In the classic strength reduction method (SRM)

there is only one strength reduction parameter which can be proved to be equal to the definition of factor of safety (FOS) by strength reservation. Some double reduction methods (DRM)

in which distinct reduction parameters are used for friction angle and cohesion force

have been presented by researchers. In this paper

a new basis is established to support the rationality of the double reduction methods

and also a specific definition of FOS is built for a recently presented DRM by the authors. A comparison is made between the DRM and the SRM through rigid mathematical proving

which shows that the FOS of the DRM is almost always smaller than that of the classic SRM. This conclusion is verified by four numerical examples. The research shows that the possibility that the classic strength reduction method (SRM) may overestimate the safety of a slope exists. It is advised that the presented DRM be adopted as an additional option in the slope stability evaluations although more application experience is expected.