Abstract
Two methods (i.e., direct tensile test and the Brazilian test) are commonly adopted to measure the tensile strength of rock, but the tensile strengths obtained by the two methods are obviously different. Taking Beishan granite as physical background, this study systematically investigates the discrepancies between the Brazilian test and direct tensile test with the use of three-dimensional Flat-joint model (FJM3D) simulation. Simulation results indicate that the Brazilian disc is under a complex three-dimensional stress state, and produce some shear cracks, which is significantly different from direct tensile test. By assigning different micro parameters to the FJM, the influences of the heterogeneity of the microstructure (particles size and pre-existing cracks) and micro-strength (bond strength) on the direct tensile strength (DTS) and the Brazilian tensile strength (BTS) are investigated. The heterogeneity of particles size, pre-existing cracks, and bond strength have negatively effects on both DTS and BTS, and that the ratio between DTS and BTS decreases with the increase of heterogeneity of pre-existing cracks and bond strength. The statistical analyses reveal that in the Brazilian disc, the contact normal stresses obey the normal distribution, but in the direct tensile specimen, the contact normal stresses obey the log-normal distribution. The three heterogeneities have minor effects on the dip direction of cracks, but significantly affect the dip angle of cracks. The heterogeneity of microstructure affects the local stress concentration, which reduces the tensile strength, and changes the orientation of cracks.
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Abbreviations
- FJM3D:
-
The three-dimensional Flat-joint model
- BTS:
-
Brazilian tensile strength (MPa)
- DTS:
-
Direct tensile strength (MPa)
- P :
-
Loading force (N)
- D :
-
The Brazilian disc’s diameter (mm)
- t :
-
The Brazilian disc’s thickness (mm)
- E :
-
The Young’s modulus (GPa)
- UCS:
-
The Uniaxial compressive strength (MPa)
- \(\nu\) :
-
The Poisson’s ratio
- HPS:
-
Heterogeneity of particles size
- HPC:
-
Heterogeneity of pre-cracks
- HBS:
-
Heterogeneity of bond strength
- d max/d min :
-
The ratio between the maximum and minimum particle diameter
- Covbs :
-
The coefficient of variance of bond strength
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Acknowledgements
This work is supported by the National Natural Science Foundation of China (No.:51909138) and the Shandong Provincial Natural Science Foundation (No.:ZR2020YQ44).
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Jiang, R., Duan, K. & Zhang, Q. Effect of Heterogeneity in Micro-Structure and Micro-Strength on the Discrepancies Between Direct and Indirect Tensile Tests on Brittle Rock. Rock Mech Rock Eng 55, 981–1000 (2022). https://doi.org/10.1007/s00603-021-02700-y
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DOI: https://doi.org/10.1007/s00603-021-02700-y