Seismic Stability of Non-homogenous Cohesive Soil by Using Calculus of Variation

In this article, the factor of safety of a cohesive soil slope subjected to seismic load is determined by employing the variational method and pseudostatic analysis. Unlike the conventional limit equilibrium method, there is no requirement to consider any kinematical or static assumption in the variational method. The factor of safety (F) is defined as a functional which is minimized by using the Euler–Lagrangian equation. The (i) transversality and boundary conditions are imposed at the intersection of slip surface, and the slope surface, and (ii) continuity and natural boundary states are forced at the intermediate point of the slip surface. The soil is considered to be completely saturated and loaded under undrained conditions. The cohesion of the soil is assumed to increase linearly with depth. The critical slip surface and consequently critical factor of safety, F_s is being obtained by varying the slope geometry, soil properties, and seismic loadings. The available solutions compare quite well with the convenient solution for the pseudostatic slope stability analysis. The proposed design charts will be quite useful to practicing engineers.