Stability assessment of soil slopes in three dimensions: The effect of the width of failure and of tension crack

Abstract

This paper investigates the effect of the width of failure and tension crack (TC) on the stability of cohesive-frictional soil slopes in three dimensions. Working analytically, the slip surface and the tension crack are considered to have spheroid and cylindrical shape respectively, although the case of tension crack having planar, vertical surface is also discussed; the latter was found to return higher safety factor values. Because at the initiation of a purely rotational slide along a spheroid surface no shear forces develop inside the failure mass, the rigid body concept is conveniently used; in this respect, the validity of the rigid body concept is discussed, whilst it is supported by comparison examples. Stability tables are given for fully drained and fully saturated slopes without TC, with non-filled TC as well as with fully-filled TC. Among the main findings is that, the width of failure corresponding to the minimum safety factor value is not always infinite, but it is affected by the triggering factor for failure (e.g., water acting as pore pressures and/or as hydrostatic force in the TC). More specifically, it was found that, when a slope is near its limit equilibrium and under the influence of a triggering factor, the minimum safety factor value corresponds to a near spherical failure mechanism, even if the triggering factor (e.g., pore-water pressures) acts uniformly along the third dimension. Moreover, it was found that, the effect of tension crack is much greater when the stability of slopes is studied in three dimensions; indeed, safety factor values comparable to the 2D case are obtained.