A multi-phase thermo-mechanical model for rock-ice avalanche

TL;DR

This work addresses the complexity of rock-ice avalanches by deriving a physically grounded, multi-phase thermo-mechanical framework that couples rock, ice, and fluid with a novel temperature evolution equation. It combines a general advection–diffusion–decay–source temperature model with depth-averaged closures, boundary heat exchange, frictional heating, and ice-melt processes to produce a ten-variable conservative system compatible with existing tools like $\text{r.avaflow}$. The authors provide both exact analytical solutions for a simplified temperature equation and comprehensive numerical realizations, including Chamoli 2021-based simulations across multiple scenarios to reveal how ice-melt efficiency, ice content, and friction modulate melting, flow transformation, and mobility. The model offers a new, physically consistent mechanism for predicting rock-ice avalanche behavior, with practical implications for hazard assessment and engineering planning in mountainous regions.

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.

Figures (9)

• Figure 1: Temperature evolution in rock-ice avalanche given by the solution (\ref{['Equation_AdvecDiffDecSource_Soln']}), involving: (A) Advection-diffusion, (B) advection-diffusion-decay processes, respectively. The top dotted-line segments indicate the actual positions of the 100 m long rock-ice mass propagating at the speed of $43.2$ md$^{-1}$.
• Figure 2: Temperature evolution in rock-ice avalanche given by the solution (\ref{['Equation_AdvecDiffDecSource_Soln']}): (A) Advection-diffusion, (B) advection-diffusion-source, (C) advection-diffusion-decay, (D) advection-diffusion-decay-source, respectively. The top dotted-line segments indicate the actual positions of the propagating rock-ice mass.
• Figure 3: Temperature evolution in rock-ice avalanche of length 100 m given by the solution (\ref{['Equation_AdvecDiffDec_Soln2']}), involving: (A) Advection-diffusion, (B) advection-diffusion-decay processes, respectively. The horizontal gray line represents the ambient temperature. Top dotted-line segments indicate the actual positions of propagating rock-ice mass.
• Figure 4: Temperature evolution in rock-ice avalanche given by the solution (\ref{['Equation_AdvecDiffDec_Soln2']}): (A) Advection-diffusion, (B) advection-diffusion-source, (C) advection-diffusion-decay, (D) advection-diffusion-decay-source, respectively. The horizontal gray line represents the ambient temperature. The top dotted-line segments indicate the actual positions of the propagating rock-ice mass.
• Figure 5: The control of ice-melt-efficiency $l_s$ on the dynamics, spreading and mobility of the rock-ice avalanche. Increased melt-efficiency results in enhanced flow spreading and mobility. $P_1, P_2, P_3$ indicate the actual rock, ice and fluid fractions with red, green and blue color maps. Also displayed are the corresponding reach time.