IntroductionWedge failure is one of the most common mode of rock slope failure. In most previous engineering applications, the approach to analyzing rock slope stability has been to simply study known wedges, which have a definite shape, size, and location and good persistence, to obtain a stability coefficient. The stereographic projection method [7] are all based on mature theories, are well developed, and are widely used in engineering.However, excavation differs in that there are not yet any good methods for conducting a specific investigation of all structural planes within a rock slope; thus, the wedges exposed in an excavation surface are stochastic and finite persistent. In addition, excavation surfaces are dynamically changing. All of these factors create unpredictability and risk regarding rock slope stability that cannot be addressed using existing methods. Thus, we need a new approach that takes into account the stochasticity and finite persistence of wedges within a rock slope to dynamically analyze the stability of a rock slope excavation, estimate the risk, and guide the construction.Recently, many scholars have presented the concept of stochastic structural-plane network simulation and reliability analysis based on statistics and probability theory. These techniques can be used to describe the spatial distribution of structural planes statistically and to quantify the uncertainty. These two methods have been applied successfully in rock mechanics. [14]. In addition, ever since probability theory was applied to slope engineering in the 1970s, great achievements have been made, including the analysis of rock slope stability using probability theory by . All of these methods effectively address stochasticity in rock slope stability analysis.The effect of finite persistence on rock slope stability cannot be ignored because in practice larger wedges tend to be more stable due to the rock bridge between structural planes. Lajtai