Failure characteristics of rock-like materials with single flaws under uniaxial compression

  • Cheng Zhao
  • Jialun Niu
  • Qingzhao ZhangEmail author
  • Chunfeng Zhao
  • Yimeng Zhou
Original Paper


A uniaxial compression test was conducted with a servo loading apparatus to study the failure of a rock-like specimen with a pre-existing single flaw. The evolution of cracks was monitored with digital image correlation technology and simulated with the expanded distinct element method based on the strain strength criterion. The concentration and evolution of the principal strain field were found to be consistent with the initiation, propagation, and coalescence of cracks. As the inclination angle increased, the position of the maximum principal strain concentration changed from within the flaw to the flaw tips, and the distribution of the horizontal displacement field changed from symmetric to antisymmetric. The initiation stress and peak strength were affected by the inclination angle; they were minimum when the inclination angle was 60°. As the inclination angle increased, the failure mode of the specimens transformed from mostly tensile failure to mostly shear failure.


Single flaw Uniaxial compression Digital image correlation method (DIC) Strain field Expanded distinct element method (EDEM) 



The authors would like to acknowledge the financial support of the National Key Research and Development Plan [grant number 2017YFC0805004], National Natural Science Foundation of China [grant number 41202193,41572262], and the Shanghai Rising-Star Program [grant number 17QC1400600].


  1. Agwai A, Guven I, Madenci E (2011) Predicting crack propagation with peridynamics: a comparative study. Int J Fract 171(1):65–78CrossRefGoogle Scholar
  2. Ashby MF, Hallam SD (1986) The failure of brittle solids containing small cracks under compressive stress states. Acta Metall 34(3):497–510CrossRefGoogle Scholar
  3. Basu A, Mishra DA, Roychowdhury K (2013) Rock failure modes under uniaxial compression, Brazilian, and point load tests. Bull Eng Geol Environ 72(3–4):457–475CrossRefGoogle Scholar
  4. Bieniawski ZT (1967) Mechanism of brittle fracture of rock, part II—experimental studies. Int J Rock Mech Min Sci 4(4):407–423CrossRefGoogle Scholar
  5. Bobet A, Einstein HH (1998) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci 35(7):863–888CrossRefGoogle Scholar
  6. Brace WF, Bombolakis EG (1963) A note on brittle crack growth in compression. J Geophys Res 68(12):3709–3713CrossRefGoogle Scholar
  7. Cao P, Liu T, Pu C, Lin H (2015) Crack propagation and coalescence of brittle rock-like specimens with pre-existing cracks in compression. Eng Geol 187:113–121CrossRefGoogle Scholar
  8. Chaker C, Barquins M (1996) Sliding effect on branch crack. Phys Chem Earth 21(4):319–323CrossRefGoogle Scholar
  9. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65CrossRefGoogle Scholar
  10. Fan LF, Wu ZJ, Wan Z, Gao JW (2017) Experimental investigation of thermal effects on dynamic behavior of granite. Appl Therm Eng 125:94–103CrossRefGoogle Scholar
  11. Gui YL, Bui HH, Kodikara J, Zhang QB, Zhao J, Rabczuk T (2016) Modelling the dynamic failure of brittle rocks using a hybrid continuum-discrete element method with a mixed-mode cohesive fracture model. Int J Impact Eng 87:146–155CrossRefGoogle Scholar
  12. Gui YL, Zhao ZY, Zhang C, Ma SQ (2017) Numerical investigation of the opening effect on the mechanical behaviours in rocks under uniaxial loading using hybrid continuum-discrete element method. Comput Geotech 90:55–72CrossRefGoogle Scholar
  13. Guo SF, Qi SW, Cai M (2016) Influence of tunnel wall roughness and localized stress concentrations on the initiation of brittle spalling. Bull Eng Geol Environ 75(4):1597–1607CrossRefGoogle Scholar
  14. Hoek E, Bieniawski ZT (1965) Brittle fracture propagation in rock under compression. Int J Fract 1(3):137–155CrossRefGoogle Scholar
  15. Horii H, Nemat-Nasser S (1985) Compression-induced microcrack growth in brittle solids: axial splitting and shear failure. J Geophys Res 90(B4):3105–3125CrossRefGoogle Scholar
  16. Hu M, Liu Y, Ren J, Wu R, Zhang Y (2017) Laboratory test on crack development in mudstone under the action of dry-wet cycles. Bull Eng Geol Environ 2017(4):1–14Google Scholar
  17. Huang J, Chen G, Zhao Y, Wang R (1990) An experimental study of the strain field development prior to failure of a marble plate under compression. Tectonophysics 175(1):269–284Google Scholar
  18. Huang ML, Tang CA, Zhu W (2000) Numerical simulation on failure process of rock. Chin J Rock Mech Eng 19(4):468–471Google Scholar
  19. Jia CJ, Xu WY, Wang SS, Wang RB, Yu J (2018) Experimental analysis and modeling of the mechanical behavior of breccia lava in the dam foundation of the Baihetan hydropower project. Bull Eng Geol Environ.
  20. Jiang MJ, Chen H, Zhang N, Fang R (2014) Distinct element numerical analysis of crack evolution in rocks containing pre-existing double flaw. Rock Soil Mech 35(11):3259–3268Google Scholar
  21. Jiang Y, Li B, Yamashita Y (2009) Simulation of cracking near a large underground cavern in a discontinuous rock mass using the expanded distinct element method. Int J Rock Mech Min Sci 46(1):97–106CrossRefGoogle Scholar
  22. Lin Q, Labuz JF (2013) Fracture of sandstone characterized by digital image correlation. Int J Rock Mech Min Sci 60:235–245CrossRefGoogle Scholar
  23. Liang CY, Zhang QB, Li X, Xin P (2016) The effect of specimen shape and strain rate on uniaxial compressive behavior of rock material. Bull Eng Geol Environ 75(4):1669–1681CrossRefGoogle Scholar
  24. Morgan SP, Johnson CA, Einstein HH (2013) Cracking processes in Barre granite-fracture process zones and crack coalescence. Int J Fract 180(2):177–204CrossRefGoogle Scholar
  25. Petit J, Barquins M (1988) Can natural faults propagate under mode II conditions? Tectonics 7(6):1243–1256CrossRefGoogle Scholar
  26. Reyes O, Einstein HH (1991) Failure mechanisms of fractured rock—a fracture coalescence model. Proc seventh Int Congr. Rock Mech 1:333–340Google Scholar
  27. Sagong M, Bobet A (2002) Coalescence of multiple flaws in a rock-model material in uniaxial compression. Int J Rock Mech Min Sci 39(2):229–241CrossRefGoogle Scholar
  28. Shen B, Stephansson O, Einstein HH, Ghahreman B (1995) Coalescence of fractures under shear stress experiments. J Geophys Res 100(B4):5975–5990CrossRefGoogle Scholar
  29. Tang CA, Lin P, Wong RHC, Chau KT (2001) Analysis of crack coalescence in rock-like materials containing three flaws—part II: numerical approach. Int J Rock Mech Min Sci 38(7):925–939CrossRefGoogle Scholar
  30. Tarokh A, Blanksma DJ, Fakhimi A, Labuz JF (2016) Fracture initiation in cavity expansion of rock. Int J Rock Mech Min Sci 85:84–91CrossRefGoogle Scholar
  31. Vesga LF, Vallejo LE, Lobo-Guerrero S (2008) DEM analysis of the crack propagation in brittle clays under uniaxial compression tests. Int J Numer Anal Met 32(11):1405–1415CrossRefGoogle Scholar
  32. Wong LNY, Einstein HH (2006) Fracturing behavior of prismatic specimens containing single flaws. In: Proceedings of the 41st US symposium on rock mechanics, 17–21 June 2006, Golden, ColoradoGoogle Scholar
  33. Wong LNY, Einstein HH (2009a) Crack coalescence in molded gypsum and Carrara marble: part 1. Macroscopic observations and interpretation. Rock Mech Rock Eng 42:475–511CrossRefGoogle Scholar
  34. Wong LNY, Einstein HH (2009b) Crack coalescence in molded gypsum and Carrara marble: part 2. Microscopic observations and interpretation. Rock Mech Rock Eng 42:513–545CrossRefGoogle Scholar
  35. Wong RHC, Chau KT (1998) Crack coalescence in a rock-like material containing two cracks. Int J Rock Mech Min Sci 35(2):147–164CrossRefGoogle Scholar
  36. Wong RHC, Chau KT, Tang CA, Lin P (2001) Analysis of crack coalescence in rock-like materials containing three flaws—part I: experimental approach. Int J Rock Mech Min Sci 38(7):909–924CrossRefGoogle Scholar
  37. Wu ZJ, Fan LF, Liu QS, Ma GW (2017) Micro-mechanical modeling of the macro-mechanical response and fracture behavior of rock using the numerical manifold method. Eng Geol 225:49–60CrossRefGoogle Scholar
  38. Wu ZJ, Wong LNY (2013) Modeling cracking behavior of rock mass containing inclusions using the enriched numerical manifold method. Eng Geol 162:1–13CrossRefGoogle Scholar
  39. Yang SQ, Huang YH, Tian WL, Zhu JB (2017) An experimental investigation on strength, deformation and crack evolution behavior of sandstone containing two oval flaws under uniaxial compression. Eng Geol 217:35–48CrossRefGoogle Scholar
  40. Yang SQ, Jing HW (2011) Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression. Int J Fract 168(2):227–250CrossRefGoogle Scholar
  41. Yang SQ, Tian WL, Huang YH, Ranjith PG, Ju Y (2016) An experimental and numerical study on cracking behavior of brittle sandstone containing two non-coplanar fissures under uniaxial compression. Rock Mech Rock Eng 49(4):1497–1515CrossRefGoogle Scholar
  42. Zhang XP, Wong LNY (2012) Cracking processes in rock-like material containing a single flaw under uniaxial compression: a numerical study based on parallel bonded-particle model approach. Rock Mech Rock Eng 45(5):711–737Google Scholar
  43. Zhang XP, Wong LNY (2014) Displacement field analysis for cracking processes in bonded-particle model. Bull Eng Geol Environ 73(1):13–21CrossRefGoogle Scholar
  44. Zhang XP, Wong LNY, Wang S (2015) Effects of the ratio of flaw size to specimen size on cracking behavior. Bull Eng Geol Environ 74(1):181–193CrossRefGoogle Scholar
  45. Zhao C, Ma CC, Zhao CF, Du SG, Bao C (2017) Crack propagation simulation of rock-like specimen using strain criterion. Eur J Environ Civ Eng.
  46. Zhao C, Matsuda H, Lou S, Guan ZC, Tian JS (2013) Visualization of buckling on thin-walled cylindrical shell by digital image correlation method. Appl Math Inform Sci 7(3):999–1004CrossRefGoogle Scholar
  47. Zhao C, Niu JL, Zhang QZ, Zhao CF, Xie JF (2018a) Buckling behavior of a thin-walled cylinder shell with the cutout imperfections. Mech Adv Mater Struct.
  48. Zhao C, Zhou YM, Zhao CF, Bao C (2018b) Cracking processes and coalescence modes in rock-like specimens with two parallel pre-existing cracks. Rock Mech Rock Eng.
  49. Zhao F, He MC (2017) Size effects on granite behavior under unloading rockburst test. Bull Eng Geol Environ 76(3):1183–1197CrossRefGoogle Scholar
  50. Zheng Y, Chen CX, Liu TT, Zhang W, Song YF (2018) Slope failure mechanisms in dipping interbedded sandstone and mudstone revealed by model testing and distinct-element analysis. Bull Eng Geol Environ 77(1):49–68CrossRefGoogle Scholar
  51. Zou C, Wong LNY (2014) Experimental studies on cracking processes and failure in marble under dynamic loading. Eng Geol 173:19–31CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Geotechnical Engineering and Key Laboratory of Geotechnical and Underground Engineering of Ministry of EducationTongji UniversityShanghaiChina
  2. 2.College of EngineeringTibet UniversityLhasaChina

Personalised recommendations