Slider-Block Friction Model for Landslides: Application to Vaiont and La Clapière Landslides

Accelerating displacements preceding some catastrophic landslides have 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 peak of slope acceleration that followed decades of ongoing accelerating displacements, 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.