A Parabolic Failure Criterion for Transversely Isotropic Rock: Modification and Verification

Abstract

It is of great significance to develop a failure criterion that can describe the orientation-dependent behavior of transversely isotropic rocks. This paper presents a simplified parabolic model that is successful in predicting the strengths of rocks under different confining pressures and bedding angles. The model is a modified version of the normal parabolic criterion for intact rocks. The two orientation-dependent parameters (σcβ and kβ) in the model show trigonometric relationships with the bedding angle, and they can be readily determined through uniaxial and triaxial compression tests. The shape of the failure envelope is determined by kβ, and σcβ only affects the level of rock strength. With application to 446 experimental data, the predicting results by the parabolic criterion are highly consistent with the experimental data, and the predictive capacity of the proposed criterion is better than those of the McLamore-Gray and Tien-Kuo criteria. Besides, the prediction errors for the high confining pressure condition and the bedding-sliding failure mode are smaller than those for the low confining pressure and the non-bedding-sliding failure. Moreover, the prediction error almost remains steady with the decrease of data set, indicating that the proposed criterion is of high precision even if the experimental data are limited.

Morphometric description of strength and degradation in porous media

“…9), where the best fit function is a parabola. This recovers the parabolic failure criterion, recently suggested and experimentally verified (see Yuan et al (2020), Wang et al (2019), Singh and Rao (2005)). This also captures the transition from a linear behavior at low confining pressures to a pressure-insensitive behavior for high confinement (Yuan et al (2020)).…”

Mathematical modelling of displacement during the potash ores mining by longwall faces

“…Mechanical properties of the rocks that make up the geological section were taken in accordance with the laboratory test results [27,28]. Determination of the stress-strain state of rocks was based on the model of an ideal elastic-plastic medium, which, in the area of compressive stresses, was implemented in the variant of the parabolic Coulomb -Mohr criterion [29]:…”