The accuracy of equilibrium methods of slope stability analysis

Abstract

Equilibrium methods of slope stability analysis all involve assumptions because the number of equilibrium equations available is smaller than the number of unknowns involved. Furthermore, a number of widely used methods do not satisfy all conditions of equilibrium, and thus do not employ all of the available equations of equilibrium. This paper discusses the inaccuracies which arise from these inevitable assumptions and these neglected conditions of equilibrium. Comparative analyses have shown that all of the methods which satisfy all conditions of equilibrium result in the same value of safety factor with an accuracy no worse than ± 5%, which is perfectly acceptable for practical purposes. Furthermore, within this range of accuracy, this may be considered to be the ‘correct’ answer. Bishop's modified method, which does not satisfy all conditions of equilibrium, has been found to be as accurate as the methods which do so, and thus to be an effective and simple means of analyzing circular slip surfaces. The ordinary method of slices, which satisfies only one condition of equilibrium, gives factors of safety which may be as much as 50% smaller than the correct value for flat slopes with high pore pressures. Force equilibrium procedures with ill-chosen side force assumptions may give factors of safety which are 30% larger than the correct value for slopes in cohesive soils. The results of the study show how equilibrium methods may be selected which avoid significant errors arising from the mechanics of the analysis, and thus allow the engineer performing the analysis to devote his attention and effort to correct evaluation of shear strength.