Stability Analyses of Initial Collapse and Earthquake-Induced Secondary Failure Using Discretization-Based Kinematic Analysis

A stability analysis of slopes is presented using the discretization-based kinematic analysis. By generating a discretized failure mechanism satisfying the kinematic admissibility condition with the use of a discretization technique, the initial analysis of the stability of a steep slope is performed, with the upper bound solutions of critical slope height and stability factor γH/c formulated according to the work rate-based balance equation. Nonuniformity of soil properties is accounted for in the analysis. The log-spiral kinematic solution is also calculated considering the pore water effect and a linearly increased soil cohesion with depth, which shows good agreement with numerical results obtained from different approaches. To analyze a secondary failure due to seismic loading following an initial collapse, the initial failure block is removed, and secondary failure analysis is performed based on the remaining curved sloping surface. Such a slope is deemed stable unless sufficient additional driving forces, such as earthquake loading, cause the slope to fail the second time. In this secondary failure, the focus is placed on the determination of yield seismic acceleration at ultimate failure. Because of the short duration of an earthquake, an undrained stability analysis is presented with a circular rotational failure mechanism; hence, it is not affected by the pore water effect. Following a similar kinematic procedure, the critical seismic acceleration is derived using the work rate-based formula. A parametric study specific to initial and secondary failure is performed to better understand the implications of influential factors affecting slope stability.