Abstract: A thermodynamically consistent extension of the constitutive equations of saturated soils to unsaturated conditions is often worked out through the use a unique ’effective’ interstitial pressure, accounting equivalently for the pressures of the saturating fluids acting separately on the internal solid walls of the pore network. The natural candidate for this effective interstitial pressure is the space averaged interstitial pressure. In contrast experimental observations have revealed that, at least, a pair of stress state variables was needed for a suitable framework to describe stress–strain–strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the invasion of the soil by the liquid water phase through the retention curve; two effective stresses, which are required to describe the soil deformation at water saturation held constant. However a simple assumption related to the plastic flow rule leads to the final need of only a Bishop-like effective stress to formulate the stress–strain constitutive equation describing the soil deformation, while the retention properties still involve the suction and possibly the deformation. Commonly accepted models for unsaturated soils, that is the Barcelona Basic Model and any approach based on the use of an effective averaged interstitial pressure, appear as special extreme cases of the thermodynamic formulation proposed here.
Abstract: In this paper two rate dependent constitutive models for porous chalks are presented. The common background of both models formulation is the isotach approach, which is first introduced. The theoretical basis and the mathematical formulation of the models are then proposed. Finally, numerical predictions of both models are compared with experimental results and discussed. The two formulations include strain rate and creep effects. Suction dependency on creep is also discussed. Some perspectives about the constitutive modelling of time-dependent behaviour of partially saturated chalks are given with respect to the description of the coupled effect of suction and time.
Abstract: Current alternative choices of stress state variables in unsaturated soils are described and compared with a special focus on the use of an effective stress. Experimental data about stiffness and shear strength evolution with suction suggests that the proportion of suction contributing to the effective stress is often much smaller than predicted by the term "suction times degree of saturation" generally used in effective stress expressions of Bishop’s type. It is suggested that effective stress in unsaturated soils should be related to soil microstructure. An effective degree of saturation is defined to describe the volume of water filling partially the soil macroporosity. This effective degree of saturation defines the proportion of prevailing suction which actually contributes to the effective stress. Two alternative expressions (piece-wise linear and nonlinear) are proposed for the effective degree of saturation. They offer a similar performance. Available data on stiffness and shear strength variation with suction of a few different soils ranging from a markedly granular material to high plasticity clay have been analyzed. The analysis made supports the proposed microstructural interpretation of the effective stress. Indeed, for granular soils the effective degree of saturation is almost equal to the total degree of saturation and therefore, Bishop’s type expression generally used as an effective stress is recovered. As the soil becomes more plastic the proportion of free water reduces and the contribution of suction to the effective stress reduces. At the limit, when the proportion of free water is negligible (this is the case of high plasticity clays at high values of suction) the proposed effective stress reduces to the net stress (excess of total stress over the air pressure). The proposed effective stress equation may be identified if information on the amount of immobile water is available for a given soil. Water retention or porosimetry data provides this information. This has been shown by comparing the present proposal with independently obtained information about immobile water in high plasticity clays.
Abstract: On the basis of plastic bounding surface model, the damage theory for structured soils and unsaturated soil mechanics, an elastoplastic model for unsaturated loessic soils under cyclic loading has been elaborated. Firstly, the description of bond degradation in a damage framework is given, linking the damage of soil’s structure to the accumulated strain. The Barcelona Basic Model (BBM) was considered for the suction effects. The elastoplastic model is then integrated into a bounding surface plasticity framework in order to model strain accumulation along cyclic loading, even under small stress levels. The validation of the proposed model is conducted by comparing its predictions with the experimental results from multi-level cyclic triaxial tests performed on a natural loess sampled beside the Northern French railway for high speed train and about 140 km far from Paris. The comparisons show the capabilities of the model to describe the behaviour of unsaturated cemented soils under cyclic loading.
Abstract: This paper studies the sedimentation-consolidation of a double porosity material, such as lumpy clay. Large displacements and finite strains are accounted for in a multidimensional setting. Fundamental equations are derived using a phenomenological approach and non-equilibrium thermodynamics, as set out by Coussy [Coussy, Poromechanics, Wiley, Chichester, 2004]. These equations particularise to three non-linear partial differential equations in one dimensional context. Numerical implementation in a finite element code is currently being undertaken.
Abstract: This paper proposes a general formulation of an elastoplastic model adapted to unsaturated soils. This formulation enters within the framework of two independent state variables descriptions. The choice of a particular effective stress combined with suction is made. The definition of this effective stress is based on the formulation of an equivalent pore pressure which is an essential point of this type of models. It will be discussed in this paper. This general formulation can be seen as a methodology allowing to adapt in a straightforward way most of elastoplastic behaviour models classically used in saturated soils mechanics to unsaturated states. It is shown that this synthesis can include most of recent models developed within the same framework. The last part of this paper is devoted to the adaptation of an existing complex elastoplastic model (CJS model) to unsaturated states using the methodology previously exposed. The model thus obtained is validated on various loading paths including oedometric, isotropic or triaxial compressions and also wetting tests simulating collapse phenomenon. This model extension shows the easiness introduced by the proposed methodology to adapt a given elastoplastic model to unsaturated states. Its validation illustrates by the way the abilities of the extended model to reproduce complex volumetric responses of an unsaturated soil.
Abstract: Constitutive equations of unsaturated soils are often derived in a thermodynamically consistent framework through the use a unique ’effective’ interstitial pressure. This later is naturally chosen as the space averaged interstitial pressure. However, experimental observations have revealed that two stress state variables were needed to describe the stress-strain-strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the retention properties of the soil and two effective stresses, which are required to describe the soil deformation at water saturation held constant. Actually, it is shown that a simple assumption related to internal deformation leads to the need of a unique effective stress to formulate the stress-strain constitutive equation describing the soil deformation. An elastoplastic framework is then presented and it is finally shown that the Barcelona Basic Model, a commonly accepted model for unsaturated soils, as well as all models deriving from it, appear as special extreme cases of the thermodynamic framework proposed here.
Abstract: In this paper a rate dependent model for geomaterials saturated by a mixture of immiscible fluids is presented. The proposed constitutive law generalizes the isotach approach to the elastoplastic strain hardening based constitutive laws for partially saturated soils. The formulation encompasses rate and creep effects together with suction dependency on creep. Some perspectives about the constitutive modelling of time-dependent behaviour of geomaterials saturated by a single or two fluids, including soft rocks are proposed. Practical applications include modelling of underground carries submitted to humidity changes, oil reservoir formations or geological storage of CO2. In this study, the model formulation is presented and numerical predictions are compared with available experimental results on oil reservoir chalk.
Abstract: In this paper a rate dependent model for partially saturated geomaterials is presented. The formulation and numerical predictions are compared with available experimental results and discussed. The constitutive laws for the description of the time-dependent mechanical behaviour of saturated and partially saturated geomaterials generalize the isotach approach to the elastoplastic strain hardening based constitutive laws for partially saturated soils. The formulation encompasses rate and creep effects together with suction dependency on creep. Some perspectives about the constitutive modelling of time-dependent behaviour of saturated and partially saturated geomaterials, including soft rocks are proposed.
Abstract: High speed railway from Northern France has encountered several stability problems in zones where loessic soils are present. Important sinkholes have been observed and were mainly due to the collapse susceptibility of the encountered loess when submitted to the cyclic loadings imposed by the passage of the high speed trains. This collapse susceptibility seems to be related to the degradation of the cemented bonds and to either the collapse under wetting at constant applied load or liquefaction depending on the natural water content of the soil. In this paper, a constitutive model is developed to gain insight into cyclic behaviour of theses soils. This model is an extension of a model previously proposed by the authors for modelling degradation of bonds and liquefaction potential of natural cemented soils under saturated states. The platform model, from which the extension is carried out, is based from one hand on the bounding surface plasticity theory for the description of the cyclic response of the soil and is inspired on the other hand from the work of Vaunat & Gens (2003) concerning bond degradation modelling. Influence of non-saturation effects is introduced following an approach similar to that of the Barcelona Basic Model (Alonso et al. 1990). The developed model is thus capable to describe the mechanical behaviour of unsaturated bonded soils under cyclic loading.
Abstract: A refined constitutive model for unsaturated soils is presented. It is based on a complex model (CJS) formerly proposed for saturated materials. Its extension is carried out within a general framework proposed by the authors. This framework is based on a formulation using two stress state variables: a constitutive stress and suction. It can be seen as a methodology allowing the extension in a straightforward manner of existing elasto-plastic models to unsaturated states. After a brief description of this methodology, the extended model is described. In a second part, the implementation of this extended model into a Finite Element code accounting for hydro-mechanical couplings is presented. The code simulates cavity expansion problems under simplified geometry hypotheses. Simulations of pressuremeter tests, a well know in situ geotechnical test, are then presented.
Abstract: This paper proposes a general formulation which allows to adapt existing constitutive models developed for dry or saturated soils to take into account suction effects. The main advantages of such a conceptualisation is to reuse reliable models presenting good capacities to closely simulate soil behaviour under complex loading paths. These loading paths may lead to sophisticated behaviour (contractancy followed by dilatancy in the course of loading etc.) well simulated by such models. The choice of a particular effective stress, combined with suction, is made. The definition of this effective stress is based on the formulation of an equivalent pore pressure. Following the approach presented, an existing elastoplastic model (CJS model), is extended to cover unsaturated states. A classic geotechnical in situ investigationmethod (pressuremeter) is then simulated. This simulation allows to determine the effects of suction on the mechanical behavior of the soil.
Abstract: The pressuremeter, a classic geotechnical investigation method, supplies useful information concerning the mechanical behavior of in situ soils. Its methods of analysis have been the subject of many studies using both experimental and theoretical approaches. In particular, correlations between pressuremeter measurements and other soil parameters obtained otherwise have been established. Although the effects of partial saturation are frequently encountered in practical engineering applications, they are not always accounted for in the calculations. In particular, such is the case in the modeling and interpretation of pressuremeter tests. As a matter of fact, mechanical behavior of unsaturated soils and its modeling still contain a lot of open questions and are subjects of intensive studies. The present paper presents an attempt to model the soil response during pressuremeter tests, taking into consideration different saturation states and suction effects. The pressuremeter testing is numerically simulated by an undrained cylindrical cavity expansion under plane strain conditions. A constitutive model, well-adapted to soils, has been implemented in the computer code developed. Its development is based on a classic elastoplastic model, with additional features introduced to account for unsaturation effects. Suction and a particular definition of effective stress have been chosen to be the independent stress variables. The plastic yield criterion and the flow potential are taken from modified Camclay model. Variations of suction and other constitutive parameters, such as volume compressibility, depending on the water content are accounted for. A parametric study is carried out, in order to highlight the predominant mechanisms conditionning the soil responses in a partial saturation context, during pressuremeter tests. These factors have to be accounted for in order to obtain a realistic modeling of soils.
Abstract: A refined constitutive model for unsaturated soils is presented. It is based on a complex model (CJS) formerly proposed for saturated materials. Its extension is carried out within a general framework proposed by the authors. This framework is based on a formulation using two stress state variables: a constitutive stress and suction. It can be seen as a methodology allowing the extension in a straightforward manner of existing elasto-plastic models to unsaturated states. After a brief description of this methodology, the extended model is described. In a second part, the implementation of this extended model into a Finite Element code accounting for hydro-mechanical couplings is presented. The code simulates cavity expansion problems under simplified geometry hypotheses. Simulations of pressuremeter tests, a well know in situ geotechnical test, are then presented.
Abstract: Taking into account unsaturation effects in modelling the behaviour of geomaterials is a key issue in many civil engineering applications. After a synthesis of the main characteristics of unsaturated soils behaviour and of several recently proposed constitutive models, a general framework for modelling purposes is proposed. This framework constitutes a methodological tool allowing an easier extension of existing elastoplastic models to unsaturated states. This methodology is then used to extend a complex elastoplastic model (CJS). The obtained model is validated using laboratory tests. In addition to this rheological contribution, a computational code using the finite element method has been developed. The boundary value problem discretization is presented. Simulations of pressure-meter tests and underground cavity deconfinement with this numerical tool are proposed and analysed. They contribute to evaluate the effects of a partial saturation on the behaviour of the ground surrounding the work.
