根据广义Hook定律、Fredlund的双应力状态变量及Brooks和Corey关于基质吸力与饱和度之间的经验关系,建立了K0状态下非饱和土的一维本构模型。将这一模型与分层总和法相结合,可以计算基质吸力变化时土的竖向变形。通过研究发现,非饱和土的地面变形不仅取决于土的性质与土层的厚度,而且依赖于土中吸力变化前后的分布及应力状态等因素。所建议的一维本构模型可以用于非饱和土地基上基础的沉降估算。     

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.