Experimental Investigation on the Tensile Mechanical Behavior of Layered Shale Using Direct and Indirect Test Methods
Abstract
:1. Introduction
2. Experimental Methodology
2.1. Specimen Preparation
2.2. Testing Procedure
3. Results
3.1. Load–Displacement Curve
3.2. Tensile Strength
3.3. Anisotropy of Acoustic Emission
3.4. Failure Mode
4. Discussion
4.1. Anisotropic Tensile Strength Criterion for Layered Shale
- (1)
- H-B criterion
- (2)
- N-Z criterion
- (3)
- SPW criterion
- (4)
- L-P criterion
- (5)
- CPA criterion
- (6)
- Phenomenological criterion
- (7)
- SS criterion
4.2. The Comparison Between Direct and Indirect Tensile Strength
4.3. The Typical Failure Mode of DTT and BST Specimens
5. Conclusions
- (1)
- Anisotropy significantly impacts the tensile strength of layered shale. Both the BST and DTT demonstrated that tensile strength increases with the loading angle (β). At β = 90°, the maximum tensile strengths for BST and DTT are 10.45 MPa and 9.60 MPa, respectively. Conversely, at β = 0°, the minimum tensile strengths for BST and DTT are 6.89 MPa and 4.06 MPa, respectively. The anisotropy ratios for BST and DTT are 1.52 and 2.36, respectively, indicating the significant impact of the loading angle on tensile strength.
- (2)
- The accumulated AE energy and ringing counts for DTT and BST specimens exhibit distinct trends under different loading angles. For DTT specimens, the accumulated AE energy and ringing counts are generally higher than those of BST specimens. Most DTT specimens display varying degrees of progressive failure characteristics. In contrast, BST specimens typically do not generate significant AE energy or ringing counts during the loading process, with a sharp increase observed only during the final failure stage.
- (3)
- Anisotropy also significantly affects the failure modes of DTT and BST specimens. For DTT specimens, the primary failure mode is tensile–shear mixed failure, with pure tensile failure across the bedding plane observed only at loading angles of β = 60° and 90°. Similarly, BST specimens predominantly exhibit tensile–shear mixed failure, except for tensile failure along the bedding plane at β = 0° and tensile failure across the bedding plane at β = 90°.
- (4)
- The difference between direct and indirect tensile strength is influenced by rock anisotropy, the testing method, and specimen geometry. The results obtained from the L-P criterion, SS criterion, and CPA criterion show good agreement with the measured results of both direct and indirect tensile strength. Furthermore, based on the statistical analysis in this study, estimating the indirect tensile strength as 1.11 times the direct tensile strength provides a reliable approximation for most cases.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Wang, Y.M.; Wang, Z.L.; Zhang, Z.C.; Yao, S.S.; Zhang, H.; Zheng, G.Q.; Luo, F.F.; Feng, L.L.; Liu, K.Q.; Jiang, L.L. Recent techniques on analyses and characterizations of shale gas and oil reservoir. Energy Rev. 2024, 3, 100067. [Google Scholar] [CrossRef]
- Zhang, Y.; Kleit, A.; Morgan, E.; Wang, J. Analysis of ultimate gas recovery in shale reservoirs. J. Energy Resour. Technol. 2024, 146, 083001. [Google Scholar] [CrossRef]
- Zhou, J.; Wu, G.A.; Geng, Y.N.; Guo, Y.T.; Chang, X.; Peng, C.Y.; Ai, C.Z. Laboratory study of the factors affecting hydraulic fracturing effect for inter-salt oil shale layers, Qianjiang Depression, China. Pet. Sci. 2023, 20, 1690–1706. [Google Scholar] [CrossRef]
- Dan, D.Q.; Konietzky, H.; Herbst, M. Brazilian tensile strength tests on some anisotropic rocks. Int. J. Rock Mech. Min. Sci. 2013, 58, 1–7. [Google Scholar] [CrossRef]
- Li, C.B.; Yang, D.C.; Xie, H.P.; Ren, L.; Wang, J. Size effect of fracture characteristics for anisotropic quasi-brittle geomaterials. Int. J. Min. Sci. Technol. 2023, 33, 201–213. [Google Scholar] [CrossRef]
- Wang, H.N.; Ma, T.S.; Liu, Y.; Wu, B.S.; Ranjith, P.G. Numerical and experimental investigation of the anisotropic tensile behavior of layered rocks in 3D space under Brazilian test conditions. Int. J. Rock Mech. Min. Sci. 2023, 170, 105558. [Google Scholar] [CrossRef]
- Liu, Z.D.; Li, D.Y.; Liu, Y.P.; Yang, B.; Zhang, Z.X. Prediction of uniaxial compressive strength of rock based on lithology using stacking models. Rock Mech. Bull. 2023, 2, 100081. [Google Scholar] [CrossRef]
- Chong, Z.; Yao, Q.; Li, X. Experimental investigation of fracture propagation behavior induced by hydraulic fracturing in anisotropic shale cores. Energies 2019, 12, 976. [Google Scholar] [CrossRef]
- Ma, T.S.; Wang, H.N.; Liu, Y.; Shi, Y.F.; Ranjith, P.G. Fracture-initiation pressure model of inclined wells in transversely isotropic formation with anisotropic tensile strength. Int. J. Rock Mech. Min. Sci. 2022, 159, 105235. [Google Scholar] [CrossRef]
- Luo, N.; Zhang, H.; Chai, Y.; Li, P.; Zhai, C.; Zhou, J.; Ma, T. Research on damage failure mechanism and dynamic mechanical behavior of layered shale with different angles under confining pressure. Deep. Undergr. Sci. Eng. 2023, 2, 337–345. [Google Scholar] [CrossRef]
- Zhang, Y.K.; Chen, S.B.; Zhai, X.H.; Khan, J.; Zhang, Y.H. Brazilian splitting experiment and finite element simulation analysis of the influence of bedding loading angle on shale fracture mode. Nat. Gas Ind. B 2023, 10, 602–612. [Google Scholar] [CrossRef]
- Zhao, H.; Li, P.; Li, X.; Yao, W. Fracture propagation and evolution law of indirect fracturing in the roof of broken soft coal seams. Int. J. Coal Sci. Technol. 2024, 11, 4. [Google Scholar] [CrossRef]
- Perras, M.A.; Diederichs, M.S. A review of the tensile strength of rock: Concepts and testing. Geotech. Geol. Eng. 2014, 32, 525–546. [Google Scholar] [CrossRef]
- Ma, T.S.; Peng, N.; Zhu, Z.; Zhang, Q.B.; Yang, C.H.; Zhao, J. Brazilian tensile strength of anisotropic rocks: Review and new insights. Energies 2018, 11, 304. [Google Scholar] [CrossRef]
- Efe, T.; Demirdag, S.; Tufekci, K.; Sengun, N.; Altindag, R. Estimating the direct tensile strength of rocks from indirect tests. Arab. J. Geosci. 2021, 14, 1343. [Google Scholar] [CrossRef]
- Tan, X.; Konietzky, H.; Frühwirt, T.; Dan, D.Q. Brazilian tests on transversely isotropic rocks: Laboratory testing and numerical simulations. Rock Mech. Rock Eng. 2015, 48, 1341–1351. [Google Scholar] [CrossRef]
- Zhong, S.; Zuo, S.; Mao, L.; Luo, S.; Wang, X. Mechanism of anisotropic characteristics of layered limestone and a constitutive model for different bedding angles based on a Brazilian tensile test. Arab. J. Geosci. 2020, 13, 1228. [Google Scholar] [CrossRef]
- Li, C.; Zou, B.; Zhou, H.; Wang, J. Experimental investigation on failure behaviors and mechanism of an anisotropic shale in direct tension. Geomech. Geophys. Geo-Energy Geo Resour. 2021, 7, 98. [Google Scholar] [CrossRef]
- Liu, P.; Liu, Q.; Huang, X.; Hu, M.; Bo, Y.; Yuan, D.; Xie, X. Direct tensile test and FDEM numerical study on anisotropic tensile strength of Kangding slate. Rock Mech. Rock Eng. 2022, 55, 7765–7789. [Google Scholar] [CrossRef]
- Alencar, A.; Muñiz-Menéndez, M.; Pérez-Rey, I.; Galindo, R. An experimental study of tensile stress and deformation in an anisotropic rock. IOP Conf. Ser. Earth Environ. Sci. 2024, 1295, 012010. [Google Scholar] [CrossRef]
- Huang, Z.; Zhang, Y.; Li, Y.; Zhang, D.; Yang, T.; Sui, Z. Determining tensile strength of rock by the direct tensile, Brazilian splitting, and three-point bending methods: A comparative study. Adv. Civ. Eng. 2021, 2021, 5519230. [Google Scholar] [CrossRef]
- Fuenkajorn, K.; Klanphumeesri, S. Laboratory determination of direct tensile strength and deformability of intact rocks. Geotech. Test. J. 2011, 34, 97–102. [Google Scholar] [CrossRef]
- Liu, J.; Lyu, C.; Lu, G.; Shi, X.; Li, H.; Liang, C.; Deng, C. Evaluating a new method for direct testing of rock tensile strength. Int. J. Rock Mech. Min. Sci. 2022, 160, 105258. [Google Scholar] [CrossRef]
- Claesson, J.; Bohloli, B. Brazilian test: Stress field and tensile strength of anisotropic rocks using an analytical solution. Int. J. Rock Mech. Min. Sci. 2002, 39, 991–1004. [Google Scholar] [CrossRef]
- Ma, T.S.; Wang, H.N.; Liu, Y.; Fu, C.L.; Ranjith, P.G. Experimental investigation on the anisotropy of mode-I fracture and tensile failure of layered shale. Eng. Fract. Mech. 2023, 290, 109484. [Google Scholar] [CrossRef]
- Hobbs, D.W. Rock tensile strength and its relationship to a number of alternative measures of rock strength. Int. J. Rock Mech. Min. Sci. 1976, 4, 115–127. [Google Scholar] [CrossRef]
- Barron, K. Brittle fracture initiation in and ultimate failure of rocks: Part I—Anisotropic rocks: Theory. Int. J. Rock Mech. Min. Sci. 1971, 8, 553–563. [Google Scholar] [CrossRef]
- Nova, R.; Zaninetti, A. An investigation into the tensile behaviour of a schistose rock. Int. J. Rock Mech. Min. Sci. 1990, 27, 231–242. [Google Scholar] [CrossRef]
- Lee, Y.K.; Pietruszczak, S. Tensile failure criterion for transversely isotropic rocks. Int. J. Rock Mech. Min. Sci. 2015, 79, 205–215. [Google Scholar] [CrossRef]
- Liu, P.; Liu, Q.S.; Deng, P.H.; Huang, X.; Xie, X.Q. A new phenomenological anisotropic tensile failure criterion and its application in FDEM simulations. Eng. Fract. Mech. 2023, 289, 109359. [Google Scholar] [CrossRef]
- Nejati, M.; Aminzadeh, A.; Driesner, T.; Saar, M.O. On the directional dependency of mode I fracture toughness in anisotropic rocks. Theor. Appl. Fract. Mech. 2020, 107, 102494. [Google Scholar] [CrossRef]
- Jaeger, J.C. Failure of rocks under tensile conditions. Int. J. Rock Mech. Min. Sci. Geomech. Abstracts 1967, 4, 219–227. [Google Scholar] [CrossRef]
- Mellor, M.; Hawkes, I. Measurement of tensile strength by diametral compression of discs and annuli. Eng. Geol. 1971, 5, 173–225. [Google Scholar] [CrossRef]
- Efimov, V.P. The rock strength in different tension conditions. J. Min. Sci. 2009, 45, 569–575. [Google Scholar] [CrossRef]
- Pandey, P.; Singh, D.P. Deformation of a rock in different tensile tests. Eng. Geol. 1986, 22, 281–292. [Google Scholar] [CrossRef]
- Briševac, Z.; Kujundžić, T.; Čajić, S. Current cognition of rock tensile strength testing by Brazilian test. Min. Geol. Pet. Eng. Bull. 2015, 30, 101–128. [Google Scholar] [CrossRef]
- Cacciari, P.P.; Futai, M.M. Assessing the tensile strength of rocks and geological discontinuities via pull-off tests. Int. J. Rock Mech. Min. Sci. 2018, 105, 44–52. [Google Scholar] [CrossRef]
- Unlu, T.; Yilmaz, O. Development of a new push–pull direct tensile strength testing apparatus (PPTA). Geotech. Test. J. 2014, 37, 60–70. [Google Scholar] [CrossRef]
- Read, S.A.L.; Richards, L.R. Correlation of direct and indirect tensile tests for use in the Hoek-Brown constant mi. In Proceedings of the ISRM Regional Symposium–EUROCK 2014, Vigo, Spain, 27–29 May 2014. [Google Scholar]
Mean Error for BST (%) | Mean SD for BST (MPa) | Mean Error for DTT (%) | Mean SD for DTT (MPa) | |
---|---|---|---|---|
H-B criterion | 6.62 | 0.29 | 15.14 | 0.53 |
N-Z criterion | 2.74 | 0.12 | 13.26 | 0.45 |
SPW criterion | 7.55 | 0.32 | 14.11 | 0.49 |
L-P criterion | 2.35 | 0.11 | 10.36 | 0.36 |
CPA criterion | 3.23 | 0.14 | 9.50 | 0.33 |
Phenomenological criterion | 7.96 | 0.37 | 24.35 | 0.87 |
SS criterion | 2.35 | 0.11 | 10.36 | 0.36 |
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Fadhel, A.M.; Ma, T.; Wang, H. Experimental Investigation on the Tensile Mechanical Behavior of Layered Shale Using Direct and Indirect Test Methods. Appl. Sci. 2025, 15, 2669. https://doi.org/10.3390/app15052669
Fadhel AM, Ma T, Wang H. Experimental Investigation on the Tensile Mechanical Behavior of Layered Shale Using Direct and Indirect Test Methods. Applied Sciences. 2025; 15(5):2669. https://doi.org/10.3390/app15052669
Chicago/Turabian StyleFadhel, Ali. M., Tianshou Ma, and Haonan Wang. 2025. "Experimental Investigation on the Tensile Mechanical Behavior of Layered Shale Using Direct and Indirect Test Methods" Applied Sciences 15, no. 5: 2669. https://doi.org/10.3390/app15052669
APA StyleFadhel, A. M., Ma, T., & Wang, H. (2025). Experimental Investigation on the Tensile Mechanical Behavior of Layered Shale Using Direct and Indirect Test Methods. Applied Sciences, 15(5), 2669. https://doi.org/10.3390/app15052669