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.     

非饱和土的清华弹塑性模型

为研究土在非饱和增湿情况下的应力、应变和强度关系,提出将含水率引入清华模型的硬化参数中建立非饱和土的清华弹塑性模型。通过在干土中掺加冰屑的方法进行增湿试验,表明该模型可以预测不同含水率的非饱和土的应力-变形和强度关系,从天然风干状态增湿到其他含水率的应力-应变全过程的计算结果也与试验结果相符合。将含水率直接引入弹塑性模型而不去研究复杂的基质吸力,可能是非饱和土本构模型工程应用的一条简便途径。     

On constitutive modelling of unsaturated soils

The paper presents a review of constitutive modelling of unsaturated soils. After a brief historical perspective, a number of existing constitutive models are classified and discussed according to the type of stress variables adopted in their formulation. Afterwards, attention is given to recent developments in the proposal of coupled hydraulic-mechanical models and the possibility of casting them in a sound thermodynamical framework. Finally, a double structure model for expansive soils is described. The incorporation of microstructural considerations and its use as a platform for incorporating the influence of new variables are highlighted.     

Thermo-elastoplastic constitutive model for unsaturated soils

This study presents a simple approach to modelling the effect of temperature on the deformation and strength of unsaturated/saturated soils by using the average skeleton stress and degree of saturation. The concept of thermo-induced equivalent stress is introduced to consider the influence of temperature on the pre-consolidated stress. A skeleton stress–saturation framework is applied to enable the model to describe the thermo-elastoplastic behaviour of both unsaturated and saturated soils, as the skeleton stress can smoothly shift to Terzaghi’s effective stress if saturation changes from the unsaturated to the saturated condition. The new model only employs seven parameters, of which five parameters are the same as those used in the Cam-Clay model. The other two parameters can be easily determined by oedometer tests and simple thermo-mechanical tests. Numerical simulations of isotropic loading tests and triaxial shear tests under different conditions are conducted to illustrate the performance of the proposed model. By comparing with experimental temperature controlled oedometer tests and triaxial tests, it is confirmed that the proposed model is able to capture the thermo-mechanical behaviour of unsaturated/saturated normally and over-consolidated soils with a set of unified parameters.     

考虑温度影响的重塑非饱和膨胀土非线性本构模型

以非饱和土的非线性模型为基础,通过对土性参数的修正和考虑温度本身引起的土的变形,建立了考虑温度效应的重塑非饱和膨胀土的本构模型。该模型包括土骨架的本构关系和水量变化的本构关系两个方面,涉及18个参数,都可用非饱和土三轴试验确定。共做了13个重塑非饱和膨胀土温控三轴试验,分析了温度对土的强度和变形的影响,研究了模型参数的变化规律。     

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。     

An evolutionary approach to modelling the thermomechanical behaviour of unsaturated soils

A new data‐mining approach is presented for modelling of the stress–strain and volume change behaviour of unsaturated soils considering temperature effects. The proposed approach is based on the evolutionary polynomial regression (EPR), which unlike some other data‐mining techniques, generates a transparent and structured representation of the behaviour of systems directly from raw experimental (or field) data. The proposed methodology can operate on large quantities of data in order to capture nonlinear and complex relationships between contributing variables. The developed models allow the user to gain a clear insight into the behaviour of the system. Unsaturated triaxial test data from the literature were used for development and verification of EPR models. The developed models were also used (in a coupled manner) to produce the entire stress path of triaxial tests. Comparison of the EPR model predictions with the experimental data revealed the robustness and capability of the proposed methodology in capturing and reproducing the constitutive thermomechanical behaviour of unsaturated soils. More importantly, the capability of the developed models in accurately generalizing the predictions to unseen data cases was illustrated. The results of a sensitivity analysis showed that the models developed from data are able to capture and represent the physical aspects of the unsaturated soil behaviour accurately. The merits and advantages of the proposed methodology are also discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

非饱和土固结理论新进展

总结了国内外多年来在非饱和土固结理论领域研究的主要理论成果,内容包括国内外非饱和土固结理论研究的概况,涉及线性、非线性、弹塑性和结构性等方面,非饱和土固结理论的研究具有非常好的应用前景。但非饱和土固结理论还很不成熟,有待广大科研工作者的进一步研究。     

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。     

Constitutive modelling of state-dependent behaviour of unsaturated soils: an overview

An unsaturated soil is a three-phase material that is ubiquitous on the earth’s surface. The fully saturated and completely dry states are just two limiting conditions of an unsaturated soil. The state and properties of unsaturated soils can change significantly with external loads, weather conditions and groundwater level. Proper modelling of the state-dependent behaviour of unsaturated soils is crucial for analysing the performance of almost all civil engineering structures. So far, there are many unsaturated soil models and several relevant review papers in the literature. None of the existing review papers, however, focused on the state dependency of unsaturated soil behaviour. Moreover, some aspects of soil behaviour have not been reviewed, including small strain stiffness, dilatancy and stress-dependence of water retention curve. In the current review paper, the state dependency of unsaturated soil behaviour is reviewed, with a particular attention to the three missing parts. The review is carried out in a unified and relatively simple constitutive framework, which adopts a three-by-three compliance matrix to link incremental volumetric strain, deviator strain and degree of saturation to incremental mean net stress, deviator stress and suction. All of the nine variables in the proposed three-by-three compliance matrix have clear physical meanings and can be measured through compression, shearing and water retention tests. Theoretical models based on other constitutive stress variables can be also converted to this framework by matrix transformation.

     

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.     

Poroelastic behaviour of fine compacted soils in the unsaturated to saturated transition zone

The behaviour of quasi-saturated materials is important to consider when designing cuttings and embankments in which earthwork materials are compacted to the optimum proctor density. Under this condition, the in-pore gaseous phase takes the form of air pockets and bubbles embedded within the liquid phase, which significantly affects the overall behaviour of the soil. The assessment of highly saturated soils thus requires a precise understanding of hydro-chemo-mechanical couplings between the entrapped air, the in-pore liquid and the solid skeleton. This paper presents a fully coupled poromechanical model that separates the kinematics and the mechanical behaviours of the phases in their interactions with each other (e.g., liquid water, dissolved air, gaseous air and solid matrix). The assumptions about the entrapped air behaviour are defined from a bibliographic study, and linear elastic behaviour is used for both the liquid phase and the solid skeleton. The model is implemented in the FEM code COMSOL and is subsequently used to simulate oedometric tests under different loading paths: undrained compression or imposed liquid pressure variation at constant stress. The behaviour, which shows a continuous transition from unsaturated to saturated, is logical and consistent with available experimental data.     

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。     

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。     

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.     

A unified bounding surface plasticity model for unsaturated soils

A unified constitutive model for unsaturated soils is presented in a critical state framework using the concepts of effective stress and bounding surface plasticity theory. Consideration is given to the effects of unsaturation and particle crushing in the definition of the critical state. A simple isotropic elastic rule is adopted. A loading surface and a bounding surface of the same shape are defined using simple and versatile functions. The bounding surface and elastic rules lead to the existence of a limiting isotropic compression line, towards which the stress trajectories of all isotropic compression load paths approach. A non‐associated flow rule of the same general form is assumed for all soil types. Isotropic hardening/softening occurs due to changes in plastic volumetric strains as well as suction for some unsaturated soils, enabling the phenomenon of volumetric collapse upon wetting to be accounted for. The model is used to simulate the stress–strain behaviour observed in unsaturated speswhite kaolin subjected to three triaxial test load paths. The fit between simulation and experiment is improved compared to that of other constitutive models developed using conventional Cam‐Clay‐based plasticity theory and calibrated using the same set of data. Also, the model is used to simulate to a high degree of accuracy the stress–strain behaviour observed in unsaturated Kurnell sand subjected to two triaxial test load paths and the oedometric compression load path. For oedometric compression theoretical simulations indicate that the suction was not sufficiently large to cause samples to separate from the confining ring. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical hysteresis model for intermittent studies in unsaturated soils

In the present study, the use of one of the recent dependent domain models of capillary hysteresis in the numerical analysis of intermittent infiltration and redistribution of water in two types of soils (a sand and Rubicon Sandy Loam) has been shown. The numerical results for both the soils have been presented in terms of pressure head depth, moisture content depth and the pressure head-moisture content relationships. The capillary hysteresis model has been found to be very useful for the prediction of both wetting and drying scanning curves of various orders.     

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.