Relationship between critical seismic acceleration coefficient and static factor of safety of 3D slopes

Many analytical methods have been adopted to estimate the slope stability by providing various stability numbers, e.g. static safety of factor (static FoS) or the critical seismic acceleration coefficient, while little attention has been given to the relationship between the slope stability numbers and the critical seismic acceleration coefficient. This study aims to investigate the relationship between the static FoS and the critical seismic acceleration coefficient of soil slopes in the framework of the upper-bound limit analysis. Based on the 3D rotational failure mechanism, the critical seismic acceleration coefficient using the pseudo-static method and the static FoS using the strength reduction technique are first determined. Then, the relationship between the static FoS and the critical seismic acceleration coefficient is presented under considering the slope angle beta, the fractional angle phi, and the dimensionless coefficients B/H and c/gamma H. Finally, a fitting formula between the static FoS and the critical seismic acceleration coefficient is proposed and validated by analytical and numerical results.