A hydrodynamic-plastic formulation for modelling sand using a minimal set of parameters

Abstract

Conventional plasticity models follow rich mathematical formulations. However, they typically lack a physical basis, so their predictive quality is strongly correlated with the number of fitting parameters used. More recent hydrodynamic principles inject physical clarity by separating scales using distinct thermal and granular temperatures. However, existing hydrodynamic models also require many parameters to reproduce a wide variety of experimental observations. This paper combines the advantages of these two approaches to construct a new physics-based hydrodynamic-plasticity model formulation, which is comprehensively predictive. An illustrative model is developed that relies on only five parameters, all of which have been previously defined and calibrated. Four parameters are easily determined from common geotechnical experiments and address diverse rate-independent phenomena, including pressure and density dependent elasticity, pressure- and density-dependent dilation behaviours, critical state relationships under continuous shearing, liquefying cyclic hystereses, and initial stress-ratio dependent extensional shear response. The one remaining parameter enables the recovery of the rate-dependent rheology of friction and density during steady flow, as well as material response during transient loading. A key feature that further distinguishes the current formulation from previous hydrodynamic ones is that here granular temperature is being related to the measurable kinetic pressure.