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.     

Work and energy equations and the principle of generalized effective stress for unsaturated soils

The effective stress principle has been efficiently applied to saturated soils in the soil mechanics and geotechnical engineering practice; however, its applicability to unsaturated soils is still under debate. The appropriate selection of stress state variables is essential for the construction of constitutive models for unsaturated soils. Owing to the complexity of unsaturated soils, it is difficult to determine the deformation and strength behaviors of unsaturated soils uniquely with the previous single‐effective‐stress variable theory and two‐effective‐stress‐variable theory in all the situations. In this paper, based on the porous media theory, the specific expression of work is proposed, and the effective stress of unsaturated soils conjugated with the displacement of the soil skeleton is further derived. In the derived work and energy balance equations, the energy dissipation in unsaturated soils is taken into account. According to the derived work and energy balance equations, all of the three generalized stresses and the conjugated strains have effects on the deformation of unsaturated soils. For considering these effects, a principle of generalized effective stress to describe the behaviors of unsaturated soils is proposed. The proposed principle of generalized effective stress may reduce to the previous effective stress theory of single‐stress variable or the two‐stress variables under certain conditions. This principle provides a helpful reference for the development of constitutive models for unsaturated soils. Copyright © 2009 John Wiley & Sons, Ltd.     

Equivalent stress approach in modelling unsaturated soils

This article presents an equivalent stress approach that can be used in many elastoplastic constitutive models for unsaturated soils. The use of the equivalent stress leads to a modified yield locus that is independent of the suction. In addition, the equivalent stress becomes the major stress variable, with suction required only as an additional variable in calculations. The model on the basis of equivalent stress predicts exactly the same soil behaviour, with the sole difference being the use of equivalent stress instead of original stress variables. This article also presents the equivalent stress formulations of several constitutive models for unsaturated soils, including the Barcelona Basic Model. The predictions from these models remain unchanged, with the only difference being in their implementation. Finally, the equivalent stress approach and the net stress approach are compared for the Barcelona Basic Model. Copyright © 2011 John Wiley & Sons, Ltd.     

Cavity expansion in unsaturated soils exhibiting hydraulic hysteresis considering three drainage conditions

Cavity expansion theory assists in the interpretation of in situ tests including the cone penetration test and pressuremeter test. In this paper, a cavity expansion analysis is presented for unsaturated silty sand exhibiting hydraulic hysteresis. The similarity technique is used in the analysis. The soil stress–strain behaviour is described by a bounding surface plasticity model. Results of oedometric compression tests, isotropic compression tests and triaxial shear tests for both saturated and unsaturated states are used to calibrate the model. The void ratio, suction, degree of saturation and effective stress are fully coupled in the analysis. The influence of where the initial hydraulic state is located on the soil–water characteristic curve on the cavity wall pressure is investigated and found to be significant. Also, the effects of three different drainage conditions (constant suction, constant moisture content and constant contribution of suction to the effective stress) on cavity wall pressure are studied. It is found that the drainage condition in which the contribution of suction to the effective stress is constant offers a good approximation to the other two. This may simplify interpretation of in situ tests. When testing occurs quickly, meaning a constant moisture content condition prevails, a constant contribution of suction condition can be assumed without loss of significant accuracy. The contribution of suction assumed in the interpretation can be taken as being equal to the in situ value, although this discovery may not be applicable to all soil types, constitutive models and soil–water characteristic curves. Copyright © 2015 John Wiley & Sons, Ltd.     

A hypoplastic model for mechanical response of unsaturated soils

A new constitutive model is developed for the mechanical behaviour of unsaturated soils based on the theory of hypoplasticity and the effective stress principle. The governing constitutive relations are presented and their application is demonstrated using several experimental data from the literature. Attention is given to the stiffening effect of suction on the mechanical response of unsaturated soils and the phenomenon of wetting‐induced collapse. All model parameters have direct physical interpretation, procedures for their quantification from test data are highlighted. Quantitative predictions of the model are presented for wetting, drying and constant suction tests. Copyright © 2008 John Wiley & Sons, Ltd.     

非饱和土广义有效应力原理

综述了非饱和土有效应力的沿革,并就非饱和土有效应力的研究和发展中存在的问题进行了讨论。基于多相孔隙介质理论推导得到的变形功的表达式,提出了非饱和土广义有效应力原理。该原理认为,由非饱和土中的单应力变量的有效应力或双应力变量理论很难唯一地确定非饱和土的变形和强度。广义有效应力原理实质上就是要综合考虑影响非饱和土变形和强度的三种广义应力以及与其对偶的广义变形,给出考虑因素更为全面、理论基础更为坚实的广义有效应力原理。它为非饱和土基本性质的研究和本构方程的建立奠定了坚实而科学的理论基础。     

非饱和土土-水特征曲线的温度效应

基于热力学的理论,利用van Genuchten的土-水特征曲线表达式,建立了一种能考虑温度影响的土-水特征曲线方程,并给出了推导过程。该表达式综合考虑了温度对表面张力和浸润系数的影响。相对于根据试验数据拟合的表达式,该表达式具有更加坚实的理论基础,更具适用性和一般性。选用MX-80斑脱土和黄土土样的试验结果,将该方程预测结果和试验结果进行了比较;可以看到,所提出的方程能较好地反映非饱和土土-水特征曲线随温度而变化的情况。     

Predicting the dependency of a degree of saturation on void ratio and suction using effective stress principle for unsaturated soils

The paper presents an approach to predicting variation of a degree of saturation in unsaturated soils with void ratio and suction. The approach is based on the effective stress principle for unsaturated soils and several underlying assumptions. It focuses on the main drying and wetting processes and does not incorporate the effects of hydraulic hysteresis. It leads to the dependency of water retention curve (WRC) on void ratio, which does not require any material parameters apart from the parameters specifying WRC for the reference void ratio. Its validity is demonstrated by comparing predictions with the experimental data on four different soils taken over from the literature. Good correlation between the measured and predicted behaviour indirectly supports applicability of the effective stress principle for unsaturated soils. Copyright © 2009 John Wiley & Sons, Ltd.     

A fully coupled simple model for unsaturated soils

Different phenomena influence the strength and volumetric behavior of unsaturated soils. Among the most important are suction hardening, hydraulic hysteresis, and the influence of volumetric strain on the soil-water retention curves. Fully coupled hydro-mechanical models require including all three phenomena in their constitutive relationships. Among these phenomena, suction hardening is the most influencing as it determines the apparent preconsolidation stress, the position of the loading-collapse yield surface, and the shift of both the isotropic consolidation and the critical state lines. In this paper, a fully coupled hydro mechanical model is presented. It is based on the modified Cam-Clay model but includes a yield surface with anisotropic hardening that takes account of the shift of the critical state line with suction. For highly overconsolidated materials, the sub-loading surface concept has been included in order to increase the precision of the model for these materials. The shift of the retention curves produced by volumetric strains is simulated using a hydraulic model based on the grain and current pore size distribution of the soil.     

Effective stress concept in unsaturated soils: Clarification and validation of a unified framework

The effective stress principle, conventionally applied in saturated soils, is reviewed for constitutive modelling purposes. The assumptions for the applicability of Terzaghi's single effective stress are recalled and its advantages are inventoried. The possible stress frameworks applicable to unsaturated soil modelling are reassessed in a comparative manner, specifically the Bishop's single effective stress, the independent stress variables approach and the generalized stress framework. The latter considerations lead to the definition of a unified stress context, suitable for modelling soils under different saturation states. In order to qualify the implications brought by the proposed stress framework, several experimental data sets are re‐examined in the light of the generalized effective stress. The critical state lines (CSLs) at different saturation states tend to converge remarkably towards a unique saturated line in the deviatoric stress versus mean effective stress plane. The effective stress interpretation is also applied to isotropic paths and compared with conventional net stress conception. The accent is finally laid on a second key feature for constitutive frameworks based on a unified stress, namely the sufficiency of a unique mechanical yield surface besides the unique CSL. Copyright © 2007 John Wiley & Sons, Ltd.     

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。     

低饱和度非饱和土的抗剪强度理论及其应用

从非饱和土的微观结构入手,提出并推导了土颗粒间毛细吸力引起的基质吸力与附加有效应力关系的近似解,并进一步得到了低饱和度非饱和土的抗剪强度公式。通过试验资料和理论分析验证了所推公式的合理性、正确性。最后分析了土颗粒半径差异、土体平均粒径大小对非饱和土强度的影响。     

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.     

非饱和土力学中几个基本问题的探讨

近些年非饱和土力学的研究非常活跃,但对一些基本问题的认识并不一致,有时甚至概念混淆。针对非饱和土力学的几个基本问题：非饱和土状态变量的选择、非饱和土有效应力变量的选择、吸力概念的界定和轴平移技术的局限性、非饱和土的结构的表征方法等问题进行了分析和探讨。其中非饱和土状态变量和有效应力的选择对于非饱和土力学的理论和相应本构模型的建立具有重要影响,因此,首先深入讨论了这一问题,概括论述了非饱和土有效应力的演变并深入探讨了目前各种形式有效应力的优缺点。其次,指出由于受负压孔隙水气化（液-气相变化）的影响,在实际场地中大于某一界限值的基质吸力是不存在的;目前被广泛使用的轴平移试验技术却掩盖了这一情况,而基于此所建立的非饱和土强度和变形理论的适用性需要进一步的研究和论证。再次,指出非饱和土的结构除了包括组构和颗粒之间作用力的综合效应外,还建议增加孔隙水和孔隙气的分布以及各相之间的相互作用和物理-化学作用。最后对一些容易混淆的概念进行了梳理。其目的是希望国内同行在今后的研究中对这些问题加以关注,并建立正确的认识,促进非饱和土力学沿着正确的方向发展。     

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。     

非饱和土的应力状态变量研究

以热力学和连续介质力学的应力理论为基础,从非饱和土的土骨架平衡方程出发,导出了一系列应力状态变量,目前文献中所使用的应力状态变量都在其中。研究发现：非饱和土的应力状态变量有多种组合形式（5组以上）,不是惟一的;大多数应力状态变量与土的孔隙率、饱和度等物性指标孪生相伴;所有应力状态变量都具有应力的量纲,单纯孔隙率或饱和度及其组合都不构成应力状态变量;简化的Bishop有效应力公式和Fredlund倡导的两个应力状态变量都是简化了的应力状态变量,前者忽略了孔隙率的影响,而后者忽略了与孔隙率及饱和度的关联性。在选择应力状态变量时应考虑理论合理、应用方便、逻辑关系正确的原则,还应做一定的验证工作。     

非饱和土三剪强度准则及验证

基于材料三剪强度准则和非饱和土力学特性,提出了非饱和土的单应力变量和双应力变量三剪强度准则,并对其做了特征分析。分析表明,通过改变准则中的主应力影响系数b,所提准则就可以对其他强度准则进行非线性近似表达。在π平面的极限线中,所提强度准则覆盖了由内边界的单剪强度准则到外边界的三剪统一强度准则之间的所有外凸区域。因此,其适用于各种复杂应力状态下的非饱和土体,也能反映非饱和土单轴抗拉抗压强度不等的特征。另外,还用其他文献的真三轴试验数据对所提准则做了试验验证,其中,非饱和黏土砂的真三轴试验值与中主应力影响系数b=0.6时的三剪强度准则预测值吻合较好,双应力变量下准则的预测值比单应力变量下的预测值更符合试验值;非饱和黄土真三轴试验值与中主应力影响系数b=0.2时的三剪强度准则预测值吻合较好,两种应力变量下的三剪强度准则预测值差别较小。     

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 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.