A continuum mixture theory applied to stress waves in snow

Abstract

In avalanche control work the types of explosives and delivery methods used are primarily determined by trial and error. Understanding the propagation of stress waves in snow is a step towards eliminating some of this guesswork. A continuum theory of mixtures is applied to model snow as a mixture of an elastic solid and an elastic fluid. Three wave types, two dilational and one rotational wave are shown to exist. Theoretical expressions are developed for the wave attenuation and propagation velocity of each of the wave types. Numerical evaluation shows velocity and attenuation increasing with frequency for all three waves. Wave velocity increases with increasing density while attenuation decreases with increasing density for all three waves. The first dilational wave has a slow wave speed and is highly attenuated. This wave exhibits diffusive behavior at low frequencies and nondispersive behavior at high frequencies. The second dilation wave is the fastest of the three wave types and does not appreciably attenuate. Nondispersive wave behavior characterizes this wave at low and high frequencies. The rotational wave is the least attenuated of all three waves and propagates at velocities greater than that of the first dilational . wave but less than that of the second dilational wave. The rotational wave exhibits nondispersive behavior at low and high frequencies. Wave velocities and attenuation show behavior that is in agreement with existing experimental data.