Constitutive Model For Unsaturated Soils Research Articles

유효응력에 근거한 불포화토의 역학적 구성모델

다양한 지반공학적 문제들에서 불포화 상태의 중요성이 강조되면서, 불포화 지반의 열-수리-역학적 현상들에 대한 거동특성을 모사하기 위한 역학적 구성모델 개발이 진행되고 있다. 본 연구에서는 Bishop의 유효응력 정의에 근거한 불포화 지반의 역학적 탄소성 구성모델을 제시하였다. 유효응력에 근거한 구성관계는 유효응력과 온도를 주 변수로 증분 형식으로 표현되었으며, 이를 이용하여 응력 갱신과 강성 텐서를 산정하였다. 개발된 구성모델을 이용하여 THM 현상을 포함하는 불포화토의 1차원 거동, 불포화토의 삼축 압축시험, 그리고 고준위 방사성폐기물 시설의 완충재의 거동 특성에 관한 예제 해석을 수행하여 해의 안정성과 구성모델의 적용성에 대하여 논의하였다. 수치해석결과는 개발된 역학적 구성모델이 THM 현상의 매우 복잡한 거동을 효과적으로 모사할 수 있었으며, 일반적인 불포화토의 거동 해석뿐만 아니라 다양한 환경 조건하에서의 THM 거동 해석에 적용이 가능할 것으로 판단된다. The importance of unsaturated state in various geo-engineering problems has led to the advance of mechanical constitutive model emulating behavior of unsaturated soils in response to thermo-hydro-mechanical loading. Elasto-plastic mechanical constitutive model for unsaturated soil is formulated based on Bishop's effective stress. Effective stress and temperature are main variables in constitutive equation, and incremental formulation of constitutive relationship is derived to compute stress update and stiffness tensor. Numerical simulations involving coupled THM processes are conducted to discuss numerical stability and applicability of developed constitutive model: one-dimensional test, tri-axial compression test, and clay-buffering at high level radioactive waste disposal. Numerical results demonstrated that developed model can predict very complex behavior of coupled THM phenomena and is applicable to geo-engineering problems under various environmental conditions, as well as interpret typical behavior of unsaturated soils.

Analysis of the FEBEX multi‐barrier system including thermoplasticity of unsaturated bentonite

SUMMARYDeep geological repository involving a multibarrier system constitutes one of the most promising options for isolating high‐level radioactive waste from the human environment. To certify the efficiency of waste isolation, it is essential to understand the behaviour of confining geomaterial under a variety of environmental conditions. To this end, results from a near‐to‐real experiment, the full‐scale engineered barriers in situ experiment, are studied by means of a thermo–hydro–mechanical finite element approach, including a consistent thermoplastic constitutive model for unsaturated soils. Laboratory tests are simulated to calibrate model parameters. The results of the numerical simulations are compared with sensor measurements and show the ability of the model to reproduce the main behavioural features of the system. The influence of the hysteretic and temperature‐dependent retention of water on the mechanical response is exhibited. Finally, those results are interpreted in the light of thermoplasticity of unsaturated soils, which reveals the highly coupled and non‐linear characters of the processes encountered. Copyright © 2011 John Wiley & Sons, Ltd.

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

AbstractA 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.

Equivalent stress approach in modelling unsaturated soils

SUMMARY 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.

Volume change behavior of unsaturated soils under non-isothermal conditions

With the development of modern geotechnical engineering practices such as the construction of high level radioactive waste repositories, exploitation and utilization of geothermal resources, energy-saving buildings and underground storage of CO2, research into the influence of temperature on the basic mechanical properties of unsaturated soils has become an important issue internationally. By using the work expression and considering the influence of temperature on the basic properties of unsaturated soils, the average soil skeleton stress, modified suction and temperature were selected as state variables of generalized forces in thermodynamics and the soil skeleton strain, saturation and entropy were chosen as state variables of generalized flows conjugate to the variables of generalized forces. Based on the nonlinear multi-field coupled model and by using existing experimental results, an elastic-plastic constitutive model of unsaturated soils under non-isothermal conditions was developed to analyze the influence of temperature on the deformation properties of unsaturated soils. The model was used to predict and analyze the influence of suction and temperature on the deformation properties of unsaturated soils under isotropic conditions, and was successfully verified using experimental results.

Coupling hydraulic with mechanical models for unsaturated soils

This paper presents an alternative method to couple the hydraulic component with the mechanical component in a constitutive model for unsaturated soils. Some pioneering work on hydromechanical coupling is reviewed. Generalized constitutive relations on coupled hydromechanical behaviour are introduced. These generalized constitutive relations are then incorporated into existing mechanical and hydraulic models for unsaturated soils. A new coupling mechanism is proposed based on the fact that soil-water characteristic equations are usually obtained for constant stress, not constant volume. The proposed coupling mechanism also satisfies the intrinsic relationship between the degree of saturation and the volumetric strain for undrained compression. Numerical examples are presented to show the performance of the proposed model in predicting soil behaviour along drying and loading paths. Finally, the model is validated against experimental data for different soils.

Benchmark of constitutive models for unsaturated soils

The paper presents a collaborative piece of research undertaken by seven research teams from different universities within the ‘Mechanics of Unsaturated Soils for Engineering' (MUSE) network. The objective is to benchmark different approaches to constitutive modelling of mechanical and water retention behaviour of unsaturated soils by comparing simulations of suction-controlled and constant water content laboratory tests. A set of 13 triaxial and oedometer laboratory tests, covering the mechanical and water retention behaviour of an unsaturated compacted silty soil under a variety of stress paths, has been provided by one of the seven participating teams. This data set has been used by the other six teams for calibrating a constitutive model of their choice, which has been subsequently employed for predicting strains and degree of saturation in three of the 13 tests used for calibration, as well as in one ‘blind' test for which experimental results had not been previously disclosed. By comparing predictions from all teams among themselves and against experimental data, the work highlights the capability of some of the current modelling approaches to reproduce specific features of the mechanical and water retention behaviour of unsaturated soils helping to identify potential areas of weakness where future research should focus. It also demonstrates the dispersion of results to be expected when different constitutive models, independently calibrated by different teams of researchers, are used to predict soil behaviour along the same stress path.

Transfer model of water-soluble material in saturated/unsaturated ground

The ground pollution is one of the most serious environmental issues all over the world now. Industrial wastes discharged from various human activities infiltrate to the ground, diffuse and damage to plants and animals indirectly. Therefore, it is strongly requested to know the transfer behavior of contaminant movement in the ground. In this study, continuous equations and advection-dispersion equation are derived from mass conservation laws in soil, water, air and dissolved material phases. These governing equations are applied to the constitutive model for unsaturated soil and formulated in the framework of the initial boundary value problems with the finite element method The soil/water/air coupled analysis program, DACSAR-M_ad, applied mass transfer equation to is coded. Here, the mass within the ground due to loading is simulated with this code.

Modelling the effect of temperature on unsaturated soil behaviour

A simple thermohydromechanical (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.

Limitations in the Constitutive Modeling of Unsaturated Soils and Solutions

Over the past six decades, significant attention has been paid to the elastoplastic behavior of unsaturated soils. In the past two decades alone, elastoplastic theory for unsaturated soils has been established and experimental techniques for measuring the elastoplastic behavior of unsaturated soils have become more sophisticated. However, less effort has been directed at developing the best strategy for constitutive modeling of unsaturated soils. At present, there is no standard method for developing constitutive models for unsaturated soils from experimental data, and owing to the extreme complexity of unsaturated soil behavior, there are limitations in the existing modeling methods. If these limitations are not recognized, misleading results in the constitutive modeling of unsaturated soil behavior may occur. This paper discusses the origins of and possible solutions to these limitations. Experimental data from the recent literature are used to demonstrate the use of existing methods for the constitutive modeling of unsaturated soils and potential associated problems. A modified state-surface approach (MSSA), recently proposed to model the elastoplastic behavior of unsaturated soils under isotropic conditions, was applied to overcome the limitations and develop a constitutive model that can best represent the behavior of unsaturated soil. A comparison of the proposed method and existing methods is discussed, and from this discussion, the capability and effectiveness of the proposed method are evaluated.

A 13-parameter model for unsaturated soil based on bounding surface plasticity

A few constitutive models for unsaturated soils have already been proposed, however, many classic models such as the Barcelona basic model can simulate neither complex volumetric soil behaviour (without forgetting its supreme merit of being the first consistently and rigorously formulated model) nor post-peak softening, and most advanced models generally comprise a large number of parameters making them more difficult to be applied to practical situations. In this paper, we present a new model for unsaturated soils based on an existing model developed originally for saturated soils. It comprises a minimum number of constitutive parameters. The extension to unsaturated state is achieved by following a general methodology previously developed in our laboratory. The capacities of this simple model are tested. With only 13 parameters, it can reproduce the basic behaviour of unsaturated soils such as rebound or collapse upon wetting, depending on the stress levels. It can also reproduce post-peak softening and transition from contractant to dilatant volumetric behaviour during undrained shear. Overall, the first tentative of validation gives a good correlation between simulations and experimental data, and shows encouraging signs for future developments.

Evolution of microstructure in compacted London Clay during wetting and loading

The influence of fabric on mechanical behaviour is explicitly considered in some of the current constitutive models for unsaturated soils. These are based on assumptions regarding the interaction between different levels of structure, which still require experimental validation. A study has been carried out to investigate the evolution of fabric in a compacted natural clay during wetting and loading, and the results are presented in this paper. Samples of London Clay were statically compacted to the same initial conditions, dry of optimum moisture content in a Proctor plot, and subsequently taken along complex stress paths involving wetting, loading, or a combination of both. Mercury intrusion porosimetry (MIP) and environmental scanning electron microscopy (ESEM) microstructure investigations were carried out to observe and quantify the change in fabric associated with each path. The soil fabric was observed to change from an aggregate to a matrix type structure along all wetting paths. This transition was found to take place only when the suction was reduced to a value close to zero kPa. Results also showed that fabric changes during yielding were stress path-dependent. It was not possible to find a correspondence between the volume of free porosity and the volume of intra-aggregate pores, as suggested by some authors. Finally, the volume of pore water was found to agree closely with the volume of intra-aggregate pores, providing support to the assumption that in an unsaturated aggregate microstructure the clay aggregations are saturated.

An unsaturated soil model with minimal number of parameters based on bounding surface plasticity

AbstractThis paper presents a constitutive model for unsaturated soils with only 13 parameters. Its development is based on the concept of bounding surface plasticity under a critical state framework. The definition of effective stress via an equivalent pore pressure and the introduction of suction effects into a general plastic hardening mechanism are inspired from the work of Pereira et al. (Ph.D. Thesis, 2005) and that of a few others. Despite the minimal number of parameters, this model can simulate correctly complex volumetric behaviour and post‐peak softening, as well as a few other classic typical behaviours of unsaturated soils. The model is validated using experimental data both on saturated and unsaturated soils. Its efficiency has been highlighted by comparing its outputs with those from the Barcelona Basic Model and from another advanced model CJS‐NS. The numerical studies revealed the necessity of additional experimental data for a more complete validation of the model and its future improvement. Copyright © 2009 John Wiley & Sons, Ltd.

A four elements porous model to estimate the strength of unsaturated soils

One of the most prevalent relationships for effective stresses on unsaturated soils was proposed by Bishop in the middle of the last century. However, only recently Bishop’s effective stress equation has been implemented in various constitutive models for unsaturated soils. These models have the advantage of naturally including the hydro-mechanical coupling that has been experimentally observed on these materials. Unfortunately, the problem of properly evaluating Bishop’s parameter χ still remains unsolved. This paper presents the results of a solid-porous model used to determine the value of Bishop’s parameter χ and evaluate the strength of unsaturated soils. These theoretical results are compared with a series of triaxial test performed on a silty sand subjected to different suctions in wet and dry paths. These comparisons show that the porous model proposed herein can be used to estimate the strength of unsaturated soils for both the wetting and the drying paths.

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

AbstractThe 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.

Explicit stress integration with error control for the Barcelona Basic Model: Part I: Algorithms formulations

The numerical integration of the stress–strain relationship is an important part of many finite element code used in geotechnical engineering. The integration of elasto-plastic models for unsaturated soils poses additional challenges associated to the presence of suction as an extra constitutive variable with respect to traditional saturated soil models. In this contribution, a range of explicit stress integration schemes are derived with specific reference to the Barcelona Basic Model (BBM), which is one of the best known elasto-plastic constitutive models for unsaturated soils. These schemes, however, do not address possible non-convexity of the loading collapse (LC) curve and neglect yielding on the suction increase (SI) line. The paper describes eight Runge–Kutta methods of various orders with adaptive substepping as well as a novel integration scheme based on Richardson extrapolation. The algorithms presented also incorporate two alternative error control methods to ensure accuracy of the numerical integration. Extensive validation and comparison of different schemes are presented in a companion paper. Although the algorithms presented were coded for the Barcelona Basic Model, they can be easily adapted to other unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.

Discussion on “On the use of the generalized effective stress in the constitutive modelling of unsaturated soils” by L. Laloui and M. Nuth [Computers and Geotechnics 36 (2009) 20–23

Discussion on “On the use of the generalized effective stress in the constitutive modelling of unsaturated soils” by L. Laloui and M. Nuth [Computers and Geotechnics 36 (2009) 20–23

Reply to Discussion on “On the use of generalised effective stress in the constitutive modelling of unsaturated soils”: [Computers and Geotechnics 36 (2009) 20–23

Reply to Discussion on “On the use of generalised effective stress in the constitutive modelling of unsaturated soils”: [Computers and Geotechnics 36 (2009) 20–23

Fully coupled finite element model for dynamics of partially saturated soils

Understanding the response of partially saturated earth structures under various static and dynamic loads is important for the design and construction of economical and safe geotechnical engineering structures. In this study, the numerical approach is used to understand the dynamics of partially saturated soils. The mathematical equations governing the dynamics of partially saturated soils are derived based on the theory of mixtures and implemented within a finite element framework. The stress–strain behavior of the soil is represented by an elasto-plastic constitutive model for unsaturated soil based on bounding surface concept and the moisture-suction behavior is modeled using van Genuchten model. Fully coupled finite element simulations are performed to study the response of partially saturated soil embankment under earthquake loading and validated with centrifuge test results available in the literature. The predicted displacement responses are in good agreement with the measured responses. The pore water pressure, pore air pressure, matric suction, the degree of saturation in various elements and the response of the embankment under different initial moisture content are also discussed.

Unsaturated soil mechanics: Critical review of physical foundations

Most constitutive models for unsaturated soils are based on identification of soil-water suction with the capillary component of the matrix potential, ignoring the contribution of adsorption to this potential. Identification of potential (energy per unit volume) with stress (or suction), is questioned, since these quantities have different physical significance despite their common dimensions. It is suggested that the identification of matrix potential with ( u a − u w) results from neglecting the adsorption potential, and adopting an unrealistic pore space model. This identification was probably motivated by the laboratory axis translation technique, but it is not valid under normal field conditions where the air pressure is usually atmospheric, and soil water cannot develop high tension without cavitating. Axis translation alters soil behavior by preventing cavitation, thus casting doubt on the relevance of laboratory results obtained from these tests to actual field conditions. Specifically, in soils having large specific surface areas, there is a range of conditions, relevant to geotechnical engineering, in which capillary potential appears to account for only a small part of matrix potential, the major contribution resulting from water adsorption onto the soil particles. Consideration of a double porosity model and cavitation of water under the tension generated by capillary mechanism appear indispensable for the interpretation of unsaturated soil behavior.