Rapid dry granular flows down an incline: a constitutive theory with an independent kinematic internal length

Abstract

Rapid, isothermal, gravity-driven dry granular flows with incompressible solid grains down an incline are investigated by the thermodynamically consistent constitutive model. To this end, the revised Goodman-Cowin theory is applied for the time evolution of the volume fraction, in which a kinematic internal length is introduced. The Müller-Liu entropy principle is carried out to derive the equilibrium constitutive models, with their dynamic responses postulated in the context of a quasi-static theory. Numerical simulations show that both the volume fraction and velocity increase from the minimum values on the plane toward the maximum values on the free surface with an ''exponential-like'' tendency, while the internal length increases in a logarithmic manner. With the equilibrated stress system in the revised Goodman-Cowin theory, the kinematic internal length is recognized as a characteristic length of the long-term enduring frictional contact and sliding between the grains (a characteristic length of the inelastic network among the grains).