A mechanical model for phase separation in debris flow

Abstract

Understanding the physics of phase-separation between solid and fluid phases as a mixture mass moves down slope is a long-standing challenge. Here, we propose an extension of the two phase mass flow model (Pudasaini, 2012) by including a new mechanism, called separation-flux, that leads to strong phase-separation in avalanche and debris flows while balancing the enhanced solid flux with the reduced fluid flux. The separation flux mechanism is capable of describing the dynamically evolving phase-separation and levee formation in a multi-phase, geometrically three-dimensional debris flow. These are often observed phenomena in natural debris flows and industrial processes that involve the transportation of particulate solid-fluid mixture material. The novel separation-flux model includes several dominant physical and mechanical aspects such as pressure gradients, volume fractions of solid and fluid phases and their gradients, shear-rates, flow depth, material friction, viscosity, material densities, topographic constraints, grain size, etc. Due to the inherent separation mechanism, as the mass moves down slope, more and more solid particles are transported to the front and the sides, resulting in solid-rich and mechanically strong frontal surge head, and lateral levees followed by a weaker tail largely consisting of viscous fluid. The primary frontal solid-rich surge head followed by secondary fluidrich surges is the consequence of phase-separation. Such typical and dominant phase-separation phenomena are revealed for two-phase debris flow simulations. Finally, changes in flow composition, that are explicitly considered by the new modelling approach, result in significant changes of impact pressure estimates. These are highly important in hazard assessment and mitigation planning and highlight the application potential of the new approach.

A Multi‐Phase Mass Flow Model

“…Interactions with the basal sliding surface and with water bodies are most relevant for rapid gravity-driven mass flows. Even though advanced approaches to dynamically simulate entrainment and also deposition do exist in theory (Pudasaini & Fischer, 2016a), they still have to be implemented in r.avaflow (Mergili et al, 2017) in a way to also be suitable for real-world applications. Erosion of the bed materials enters the mass and momentum balance equations as additional mass and momentum production terms on the right-hand sides of (13a)-(13c) and (14a)-(14c), respectively.…”

“…Erosion of the bed materials enters the mass and momentum balance equations as additional mass and momentum production terms on the right‐hand sides of and , respectively. Thereby, nonlinear coupling and feedback mechanisms accounting for erosion, deposition, phase‐separation, and particle sorting should be considered (Conway et al, ; de Haas et al, ; Johnson et al, ; Major & Iverson, ; McArdell et al, ; Pudasaini & Fischer, ; Schneider et al, ; Steinkogler et al, ). Phase transformations are important aspects. Theoretical concepts do exist also for transformations between phases (see, e.g., Pudasaini & Krautblatter, ).…”

“…One‐ and two‐phase models serve for various purposes but cannot appropriately represent many important aspects of very complex mass flows in terms of material composition. The rheological properties and flow dynamics are governed by both coarse and fine solids, and viscous fluid, that is, typically three phases (de Haas et al, , ; Iverson, ; Kowalski & McElwaine, ; Pierson, , ; Pudasaini & Fischer, ). Consequently, the most complex model family for geophysical mass flows should aim at describing the flow as (typically or ideally) a three‐phase mixture, as often observed in the field and experiments (Conway et al, ; de Haas & van Woerkom, ; de Haas et al, , ; Iverson, ; Johnson et al, ; Major & Iverson, ; McArdell et al, ; Schneider et al, ; Steinkogler et al, ).…”

Granular flow on a rotating and gravitating elliptical body

“…Recent works (Maurel et al 2017;Chujo et al 2018) show that mechanisms leading to inverse grading remain active on small bodies, but their efficacy in retaining this structure in flowing conditions is not yet known. In this context, we mention the recent separation-flux model of Pudasaini & Fischer (2020). This model overcomes the shortcomings of previous works in that it does not presume inverse grading, does not require grains with similar material properties and makes no assumptions about the bulk velocity.…”

A mathematical framework for modelling rock–ice avalanches

“…Drahun & Bridgwater (1983), Iverson (1997), Gray & Thornton (2005), Johnson et al. (2012) and Pudasaini & Fischer (2020)). More precisely, the mathematical approaches derived applying the isokinetic condition to rock and ice (PI-RIW, TP-RIW) can simulate the phase separation, but not the phenomenon of segregation.…”