Rock Tensile Properties and Modification of Tensile Strength Criterion Under Confining Pressure
Authors: Sun Wei , Zhang Guangqing , Xue Xiaojia , Chen Wenbin 
Published: September 2023

ABSTRACT
To reveal the influence of confining pressure on the tensile properties of rock, Brazilian disc tests for tight sandstone and granite under different confining pressures were carried out. The tensile failure characteristics were analyzed, and the tensile strength-confining pressure curves were obtained. The maximum tensile stress criterion was modified considering the influence of confining pressure, which was incorporated into ABAQUS, and characteristics of hydraulic fractures under different in-situ stress conditions were studied. The results reveal that (1) under the confining pressure of 0-25 MPa, the failure mode of tight sandstone changes from tensile failure to tensile-shear failure, while granite only exhibits tensile failure; (2) under the tensile failure mode, the relationship between tensile strength and confining pressure is linear, and the confining pressure has a more significant influence on granite; (3) the modified maximum tensile stress criterion is expressed as multiple sets of nested vertical planes in the principal stress space; (4) ignoring the influence of confining pressure on tensile strength, the breakdown pressure is underestimated, the fracture length is overestimated, and the maximum fracture width is underestimated.

INTRODUCTION
The tensile failure of rocks in hydraulic fracturing occurs under the in-situ stress environment, which belongs to confined tensile failure (Chen et al., 2023). Conventional rock tensile tests have gradually expanded to confined rock tensile tests. The confined direct tensile test is an experimental method in which the specimen is directly tensioned under confining pressure. You et al. (2006) conducted direct tensile tests under confining pressure by bonding the cylindrical specimen to the squeeze head. The results showed that the tensile strength decreases with the increase of confining pressure, and the Griffith criterion in the tensile stress region is not valid for rocks. However, the failure surfaces were not in the middle of the test piece, but closer to the end. Liu et al. (2019) compared the results of triaxial tension and triaxial compression tests of cylindrical sandstone specimens. It is considered that confining pressure can improve the compressive strength of sandstone and reduce its tensile strength, and the impact on the former is greater than the latter. Because of the uncertainty of the failure section of the cylindrical specimen, the direct tensile tests of the dog-bone specimen were carried out (Ma et al., 2018; Lan et al., 2019; Tarokh et al., 2022). Compared with the cylindrical specimen, the sections of the dog-bone specimen are primarily located in the middle of the specimen. With the increase of the confining pressure, the specimen section gradually inclines. The failure mode transits from tensile failure to tension-shear failure. The confined hollow cylinder tensile test is an experimental method of obtaining tensile strength by hydraulic fracturing. A significant positive correlation between rock tensile strength and confining pressure (Zhang et al., 2020; Li et al., 2019). Li et al. (2019) indicated that increasing confining pressure can decrease rock brittleness, enhance its toughness, and increase the energy required for microcracks to continue expanding. This results in an increase in macroscopic tensile strength and fracture toughness of rocks. The confined Brazilian disc test is widely used to obtain tensile strength indirectly. Mighani et al. (2015) suggested that confining pressure hinders the nucleation of microfractures, resulting in an increase in tensile strength as the confining pressure increases. Li et al. (2020) obtained the tensile failure envelope through multistage Brazilian disc tests on sandstone. Li et al. (2018) used the copper jacket to wrap Brazilian disc specimens to isolate fluid and rock. The experimental results indicate that the inclination of the failure surface increases with the increase of confining pressure, and the failure mode changes from tensile failure (low confining pressure) to shear failure (high confining pressure). Hagengruber et al. (2021) demonstrated an increase in the intermediate principal stress can significantly enhance the strength of sandstone, and as the confining pressure increases, the characteristics of shear failure gradually become more apparent. Wu et al. (2016) indicated the dynamic tensile strength increased with the increase of the confining pressure. Moreover, under equivalent levels of confining pressure, the dynamic tensile strength of rock increases with the loading rate.