Statistical treatment of jointed rock masses: Spherical statistics and orientation data simulation

A probabilistic method for analysing the stability of underground excavations in a fractured rock mass is presented. By adopting a probabilistic approach in stability analysis, the distribution of safety factor can be established. The state-of-the-art in spherical statistics is reviewed in detail with emphasis on random number generation and simulation techniques. A best fit-probability density model that maps data clusters on the unit sphere or stereonet is described and tested. The statistics are then applied to Monte Carlo simulation of spherical data clusters. Application of the method to deterministic wedge stability analysis is then described. Several data sets are analysed. Finally, suggestions on how to upgrade the software package DIPS are discussed. A broader method to include more geotechnical parameters is discussed for implementation into DIPS.