Upper-Bound Multi-Rigid-Block Solutions for Seismic Performance of Slopes with a Weak Thin Layer

The presence of a weak layer has an adverse influence on the seismic performance of slopes. The upper-bound solution serves as a rigorous method in the stability analysis of geotechnical problems. In this study, a multi-rigid-block solution based on the category of the upper-bound theorem of limit analysis is presented to examine the seismic performance of nonhomogeneous slopes with a weak thin layer. Comparison of the static factors of safety is conducted with various solutions (i.e., limit analysis with a different failure mechanism, limit equilibrium solution, and numerical method), and the results exhibit reasonable consistency. An analytical solution in estimating the critical yield acceleration coefficient is derived, and the influence of slope angle, slope height, and soil strength on the critical yield acceleration coefficient and failure mechanism is analyzed. Subsequently, Newmark’s analytical procedure is employed to evaluate cumulative displacement with various real earthquake acceleration records as input motion. Results show that the strength and geometric parameters have a remarkable influence on the critical yield acceleration coefficient, and the cumulative displacement increases with the increasing slope angle.