New method to identify optimal discontinuity set number of rock tunnel excavation face orientation based on Fisher mixed evaluation

Discontinuity is critical for strength, deformability, and permeability of rock mass. Set information is one of the essential discontinuity characteristics and is usually accessed by orientation grouping. Traditional methods of identifying optimal discontinuity set numbers are usually achieved by clustering validity indexes, which mainly relies on the aggregation and dispersion of clusters and leads to the inaccuracy and instability of evaluation. This paper proposes a new method of Fisher mixed evaluation (FME) to identify optimal group numbers of rock mass discontinuity orientation. In FME, orientation distribution is regarded as the superposition of Fisher mixed distributions. Optimal grouping results are identified by considering the fitting accuracy of Fisher mixed distributions, the probability monopoly and central location significance of independent Fisher centers. A Halley-Expectation-Maximization (EM) algorithm is derived to achieve an automatic fitting of Fisher mixed distribution. Three real rock discontinuity models combined with three orientation clustering algorithms are adopted for discontinuity grouping. Four clustering validity indexes are used to automatically identify optimal group numbers for comparison. The results show that FME is more accurate and robust than the other clustering validity indexes in optimal discontinuity group number identification for different rock models and orientation clustering algorithms.