Location of critical failure surface and some further studies on slope stability analysis

The search for critical failure surface of a general soil slope is difficult as the objective function of the factor of safety is non-convex and multiple minima exist in general. For this problem, the author proposes to use simulated annealing method and transforms the constraints of the problem to the determination of the dynamic upper and lower bounds of the control variables. The critical failure surface can then be located with high precision with reasonable computer time under the present proposal. The author has demonstrated that the proposed method is effective and efficient in analysis. Furthermore, the author has also proposed a double QR factorization method in the evaluation of factor of safety and has demonstrated that this new approach is much better in convergence.