Earthquakes contribute to the failure of anti-dip bedding rock slopes (ABRSs) in seismically active regions. The pseudo-static method is commonly employed to assess the ABRSs stability. However, simplifying seismic effects as static loads often underestimates rock slope stability. The development of a practical stability analysis approach for ABRSs, particularly in slope engineering design, is imperative. This study proposes a stability evaluation model for ABRSs, incorporating the viscoelastic properties of rock, to quantitatively assess the safety factor and failure surface under seismic conditions. The mathematical description of the pseudo-dynamic method, derived in this study, accounts for the viscoelastic properties of ABRSs and integrates the Hoek-Brown failure criterion with the Kelvin-Voigt stress-strain relationship of rocks. Furthermore, to address concurrent translation-rotation failure in ABRSs, upper bound limit analysis is utilized to quantify the safety factor. Through a comparison with existing literature, the proposed method considers the effect of harmonic vibration on the stability of ABRSs. The obtained safety factor is lower than that of the quasi-static method, with the resulting percentage change exceeding 5%. The critical failure surface demonstrates superior positional accuracy compared to the Aydan and Adhikary basal planes, with minimal error observed between the physical model test and the numerical simulation test. The parameter sensitivity analysis reveals that the inclination of ABRSs exhibits the highest sensitivity (Sk) value across the three levels of horizontal seismic coefficient (kh). The study aims to devise an expeditious calculation approach for assessing the stability of ABRSs during seismic events, intending to offer theoretical guidance for their stability analysis. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).

Earthquakes and groundwater are pivotal factors affecting slope stability. However, the majority of previous studies have focused on these factors individually, neglecting their combined effects. Hence, this paper aims to develop a framework using the kinematic approach of limit analysis to investigate the stability of slopes in partially saturated soils under the combined effects of seismic force and pore-water pressure. The pseudodynamic method (PDM) was employed to capture the temporal-spatial effect of horizontal and vertical seismic waves. Variations in suction and effective unit weight profiles with moisture content under steady-state unsaturated flow were considered. External rates arising from both static pore-water pressure and earthquake-induced excess pore-water pressure were incorporated into the energy-balance equation. With the aid of gravity increase method (GIM), an explicit expression of safety factor (FS) was derived and optimized using a genetic algorithm (GA). The validity of this approach was verified through a comparison with existing solutions. Parametric analyses were conducted to explore the influence of varying groundwater level, seismic coefficients, suction, threedimensional effects, excess pore water pressure, unsaturated flow types, and pseudo-dynamic parameters, on the FS and critical sliding surface of slopes in partially saturated slopes. This framework can provide a good reference for the safety design of reservoir slope under the combined effects of earthquakes and groundwater.