Development of three-dimensional numerical manifold method for jointed rock slope stability analysis

• An advanced hybrid continuum-discontinuum numerical approach called 3-D numerical manifold method (NMM) has been developed for rock engineering applications.
• A 3-D contact detection and modeling algorithm has been customized for 3-D NMM.
• The validity and accuracy of the 3-D NMM has been verified through a series of examples.
• Potential application of 3-D NMM to rock engineering applications is clearly seen through the last slope example
• The distinctions of the 3-D NMM compared with other slope analysis tools are highlighted

This paper presents a three-dimensional numerical manifold method (NMM) for jointed rock slope stability analysis. The main barriers for realistic rock slope stability analysis are discussed, and the unique features of the NMM which make it stand out in slope analysis are emphasized. The framework of the 3-D NMM is established via a regularly-patterned tetrahedral mesh-based mathematical cover system. A contact detection algorithm is then customized to fit the 3-D NMM characteristics. The developed code is first calibrated by two simple cases: inclined plane sliding and tetrahedral wedge sliding, and then applied to a more complex slope scenario. The complete failure process involving large displacement and rotation of multiple interaction blocks is exhibited dynamically. Two typical stabilization/protection techniques are also investigated. The developed 3-D NMM could be potentially used to find the trigger/failure mechanism of jointed rock slopes, so as to optimize the slope stabilization or protection design.