A procedure for the direct determination of Bishop's χ parameter from changes in pore size distribution

Most of the recent works relating to the concept of effective stress in unsaturated soils focus on the proposal by Bishop, and, more particularly, on the search for suitable relationships between Bishop's χ parameter and the main controlling variables. These relationships are generally formulated by theoretical derivations and back-analyses of the dependency of mechanical parameters on hydraulic variables such as suction or saturation. In this note, a new procedure is proposed to evaluate directly, and without any a priori assumptions, values for Bishop's χ parameter. In the first part, a general derivation based on the definition of work conjugated variables allows the χ parameter to be defined as the ratio of the change of water volume over the change in pore volume during a process at constant suction. This definition is further exploited to evaluate Bishop's parameter from the changes suffered by material pore size distribution during loading. The method is applied to data obtained by mercury intrusion porosimetry tests on low-plasticity silt (Jossigny silt), low-plasticity sandy clay (lean clay) and highly plastic clay (Febex clay). Values obtained for these materials show that the χ parameter is close to the effective degree of saturation rather than the total degree of saturation.