A Model of Stability of Slopes

Abstract

A model of slope stability is presented using a non-homogeneous Bingham model. The constitutive parameters can be calibrated from in situ observations only (inclinometers). It is shown that the yield stress is varying nonlinearly with depth. An example is given. The case of possible slip at the bed rock is discussed. Introduction Gravitational creep flow of geomaterials as for instance slope movements, submarine landslides, snow avalanches, debris flow, volcanic lava flow, etc., has been studied by many authors. From the various aspects studied let as mention: deep-seated landslides at low strain rates (Petley & Allison [1997], Chiriotti [ 1999]), the study of the order of magnitude of the velocities of various land slides (Guzzetti [1998]), very large slope failures (Sousa & Voight, [1991]), snow slope stability during storms (Conway H., Wilbour C.[1999]), the influence of the water table depth on landslides velocity (Russo & Urciuoli [1999]), McDougall et a1.[1999]), to mention just a few. Several models have been used to describe landslides (Vulliet [1999]), the most successful seems to be the viscoplastic constitutive equation (Desai et al. [1995], Samtani et al. [1996]), or Bingham models (Liu & Mei [1989], Sousa & Voight [1991]). In the present paper the creep flow of a landslide is described starting from the idea that due to the gravitational forces the geomaterial compacts under its own weight. Thus, the mechanical properties of the layers vary with the depth. In particular the density and the yield stress are varying with depth. This is further analyzed to determine the depth where the sliding is incipient and the distribution with depth of the landslide velocity. k Graduate Research Professor, Dept. of Aerospace Engineering, Mechanics & Engineering Science, University of Florida, P.O.Box 116250, Gainesville, FI. 32611-6250. 86 SLOPE STABILITY 2000 87 Formulation of the problem Let us consider a stratum of thickness h inclined with the angle 0 to the horizontal (Fig.l). A geometrical deposited on this inclined slope will compact in