A method to evaluate the capillary stress tensor at failure in unsaturated soils

This paper aims to provide a better understanding of the mechanisms that make it difficult to interpret the behavior of unsaturated soils using an effective stress principle. The main difficulty is that some deformed states of the unsaturated medium may not be statically admissible in saturated conditions. Therefore, we introduce the notions of total strain, which is measured at the boundary of the sample; effective strain, which is conjugated to the effective stress of the solid skeleton; and capillary strain, which results from the capillary forces. Recent results using the discrete element method prove that the effective strain can still be identified with the total strain in ‘small’ strains and at failure. Consequently, we propose to interpret the behavior of unsaturated soils on the basis of the principle of effective stress revisited with the theory of multiphase media and to identify the total and effective strain tensors in a first simplified approach. A conceptual experimental procedure is proposed to assess what we call the capillary tensor, using existing experimental devices. We propose certain hypotheses that allow engineers to numerically bound this capillary tensor at failure by knowing the total stress state measured at failure and the effective failure envelope in saturated conditions.