Improved analysis of rock mass geometry using mathematical and photogrammetric methods

Most engineering in, or on, rock close to the surface of the Earth is affected by the presence of discontinuities. Hence, an accurate and complete description of rock mass geometry in terms of the geometry of these features is essential for economic operations. Here, a review of customary methods for the measurement and analysis of rock mass geometry has been presented, and has revealed that they are deficient in a number of ways. Detailed reviews of photogrammetry and cluster identification schemes have shown that the integrated use of modern non-metric photogrammetric techniques with fuzzy partitioning algorithms promises improved methods of the analysis of rock mass geometry, and this has led to further development in these fields. A high-performance analytical plotter, incorporating sophisticated closed-loop control systems, has been designed and constructed to allow determination of photograph coordinates at a resolution appropriate for the measurement of rock mass geometry. This instrument, in conjunction with an original method of introducing high-accuracy photogrammetric control at a rock face, has allowed development of simplified procedures for photogrammetric surveying. A novel computer program is introduced that implements a sequential application of three fuzzy partitioning algorithms—namely; fuzzy c-means, fuzzy covariance and fuzzy maximum likelihood estimation—for the analysis of discontinuity orientation. Exhaustive tests on both synthetic and natural data sets reveals the enhanced form of the analysis over customary methods. This analysis leads to the generation of two new types of hemispherical projection— viz. cluster assignment plots and membership level plots—which together allow improved assimilation of rock mass structure. A report of the application of the new techniques at two quarry sites within the UK demonstrates their overall efficacy. It has been found that photogrammetric methods permits surveying of the entire rock face at an accuracy sufficient for the computation of discontinuity orientation, and the use of fuzzy partitioning algorithms allows an improved analysis of rock mass structure in terms of discontinuity orientation