The authors of this paper have previously, in 1987, outlined the development of a set of constitutive equations representing the behaviour of avalanching snow, and the resulting equations for fully developed steady shear flow. The present paper considers the development of non-steady two-dimensional shear flow together with the use of a finite-difference programme to calculate snow-avalanche velocities and flow heights in the run-out zone. The numerical results thus obtained are compared with full-scale experimental data. These comparisons indicate that front velocity and run-out distance are simulated well by the model, and that the predicted snow deposits are fairly well in agreement with those actually observed.
The authors of this paper have previously, in 1987, outlined the development of a set of constitutive equations representing the behaviour of avalanching snow, and the resulting equations for fully developed steady shear flow. The present paper considers the development of non-steady two-dimensional shear flow together with the use of a finite-difference programme to calculate snow-avalanche velocities and flow heights in the run-out zone. The numerical results thus obtained are compared with full-scale experimental data. These comparisons indicate that front velocity and run-out distance are simulated well by the model, and that the predicted snow deposits are fairly well in agreement with those actually observed.
This paper explores the computational problem of finding suitable numbers to use in a two-parameter model of snow avalanche dynamics. The two parameters are friction, μ, and a ratio of avalanche mass to drag, M/D. Given a path profile, and a maximum avalanche speed, then it is possible to compute unique values for u and M/D. If only the path profile and the stopping position are known, then it is possible to compute tables of pairs {μ, M/D} which can be tested as predictors of avalanche speeds. To generate these tables it is convenient to scale M/D in multiples of the total vertical drop of the path. The computations were tested on 136 avalanche paths. Values of {μ, M/D} were stratified, and certain values were rejected as unrealistic.
Two models simulating snow avalanches impacting retaining dams at oblique angles of incidence are presented.First, a lumped-mass model applying the Voellmy-Perla equation is used to calculate the path of the centre-of-mass along the side of a retaining dam.Secondly, a one-dimensional continuum model, applying depth-integrated equations of balance of mass and linear momentum, is expanded to take into account that real avalanche flows are three-dimensional. The centre-line of the avalanche path is determined by the flowing material as it progresses down the channelized avalanche path. The nonlinear constitutive equations comprise viscosity, visco-elasticity and plasticity.Both models are calibrated by simulations of a registered avalanche following a strongly curved channel. The path and the run-up height of the avalanche on the natural deflecting dam with oblique angle of incidence as calculated by the two models, are compared with the observations made.
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