A five-parameter hydrodynamic-plastic model for crushable sand

Sand tends to dilate when sheared under small confining stresses, and compact under high stresses. This has been attributed to grain crushing, and associated with the development of a non-unique critical state in a stress-density space. This paper tackles a wide scope of crushable granular material phenomena that arise due to this interplay between crushing and dilation, by extending the recently proposed hydrodynamic-plastic formulation. The thermodynamic evolution of the state variables are defined by combining the mathematical frameworks of breakage mechanics, hypoplasticity and bounding surface plasticity. Accordingly, the model is distinguished from previous breakage models in that its stress-strain response is incrementally nonlinear, with possible plastic strain developing at any stress level. The model relies on only five mechanical constants which can be determined from typical geotechnical experiments. The predictions of the model are qualitatively compared against experimental tests under monotonic and cyclic compression and shear loading conditions, where it captures a broad range of sand phenomena.