A theoretical strain relationship for identifying the failure of laboratory-scale rocks under triaxial compression

ABSTRACT

A theoretical strain relationship between peak strain (ε_peak) and crack damage strain (ε_cd) is established for identifying the failure of the rock under triaxial compression. The relationship is derived from the two-dimensional renormalisation group theory with consideration of the rock heterogeneous microstructures. It is afunction of five parameters, including the confining stress (σ₃), Young’s modulus (E), friction angle (φ), Poisson’s ratio (γ) and homogeneity index of Weibull distribution (m). The σ₃, E, φ and γ values can be readily obtained from the stress–strain data, and amethod for obtainingmvalue using σ₃, σ_cd, ε_cd, E, φ and γ values is proposed. Comparison with the triaxial compression test results of 48 shale specimens with four bedding dip angles shows the failure identifications using the established relationship well agree with the experimental measurements, demonstrating the ability of the established relationship to identify the failure of the laboratory-scale rock specimens under triaxial compression. Single-parameter sensitivity analysis shows that the established relationship between the ε_cd and ε_peak is affected by the parameters with different sensitivity. The highest to lowest sensitivity of the parameters are φ, σ₃, E, γ andm, respectively.

KEYWORDS:

• Rock
• triaxial compression test
• failure identification
• strain
• renormalisation group theory
• weibull distribution

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences [XDB10030302], the open fund of SINOPEC Key Laboratory of Geophysics [33550006-16-FW0399-0026], the National Natural Science Foundation of China [41807224] and the Natural Science Foundation of Zhejiang Province [LQ17D020001].