Abstract: The rapid calculation of seismic stability of rock slopes remains a prominent and challenging focus among scholars. Historically, the chart method has been predominant in acquiring safety factors to swiftly evaluate the seismic stability of such slopes. However, approaches for promptly determining the critical acceleration of rock slopes are in lack. Establishing a model for critical acceleration is a prerequisite for computing the permanent displacement of slopes. To address this issue, we present a novel approach for swiftly computing the critical acceleration of rock slopes by employing the finite element limit analysis method (mean bound solution) and the generalized Hoek-Brown strength criterion. We obtained the diagram of critical acceleration based on 1 960 case calculations via numerical simulations for a generalized rock slope. Subsequent to two fitting statistical analyses, we derived a functional relationship between the critical acceleration of rock slopes and their geometric attributes and strength parameters. Comparisons of the results of the proposed method with those of the Newmark model and numerical solutions demonstrate that the computational accuracy of the proposed method aligns more closely with numerical solutions compared to the Newmark model. The developed method for calculating permanent displacement in rock slopes proves efficient and convenient. It not only facilitates the rapid assessment of seismic stability for individual slopes but also offers technical support for calculating permanent displacement across a large number of slopes on regional scale.

Key words: rock slope, stability charts, finite element limit analysis, generalized Hoek-Brown strength criterion, critical acceleration, Newmark model, permanent displacement, rapid calculation