Analytical expressions for determining the stability of cohesionless soil slope under generalized seismic conditions

In recent major earthquakes, the researchers have found the need for consideration of vertical seismic acceleration for the stability analysis of the man-made and natural slopes. However, in most past studies, the performance of slopes has been assessed by accounting only the horizontal seismic component of the ground motion, without giving due weightage to the effect of vertical component. In the present study, analytical expressions are derived to determine the factor of safety, yield seismic coefficient and consequently the seismic displacement of cohesionless soil slope under combined horizontal and vertical components of the ground motion. The derivation uses the Newmark's sliding block approach, in which the soil slope with a planar failure surface within the framework of conventional pseudo-static analysis is assumed to follow the Mohr-Coulomb failure criterion. The effects of vertical seismic coefficient on the stability of cohesionless slope have been studied through a set of graphical presentations for a specific range of soil parameters. It is observed that overlooking the effect of the vertical component of the ground motion on factor of safety and the displacement while designing the slope may be detrimental, resulting in the slope failure. The general expressions presented in this paper may be highly useful in the field of earthquake geotechnical engineering practice for designing the cohesionless soil slopes under combined horizontal and vertical seismic loads.