The optimal upper-bound solution for factor of safety of slope by linear programming

A new method is proposed for determining the optimal upper-bound solution for the factor of safety of a slope based on linear programming. Unlike the conventional limit analysis, which directly searches the lowest value of factor of safety by using complicated nonlinear optimization procedure, this method chooses the horizontal seismic coefficient as the objective function and the normal stresses acting upon the slip surface as the unknown variables. The constraint conditions are established based on the force equilibrium condition and the failure criterion both on the interslice surfaces and on the slip surface. With a prescribed value of factor of safety, both the objective function and constraints are linearly related to the unknown variables; thus, the linear programming can be adopted for determining the largest value of horizontal seismic coefficient along with the optimal combination of the sliding mechanism. By use of an iterative procedure, the minimal upper-bound solution of factor of safety is finally obtained with the actual value of horizontal seismic coefficient.