A microstructurally based effective stress for unsaturated soils

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 on stiffness and shear strength evolution with suction suggest 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 the Bishop type. It is suggested that effective stress in unsaturated soils should be related to soil microstructure. An effective degree of saturation is defined as describing the volume of water partially filling the soil macroporosity. This effective degree of saturation defines the proportion of the prevailing suction that actually contributes to the effective stress. Two alternative expressions (piecewise linear and non-linear) 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 analysed. The analysis 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 the Bishop-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 provide this information. This has been shown by comparing the present proposal with independently obtained information about immobile water in high-plasticity clays.