Reply to “Discussion of “The relation between dilatancy, effective stress and dispersive pressure in granular avalanches” by P. Bartelt and O. Buser (DOI: 10.1007/s11440-016-0463-7)” by Richard Iverson and David L. George (DOI: 10.1007/s11440-016-0502-4)

Abstract

Iverson and George largely agree with our mathematical description of the dispersive pressure and dilatancy for a dry granular avalanche; however, they disagree with our views of effective stress and pore-fluid pressure in a debris flow containing solid granular material fully or partially submerged in a muddy fluid. Here we counter their concerns by deriving time-dependent relations for pore-fluid pressure in a two-component debris flow in which the solid phase is undergoing dilations and contractions. This analysis was not contained in our original paper. We explicitly show how the excess fluid pressure arises from dispersive accelerations associated with changes in configuration of the solid material. Additional contributions to the pore-fluid pressure are associated with the solid–fluid drag and buoyancy. In our analysis, we find that pore-fluid pressures can only be calculated (1) by modelling their time-dependent source, the frictional work rate, and (2) by accounting for the time-dependent inertial forces associated with the solid configuration’s center of mass. This leads to an alternative physical description of pore-fluid pressure, especially when the debris flow is far from equilibrium.