Evaluation of Interslice Force Function and Discussion on Convergence in Slope Stability Analysis by the Lower Bound Method

The interslice force function $f\left(x\right)$ is a major assumption of the limit equilibrium method, which is important but has not been adequately considered in the past. In this paper, $f\left(x\right)$ is taken as the control variable, and the upper and lower limits of the factor of safety for a general slope will be determined by a global optimization analysis. Based on this approach, $f\left(x\right)$ will be determined and investigated. We demonstrate that $f\left(x\right)$ cannot be arbitrarily assigned if a set of acceptable internal forces is required. The present approach can be presented practically as a lower bound approach with the advantage that failure to converge is virtually eliminated, which is not possible with all other existing “rigorous” methods. The “present proposal” attempts to answer several important questions in the basic theory of slope stability analysis, and provides a $f\left(x\right)$ based on the lower bound approach statically admissible forces throughout the whole failure zone. Currently, different assumptions will give different factors of safety to the same problem, and this situation will be overcome by the use of the present proposal. The present proposal is also proven to give a result equal to the slip line solution for a simple footing on clay which is not possible for other classical slope stability methods, which has demonstrated that the applicability of the “present proposal” for general difficult problems.