Determination of statistical discontinuity persistence for a rock mass characterized by non-persistent fractures

The discontinuity persistence is an important parameter that affects the strength of rock masses and stability in rock engineering. However, determining the 3D discontinuity persistence in practical field projects remains difficult. This study proposes an approach to determine the 3D discontinuity persistence (percentage of total discontinuity area to the area of the potential failure surface) on the basis of Dijkstra's shortest-path algorithm and Bayesian bootstrap method. First, Dijkstra's shortest-path algorithm is used to determine the linear discontinuity persistence (percentage of total discontinuity trace length to the length of 2D potential failure surface), which is essential to determining 3D discontinuity persistence. Second, geological analysis is performed to deduce 3D discontinuity persistence as a function related to two linear discontinuity persistence in two vertical directions. Lastly, Bayesian bootstrap method is used to analyze the linear and 3D discontinuity persistence. This approach can substantially simplify the process of determining discontinuity persistence and comprehensively considers the uncertainty of the fracture network. The mean, standard deviation, and p-value (i.e., value at the 95% confidence limit) are used as the statistical parameters of the linear and 3D discontinuity persistence.