Determination of discontinuity persistent ratio by Monte-Carlo simulation and dynamic programming

Using measured data of over 100,000 discontinuities in 35 hydropower projects, this study conducts in-depth analyses on the statistical characteristics of geometric parameters of rock discontinuities and makes an improvement of Monte Carlo network simulation of discontinuities. A new method of determining the discontinuity persistent ratio is developed. The persistent ratio is defined as the percentage of discontinuity planes along the failure surface when the rock mass sheared in a defined direction. This definition overcomes the inadequacies of the traditional geometric projection method, and reduces the determination of the persistent ratio to the identification of the combined failure surface formed by discontinuity planes and rock bridges only. Lajtai (1969) strength theory for rock bridges is used in combination with the conventional failure mechanism of a joint. Dynamic programming is used to resolve the difficulties of identifying failure path in complicated discontinuity network. Finally, the joint persistent ratio can be determined and the methods have been widely applied in engineering practices.