A critical state based viscoplastic model for crushable granular materials

Experimental studies have confirmed that the critical state of a granular material varies with alteration in granular fabric, particle shape and grain size. On the other hand, granular materials demonstrate significant strain rate dependency in the presence of particle crushing. While the first feature is well explored, the strain rate effects on the crushability of granular material and consequent critical state alteration are less ventured. This study highlights the strain rate dependence of the critical state of crushable granular materials like sand. A rate-dependent model is proposed bridging the macro and microscopic understanding. The model follows a consistent viscoplastic formulation without using any overstress function. The proposed model considers various loading rate effects at different porosities, confinements and pore water drainage conditions. Further, it can predict the strain rate-dependent particle crushing and dilation features that affect the critical state of granular materials. The model has been validated by comparing its responses with both the experimental and discrete particle simulations for drained and undrained triaxial conditions. An implicit stress return integration scheme is devised to enable accurate numerical response from the model.  Finally, a parametric study is presented that envisages the evolution of critical state due to coupled strain rate and particle crushing effect.