Research on a two-parameter reduction method that strictly satisfies the upper and lower limit theorem

The traditional strength reduction method (SRM) uses a single reduction parameter to reduce the cohesion (c) and friction coefficient (tanφ) of a slope. However, this paper develops a new SRM using two different reduction parameters to reduce c and tanφ, by which the critical state of the slope can strictly simultaneously satisfy the upper and lower limit theorem. First, two types of critical state curves (CSCs) are established based on the upper and lower limit theorems, respectively, which are used to depict the sufficient conditions for the slope in the critical state. The intersection of two CSCs is considered the most appropriate combination of c/γH and tanφ to lead a slope to the critical state. Second, it is supposed that the most appropriate reduction path is that c and tanφ are reduced towards the intersection of two CSCs. Finally, the differences between the traditional SRM and the proposed method are discussed by analysing five examples with different slope angles. The results show that the potential sliding area of the slope acquired by the proposed method is larger than those obtained from the traditional SRM. The sliding surface of the slope at the critical state acquired by the proposed method can preferably represent the drawing open surface of the back edge. Thus, the traditional SRM may underestimate the sliding range of a slope.