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Analytical insights in the micromechanics of unsaturated granular materials

The mechanical behaviour of granular materials with low moisture content is micro-mechanically analyzed. Such materials involve a mixture of gas, liquid, and solid grains, which leads to a drastically different behaviour from two-phase systems encompassing solid with liquid or gas phases. Low degrees of saturation are considered, so that the three-phase medium can be considered in the pendular regime where the liquid phase forms distinct menisci that join solid grain pairs.

The various internal forces that arise in such a three-phase medium are analytically derived according to the liquid bridge distribution and their geometrical properties, as well as grain packing. As such, a capillary stress tensor is obtained that distinguishes the total stress tensor from the grain-grain internal forces, i.e. the so-called effective stress tensor. The resulting analytical expressions highlight the non-spherical nature of the capillary stress tensor, contrary to the classical description of the air-water action with a spherical stress tensor (Bishop, 1959).

Furthermore, distinct contributions to this newly derived capillary stress tensor arise in our derivations. The first one relates to the unequal loading applied onto the solid grains by the gas and liquid phases with a pressure difference known as matric suction. The second contribution is due to contractile skin effects where surface tension forces act along wetted contours of grains because of liquid-gas interfaces (Wan et al. 2014).

Discrete numerical simulations show the relevancy of such proposed tensorial formulation of effective stress in the pendular regime. A discrete element model involving capillary forces (Scholtès et al. 2009) arising from liquid bridges is used for the verification of analytically derived expressions within a range of validity that is discussed.
It is shown that the proposed effective stress is the adequate variable to express the strength of the unsaturated material for various loading paths and saturations.


References

(Bishop, 1959) A. W. Bishop, “The principle of effective stress”, Teknisk Ukeblad, vol. 106, pp. 859-863, 1959.

(Wan et al. 2014) R. Wan, S. Khosravani and M. Pouragha, “Micromechanical Analysis of Force Transport in Wet Granular Soils”, Vadose Zone Journal, vol. 13(5), pp. 1-12, 2014.

(Scholtès et al. 2009) L. Scholtès, B. Chareyre, F. Nicot and F. Darve, “Micromechanics of granular materials with capillary effects”, International Journal of Engineering Science, vol. 47(1), pp. 64-75, 2009

Author(s):

Jerome Duriez    
University of Calgary
Canada

Richard Wan    
University of Calgary
Canada