Rock Avalanche Volume-Mobility Relation

If Heim's ratio were a friction coefficient it would be a property of the rock and would not care how much of it fell. Plot $H/L$ against volume for a few hundred documented rock avalanches and it cares a great deal: the cloud of points slopes downwards, and a straight line through it on log-log axes is the relation this page computes. Scheidegger fitted the classic version in 1973 (Rock Mechanics 5, 231) as $\log_{10}(H/L) = 0.62419 - 0.15666\log_{10}V$, with $V$ in cubic metres, which is the same thing as $H/L = kV^{-n}$ with $k = 4.209$ and $n = 0.157$.

Read what it says. At 10³ m³ the fit gives $H/L \approx 0.70$, a travel angle of 35°, which is simply the friction angle of broken rock — a small fall stops on its own talus. At 10⁶ m³ it gives 0.48. At 10⁷ it gives 0.34, and at 10⁹ it gives 0.17, a travel angle under 10°. The bigger the event, the less like friction it behaves, and by the largest sizes it is behaving three or four times more mobile than any coefficient of friction permits.

The scatter is the headline, not the line. Scheidegger's fit — and every regional fit made since — explains roughly half the variance in its own dataset and no more. Individual events sit a factor of two either side of the fitted $H/L$, and a factor of two in $H/L$ is a factor of two in runout distance. What is missing from the equation is most of what actually governs the event: whether the path was confined in a valley or spread across an open slope, what the mass ran over, how wet it was, how far it fell before it started travelling, whether it ran onto a glacier. A single power law through a point cloud spanning eight orders of magnitude in volume is a description of a trend. It is not a prediction of an event.

Two arithmetic traps are worth naming. First, the coefficient $k$ is convention-bound and is not a dimensionless constant: since $H/L$ is a ratio and $V$ is a volume, $k$ carries dimensions of length to the power $3n$, and its numerical value depends entirely on the volume unit the fit was made in. Every published value assumes cubic metres. Taking a coefficient from a paper that worked in cubic kilometres and using it with a volume in cubic metres is a silent error of many orders of magnitude, and the answer will not look obviously absurd. Second, inverting the relation for volume is arithmetically trivial and epistemically hopeless. The exponent is about 0.157, so the inverse exponent is about 6.4, and a 10 % error in $H/L$ becomes a factor of 1.9 in volume. Since real events scatter by a factor of two in $H/L$ anyway, a volume back-figured this way is uncertain by well over an order of magnitude.

And the mechanism behind the trend remains unexplained. Acoustic fluidisation, basal air-layer lubrication, self-lubrication by dynamic fragmentation, mechanical fluidisation in a dense granular flow, and undrained loading of entrained saturated substrate have all been proposed, each is supported by some events and contradicted by others, and none is settled. That is not a gap this page fills, and picking a winner would misrepresent the state of the subject.

This is a planning tool, not permission. A ratio from a power law does not define a safe location. Use it to bound an order of magnitude and to sanity-check a modelled runout. Hazard mapping is the job of a qualified practitioner with local event records.