A study on rapid calculation methods for seismic safety factors of three-dimensional slopes

Seismic activity is a major factor in triggering slope instability and failure. Consequently, building on previous research into rapid calculation methods for the safety factor of three-dimensional homogeneous slopes, this paper further investigates rapid calculation methods for the safety factor of three-dimensional slopes under seismic loading conditions. To investigate the relationship between this and the method for calculating the safety factor for a pitched roof without overloading, and thereby derive an expression for the rapid calculation of the safety factor under seismic loads. First, a numerical slope model is established to simulate seismic effects, and the variation laws of soil and geometric parameters are analyzed for slopes approaching the critical instability state under seismic loading. To further investigate the patterns of change in soil parameters under seismic loading and the functional relationship between these parameters and those at the crest of the slope when there is no horizontal overload. On this basis, and taking into account the definition of the safety factor, a formula for the rapid calculation of the safety factor under seismic loads has been derived. Finally, engineering examples are adopted to verify the validity and feasibility of this safety‑factor formula.