[Paper Review] A multi-phase thermo-mechanical model for rock-ice avalanche

Shiva P. Pudasaini|arXiv (Cornell University)|Apr 9, 2024

Landslides and related hazards10 citations

TL;DR

The paper develops a novel, physically-based multi-phase (rock-ice-fluid) thermo-mechanical model for rock-ice avalanches, deriving a general temperature equation and unified ice-melt formulation that couples heat transfer, ice melting, entrainment, and mass/momentum exchanges across rock, ice, and fluid phases.

ABSTRACT

We propose a novel multi-phase thermo-mechanical rock-ice avalanche model. It considers rock, ice and fluid; includes rigorously derived ice melt rate, melting efficiency dependent fluid production rate and a general temperature equation. It explains advection-diffusion of heat including heat exchange across the avalanche, basal heat conduction, production and loss of heat due to frictional shearing and changing temperature, and temperature enhancement due to entrainment. Temperature equation couples rates of thermal conductivity and temperature. Ice melt intensity determines these rates as mixture conductivity evolves, characterizing thermo-mechanical processes. The model includes interfacial mass and momentum exchanges and mass and momentum productions due to entrainment. The latter significantly changes the state of temperature; yet, the former characterizes the rock-ice avalanche. Phase mass and momentum balances and temperature are coupled. New model offers the first-ever complete dynamical solution for rock-ice avalanche with changing temperature and ice melting. We develop an advection-diffusion-decay-source model and its analytical solutions providing novel understanding of temperature evolution. The 2021 Chamoli event simulations with r$.$avaflow (https://www.landslidemodels.org/r.avaflow/) illustrate the functionality of thermo-mechanical rock-ice avalanche model. Four scenarios are considered: variations in ice-melt-efficiency; fraction of ice; ice and rock frictions; governing the process of melting, flow transformation, spreading and mobility. Ice melting designates the motion and explains the rock-ice avalanche mobility: a phenomenal thermo-mechanical play. Essentially different controls of ice and rock frictions on the state of flow mobility are revealed, explaining complex thermo-mechanical processes. This provides a useful method for practitioners and engineers in solving problems associated with rock-ice avalanches.

Motivation & Objective

• Motivate the need to model rock-ice avalanches as multi-phase systems with changing temperature.
• Derive a general, dynamically evolving temperature equation for the avalanche bulk mass.
• Incorporate ice melting, basal entrainment, and inter-phase mass/momentum exchanges into a unified model.
• Present depth-averaged closures for thermo-mechanical processes to enable practical simulations.

Proposed method

• Extend a multi-phase mass flow framework to include rock, ice, and fluid as three constituents.
• Derive and depth-average a general temperature equation with heat production and loss terms, including boundary heat exchange and basal conduction.
• Formulate frictional shear heating and ice-melt dissipation terms with depth-averaged closures.
• Derive two ice-melt mechanisms (frictional heating and temperature-change-driven melting) and propose a unified, linear combination for the total melt rate.
• Incorporate internal mass and momentum exchanges, entrainment from the bed, and a coupling between phase dynamics and temperature evolution.

Experimental results

Research questions

• RQ1 How can rock-ice avalanches be modeled as a truly three-phase system including temperature evolution?
• RQ2 What is a general, dynamically evolving temperature equation for the avalanching mass, and how does ice melting feed back into the dynamics?
• RQ3 How do frictional heating, boundary heat exchange, and entrainment influence the ice-melt rate and the overall thermo-mechanical state?
• RQ4 How can the Ice-melt rate be unified and embedded into the depth-averaged mass and momentum balances?
• RQ5 What are the key thermo-mechanical closures required to simulate rock-ice avalanches with changing temperature?

Key findings

• A novel multi-phase thermo-mechanical model that couples rock, ice, and fluid with a dynamically evolving temperature equation.
• A depth-averaged framework for advection-diffusion heat transport, including boundary heat exchange and basal conduction.
• A rigorously derived frictional heat production term and associated ice-melt rate, with a formal melt-dissipation mechanism tied to ice properties and shear.
• A unified ice-melt rate combining frictional heating and temperature-change effects through a linear mixing parameter.
• Demonstrates strong coupling between phase mass/momentum balances and the temperature equation, enabling a complete dynamical solution for rock-ice avalanche simulations.