Analysis of wedge stability using different methods

Abstract

The stability problem of a rock slope containing a wedge resting on two intersecting discontinuities is of great interest in rock slope engineering. It is a statistically indeterminate problem with two extra unknowns according to the force (stress) equilibrium analysis. The widely used limit equilibrium methods in practice assume that the directions of the shear forces acting on the two discontinuities are parallel to their line of intersection. The validity of this assumption, however, has not been verified theoretically. This paper presents a general limit equilibrium method that determines the directions of the shear forces by using Pan's "Maximum principle" and an upper bound method that applies the classic upper bound theorem of limit analysis to avoid making extra assumptions. The formulations of the two methods are derived. A non-symmetric wedge and a symmetric wedge are analyzed using the two derived methods. To further explore the influence on stability due to the direction of the shear force acting on the two discontinuities, three-dimensional finite-element analyses are also conducted. The results are compared and discussed.