Cohesion and friction angle are reduced by the same amount in the traditional strength reduction method

and the reduction parameter at the critical state of the slope is considered as the safety factor of this slope. Thus

the strength reduction method based on single reduction parameter is defined as equivalent proportional reduction method. For a target slope with the certain slope configuration and rock density

the combination of cohesive and friction coefficient

at which the slope is at the critical state

is not unique. The strength reduction by the same amount is simply one of possible choice

but not necessarily the best one. Based on the above understanding

the - critical state curve is first established under different slopes shapes and rock mass densities; then it is proposed that cohesive and friction coefficient are reduced along the short path from the current coordinate of strength parameter to - critical state curve

and a scheme of matching reduction is proposed; finally

the difference between these two reduction methods is analyzed through three examples. The results show the critical states of equivalent proportional reduction method and double reduction method are not the same

the range of the former is larger than the that of the latter