Deterministic and probabilistic analysis of rock slope stability under earthquake loading conditions

The purpose of this research is to elucidate earthquake effects on rock slopes. To accomplish this purpose, the pseudostatic analysis and the earthquake-induced displacement method were performed on plane and wedge failures of rock slopes, both deterministically and probabilistically. In the deterministic analysis, the pseudostatic factor of safety and earthquake-induced displacement were calculated using fixed values of parameters. For the probabilistic analysis, the uncertainty of rock slopes and of earthquake ground motions were considered using the First-Order Second-Moment method and regression analysis. Regarding earthquake forces acting on the rock slopes, equations for pseudostatic factor of safety in plane and wedge failures were derived using the limit equilibrium method, and these equations were used for parametric studies. Using the pseudostatic method, critical earthquake accelerations were calculated for both plane and wedge failures. The earthquake-induced displacements were determined using double integration of those parts of the accelerograms that lie above the critical earthquake coefficient. In the probabilistic analysis, to estimate the mean and variance of the displacement in rock slopes, 23 corrected accelerograms were obtained from 8 earthquakes ranging from 5.3 to 7.0 in magnitude and from 16.7 to 50.0 km in epicentral distance. Based on the empirical equation obtained from regression analysis, the probability that displacement exceeds a specific value (10 cm) was calculated for both plane and wedge failures under various conditions. Stability of rock slopes under post-earthquake conditions was evaluated using the residual shear strength of discontinuities. Results obtained from pre- and post-earthquake stability analyses were compared in terms of the factor of safety (deterministic) and the probability of failure. Finally, as a case study, the Madison Canyon rockslide caused by the Hebgen Lake earthquake of 1959 was evaluated using the methods developed in the current study. Both the deterministic and probabilistic procedures showed that the rock slope was unstable under that earthquake loading