Stability Assessment of a Rock Slope With Tension Cracks Subjected to Earthquakes

ABSTRACT The presence of a tension crack at the slope crest indicates a reduction in slope stability, particularly under seismic conditions. Therefore, the seismic stability of slopes with cracks requires special attention. In this study, the seismic stability of cracked rock slopes governed by the Hoek–Brown criterion is investigated within the framework of the kinematic approach of limit analysis. The strength nonlinearity of rock masses is represented by two stress variables on the slip surface using the pointwise equivalence strategy, instead of the single‐ or multi‐tangent technique. Seismic acceleration is incorporated through the classical pseudo‐static method. A discretization‐based approach is applied to construct the failure mechanism following the associative flow rule. The critical depth of a vertical crack under seismic loading is re‐derived and used as a boundary condition for the subsequent optimization. Closed‐form solutions for the stability number and the yield seismic coefficient are then obtained from the energy balance equation. Stability charts are presented for different seismic coefficients and combinations of rock strength parameters. The influence of slope inclination and rock strength on the yield seismic coefficient is also examined. Finally, two well‐recorded seismic waves are employed to estimate seismic permanent displacements using Newmark's method.