Realization of Pan Jiazheng′s extremum principle with optimization methods

Slope stability analysis based on the limit equilibrium method is statically indeterminate,which requires various assumptions to evaluate the factor of safety. The interslice force function f (x) is a major assumption that is important but is not adequately considered in the past. The authors propose that the factor of safety and the interslice force function can be determined in accordance with the Pan Jiazheng′s extremum principle from an optimization analysis. For any prescribed failure surface,the interslice force function f ( xi)is taken as the control variable;and the maximum factor of safety will be computed by tuning function f ( xi)with the simulated annealing method,which is actually equivalent to a lower bound approach. For locating the critical failure surface, the particle swarm or the harmony method is used,which is an upper bound approach. In addition,the problem of convergence in evaluating the factor of safety is investigated;and it is demonstrated that interslice force function f (x) cannot be arbitrarily assigned if consistent and acceptable internal forces are required. The presented approach has a further advantage that convergence during the stability analysis is greatly reduced which is not possible with all the other existing"rigorous"methods,and an interslice force function is not required in the analysis.