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

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.