A simple formalism is presented to model the behaviour of expansive clays. Two levels of structure are considered. The behaviour of the macrostructure follows the model developed for unsaturated materials by Alonso et al. [Géotechnique 40 (3) (1990) . The behaviour of the microstructure is adapted from the work of Gens and Alonso [Can. Geotech. J. 29 (1992) 1013-1032] in order to include the possibility of the micropores being partially saturated. Mechanical coupling between both levels of structure are defined through two functions, one for wetting and the other for drying. They express the change in macrostructural void ratio due to a change in microstructural void ratio, and their value depends on the state of compaction of the macrostructure. The general shape of these curves is discussed on the basis of experimental evidence. Phenomena such as the dependency of strain on stresssuction path, accumulation of expansion strain during suction cycles at low confining stress, accumulation of compression strain during suction cycles at high confining stress, strain fatigue during drying-wetting cycles, macropore invasion by expanded microstructure and development of macroporosity during strong drying can be represented. A mathematical formulation of the model is described and its performance finally assessed by comparison with laboratory tests.

Citation for published item:qllipoliD hF nd qensD eF nd hrmD F nd untD tF @PHHQA 9en elstoEplsti model for unsturted soil inorporting the e'ets of sution nd degree of sturtion on mehnil ehviourF9D q¡ eotehniqueFD SQ @IAF ppF IPQEIQTF Further information on publisher's website: httpXGGwwwFthomstelfordFomGjournlsGstrtFspctournlitleaq¡ eotehniqueertileshaIQITtournlwenuatruetourn Publisher's copyright statement:Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour D. GA LLIPOLI, Ã A . GENS, Ã R. SH ARMA{ and J. VAUNAT Ã The paper presents an elasto-plastic model for unsaturated soils that takes explicitly into account the mechanisms with which suction affects mechanical behaviour as well as their dependence on degree of saturation. The proposed model is formulated in terms of two constitutive variables directly related to these suction mechanisms: the average skeleton stress, which includes the average fluid pressure acting on the soil pores, and an additional scalar constitutive variable, î, related to the magnitude of the bonding effect exerted by meniscus water at the inter-particle contacts. The formulation of the model in terms of variables closely related to specific behaviour mechanisms leads to a remarkable unification of experimental results of tests carried out with different suctions. The analysis of experimental isotropic compression data strongly suggests that the quotient between the void ratio, e, of an unsaturated soil and the void ratio e s , corresponding to the saturated state at the same average soil skeleton stress, is a unique function of the bonding effect due to water menisci at the inter-particle contacts. The same result is obtained when examining critical states at different suctions. Based on these observations, an elastoplastic constitutive model is developed using a single yield surface the size of which is controlled by volumetric hardening. In spite of this simplicity, it is shown that the model reproduces correctly many important features of unsaturated soil behaviour. It is especially remarkable that, although only one yield surface is used in the formulation of the model, the irreversible behaviour in wetting-drying cycles is well captured. Because of the behaviour normalisation achieved by the model, the resulting constitutive law is economical in terms of the number of tests required for parameter determination.KEYWORDS: clays; constitutive rela...

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.

The authors should be commended for presenting such an innovative, elaborate elasto-plastic framework for predicting constitutive unsaturated soil response under isotropic stress states. One of the key aspects of the work is the authors' deep knowledge of the physical interactions that lie behind the mechanical behaviour of unsaturated soils. The proposed constitutive model and their associated conceptual framework provide an important improved understanding of soil behaviour. The present review is intended to offer some comments that further highlight the relevance of the work and its potential for further refinement and tuning.The objective of this review is twofold:

International audienceA 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

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Citation for published item:qllipoliD hF nd qensD eF nd hrmD F nd untD tF @PHHQA 9en elstoEplsti model for unsturted soil inorporting the e'ets of sution nd degree of sturtion on mehnil ehviourF9D q¡ eotehniqueFD SQ @IAF ppF IPQEIQTF Further information on publisher's website: httpXGGwwwFthomstelfordFomGjournlsGstrtFspctournlitleaq¡ eotehniqueertileshaIQITtournlwenuatruetourn Publisher's copyright statement:Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour D. GA LLIPOLI, Ã A . GENS, Ã R. SH ARMA{ and J. VAUNAT Ã The paper presents an elasto-plastic model for unsaturated soils that takes explicitly into account the mechanisms with which suction affects mechanical behaviour as well as their dependence on degree of saturation. The proposed model is formulated in terms of two constitutive variables directly related to these suction mechanisms: the average skeleton stress, which includes the average fluid pressure acting on the soil pores, and an additional scalar constitutive variable, î, related to the magnitude of the bonding effect exerted by meniscus water at the inter-particle contacts. The formulation of the model in terms of variables closely related to specific behaviour mechanisms leads to a remarkable unification of experimental results of tests carried out with different suctions. The analysis of experimental isotropic compression data strongly suggests that the quotient between the void ratio, e, of an unsaturated soil and the void ratio e s , corresponding to the saturated state at the same average soil skeleton stress, is a unique function of the bonding effect due to water menisci at the inter-particle contacts. The same result is obtained when examining critical states at different suctions. Based on these observations, an elastoplastic constitutive model is developed using a single yield surface the size of which is controlled by volumetric hardening. In spite of this simplicity, it is shown that the model reproduces correctly many important features of unsaturated soil behaviour. It is especially remarkable that, although only one yield surface is used in the formulation of the model, the irreversible behaviour in wetting-drying cycles is well captured. Because of the behaviour normalisation achieved by the model, the resulting constitutive law is economical in terms of the number of tests required for parameter determination.KEYWORDS: clays; constitutive rela...

No abstract