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Geomechanics and Engineering Volume 36, Number 6, March25 2024 , pages 601-618 DOI: https://doi.org/10.12989/gae.2024.36.6.601 |
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A Copula method for modeling the intensity characteristic of geotechnical strata of roof based on small sample test data |
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Jiazeng Cao, Tao Wang, Mao Sheng, Yingying Huang and Guoqing Zhou
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| Abstract | ||
| The joint probability distribution of uncertain geomechanical parameters of geotechnical strata is a crucial aspect in constructing the reliability functional function for roof structures. However, due to the limited number of on-site exploration and test data samples, it is challenging to conduct a scientifically reliable analysis of roof geotechnical strata. This study proposes a Copula method based on small sample exploration and test data to construct the intensity characteristics of roof geotechnical strata. Firstly, the theory of multidimensional copula is systematically introduced, especially the construction of four-dimensional Gaussian copula. Secondly, data from measurements of 176 groups of geomechanical parameters of roof geotechnical strata in 31 coal mines in China are collected. The goodness of fit and simulation error of the four-dimensional Gaussian Copula constructed using the Pearson method, Kendall method, and Spearman methods are analyzed. Finally, the fitting effects of positive and negative correlation coefficients under different copula functions are discussed respectively. The results demonstrate that the established multidimensional Gaussian Copula joint distribution model can scientifically represent the uncertainty of geomechanical parameters in roof geotechnical strata. It provides an important theoretical basis for the study of reliability functional functions for roof structures. Different construction methods for multidimensional Gaussian Copula yield varying simulation effects. The Kendall method exhibits the best fit in constructing correlations of geotechnical parameters. For the bivariate Copula fitting ability of uncertain parameters in roof geotechnical strata, when the correlation is strong, Gaussian Copula demonstrates the best fit, and other Copula functions also show remarkable fitting ability in the region of fixed correlation parameters. The research results can offer valuable reference for the stability analysis of roof geotechnical engineering. | ||
| Key Words | ||
| coal seam roof; Gaussian copula; joint probability distribution; small sample; uncertain mechanical parameters | ||
| Address | ||
| Jiazeng Cao and Tao Wang:1State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China; National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum, Beijing 102249, China; Key Laboratory of Geohazard Prevention of Hilly Mountains, Ministry of Natural Resources, Fujian Key Laboratory of Geohazard Prevention, Fuzhou, Fujian 350002, China; Technology Innovation Center for Mine Geological Environment Restoration in the Alpine and Arid Regions, MNR, Lanzhou, Gansu, 730000, China Mao Sheng: National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum, Beijing 102249, China Yingying Huang: Key Laboratory of Geohazard Prevention of Hilly Mountains, Ministry of Natural Resources, Fujian Key Laboratory of Geohazard Prevention, Fuzhou, Fujian 350002, China Guoqing Zhou: State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China | ||