In view of the continuous deterioration of strength parameters of rock and soil during the progressive failure of slope

the strain-softening model

instead of the traditional ideal plastic model

was applied. An improved vector sum algorithm

which considers the tensile-shear progressive failure

was proposed in this paper. Both the safety factor expression and the method of searching the most dangerous sliding surface were studied. Based on vector characteristics of sliding and force

the sliding trend and safety factor expression of vector sum were improved. Moreover

the most dangerous sliding surface of slope was searched based on the improved adaptive genetic algorithm. Results of several case studies show that

when the strain-softening model was adopted

the safety factor based on the definition of vector sum and the most dangerous sliding surface shape have dynamic changes and adjustment characteristics. The proposed algorithm in this paper

which is based on the tensile-shear strain softening model

expands analytic methods of slope vector sum to a certain extent.