Approximate Solution to the Sokolovskiĭ Concave Slope at Limiting Equilibrium

The growth of precision autoguidance systems on construction equipment suggests that nonplanar slopes and landforms now can be constructed readily. Slopes with concave cross sections not only appear more like natural slopes, but can also have superior stability and erosion resistance. Thus, it is desirable to have the description of concave slopes that provide mechanical stability for a given set of soil properties. In this paper, an approximate solution that defines the geometry of critical concave slopes (factor of safety ≈1) in a frictional medium is developed, based on the slip-line field method. The approximate solution is compared with previous numerical results and validated via limit-equilibrium method and FEM analyses. The proposed solution is simple in form, and, when implemented with precision construction equipment, will allow the construction of embankments and reclaimed mine lands that appear more like those in nature and yet are more resistant to erosion.