Characterizing the Shape Effect and Stability Coefficient of an Embankment under an S-Shaped Gully

The embankment of an S-shaped gully (E-SSG) has a specific topography, which results in its unique shape effect. However, how the shape effect of the E-SSG is generated, how it relates to different geometric variables, and how it can be considered in slope stability analysis remain unknown. Hence, this study examined this shape effect using the finite-element strength reduction method to analyze the spatial stress and displacement distribution. In addition, the gray correlation method was introduced to determine the link between the shape effect and the terrain factors. Furthermore, the shape effect within the steep slope of an E-SSG was considered and a dimension-reduced (DR) slope stability analysis technique was proposed. Upon obtaining the link between the shape effect and the terrain factors, the shape effect factor ψ can be calculated. A ψ value >0.062 indicated a shape effect on the E-SSG. On this basis, the three-dimensional safety coefficient of the E-SSG can be obtained using the spatial-effect trends and the safety factor via the DR approach (i.e., the two-dimensional model). Finally, the rationality and accuracy of the proposed method were validated using engineering cases. Moreover, generation mechanisms and principal determinants of the shape effects within the steep-slope embankments under S-shaped and V-shaped gullies were compared. It was learned that the E-SSG is an asymmetric structure compared with the V-shaped gullies, and the stable right base bank is an important factor in the shape effect of the E-SSG.