Abstract
Theoretically, the direct tension (DT) test is the simplest and most effective method to determine the tensile strength of rocks, which is meaningful in the practice of rock engineering and geophysics applications. However, clamping the specimens is a problem that causes difficulty in specimen preparation and complicates the use of test equipment. The Luong core tension (LCT) test is an innovative approach to estimate the tensile strength of rocks in a laboratory and overcome the disadvantages of the conventional DT test; thus, this approach has strong practical appeal. This study first discusses the mechanics of the LCT test, and then experimentally and numerically investigates the sample shape effect and optimal sample shape range to obtain a reliable tensile strength (TS). Results show that the maximum stress near the inner and outer bottom are close to each other, and a reliable tensile strength can be obtained when the ratio of the outer ring diameter to specimen diameter, r1/R, is 0.62 ± 0.08; the ratio of the inner ring diameter to specimen diameter, r2/R, is 0.45 ± 0.12; and the ratio the of inner ring diameter to outer ring diameter, r2/r1, is 0.64 ± 0.06. Tensile strength results obtained from these tests are well consistent with that obtained from the present DT test. Furthermore, compared with results of Brazilian and hydraulic fracturing hollow-cylinder tests, this method yields the lowest standard error and minimum coefficient of variation.
Similar content being viewed by others
Abbreviations
- CAX8:
-
8-node biquadratic axisymmetric quadrilateral elements
- CEA:
-
China Earthquake Administration
- COV:
-
Coefficient of variation
- DT:
-
Direct tension
- ICD:
-
Institute of Crustal Dynamics
- inDT:
-
Indirect tension
- ISRM:
-
International Society for Rock Mechanics
- LCT:
-
Luong core tension
- SD:
-
Standard deviation
- TS:
-
Tensile strength
- c :
-
Cohesion
- E :
-
Young’s modulus
- F :
-
Load
- F a :
-
Axial load
- R :
-
Specimen radius
- r 1 :
-
Outer annular ring radius
- r 2 :
-
Inner annular ring radius
- S max1 :
-
Maximum stress at tip of outer ring
- S max2 :
-
Maximum stress at tip of inner ring
- Syy, σy :
-
Axial stress
- δ :
-
Relative difference between stresses at tips of inner and outer rings
- δ 0 :
-
Error
- σ t :
-
Uniaxial tensile strength
- v :
-
Poisson’s ratio
- Ф :
-
Coefficient of friction
References
Blümel M (2000) Improved procedures for laboratory rock testing. In: Proceedings of the EUROCK 2000 Symposium. VerlagGlückauf, Essen, pp 573–578
Boresi AP, Schmidt RJ (2003) Advanced mechanics of materials, 6th edn. John Wiley, New York
Butenuth C, Freitas MHD, Al-Samahiji D, Park HD, Cosgrove JW, Schetelig K (1993) Observations on the measurement of tensile strength using the hoop test. Int J Rock Mech Min Sci Geomech Abstr 30:157–162. https://doi.org/10.1016/0148-9062(93)90708-L
Cai M (2013) Rock mechanics and engineering. Science Press, Beijing
Chen X, Bu J, Xu L (2016) Effect of strain rate on post-peak cyclic behavior of concrete in direct tension. Constr Build Mater 124:746–754. https://doi.org/10.1016/j.conbuildmat.2016.08.012
Chen X, Bu J, Xu L (2017a) Experimental study on cyclic tensile behavior of concrete under high stress level. ACI Mater J 114:775–781. https://doi.org/10.14359/51700796
Chen X, Xu L, Bu J (2017b) Experimental study and constitutive model on complete stress-strain relations of plain concrete in uniaxial cyclic tension. KSCE J Civ Eng 21:1829–1835. https://doi.org/10.1007/s12205-016-0802-0
Chen X, Xu L, Shi D, Chen Y, Zhou W, Wang Q (2017c) Experimental study on cyclic tensile behaviour of concrete under various strain rates. Mag Concr Res 70:55–70. https://doi.org/10.1680/jmacr.17.00144
Coviello A, Lagioia R, Nova R (2005) On the measurement of the tensile strength of soft rocks. Rock Mech Rock Eng 38:251–273. https://doi.org/10.1007/s00603-005-0054-7
Diederichs M, Kaiser P (1999) Tensile strength and abutment relaxation as failure control mechanisms in underground excavations. Int J Rock Mech Min Sci 36:69–96. https://doi.org/10.1016/S0148-9062(98)00179-X
Efimov V (2009) The rock strength in different tension conditions. J Min Sci 45:569–575. https://doi.org/10.1007/s10913-009-0071-0
Erarslan N, Williams DJ (2012) Experimental and numerical studies on determination of indirect tensile strength of rocks. Rock Mech Rock Eng 45:739–751. https://doi.org/10.1007/s00603-011-0205-y
Fahimifar A, Malekpour M (2012) Experimental and numerical analysis of indirect and direct tensile strength using fracture mechanics concepts. Bull Eng Geol Environ 71:269–283. https://doi.org/10.1007/s10064-011-0402-7
Fairhurst C (1961) Laboratory measurement of some physical properties of rock. In: The 4th US Symposium on Rock Mechanics (USRMS), University Park. American Rock Mechanics Association, pp 105–118
Hawkes I, Mellor M (1970) Uniaxial testing in rock mechanics laboratories. Eng Geol 4:179–285. https://doi.org/10.1016/0013-7952(70)90034-7
He M, Hu J, Xiong W, Liu C (2005) Splitting test and analysis of rock tensile strength. Mining Research and Development 25:12–16
Li D, Wong LNY (2013) The Brazilian disc test for rock mechanics applications: review and new insights. Rock Mech Rock Eng 46:269–287. https://doi.org/10.1007/s00603-012-0257-7
Luong M (1988) Direct tensile and direct shear strengths of Fontainebleau sandstone. In: Key Questions in Rock Mechanics: Proc 29th US Symposium, Minneapolis, vol 2. Balkema, Rotterdam, pp 237–246
Masoumi H, Serati M, Williams DJ, Alehossein H (2017) Size Dependency of Intact Rocks With High Brittleness: A Potential Solution to Eliminate Secondary Fractures in Brazilian Test. Paper presented at the 51st U.S. Rock Mechanics/Geomechanics Symposium, San Francisco
Molenda M, Stöckhert F, Brenne S, Alber M (2013) Comparison of hydraulic and conventional tensile strength tests. In: Bunger AP, McLennan J, Jeffrey R (eds) Effective and sustainable hydraulic fracturing. InTech, pp 981–992. https://doi.org/10.5772/56300
Perras MA, Diederichs MS (2014) A review of the tensile strength of rock: concepts and testing. Geotech Geol Eng 32:525–546. https://doi.org/10.1007/s10706-014-9732-0
Plinninger R, Wolski K, Spaun G, Thomée B, Schikora K (2003) Experimental and model studies on the Modified Tension Test (MTT)-a new and simple testing method for direct tension tests. Paper presented at the Geotechnical Measurements and Modelling: Proceedings of the 8th International Symposium, Karlsruhe
Ye M, Xu J, Mu H, Hong H (2001) Approach to test method of rock strength in uniaxial tension. Journal of Guizhou University of Technology: Natural Science Edition 30:19–25
Acknowledgements
The authors would like to thank Enago (www.enago.cn) for the English language review.
Funding
This work is supported by the National Natural Science Foundation of China (41704096, 41574088) and Fundamental Research Fund for State Level Scientific Institutes (ZDJ2017-13).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Wang, C., Gao, G., Jia, Q. et al. Investigation of optimum sample shape for the Luong core tension test. Bull Eng Geol Environ 79, 831–844 (2020). https://doi.org/10.1007/s10064-019-01607-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10064-019-01607-x