Technical Papers
Jun 9, 2020

Influence of Two Cross-Flaws Geometry on the Strength and Crack Coalescence of Rock-Like Material Specimens under Uniaxial Compression

Publication: International Journal of Geomechanics
Volume 20, Issue 8

Abstract

Cross-flaws are very common in natural rocks. To date, the understanding of the failure process of rocks with cross-flaws is very limited. In this research, we study the influence of the cross-flaws geometry on the rock strength and coalescence modes with rock-like specimens. In this work, three groups of specimens with pre-existing cross-flaws are investigated: two aligned cross-flaws, two step cross-flaws, and two collinear primary flaws. The crack propagation and strength of specimens containing two parallel flaws are also studied to compare the results with those of specimens with cross-flaws. The results demonstrate that the cross-flaw geometry influences the rock bridge coalescence patterns in rock-like specimens. Specimens with two aligned cross-flaws and two step cross-flaws coalesce with tensile cracks in the rock bridge areas, while specimens with two collinear primary flaws coalesce with shear cracks. Specimens containing two cross-flaws may have a higher uniaxial compressive strength than specimens containing two parallel flaws, and the number of specimens with a higher uniaxial compressive strength is influenced by the cross-flaws geometry in the different groups. The cross-flaws geometry influences the strength of the specimens. In this research, specimens in the group containing two aligned cross-flaws have the highest mean uniaxial compressive strength, and specimens in the group with two step cross-flaws have the lowest strength.

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Acknowledgments

This paper was funded by the National Natural Science Foundation of China (Nos. 51879151, 51739007, and 51879153).

Notation

The following symbols are used in this paper:
α
angle between the primary flaws (i.e., Flaws ① or ③) and the horizontal direction;
β
angle between the primary and secondary flaws; and
|τ(θr)max|
maximum shear stress (absolute value).

References

Al-Shayea, N. A. 2005. “Crack propagation trajectories for rocks under mixed mode I–II fracture.” Eng. Geol. 81 (1): 84–97. https://doi.org/10.1016/j.enggeo.2005.07.013.
Bobet, A. 2000. “The initiation of secondary cracks in compression.” Eng. Fract. Mech. 66 (2): 187–219. https://doi.org/10.1016/S0013-7944(00)00009-6.
Bobet, A., and H. H. Einstein. 1998. “Fracture coalescence in rock-type materials under uniaxial and biaxial compression.” Int. J. Rock Mech. Min. Sci. 35 (7): 863–888. https://doi.org/10.1016/S0148-9062(98)00005-9.
Cao, P., T. Liu, C. Pu, and H. Lin. 2015. “Crack propagation and coalescence of brittle rock-like specimens with pre-existing cracks in compression.” Eng. Geol. 187: 113–121. https://doi.org/10.1016/j.enggeo.2014.12.010.
Chen, Y. L., J. Ni, W. Shao, Y. C. Zhou, A. Javadi, and R. Azzam. 2012. “Coalescence of fractures under uni-axial compression and fatigue loading.” Rock Mech. Rock Eng. 45 (2): 241–249. https://doi.org/10.1007/s00603-011-0186-x.
Duan, K., C. Y. Kwok, Q. Y. Zhang, and J. L. Shang. 2020. “On the initiation, propagation and reorientation of simultaneously-induced multiple hydraulic fractures.” Comput. Geotech. 117: 103226. https://doi.org/10.1016/j.compgeo.2019.103226.
Duriez, J., L. Scholtès, and F.-V. Donzé. 2016. “Micromechanics of wing crack propagation for different flaw properties.” Eng. Fract. Mech. 153: 378–398. https://doi.org/10.1016/j.engfracmech.2015.12.034.
Feng, P., F. Dai, Y. Liu, N. W. Xu, and H. B. Du. 2019. “Coupled effects of static-dynamic strain rates on the mechanical and fracturing behaviors of rock-like specimens containing two unparallel fissures.” Eng. Fract. Mech. 207: 237–253. https://doi.org/10.1016/j.engfracmech.2018.12.033.
Feng, P., F. Dai, Y. Liu, N. Xu, and T. Zhao. 2018a. “Influence of two unparallel fissures on the mechanical behaviours of rock-like specimens subjected to uniaxial compression.” Eur. J. Environ. Civ. Eng. https://doi.org/10.1080/19648189.2018.1481770.
Feng, P., F. Dai, Y. Liu, N. Xu, and T. Zhao. 2018b. “Effects of strain rate on the mechanical and fracturing behaviors of rock-like specimens containing two unparallel fissures under uniaxial compression.” Soil Dyn. Earthquake Eng. 110: 195–211. https://doi.org/10.1016/j.soildyn.2018.03.026.
Griffith, A. A. 1921. “The phenomena of rupture and flow in solids.” Philos. Trans. R. Soc. London, Ser. A 221: 163–198.
Haeri, H., K. Shahriar, M. F. Marji, and P. Moarefvand. 2014. “Experimental and numerical study of crack propagation and coalescence in pre-cracked rock-like disks.” Int. J. Rock Mech. Min. Sci. 67: 20–28. https://doi.org/10.1016/j.ijrmms.2014.01.008.
Hao, R. Q., P. Cao, Y. Chen, J. Jin, H. Wang, and X. Fan. 2018. “Mechanical and propagating behaviors of single-flawed rock samples with hydraulic pressure and uniaxial compression conditions.” Int. J. Geomech. 18 (7): 04018078. https://doi.org/http://dx.doi.org/10.1061/(ASCE)GM.1943-5622.0001176.
Hoek, E., and Z. T. Bieniawski. 1965. “Brittle fracture propagation in rock under compression.” Int. J. Fract. Mech. 1 (3): 137–155. https://doi.org/10.1007/BF00186851.
Huang, J., G. Chen, Y. Zhao, and R. Wang. 1990. “An experimental study of the strain field development prior to failure of a marble plate under compression.” Tectonophysics 175 (1): 269–284. https://doi.org/10.1016/0040-1951(90)90142-U.
Kwok, C.-Y., K. Duan, and M. Pierce. 2020. “Modeling hydraulic fracturing in jointed shale formation with the use of fully coupled discrete element method”. Acta Geotech. 15 (1): 245–264. https://doi.org/10.1007/s11440-019-00858-y.
Lajtai, E. Z. 1974. “Brittle fracture in compression.” Int. J. Fract. 10 (4): 525–536. https://doi.org/10.1007/BF00155255.
Lee, J., J.-W. Hong, and J.-W. Jung. 2017. “The mechanism of fracture coalescence in pre-cracked rock-type material with three flaws”. Eng. Geol. 223: 31–47. https://doi.org/10.1016/j.enggeo.2017.04.014.
Li, A., N. W. Xu, F. Dai, G. Gu, Z. Hu, and Y. Liu. 2018. “Stability analysis and failure mechanism of the steeply inclined bedded rock masses surrounding a large underground opening.” Tunnelling Underground Space Technol. 77: 45–58. https://doi.org/10.1016/j.tust.2018.03.023.
Li, S. C., B. Liu, Y. X. Ren, S. L. Yang, Y. K. Chen, Y. H. Wang, and P. Jiang. 2020. “Deep-learning inversion of seismic data.” IEEE Trans. Geosci. Remote Sens. 58 (3): 2135–2149. https://doi.org/10.1109/TGRS.2019.2953473.
Li, X. Z., C. Z. Qi, Z. S. Shao, and C. Xia. 2017. “Effects of crack inclination on shear failure of brittle geomaterials under compression.” Arabian J. Geosci. 10: 529–538. https://doi.org/10.1007/s12517-017-3310-8.
Li, Y.-P., L.-Z. Chen, and Y.-H. Wang. 2005. “Experimental research on pre-cracked marble under compression.” Int. J. Solids Struct. 42 (9): 2505–2516. https://doi.org/10.1016/j.ijsolstr.2004.09.033.
Liu, B., Q. Guo, S. C. Li, B. C. Liu, Y. X. Ren, Y. H. Pang, X. Guo, L. B. Liu, and P. Jiang. 2020a. “Deep learning inversion of electrical resistivity data.” IEEE Trans. Geosci. Remote Sens. https://doi.org/10.1109/TGRS.2020.2969040.
Liu, B., Y. H. Pang, D. Q. Mao, J. Wang, Z. Y. Liu, N. Wang, S. H. Liu, and X. X. Zhang. 2020b. “A rapid four-dimensional resistivity data inversion method using temporal segmentation.” Geophys. J. Int. 221 (1): 586–602. https://doi.org/10.1093/gji/ggaa019.
Liu, Y., F. Dai, P. Fan, N. W. Xu, and L. Dong. 2017a. “Experimental investigation of the influence of joint geometric configurations on the mechanical properties of intermittent jointed rock models under cyclic uniaxial compression.” Rock Mech. Rock Eng. 50: 1453–1471. https://doi.org/10.1007/s00603-017-1190-6.
Liu, Y., F. Dai, P. Feng, and N. W. Xu. 2018. “Mechanical behavior of intermittent jointed rocks under random cyclic compression with different loading parameters.” Soil Dyn. Earthquake Eng. 113: 12–24. https://doi.org/10.1016/j.soildyn.2018.05.030.
Liu, X. W., Q. S. Liu, L. Wei, and X. Huang. 2017b. “Improved strength criterion and numerical manifold method for fracture initiation and propagation.” Int. J. Geomech. 17 (5): E4016007. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000676.
Park, C. H., and A. Bobet. 2009. “Crack coalescence in specimens with open and closed flaws: A comparison.” Int. J. Rock Mech. Min. Sci. 46 (5): 819–829. https://doi.org/10.1016/j.ijrmms.2009.02.006.
Park, C. H., and A. Bobet. 2010. “Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression.” Eng. Fract. Mech. 77 (14): 2727–2748. https://doi.org/10.1016/j.engfracmech.2010.06.027.
Pu, C. Z., and P. Cao. 2012. “Failure characteristics and its influencing factors of rock-like material with multi-fissures under uniaxial compression.” Trans. Nonferrous Met. Soc. China 22 (1): 185–191. https://doi.org/10.1016/S1003-6326(11)61159-X.
Sagong, M., and A. Bobet. 2002. “Coalescence of multiple flaws in a rock-model material in uniaxial compression.” Int. J. Rock Mech. Min. Sci. 39 (2): 229–241. https://doi.org/10.1016/S1365-1609(02)00027-8.
Sagong, M., D. Park, J. Yoo, and J. S. Lee. 2011. “Experimental and numerical analyses of an opening in a jointed rock mass under biaxial compression.” Int. J. Rock Mech. Min. Sci. 48 (7): 1055–1067. https://doi.org/10.1016/j.ijrmms.2011.09.001.
Sahouryeh, E., A. V. Dyskin, and L. N. Germanovich. 2002. “Crack growth under biaxial compression.” Eng. Fract. Mech. 69 (18): 2187–2198. https://doi.org/10.1016/S0013-7944(02)00015-2.
Sharafisafa, M., and M. Nazem. 2014. “Application of the distinct element method and the extended finite element method in modelling cracks and coalescence in brittle materials.” Comput. Mater. Sci. 91: 102–121. https://doi.org/10.1016/j.commatsci.2014.04.006.
Shen, B., O. Stephansson, H. H. Einstein, and B. Ghahreman. 1995. “Coalescence of fractures under shear stresses in experiments.” J. Geophys. Res. Solid Earth 100 (6): 5975–5990. https://doi.org/10.1029/95JB00040.
Tang, C. A., P. Lin, R. H. C. Wong, and K. T. Chau. 2001. “Analysis of crack coalescence in rock-like materials containing three flaws—Part II: Numerical approach.” Int. J. Rock Mech. Min. Sci. 38 (7): 925–939. https://doi.org/10.1016/S1365-1609(01)00065-X.
Wei, M.-D., F. Dai, N.-W. Xu, and T. Zhao. 2016. “Stress intensity factors and fracture process zones of ISRM-suggested chevron notched specimens for mode I fracture toughness testing of rocks.” Eng. Fract. Mech. 168: 174–189. https://doi.org/10.1016/j.engfracmech.2016.10.004.
Wong, L. N. Y., and H. H. Einstein. 2009a. “Crack coalescence in molded gypsum and Carrara marble: Part 1. Macroscopic observations and interpretation.” Rock Mech. Rock Eng. 42 (3): 475–511. https://doi.org/10.1007/s00603-008-0002-4.
Wong, L. N. Y., and H. H. Einstein. 2009b. “Crack coalescence in molded gypsum and Carrara marble: Part 2. Microscopic observations and interpretation.” Rock Mech. Rock Eng. 42 (3): 513–545. https://doi.org/10.1007/s00603-008-0003-3.
Wong, L. N. Y., and H. H. Einstein. 2009c. “Systematic evaluation of cracking behavior in specimens containing single flaws under uniaxial compression.” Int. J. Rock Mech. Min. Sci. 46 (2): 239–249. https://doi.org/10.1016/j.ijrmms.2008.03.006.
Wong, R. H. C., and K. T. Chau. 1998. “Crack coalescence in a rock-like material containing two cracks.” Int. J. Rock Mech. Min. Sci. 35 (2): 147–164. https://doi.org/10.1016/S0148-9062(97)00303-3.
Wong, R. H. C., K. T. Chau, C. A. Tang, and P. Lin. 2001. “Analysis of crack coalescence in rock-like materials containing three flaws—Part I: Experimental approach.” Int. J. Rock Mech. Min. Sci. 38 (7): 909–924. https://doi.org/10.1016/S1365-1609(01)00064-8.
Xu, X. L., S. C. Wu, A. B. Jin, and Y. T. Gao. 2018. “Review of the relationships between crack initiation stress, mode I fracture toughness and tensile strength of geo-materials.” Int. J. Geomech. 18 (10): 04018136. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001227.
Yan, Z. L., F. Dai, Y. Liu, and P. Feng. 2019. “Experimental and numerical investigation on the mechanical properties and progressive failure mechanism of intermittent multi-jointed rock models under uniaxial compression.” Arabian J. Geosci. 12: 681. https://doi.org/10.1007/s12517-019-4737-x.
Yang, S.-Q. 2011. “Crack coalescence behavior of brittle sandstone samples containing two coplanar fissures in the process of deformation failure.” Eng. Fract. Mech. 78 (17): 3059–3081. https://doi.org/10.1016/j.engfracmech.2011.09.002.
Yang, S.-Q., X.-R. Liu, and H.–W. Jing. 2013. “Experimental investigation on fracture coalescence behavior of red sandstone containing two unparallel fissures under uniaxial compression.” Int. J. Rock Mech. Min. Sci. 63: 82–92. https://doi.org/10.1016/j.ijrmms.2013.06.008.
Yang, X.-X., H.-W. Jiang, C.-A. Tang, and S.-Q. Yang. 2017. “Effect of parallel joint interaction on mechanical behavior of jointed rock mass models.” Int. J. Rock Mech. Min. Sci. 92: 40–53. https://doi.org/10.1016/j.ijrmms.2016.12.010.
Yin, P., R. H. C. Wong, and K. T. Chau. 2014. “Coalescence of two parallel pre-existing surface cracks in granite.” Int. J. Rock Mech. Min. Sci. 68: 66–84. https://doi.org/10.1016/j.ijrmms.2014.02.011.
Zhang, B., S. C. Li, K. Xia, X. Yang, D. Zhang, S. Wang, and J. Zhu. 2016. “Reinforcement of rock mass with cross-flaws using rock bolt.” Tunnelling Underground Space Technol. 51: 346–353. https://doi.org/10.1016/j.tust.2015.10.007.
Zhang, B., S. C. Li, X. Y. Yang, K. W. Xia, J. Y. Liu, S. Guo, and S. G. Wang. 2019. “The coalescence and strength of rock-like materials containing two aligned X-type flaws under uniaxial compression.” Geomech. Eng. 17 (1): 47–56. https://doi.org/10.12989/gae.2019.17.1.047.
Zhou, X. P., H. Cheng, and Y. F. Feng. 2014. “An experimental study of crack coalescence behaviour in rock-like materials containing multiple flaws under uniaxial compression.” Rock Mech. Rock Eng. 47 (6): 1961–1986. https://doi.org/10.1007/s00603-013-0511-7.
Zhou, X. P., Y. J. Lian, L. N. Y. Wong, and F. Berto. 2018. “Understanding the fracture behavior of brittle and ductile multi-flawed rocks by uniaxial loading by digital image correlation.” Eng. Fract. Mech. 199: 438–460. https://doi.org/10.1016/j.engfracmech.2018.06.007.
Zhang, X.-P., and L. N. Y. Wong. 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): 711–737. https://doi.org/10.1007/s00603-011-0176-z.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 20Issue 8August 2020

History

Received: Mar 29, 2019
Accepted: Mar 5, 2020
Published online: Jun 9, 2020
Published in print: Aug 1, 2020
Discussion open until: Nov 9, 2020

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Professor, School of Civil Engineering, Shandong Univ., Jinan, Shandong 250061, PR China. ORCID: https://orcid.org/0000-0002-5801-2819. Email: [email protected]
School of Civil Engineering, Shandong Univ., Jinan, Shandong 250061, PR China. Email: [email protected]
Lecturer, Dept. of Construction Engineering Management, Shandong Urban Construction Vocational College, Jinan, Shandong 250014, PR China. Email: 274679821@ qq.com
S. C. Li, Ph.D. [email protected]
Professor, Research Center of Geotechnical and Structural Engineering, Shandong Univ., Jinan, Shandong 250061, PR China. Email: [email protected]
B. Liu, Ph.D. [email protected]
Professor, Research Center of Geotechnical and Structural Engineering, Shandong Univ., Jinan, Shandong 250061, PR China. Email: [email protected]; [email protected]
Z. H. Xu, Ph.D. [email protected]
Professor, Research Center of Geotechnical and Structural Engineering, Shandong Univ., Jinan, Shandong 250061, PR China (corresponding author). Email: [email protected]
Y. Pei, Ph.D. [email protected]
Postdoctoral Scholar, Research Center of Geotechnical and Structural Engineering, Shandong Univ., Jinan, Shandong 250061, PR China. Email: [email protected]; [email protected]

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