A model for frictional melt production beneath large rock avalanches

Two puzzling traits of giant rock avalanches (sturzstroms) are the decrease of the effective friction coefficient as a function of the volume (volume effect) and the remarkable preservation of large geological structures during the flow, demonstrating that the upper cap of a sturzstrom travels coherently on top of a basal shear layer. Hence, frictional heat is rapidly produced along the shear layer, which could explain the formation of sheets of molten rock inside certain landslide deposits. It has been conjectured that a molten layer could potentially self-lubricate the base of the sturzstrom. To theoretically investigate this scenario, we consider the model of a rock slab sliding on an inclined surface. We present a set of coupled differential equations to calculate the frictional heat produced, the properties of the molten layer (thickness, temperature, and velocity distribution), and the motion of the slab. Our simulations illustrate the onset of self-lubrication and show the volume effect when the melt viscosity is low, corresponding to a simulated mafic composition of the rock. For a felsic composition (and to some extent also for intermediate melts) we find that the melting introduces more resistance at the beginning of the melting process, in close similarity with frictional melting in tectonic faults. However, in contrast to faults, the rock avalanche is capable of overcoming the initial resistance in at least two situations: if the rock is rigid and the landslide is sufficiently thick or else if the material of the landslide is disintegrated. The simulations also show that although self-lubrication is a viable possibility to explain the runout of sturzstroms, there are rather stringent conditions for the formation of a molten layer of good lubricating qualities. More generally, we suggest that the properties of the Coulomb frictional law at the interfaces may change radically during sliding and that the assumption of constant friction does not represent a good model in landslide calculations.