Slider-Block Friction Model for Landslides: Implication for Prediction of Mountain Collapse

Accelerating displacements preceding some catastrophic landslides has been found empirically to follow a time-to-failure power law, corresponding to a finite-time singularity of the velocity v ∼ 1/(tc − t) [Voight, 1988]. Here, we provide a physical basis for this phenomenological law based on a slider-block model using a state and velocity dependent friction law established in the laboratory and used to model earthquake friction. This physical model accounts for and generalizes Voight’s observation: depending on the ratio B/A of two parameters of the rate and state friction law and on the initial frictional state of the sliding surfaces characterized by a reduced parameter xi, four possible regimes are found. Two regimes can account for an acceleration of the displacement. For B/A > 1 (velocity weakening) and xi < 1, the slider block exhibits an unstable acceleration leading to a finite-time singularity of the displacement and of the velocity v ∼ 1/(tc − t), thus rationalizing Voight’s empirical law. An acceleration of the displacement can also be reproduced in the velocity strengthening regime, for B/A < 1 and xi > 1. In this case, the acceleration of the displacement evolves toward a stable sliding with a constant sliding velocity. The two others cases (B/A < 1 and xi < 1, and B/A > 1 and xi > 1) give a deceleration of the displacement. We use the slider-block friction model to analyze quantitatively the displacement and velocity data preceding two landslides, Vaiont and La Clapière. The Vaiont landslide was the catastrophic culmination of an accelerated slope velocity. La Clapière landslide was characterized by a strong slope acceleration over a two years period, succeeded by a restabilizing phase. Our inversion of the slider-block model on these data sets shows good fits and suggest to classify the Vaiont (respectively La Clapière) landslide as belonging to the velocity weakening unstable (respectively strengthening stable) sliding regime. We cannot however exclude that La Clapière might also belong to the unstable velocity weakening regime; its deceleration observed after 1988 may then be interpreted as a change of surface properties that modifies the friction law parameters. For the Vaiont landslide, this model provides good predictions of the critical time of failure up to 20 days before the collapse. Tests are also presented on the prediction of the time of the change of regime for la Clapière landslide.