Dynamic reliability analysis of anchored slopes under seismic action considering acceleration amplification effect

Abstract
This paper presents a reliability analysis method for anchored slopes under seismic action. The key methodological novelty lies in the integration of an elevation-dependent acceleration amplification effect into the probabilistic limit state formulation-a significant departure from conventional pseudo-static or deterministic approaches that assume a uniform seismic coefficient. By treating the amplification coefficient as a segmentally defined function along the slope height based on design codes, the proposed framework captures the realistic distribution of seismic inertia forces, while simultaneously accounting for the inherent uncertainties in geotechnical shear strength parameters and seismic acceleration. A limit state equation incorporating acceleration amplification coefficients is established for anchored slopes. The geotechnical shear strength parameters and seismic acceleration are treated as random variables. Amplification coefficients are defined segmentally according to relevant codes to derive the calculation formula for pseudo-static seismic inertia forces. The critical slip surface search is optimized by integrating an improved horizontal slice method with a Genetic Algorithm (GA). Reliability indices and failure probabilities are computed using the checking point method (JC) and Monte Carlo simulation (MCS), with comparative validation confirming the effectiveness of the proposed approach. Results demonstrate that increasing peak seismic acceleration markedly elevates the slope failure probability. Reliability indices exhibit nonlinearly accelerated attenuation characteristics, which is consistent with the transition from linear to nonlinear dynamic response identified as a precursor to failure in experimental shaking table tests (Yan et al., Eng Geol 355:108220, 2025). When the seismic intensity reaches a critical threshold, the slope system approaches instability. Increasing the mean cohesion and internal friction angle substantially enhances slope stability. The influence of variation coefficients on failure probability remains relatively weak, confirming that geotechnical parameter dispersion is not the dominant factor. Anchor failure significantly reduces the anti-sliding capacity of the slope. Complete anchor failure scenarios show substantially higher failure probabilities than partial failure combinations.