Gravitational stability computed through the limit equilibrium method revisited

Abstract

The stability of slopes is a problem of great relevance for geologists and geophysicists as well as for geotechnical and geoenvironmental engineers. The classical approaches are the method of limit equilibrium, and the finite-element and finite-difference analyses of deformations. Since the former is computationally simpler and less expensive, it is more widely used in common practice, though it has some weakness points from a theoretical point of view. Essential in this technique is the definition and computation of the factor of safety F for the slope, a parameter indicating that the slope is stable, if it is larger than unity. The method is known to have not a unique solution, but it is common belief that the safety factors associated with all the solutions fulfilling the basic equilibrium equations do not differ more than 5–10 per cent from each other, which is a range of variability considered acceptable by most. Here the non-uniqueness of the solution is discussed, and it is shown that the magnitude range of F can be so large as to undermine the meaning of the safety factor criterion. The classical limit equilibrium methods based on the assumptions of cutting the sliding body into a set of vertical slices are revised, and the new concept of minimum lithostatic deviation (MLD) is introduced as a means to mitigate the effect of non-uniqueness. The paper suggests that the proper solution to the problem is the one that satisfies the equilibrium equations and minimizes the lithostatic deviation that is defined here as the ratio of the average intensity of the interslice forces and the total weight of the body. Accordingly, the factor of safety F associated with such a solution is suggested to be the value appropriate to evaluate the stability of the slope. Remarkably, the MLD principle gives us the means to introduce a completely revolutionary approach to study stability. We derive expressions that account for gravitational loading, and for additional effects such as seismic loading and the overpressure due to the overlying water mass in case of underwater slopes.