Geomechanics and Engineering

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A Copula method for modeling the intensity characteristic of geotechnical strata of roof based on small sample test data

  • Jiazeng Cao (State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology) ;
  • Tao Wang (State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology) ;
  • Mao Sheng (National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum) ;
  • Yingying Huang (Key Laboratory of Geohazard Prevention of Hilly Mountains, Ministry of Natural Resources, Fujian Key Laboratory of Geohazard Prevention) ;
  • Guoqing Zhou (State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology)
  • Received : 2023.01.12
  • Accepted : 2024.03.02
  • Published : 2024.03.25
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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.

Keywords

Acknowledgement

This research was supported by the National Natural Science Foundation of China (Grant No. 42371133), the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20231501), the Key Research and Development Program of Xuzhou (Grant No. KC23294), the Opening Fund of National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum, Beijing (Grant No. PRP/open-2211), the Opening Fund of Key Laboratory of Geohazard Prevention of Hilly Mountains, Ministry of Natural Resources (Fujian Key Laboratory Of Geohazard Prevention) (Grant No. FJKLGH2023K003) and the Opening Fund of Technology Innovation Center for Mine Geological Environment Restoration in the Alpine and Arid Regions (Grant No. HHGCKK2205).

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