Three-dimensional stability of triple-step slopes considering diverse hydraulic hysteresis paths

The three-dimensional (3D) stability problem of triple-step slopes is important due to their unique profiles under natural rainfall conditions. In this paper, an innovative approach was proposed for rapidly evaluating the stability of triple-step slopes, which considers the effects of diverse hydraulic hysteresis paths caused by rainfall and drought alternation. Considering diverse hydraulic hysteresis paths, a 3D upper-bound analysis (UBA) mechanical model was developed. On this basis, a new analytical solution for the stability number (NS) of 3D slopes under the influence of hydraulic hysteresis was derived through the work and energy equation. The comparisons showed that the new analytical solution and proposed method are correct. Then, ranges of the controlling parameters of triple-step slopes were designed for practical use in slope engineering. Comprehensive discussions were presented, considering four distinct hydraulic hysteresis cases within the context of two typical scenarios involving silty and sandy soils. The results could provide a reference for the design and construction of triple-step slopes where rainy and drought conditions frequently alternate.