In the coordinate system of strength parameters

utilizing the concept of strength reserve area can deduce the FOS expression of double reduction method (DRM)

which is more rational than several existing expressions

and the results do not have enormous deviations from results of existing expressions. In this new method

for the same K

adopting different mathematical expressions gets different virtual initial points. There are two approaches that are based on the ratio of reduction. The first approach only adjusts tan?

and the other only adjusts friction. In theory

these two reduction paths are different. However

this research shows that the difference has no influence on results of DRM

and selecting the shortest reduction path can reduce calculation time. The reduction strategy of traditional strength reduction method (SRM) is different from double reduction method. In DRM result

the critical friction and cohesion appear in such a way that critical friction is over initial friction

or critical cohesion is over initial cohesion

which is not reasonable. By analyzing DRM calculation results given various K

and focusing on the essence of strength reduction method to get two types of results. The first type result is the result that has to conform to calculation accuracy

and the other result is that the result has to align with the fact that critical points must embody the phenomenon of parameters of the weakening.