A New Volumetric Strain-Based Method for Determining the Crack Initiation Threshold of Rocks Under Compression

Abstract

The crack initiation stress threshold (σci\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{\\mathrm{ci}}$$\\end{document}) is an essential parameter in the brittle failure process of rocks. In this paper, a volumetric strain response method (VSRM) is proposed to determine the σci\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{\\mathrm{ci}}$$\\end{document} based on two new concepts, i.e., the dilatancy resistance state index (δci\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\delta }_{\\mathrm{ci}}$$\\end{document}) and the maximum value of the dilatancy resistance state index difference (Δδci\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left|{\\Delta \\delta }_{\\mathrm{ci}}\\right|$$\\end{document}), which represent the state of dilatancy resistance of the rock and the shear sliding resistance capacity of the crack-like pores during the compressive period, respectively. The deviatoric stress corresponding to the maximum Δδci\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left|{\\Delta \\delta }_{\\mathrm{ci}}\\right|$$\\end{document} is taken as the σci\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{\\mathrm{ci}}$$\\end{document}. We then examine the feasibility and validity of the VSRM using the experimental results. The results from the VSRM are also compared with those calculated by other strain-based methods, including the volumetric strain method (VSM), crack volumetric strain method (CVSM), lateral strain method (LSM) and lateral strain response method (LSRM). Compared with the other methods, the VSRM is effective and reduces subjectivity when determining the σci\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{\\mathrm{ci}}$$\\end{document}. Finally, with the help of the proposed VSRM, influences from chemical corrosion and confining stress on the σci\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{\\mathrm{ci}}$$\\end{document} and Δδci\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\Delta \\delta }_{\\mathrm{ci}}$$\\end{document} of the carbonate rock are analyzed. This study provides a subjective and practical method for determining σci\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{\\mathrm{ci}}$$\\end{document}. Moreover, it sheds light on the effects of confinement and chemical corrosion on σci\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{\\mathrm{ci}}$$\\end{document}.