A self-confined compression model of point load test and corresponding numerical and experimental validation

  • Qingwen Shi (School of Mine Safety, North China Institute of Science and Technology) ;
  • Zhenhua Ouyang (School of Mine Safety, North China Institute of Science and Technology) ;
  • Brijes Mishra (Department of Mining Engineering, The University of Utah) ;
  • Yun Zhao (Department of Mineral Resources, Xingfa Group)
  • Received : 2021.12.02
  • Accepted : 2023.06.20
  • Published : 2023.11.25


The point load test (PLT) is a widely-used alternative method in the field to determine the uniaxial compressive strength due to its simple testing machine and procedure. The point load test index can estimate the uniaxial compressive strength through conversion factors based on the rock types. However, the mechanism correlating these two parameters and the influence of the mechanical properties on PLT results are still not well understood. This study proposed a theoretical model to understand the mechanism of PLT serving as an alternative to the UCS test based on laboratory observation and literature survey. This model found that the point load test is a self-confined compression test. There is a compressive ellipsoid near the loading axis, whose dilation forms a tensile ring that provides confinement on this ellipsoid. The peak load of a point load test is linearly positive correlated to the tensile strength and negatively correlated to the Poisson ratio. The model was then verified using numerical and experimental approaches. In numerical verification, the PLT discs were simulated using flat-joint BPM of PFC3D to model the force distribution, crack propagation and BPM properties' effect with calibrated micro-parameters from laboratory UCS test and point load test of Berea sandstones. It further verified the mechanism experimentally by conducting a uniaxial compressive test, Brazilian test, and point load test on four different rocks. The findings from this study can explain the mechanism and improve the understanding of point load in determining uniaxial compressive strength.



The research described in this paper was financially supported by the National Nature Science Foundation of China [Grant No.52274120].


  1. ASTM Standard D3148-02 (2002), Standard Test Method for Elastic Moduli of Intact Rock Core Specimens in Uniaxial Compression, American Society for Testing and Materials,West Conshohocken, PA, USA.
  2. ASTM Standard D3967-16 (2016), Standard Test Method for Splitting Tensile Strength of Intact Rock Core Specimens, American Society for Testing and Materials, West Conshohocken, PA, USA.
  3. ASTM standard D5731-16 (2016), Standard Test Method for Determination of the Point Load Strength Index of Rock and Application to Rock Strength Classifications, American Society for Testing and Materials, West Conshohocken, PA, USA.
  4. Basu, A., Mishra, D.A. and Roychowdhury, K. (2013), "Rock failure modes under uniaxial compression, Brazilian, and point load tests", Bull. Eng. Geol. Environ., 72, 457-475.
  5. Bieniawski, Z.T. (1975), "The point-load test in geotechnical practice", Eng. Geol., 9(1), 1-11.
  6. Broch, E. and Franklin, J.A. (1972), "The point-load strength test", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 9(6), 669-676.
  7. Churcher, P.L., French, P.R., Shaw, J.C. and Schramm, L.L. (1991), "Rock properties of Berea sandstone, Baker dolomite, and Indiana limestone", The SPE International Conference on Oilfield Chemistry, Anaheim, CA, USA, February.
  8. Everall, T.J. and Sanislav, I.V. (2018), "The influence of preexisting deformation and alteration textures on rock strength, failure modes and shear strength parameters", Geosci., 8(4), 124.
  9. Franklin, J.A. (1985), "Suggested method for determining point load strength", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 22(2), 51-60.
  10. Frocht, M.M. (1974), Photoelasticity, Wiley, Hoboken, NJ, USA.
  11. Heidari, M., Khanlari, G.R., Torabi Kaveh, M. and Kargarian, S. (2012), "Predicting the uniaxial compressive and tensile strengths of gypsum rock by point load testing", Rock Mech. Rock Eng., 45, 265-273.
  12. Hoek, E. (1977), "Rock mechanics laboratory testing in the context of a consulting engineering organization", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 14(2), 93-101.
  13. Itasca Consulting Group, Inc. (2019), PFC|US Minneapolis - Itasca Consulting Group, Inc, Itasca Consulting Group, Inc., Minneapolis, MN, USA.
  14. Jaeger, J.C., Cook, N.G. and Zimmerman, R. (2009), Fundamentals of Rock Mechanics, Wiley, Hoboken, NJ, USA.
  15. Kabilan, N., Muttharam, M. and Elamathi, V. (2017), "Prediction of unconfined compressive strength for jointed rocks using point load index based on joint asperity angle", Geotech. Geol. Eng., 35, 2625-2636.
  16. Kaya, A. and Karaman, K. (2016), "Utilizing the strength conversion factor in the estimation of uniaxial compressive strength from the point load index", Bull. Eng. Geol. Environ., 75, 341-357.
  17. Koyama, T. and Jing, L. (2007), "Effects of model scale and particle size on micro-mechanical properties and failure processes of rocks-a particle mechanics approach", Eng. Anal. Bound. Elem., 31(5), 458-472.
  18. Lutton, RJ. (1970), "Tensile fracture mechanics from fracture surface morphology", The 12th U.S. Symposium on Rock Mechanics, Rolla, MO, USA, November.
  19. Lutton, R.J. (2006), "Fracture surface morphology", Structural Geology and Tectonics, Encyclopedia of Earth Science Springer, Berlin, Heidelberg.
  20. Hossein, M., Paul, C.H. and Serkan, S. (2015), "A modification to radial strain calculation in rock testing", Geotech. Test. J., 38(6), 813-822.
  21. Peng, S.S. (1976), "Stress analysis of cylindrical rock discs subjected to axial double point load", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 13(3), 97-101.
  22. Potyondy, D.O. (2017), "Simulating perforation damage with a flat-jointed bonded-particle material", The 51st U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, CA, USA, June.
  23. Potyondy, D.O. (2018), "A flat-jointed bonded-particle model for rock", The 52nd U.S. Rock Mechanics/Geomechanics Symposium, Seattle, WA, USA, June.
  24. Russell, A.R. and Wood, D.M. (2009), "Point load tests and strength measurements for brittle spheres", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 46(2), 272-280.
  25. Sahin, M., Ulusay, R. and Karakul, H. (2020), "Point load strength index of half-cut core specimens and correlation with uniaxial compressive strength", Rock Mech. Rock Eng., 53, 3745-3760.
  26. Sarici, D.E. and Ozdemir, E. (2018), "Determining point load strength loss from porosity, Schmidt hardness, and weight of some sedimentary rocks under freeze-thaw conditions", Environ. Earth Sci., 77, 1-9.
  27. Serati, M., Masoumi, H., Williams, D.J., Alehossein, H. and Roshan, H. (2018), "Some new aspects on the diametral point load testing", The 52nd U.S. Rock Mechanics/Geomechanics Symposium, Seattle, WA, USA, June.
  28. Shi, Q. and Mishra, B. (2021), "Discrete element modeling of delamination in laboratory scale laminated rock", Min. Metall. Explor., 38(1), 433-446.
  29. Shi, Q., Mishra, B. and Zhao, Y. (2022), "DEM analysis of the effect of lamination properties on the stability of an underground coal mine entry with laminated shale roof", Min. Metall. Explor., 39(2), 495-506.
  30. Sternberg, E. and Rosenthal, F. (1952), "The elastic sphere under concentrated loads", J. Appl. Mech., 19(4), 413-421.
  31. Timoshenko, S. (1951), Theory of Elasticity, McGraw-Hill Book Co., Inc., New York City, NY, UAS.
  32. Wang, Y., Tang, J., Dai, Z. and Yi, T. (2018), "Experimental study on mechanical properties and failure modes of low-strength rock samples containing different fissures under uniaxial compression", Eng. Fract. Mech., 197, 1-20.
  33. Wei, X.X., Chau, K.T. and Wong, R.H.C. (2019), "Theoretical and experimental validation of point load strength test for irregular lumps", J. Eng. Mech., 145(9), 04019065.
  34. Wen, L., Luo, Z.Q., Yang, S.J., Qin, Y.G., Ma, S.W. and Jiang, H. (2019), "A new method for evaluating the rock mass damage index based on the field point load strength", Royal Soc. Open Sci., 6(3), 181591.
  35. Wong, R.H., Chau, K.T., Yin, J.H., Lai, D.T. and Zhao, G.S. (2017), "Uniaxial compressive strength and point load index of volcanic irregular lumps", Int. J. Rock Mech. Min. Sci., 93, 307-315.
  36. Xie, H., Wang, J.A. and Kwasniewski, M.A. (1999), "Multifractal characterization of rock fracture surfaces", Int. J. Rock Mech. Min. Sci., 36(1), 19-27.
  37. Xue, Y., Gao, D. and Mishra, B. (2018), "Stochastic simulation of rock size effect with correlation length", The 52nd U.S. Rock Mechanics/Geomechanics Symposium, Seattle, WA, USA, June.
  38. Yin, J.H., Wong, R.H., Chau, K.T., Lai, D.T. and Zhao, G.S. (2017), "Point load strength index of granitic irregular lumps: Size correction and correlation with uniaxial compressive strength", Tunn. Undergr. Space Technol., 70, 388-399.
  39. Yoon, J. (2007), "Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation", Int. J. Rock Mech. Min. Sci., 44(6), 871-889.
  40. Zhang, X.P., Wu, S., Afolagboye, L.O., Wang, S. and Han, G. (2016), "Using the point load test to analyze the strength anisotropy of quartz mica schist along an exploration adit", Rock Mech. Rock Eng., 49, 1967-1975.
  41. Zhang, Y., Shao, Z., Wei, W. and Qiao, R. (2019), "PFC simulation of crack evolution and energy conversion during basalt failure process", J. Geophys. Eng., 16(3), 639-651.