Avalanche side profile: slab stability and runout (2D)

Step 1: will the slab fail?

A slab of thickness h and density rho (plus new snow) lies on a weak layer on a slope of angle theta. The weight per area is W = g (rho h + rho_n h_n). Along the slope it pulls with shear stress W sin(theta) cos(theta). The weak layer resists with the Mohr-Coulomb strength c + W cos^2(theta) tan(phi), where c is cohesion and phi the friction angle. The safety factor is the ratio, FS = (c + W cos^2 theta tan phi) / (W sin theta cos theta). Below 1 the layer cannot carry the load and the slab releases. With no cohesion FS = 1 exactly at theta = phi, which is the first model check.

Step 2: how does the released snow move?

The released mass is treated as one block with the Voellmy-Salm equation dv/dt = g (sin theta - mu cos theta) - g v^2 / (xi h) along the path, where mu is dry Coulomb friction, xi a turbulent friction coefficient and h the flow depth. The speed grows until drag balances the downslope pull at the terminal speed sqrt(xi h (sin theta - mu cos theta)). On a flat enough slope friction wins and the block stops. The path is a smooth steep start zone that eases into a valley floor.

Angles and energy

The alpha angle is the slope of the straight line from the crown to the stopping point; the beta angle is the same line to the point where the path flattens to 10 degrees. Both are standard ways to describe how far avalanches run. Energy per kilogram is tracked: the potential energy lost equals kinetic energy plus the work of friction and drag, and the page prints the residual.

Honest simplifications

• One block with constant mass and flow depth: no snow entrainment, no dense core plus powder cloud physics, no spreading or channel width, no terrain roughness across the path.
• The weak layer is one uniform layer. Real slabs fail by crack propagation along the layer, which this safety factor does not model.
• The numbers show how the model behaves, they are not a prediction for any real slope. The chalet and the trees are inanimate scenery only.

Model checks on this page

(1) Zero-cohesion critical angle equals phi. (2) The numerical terminal speed matches the formula. (3) The numerical stopping distance matches the closed form (1/2k) ln(1 + k v0^2 / a) with k = g/(xi h). (4) Potential-energy drop equals kinetic energy plus friction and drag work along the run.