Contact-dependent inertial number and μ(I) rheology for dry rock-ice granular materials

Abstract

To gain a deep understanding of the dynamics of dry rock-ice granular flows, the local rheology was investigated numerically. For mono-disperse granular materials, theoretically, the μ(I) rheology describes the relationship between the effective friction coefficient μ and inertial number I, and the solid volume fraction Φ depends linearly on the inertial number. The generality of these two relationships, however, remains unclear for the dry rock-ice granular materials that are dispersed in particle size, density, and surficial friction coefficient. This work numerically investigated the rock-ice mixtures flowing down a tilting flume using the discrete element method. A contact-dependent averaging method was proposed to determine the local inertial number integrating the contribution of all binary contacts. Moreover, a method was developed to predict the proportions of rock-rock, rock-ice, and ice-ice type of contacts, based on the coordination number. Specifically, the inter-phase coordination number ratio approaches the product of the inter-phase size and number ratios, enabling accurate predictions of contact proportions. The simulations demonstrate the numerical applicability of the μ(I) rheology and linear Φ(I) dependence to the bi- or poly-disperse dry rock-ice granular materials. Ice fragmentation significantly enhances the mixture mobility due to the increasing prevalence of ice-related contacts which exhibit lower friction. Compared with the commonly used volume-fraction averaged inertial number, the contact-proportion averaged inertial number incorporates local contact information, and its effect becomes more pronounced at higher size ratios and lower number ratios. These results underscore the importance of the particle dispersity of rock-ice granular materials, particularly in the case with substantial differences in particle size and number. The findings offer particle-scale insights for future research on friction and melting in rock-ice avalanches, while they need validation with experiments or field data.