The relation between dilatancy, effective stress and dispersive pressure in granular avalanches

Abstract

Here we investigate three long-standing principles of granular mechanics and avalanche science: dilatancy, effective stress and dispersive pressure. We first show how the three principles are mechanically interrelated: Shearing of a particle ensemble creates a mechanical energy flux associated with random particle movements (scattering). Because the particle scattering is inhibited at the basal boundary, there is a spontaneous rise in the center of mass of the particle ensemble (dilatancy). This rise is connected to a change in potential energy. When the center of mass rises, there is a corresponding reaction at the base of the flow that is coupled to the vertical acceleration of the ensemble. This inertial stress is the dispersive pressure. Dilatancy is therefore not well connected to effectivestress-type relations, rather the energy fluxes describing the configurational changes of the particle ensemble. The strict application of energy principles has far-reaching implications for the modeling of avalanches and debris flows and other dangerous geophysical hazards.

Comments on avalanche flow models based on the concept of random kinetic energy

“…Recently, applied their approach to debris flows. We chose not to include that paper in the present discussion because Iverson and George (2016) already provided a concise critique of the way the authors use the notions of excess pore pressure and particle-fluid interactions.…”

“…These papers can be characterised briefly as follows (we will refer to them henceforth as [I]–[VII]): Buser and Bartelt (2009) [Production and decay of RKE in granular snow avalanches] introduce the notion of RKE, propose a balance equation for it and fit the model to experimentally observed velocity profiles. They also indicate an exponential dependence of Voellmy's friction parameter μ on RKE. The RKE dependence is extended to g / ξ by Bartelt and Buser (2010) [Frictional relaxation in avalanches], who also discuss a number of conceptual issues. Bartelt and others (2011) [Snow avalanche flow-regime transitions induced by mass and RKE fluxes] reduce the model sketched in [II] to a block model that can be described by ordinary differential equations and study its properties as a dynamical system (fixed points, stability, flow in phase space) in detail. In this paper, [Modelling mass-dependent flow-regime transitions to predict the stopping and depositional behaviour of snow avalanches], Bartelt and others (2012) formulate the model from [II] as a depth-averaged model, solve it numerically and test it against a number of full-scale experiments. In order to account for avalanche volume expansion due to particle collisions, Buser and Bartelt (2011) [Dispersive pressure and density variations in snow avalanches] develop equations for the vertical motion of the centre-of-mass of a control column in the avalanche under the action of what they call dispersive pressure. Extending the approach in [V], Buser and Bartelt (2015) [An energy-based method to calculate streamwise density variations in snow avalanches] supplement the model from [IV] with three further conservation equations connected to dispersive pressure. Bartelt and others (2016) [Configurational energy and the formation of mixed flowing/powder-snow and ice avalanches] equip the model introduced in [VI] with a second layer for the powder-snow cloud and propose that the latter is formed by intermittent ejection of a mixture of fine snow grains with air from the dense core. Recently, Bartelt and Buser (2016) applied their approach to debris flows. We chose not to include that paper in the present discussion because Iverson and George (2016) already provided a concise critique of the way the authors use the notions of excess pore pressure and particle–fluid interactions.…”

“…Readers familiar with the literature on snow avalanche dynamics should note that the same term was used a quarter century earlier by Norem and others (1987, 1989) to designate the (always positive) pressure due to particle collisions. Iverson and George (2016) also discuss the notion of dispersive pressure in the context of a follow-up paper by Bartelt and Buser (2016) on debris-flow modelling. Configuration energy : This is a central notion in [VI]. It is otherwise probably most often used in the context of atomic and many-body physics, where it describes the potential energy of the system due to the mutual interactions between its components (usually by means of electromagnetic forces).…”

“…Readers familiar with the literature on snow avalanche dynamics should note that the same term was used a quarter century earlier by Norem and others (1987, 1989) to designate the (always positive) pressure due to particle collisions. Iverson and George (2016) also discuss the notion of dispersive pressure in the context of a follow-up paper by Bartelt and Buser (2016) on debris-flow modelling.…”

A dilatant, two-layer debris flow model validated by flow density measurements at the Swiss illgraben test site

“…3. Because the configuration of the particles in the dilated volume defines the potential energy D, we sometimes refer to the energy D as the configurational energy of the debris flow [28][29][30]. Importantly, we are making the following physical assumption: the potential energy is associated with the buoyant weight of the solid particles immersed in the inter-granular fluid.…”