Experiments and simulations on the mechanics of ice and snow

Abstract: We present experiments along with an approximate, semi-analytic, close-form solution to predict ice sintering force as a function of temperature, contact load, contact duration, and particle size during the primary stage of sintering. The ice sintering force increases nearly linear with increasing contact load but nonlinear with both contact duration and particle size in the form of a power law. The exponent of the power law for size dependence is around the value predicted by general sintering theory. The temperature dependence of the sintering force is also nonlinear and follows the Arrhenius equation. At temperatures closer to the melting point, a liquid bridge is observed upon the separation of the contacted ice particles. We also find that the ratio of ultimate tensile strength of ice to the axial stress concentration factor in tension is an important factor in determining the sintering force, and a value of nearly 1.1 MPa can best catch the sintering force of ice in different conditions. We find that the activation energy is around 41.4 KJ/mol, which is close to the previously reported data. Also, our results suggest that smaller particles are “stickier” than larger particles. Moreover, during the formation of the ice particles, cavitation and surface cracking is observed which can be one of the sources for the variations observed in the measured ice sintering force.We experimentally demonstrate the presence of a capillary bridge in contact between an ice particle and a smooth Aluminum surface at relative humidity around 50\% and temperatures below the melting point. We conduct the experiments in a freezer with a controlled temperature and consider the mechanical instability of the bridge upon separation of the ice particle from the Aluminum surface with a constant speed. We observe that a liquid bridge forms, and this formation becomes more pronounced as the temperature approaches the melting point. We also show that the separation distance is proportional to the cube root of the volume of the bridge. We use the volume of the liquid bridge to estimate the thickness of the liquid layer on the ice particle and show that the estimated value lies within the range reported in the literature. The thickness of the liquid layer decreases from nearly 56 nm at -1.7\(^{\circ}\)C to 0.2 nm at -12.7\(^{\circ}\)C. The dependence can be approximated with a power law, proportional to \({(T_M - T)}^{-\beta}\), where $\beta < 2.6$. We further observe that for a rough surface, the capillary bridge formation in the considered experimental conditions vanishes. Snow is a heterogenous, hot material which is constituted from ice particles. The bonding behavior of ice particles is an important parameter determining the macroscopic behavior of snow. Discrete Element Method (DEM) is usually used as a tool to model dry snow. The most important input data required into the DEM is bonding behavior of ice particles since ice particles can adhere to form bonds when they brought into contact. This study had two aims: first, an analytical formulation was derived to predict the bond diameter of ice-ice contacts as a function of time, compressive load, and strain rate. Using the previously published data for strain rate of ice, a solution method was developed. The results of bond diameter development with time were compared to experimental data and a good agreement was found. Second, a DEM for dry snow was developed and programmed in MATLAB and the developed bond model was employed in the simulation to study the deposition behavior of snow in a container under gravity acceleration. A specific beam element with implemented damage model was developed in implemented in the simulation using the bond data obtained from the analytical approach. The simulated parameters were macroscopic angle of repose, packing density, and surface conditions as a function of temperature and filling rate. The results showed that discrete element simulations were able to verify the existing published experimental data. Specifically, the simulation results showed that angle of repose of snow decreased rapidly with decreasing the temperature, the surface became very irregular due to the particles rotation and re-arrangement for lower falling speeds of particles, and density increased with depth of deposition. These findings were all matched with experimental observations.