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

Abstract

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.

Keywords

Rock mass discontinuity / Orientation grouping / Fisher mixed distribution / 3D point cloud / Stereo photogrammetry

CRediT authorship contribution statement

Keshen Zhang: Conceptualization, Writing - original draft, Visualization, Methodology, Validation. Wei Wu: Writing - review & editing, Supervision. Min Zhang: Funding acquisition, Data curation, Investigation. Yongsheng Liu: Funding acquisition, Resource, Investigation. Yong Huang: Funding acquisition, Resource, Investigation. Baolin Chen: Funding acquisition, Resource, Investigation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by the National Natural Science Foundation of China (Grant Nos. 42272338, 41827807 and 41902275); Shanghai Sailing Program (Grant No. 18YF1424400); Joint Fund for Basic Research of High-speed Railway of National Natural Science Foundation of China, China Railway Corporation (U1934212); China State Railway Group Co., Ltd. (P2019G038); Department of Transportation of Zhejiang Province (202213); China Railway First Survey and Design Institute Group Co., Ltd. (19-21-1, 2022KY53ZD(CYH)-10); China Railway Tunnel Group Co., Ltd. (CZ02-02-08); PowChina Hebei Transportation Highway Investment Development Co., Ltd. (TH-201908); Sichuan Railway Investment Group Co., Ltd. (SRIG2019GG0004); The Science and Technology major program of Guizhou Province [2018]3011.

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