A Potential Strain Indicator for Brittle Failure Prediction of Low-Porosity Rock: Part II—Theoretical Studies Based on Renormalization Group Theory

• Published in: Rock mechanics and rock engineering 2015-09, Vol.48 (5), p.1773-1785
• Main Authors: Xue, Lei, Qi, Meng, Qin, Siqing, Li, Guoliang, Li, Pei, Wang, Miaomiao
• Format: Article
• Language: English
• Subjects: Axial strain; Civil Engineering; Earth and Environmental Science; Earth Sciences; Failure; Failure analysis; Geophysics/Geodesy; Indicators; Mathematical models; Original Paper; Porosity; Rock; Rock deformation; Rocks; Strain; Stress analysis; Three dimensional models; Thresholds
• ISSN: 0723-2632; 1434-453X
• DOI: 10.1007/s00603-014-0681-y

This paper investigated the theoretical relationship between the axial strain thresholds at the volumetric strain reversal point ( ε 1cd ) and the strain threshold at the peak stress ( ε 1ucs ) during a uniaxial compression test. Firstly, we used renormalization group theory with the stress transfer mechanism to reveal the essence of the phase transition phenomenon at the axial strain threshold ( ε 1cd ). Then, we constructed mathematical expressions for ε 1ucs and ε 1cd , respectively. Finally, a theoretical expression for the normalized quantity ε 1ucs / ε 1cd was deduced. Results indicate that the theoretical solution of ε 1ucs / ε 1cd is a function of the shape parameter m . We determined m values in the granitic gneiss experiments presented in Part I of this paper, and then compared the experimental results with theoretical solutions for ε 1ucs / ε 1cd . It was observed that, for a given m , the experimental results were approximately consistent with the theoretical values for the two- and three-dimensional renormalization group models. This indicates that the two- and three-dimensional renormalization group models of rock fracture processes can be used to describe the mechanical behavior of laboratory-scale rock samples. Therefore, this study has thrown some light on failure prediction for laboratory-scale rock samples. Furthermore, the results show that ε 1ucs / ε 1cd can be regarded as a potential indicator for predicting the failure strain of laboratory-scale rock samples.