Key-block based analytical stability method for discontinuous rock slope subjected to toppling failure

Abstract This study introduces a simplified semi-distinct element algorithm for discontinuous rock slopes under toppling instability assessment based on block theory. The presented algorithm is developed to investigate block, flexural and block-flexural types of toppling failures which have been coded in the Python high-level programming language. In order to investigate toppling instabilities for different modes, the three modelling steps, namely, geometrical, behavioural and mechanical simulations were conducted to appoint high-order calculation trending loops. These loops were based on the analytical description of modified second-order reliability method with first-order efficiency to determine the factor of safety values for discontinuous rock slopes. Each type of toppling failure was described based on main assumptions that were modified by geometric qualifications such as the analytical procedure, single block slip, and the Voronoi diagram algorithm for the stability analysis of the three different failure types. According to the stability assessment results of the studied slopes which were verified by the distinct numerical method via UDEC software, it has been clarified that the results obtained from the algorithm and the numerical analysis were in an appropriate trend. The used algorithm is superior in pinpointing the critical sliding zones, safety factor estimation and progressive failure analyses as compared to the numerical analyses. Moreover, the block theory based algorithm has higher processing capability and speed with respect to the numerical method.