Important aspects in the formulation of solid–fluid debris-flow models. Part II. Constitutive modelling

Abstract

The intention is to see whether (i) well-known formulations of binary mixture models can be derived from the thermodynamic model, (ii) classical hypo-plasticity is deducible from the frictional evolution equation and (iii) the popular assumption of pressure equilibrium is justified. To this end, we ignore mass and volume fraction interaction rate densities, restrict considerations to isothermal processes, ignore higher order non-linearities in the constitutive relations and use the principle of phase separation. These assumptions transform the equilibrium stresses, heat flux and interaction forces to considerably simplified forms. Furthermore, the analysis shows that classical hypo-plasticity can be reconstructed with the introduction of a new objective time derivative for the stress-like variable. Non-equilibrium contributions to the stresses and interaction forces are also briefly discussed. It is, finally, shown that the assumption of pressure equilibrium precludes the application of frictional stresses in equilibrium. This unphysical assumption is, therefore, replaced by a thermodynamic closure condition that is more flexible and less restrictive. It allows for frictional stresses in thermodynamic equilibrium and, therefore, is sufficiently general for applications to mixture theories.

A general two‐phase debris flow model

“…There is a significant need for reliable methods for predicting the dynamics, runout distances, and inundation areas of such events. Debris flows are multiphase, gravity‐driven flows consisting of randomly dispersed interacting phases [ O'Brien et al , 1993; Hutter et al , 1996; Iverson , 1997; Iverson and Denlinger , 2001; Pudasaini et al , 2005; Takahashi , 2007; Hutter and Schneider , 2010a, 2010b]. They consist of a broad distribution of grain sizes mixed with fluid.…”

On Objectivity, Irreversibility and Non-Newtonian Fluids

“…They also have emerged as important constraints in other areas of fluid mechanics usually not considered to be non-Newtonian. Moreover, as noted by Hutter and Rajagopal [4], and Hutter and Schneider [5,6] both principles play complimentary roles in constraining constitutive equations.…”

Lie symmetry solutions for two-phase mass flows

“…Significant research in the past few decades has focused on different aspects of two-phase debris avalanches and debris flows [2][3][4][5][6][7][8][9][10] which was recently advanced in a comprehensive theory that accounts for the different interactions between the solid particles and the fluid [1]. This model includes several fundamentally important and dominant physical aspects, including the enhanced non-Newtonian viscous stress, the virtual mass, and the generalized drag.…”

“…Gravity mass flows and gravity currents, including avalanches, debris flows, debris floods, floods, and water waves, play important role both in environment, geophysics and engineering [2][3][4][5][6][7][8][9][10][11][12]. Debris flows are extremely destructive and dangerous natural hazards, so there is a need for reliable methods for predicting the dynamics, runout distances, and possible areas hit by such events.…”