Slope stability is one of the most important topics of engineering geology with a background of more than 300 years. So far, various stability assessment techniques have been developed which include a range of simple evaluations, planar failure, limit state criteria, limit equilibrium analysis, numerical methods, hybrid and high-order approaches which are implemented in two-dimensional (2D) and three-dimensional (3D) space. In the meantime, limit equilibrium methods due to their simplicity, short analysis time, coupled with probabilistic and statistics functions to estimate the safety factor (F.S), probable slip surface, application on different failure mechanisms, and varied geological conditions has been received special attention from researchers. The presented paper provides a review to limit equilibrium methods used for discontinuous rock slope stability analyses with different failure mechanisms of natural and cut slopes. The article attempted to provide a systematic review for rock slope stability analysis outlook based on limit equilibrium approaches.

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This study presents a fuzzy logical decision-making algorithm based on block theory to effectively determine discontinuous rock slope reliability under various wedge and planar slip scenarios. The algorithm was developed to provide rapid response operations without the need for extensive quantitative stability evaluations based on the rock slope sustainability ratio. The fuzzy key-block analysis method utilises a weighted rational decision (multicriteria decision-making) function to prepare the 'degree of reliability (degree of stability-instability contingency)' for slopes as implemented through the Mathematica software package. The central and analyst core of the proposed algorithm is provided as based on discontinuity network geometrical uncertainties and hierarchical decision-making. This algorithm uses block theory principles to proceed to rock block classification, movable blocks and key-block identifications under ambiguous terms which investigates the sustainability ratio with accurate, quick and appropriate decisions especially for novice engineers in the context of discontinuous rock slope stability analysis. The method with very high precision and speed has particular matches with the existing procedures and has the potential to be utilised as a continuous decision-making system for discrete parameters and to minimise the need to apply common practises. In order to justify the algorithm, a number of discontinuous rock mass slopes were considered as examples. In addition, the SWedge, RocPlane softwares and expert assignments (25-member specialist team) were utilised for verification of the applied algorithm which led to a conclusion that the algorithm was successful in providing rational decision-making.

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