DOI QR코드

DOI QR Code

Comparison of measurement uncertainty calculation methods on example of indirect tensile strength measurement

  • Received : 2016.08.12
  • Accepted : 2017.01.04
  • Published : 2017.06.25

Abstract

Indirect measure of the tensile strength of laboratory samples is an important topic in rock engineering. One of the most important tests, the Brazilian strength test is performed to obtain the tensile strength of rock, concrete and other quasi brittle materials. Because the measurements are provided indirectly and the inspected rock materials may have heterogeneous properties, uncertainty quantification is required for a reliable test evaluation. In addition to the conventional measurement evaluation uncertainty methods recommended by the Guide to the Expression of Uncertainty in Measurement (GUM), such as Taylor's and Monte Carlo Methods, a fuzzy set-based approach is also proposed and resulting uncertainties are discussed. The results showed that when a tensile strength measurement is measured by a laboratory test, its uncertainty can also be expressed by one of the methods presented.

Keywords

References

  1. Adl-Zarrabi, B., Christiansson, R., Emardson, R., Jacobsson, L., Pendrill, L.R., Sandstrom, M. and Schoue, B. (2009), "Quality aspects of determining key rock parameters for the design and performance assessment of a repository for spent nuclear fuel", Proceedings of the 13th International Metrology Congress, Lille, France, June. (Edited by French College of Metrology, ISTE-Wiley)
  2. Bieniawski, Z.T. and Hawkes, I. (1978), "Suggested Methods for Determining Tensile Strength of Rock Materials", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 15(3), 99-103 https://doi.org/10.1016/0148-9062(78)90003-7
  3. BIPM 2008a (2008a), Joint Committee for Guides in Metrology - 100. Evaluation of measurement data- Guide to the expression of uncertainty in measurement; BIPM, Paris, France.
  4. BIPM 2008b (2008b), Joint Committee for Guides in Metrology - 101. Evaluation of measurement datasupplement 1 - Propagation of Distributions Using a Monte Carlo Method; BIPM, Paris, France.
  5. Castro-Montero, A., Jia, Z. and Shah, S.P. (1995), "Evaluation of damage in brazilian test using holographic interferometry", ACI Mater. J., 92(3), 268-275.
  6. Chen, Y. (2012), "Uncertainty evaluation in measure results of rock permeability", Adv. Mater. Res., 508, 47-50. https://doi.org/10.4028/www.scientific.net/AMR.508.47
  7. Chen, C.S. and Hsu, S.C. (2001), "Measurement of indirect tensile strength of anisotropic rocks by the ringtest", Rock Mech. Rock Eng., 34(4), 293-321. https://doi.org/10.1007/s006030170003
  8. Claesson, J. and Bohloli, B. (2002), "Brazilian test: stress field and tensile strength of anisotropic rocks using an analytical solution", Int. J. Rock Mech. Min. Sci., 39(8), 991-1004. https://doi.org/10.1016/S1365-1609(02)00099-0
  9. Desenfant, M., Fischer, N., Blanquart, B. and Bediat, N. (2009), "Evaluation of uncertainty using Monte Carlo Simulations", Proceedings of the 13th International Metrology Congress, Lille, France, June. (Edited by French Colege of Metrology, ISTE-Wiley)
  10. Ellison, S.L.R. (2015), metRology Package; R Project (CRAN), Version 0.9-18.
  11. Erarslan, N., Liang, Z.Z. and Williams, D.J. (2012), "Experimental and numerical studies on determination of indirect tensile strength of rocks", Rock Mech. Rock Eng., 45(5), 739-751. https://doi.org/10.1007/s00603-011-0205-y
  12. Gui, Y., Bui, H.H. and Kodikara, J. (2015), "An application of a cohesive fracture model combining compression tension and shear in soft rocks", Comput. Geotech., 66, 142-157. https://doi.org/10.1016/j.compgeo.2015.01.018
  13. Hanss, M. (2005), Applied Fuzzy Arithmetic. An Introduction with Engineering Applications, Springer, Heidelberg, Germany.
  14. Hudson, J.A. and Harrison, J.P. (1997), Engineering Rock Mechanics. An Introduction to Principles; Pergamon Press.
  15. Bieniawski, Z.T. and Hawkes, I. (2007), "Suggested methods for determining tensile strength of rock materials", In: The Complete ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 1974-2006, (R. Ulusay and J.A. Hudson Eds.), pp. 177-184.
  16. Klir, G.J. (2005), Uncertainty and Information. Foundations of Generalized Information Theory, John Wiley & Sons, NJ, USA.
  17. Kuhinek, D., Zoric, I. and Hrzenjak, P. (2011), "Measurement uncertainty in testing of uniaxial compressive strength and deformability of rock samples", Measure. Sci. Rev., 11(4), 112-117.
  18. Lafarge, T. and Possolo, A. (2015), "The NIST uncertainty Machine - User's Manual", NCSLI Measure J. Measure. Sci., 10(3), 20-27.
  19. Li, D. and Wong, L.N.Y. (2013), "The Brazilian disc test for rock mechanics applications: Review and new İnsights", Rock Mech. Rock Eng., 46(2), 269-287. https://doi.org/10.1007/s00603-012-0257-7
  20. MATLAB-R2009b (2009), MATLAB 7.9; The MathWorks Inc., Natick, MA, USA.
  21. Mauris, G., Lasserre, V. and Foulloy, L. (2001), "A fuzzy approach for the expression of uncertainty in measurement", Measurement, 29(3), 165-177. https://doi.org/10.1016/S0263-2241(00)00036-1
  22. Muller, M. (2009), "Computational aspects of measurement uncertainty calculation", Ph.D. Dissertation; ETH, Zurich, Switzerland.
  23. Muller, M., Wolf, M., Rosslein, M. and Gander, W. (2009), "Limits of the uncertainty propagation: examples and solutions using the Monte Carlo Method", Proceedings of the 13th International Metrology Congress, Lille, France, June. (Edited by French College of Metrology, ISTE-Wiley)
  24. Pavese, F. (2009), An Introduction to Data modeling Principles in Metrology and Testing, in Data Modeling for Metrology and Testing in Measurement Science, (Edited by F. Pavese and A.B. Forbes), Springer, New York, NY, USA.
  25. Perras, M.A. and Diederichs, M.S. (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
  26. Rabinovich, S.G. (2013), Evaluating Measurement Accuracy. A Practical Approach, (2nd Ed.), Springer, New York, NY, USA.
  27. Rocco, C., Guinea, G.V., Planas, J. and Elices, M. (1999), "Size effect and boundary conditions in the brazilian test: Theoretical analysis", Materials & Structures/Materiaux et Constructions, 32(6), 437-444. https://doi.org/10.1007/BF02482715
  28. Rojek, J., Onate, E., Labra, C. and Kargl, H. (2011), "Discrete element simulation of rock cutting", Int. J. Rock Mech. Min. Sci., 48(6), 996-1010. https://doi.org/10.1016/j.ijrmms.2011.06.003
  29. Salicone, S. (2007), Measurement Uncertainty. An Approach via the Mathematical Theory of Evidence, Springer, New York, NY, USA.
  30. Steele, A.G. and Douglas, R.J. (2009), "Monte Carlo modeling of randomness", In: Data Modeling for Metrology and Testing in Measurement Science, (Edited by F. Pavese, A.B. Forbes), Springer.
  31. Tutmez, B. (2009), "Clustering-based identification for the prediction of splitting tensile strength of concrete", Comput. Concrete, Int. J., 6(2), 155-165. https://doi.org/10.12989/cac.2009.6.2.155
  32. Ulusay, R., Gokceoglu, C. and Binal, A. (2011), Rock Mechanics Laboratory Experiments, TMMOB. [In Turkish]
  33. Wan, L., Wei, Z. and Shen, J. (2016), "Charts for estimating rock mass shear strength parameters", Geomech. Eng., Int. J., 10(3), 257-267.
  34. Wosatko, A., Winnicki, A. and Pamin, J. (2011), "Numerical analysis of Brazilian split test on concrete cylinder", Comput. Concrete, Int. J., 8(3), 243-278. https://doi.org/10.12989/cac.2011.8.3.243
  35. Yue, Z.Q., Chen, S. and Tham, L.G. (2003), "Finite element modeling of geomaterials using digital image processing", Comput. Geotech., 30(5), 375-397. https://doi.org/10.1016/S0266-352X(03)00015-6
  36. Zimmermann, H.-J. (2010), "Fuzzy set theory", WIREs Computational Statistics, 2(3), 317-332. https://doi.org/10.1002/wics.82