By considering a drained cohesionless granular sample made up of rigid grains and submitted to a triaxial test, we derive an equation relating the dilatancy K, the deviatoric stress q and the confining pressure p to the energy losses Dplastic due to plastic yielding. We demonstrate that the system is contracting (K ≤ 0) at q=0, when q is increasing and that spontaneous uncontrolled yielding begins occurring when dilatancy K is maximum. We also demonstrate the existence of the characteristic state introduced by Luong and Habib and the existence of the critical state of Schofield and Wroth. We give at last a method to determine the plastic losses during a triaxial cell test using the experimental data.
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Evesque, P., Stefani, C. Relationship Between Dilatancy, Stresses and Plastic Dissipation in a Granular Material with Rigid Grains. MRS Online Proceedings Library 291, 473–478 (1992). https://doi.org/10.1557/PROC-291-473