Three-Dimensional Crack Recognition by Unsupervised Machine Learning
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ORIGINAL PAPER
Three‑Dimensional Crack Recognition by Unsupervised Machine Learning Chunlai Wang1 · Xiaolin Hou1,2 · Yubo Liu1 Received: 8 April 2020 / Accepted: 21 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract Many macrocracks are usually generated during the fracturing of rocks. Elucidating the spatial distribution of cracks provides the basis for understanding crack nucleation and fracture formation in rock mechanics. Considering either a single microcrack or all the microcracks provides a limited interpretation of rock mass failure that is often induced by different macrocracks. Here we recognize macrocracks based on a three-dimensional (3D) crack model, implemented using an unsupervised machine learning algorithm and microcrack coordinates. This approach recognized microcracks that coalesce to form a macrocrack in three dimensions. Rock fracturing was performed using a triaxial loading test, and the coordinate data were obtained via the acoustic emission (AE) technique. The results show that the main macrocracks are distributed throughout the whole granite specimen, and smaller macrocracks form near the unloading surface. The AE-recognized crack pattern was found to be consistent with the actual cracks. The adaptability of the proposed method and the potential research and applications were discussed. This approach provides a means to understand the formation and distribution of rock fractures. Keywords Crack recognition · 3D crack · Acoustic emission · Unsupervised machine learning List of Symbols 𝜎1 Vertical stress (MPa) 𝜎2 Horizontal stress (MPa) 𝜎3 Horizontal stress on the unloading surface (MPa) p(x) , P(x) The probability distribution function of x x, xi Microcrack coordinates expressed in matrix form 𝝁 , E(x) The expectation of x 𝚺 , Cov(x) The covariance matrix of vector x m The number of single crack models Nj The jth single crack model 𝛼j The combined coefficient of the jth single crack model 𝜀 The convergence condition � L(𝜃) , L(𝜃) The log of the likelihood function of P(x) * Chunlai Wang [email protected] 1
School of Energy and Mining Engineering, China University of Mining and Technology Beijing, Beijing 100083, People’s Republic of China
Norman B. Keevil Institute of Mining Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
2
𝛾(i, j) The posterior probability of 𝛼j 𝜃 The shorthand for parameters of P(x)
1 Introduction Subject to external loads, the defects and microcracks preexisting inside the rock are activated and propagated, generating new cracks in both micro- and macro-scale, and the resulting damage eventually leads to failure, even catastrophic hazards (Hoek and Martin 2014). Therefore, understanding the spatial distribution of different cracks inside the rock mass is not only a fundamental study of rock failure, but also a promotion way to evaluate the geotechnical disasters. In previous studies, the patterns of crack formation and distribution were deeply investigated by scholars from the failu
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