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Abstract
The ratio of crack initiation stress to the uniaxial compressive strength (SCI,B/SUC,B) and the ratio of axial strain at the crack initiation stress to the axial strain at the uniaxial compressive strength \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\left( {S_{A,S_{CI,B} } /S_{A,S_{UC,B} } } \right)$$\end{document}
were studied by performing numerical stress analysis on blocks having multi flaws at close spacing’s under uniaxial loading using PFC3D. The following findings are obtained: SCI,B/SUC,B has an average value of about 0.5 with a variability of ± 0.1. This range agrees quite well with the values obtained by former research. For joint inclination angle, β=90°, \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_{A,S_{CI,B} } /S_{A,S_{UC,B} }$$\end{document}
is found to be around 0.48 irrespective of the value of joint continuity factor, k. No particular relation is found between \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_{A,S_{CI,B} } /S_{A,S_{UC,B} }$$\end{document}
and β; however, the average \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_{A,S_{CI,B} } /S_{A,S_{UC,B} }$$\end{document}
seems to slightly decrease with increasing k. The variability of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_{A,S_{CI,B} } /S_{A,S_{UC,B} }$$\end{document}
is found to increase with k. Based on the cases studied in this work, \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_{A,S_{CI,B} } /S_{A,S_{UC,B} }$$\end{document}
ranges between 0.3 and 0.5. This range is quite close to the range of 0.4 to 0.6 obtained for SCI,B/SUC,B. The highest variability of ± 0.12 for \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_{A,S_{CI,B} } /S_{A,S_{UC,B} }$$\end{document}
is obtained for k=0.8. For the remaining k values the variability of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_{A,S_{CI,B} } /S_{A,S_{UC,B} }$$\end{document}
can be expressed within ± 0.05. This finding is very similar to the finding obtained for the variability of SCI,B/SUC,B.
Keywords
jointed rock
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multi flaws
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uniaxial loading
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PFC3D model
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crack initiation stress (SCI,B)
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\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_{A,S_{CI,B} }$$\end{document}
')">axial strain at crack initiation stress \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_{A,S_{CI,B} }$$\end{document}
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Xiang Fan, P. H. S. W. Kulatilake, Xin Chen, Ping Cao.
Crack initiation stress and strain of jointed rock containing multi-cracks under uniaxial compressive loading: A particle flow code approach.
Journal of Central South University, 2015, 22(2): 638-645 DOI:10.1007/s11771-015-2565-z
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