On the operating critical friction ratio in general stress states

Stress dilatancy provides a fundamental flow rule for constitutive models and several variations on the framework have similar operational performance. However, regardless of idealisation adopted for stress dilatancy, the scaling coefficient evolves and only attains the critical friction ratio at large strain. The scaling coefficient also depends on the proportion of intermediate principal stress. Data on stress dilatancy in triaxial compression and plane strain are reviewed. Based on these data, a simple function is proposed for stress-dilatancy scaling using an operational friction ratio M_i based on work-conjugate stress and strain invariants. The function is calibrated to soil properties measured in conventional drained triaxial tests (about three, suitably chosen, tests are needed in addition to those used to define the critical state locus) and predicts strength in plane strain to an accuracy of ∆η= ±0·03 at 80% confidence for the Brasted and Changi sands considered (i.e. about ± 3% of typical peak strength). The proposed function is suitable for any soil constitutive model that includes a critical state line and which invokes stress dilatancy.