Slider block friction model for landslides: Application to Vaiont and La Clapière landslides

Authors

  • A. Helmstetter,

    1. Laboratoire de Géophysique Interne et Tectonophysique, Observatoire de Grenoble, Université Joseph Fourier, Grenoble, France
    2. Now at Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA.
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  • D. Sornette,

    1. Laboratoire de Physique de la Matière Condensée, CNRS UMR 6622 and Université de Nice-Sophia Antipolis, Nice, France
    2. Department of Earth and Space Sciences, University of California, Los Angeles, California, USA
    3. Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA
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  • J.-R. Grasso,

    1. Laboratoire de Géophysique Interne et Tectonophysique, Observatoire de Grenoble, Université Joseph Fourier, Grenoble, France
    2. Now at U.S. Geological Survey, Western Region Earthquake Hazards Team, Menlo Park, California, USA.
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  • J. V. Andersen,

    1. Laboratoire de Physique de la Matière Condensée, CNRS UMR 6622 and Université de Nice-Sophia Antipolis, Nice, France
    2. U. F. R. de Sciences Economiques, Gestion, Mathématiques et Informatique, CNRS UMR7536 and Université Paris X-Nanterre, Nanterre, France
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  • S. Gluzman,

    1. Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA
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  • V. Pisarenko

    1. International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Science, Moscow, Russia
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Abstract

[1] Accelerating displacements preceding some catastrophic landslides have been found to display a finite time singularity of the velocity v ∼1/(tct) [Voight, 1988a, 1988b]. 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. 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/(tct), 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 other 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 restabilization. Our inversion of the slider block model in these data sets shows good fits and suggests a classification of the Vaiont landslide as belonging to the unstable velocity-weakening sliding regime and La Clapière landslide as belonging to the stable velocity-strengthening regime.

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