A Thermodynamically Consistent 3D Breakage Model Considering Intermediate Principal Stress for Granular Crushing Problems

Abstract

A thermodynamically consistent three-dimensional (3D) continuum breakage model was developed to study the effect of intermediate principal stress. Such an effect has been long overlooked in most existing constitutive models, which might result in a considerable difference in the strength estimation of crushable granular materials. Following basic thermodynamic laws, the proposed 3D breakage model was based on a new explicit mathematical expression of the original Matsuoka–Nakai failure criterion and 3D stress transformation. This proposed 3D breakage model was verified against the corresponding true triaxial constant-hydrostatic-pressure loading tests and true triaxial constant-minor-principal-stress loading tests of sand. The results confirmed that the proposed 3D breakage model accurately captures the effect of intermediate principal stress on granular crushing behaviors.