Acknowledgement
This study was supported by Shandong Provincial Natural Science Foundation of China (ZR2019BEE013), National Natural Science Foundation of China (No. 51974174 and 51974173), the Shandong Provincial Excellent Youth Scientists Fund (grant No. ZR2019YQ26). The authors are grateful to the reviewer for his/her valuable comments and suggestions.
References
- Afolagboye, L.O., He, J., and Wang, S. (2017), "Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping flaws under uniaxial compression", Acta Mech. Sinica, 33(2), 394-405. https://doi.org/10.1007/s10409-016-0624-9.
- Bobet A. and Einstein H.H. (1998), "Numerical modeling of fracture coalescence in a model rock materials", Int. J. Fracture, 92(3), 221-252. https://doi.org/10.1023/A:1007460316400.
- Bahaaddini, M., Sharrock, G. and Hebblewhite, B.K. (2013), "Numerical investigation of the effect of joint geometrical parameters on the mechanical properties of a non-persistent jointed rock mass under uniaxial compression", Comput. Geotech., 49, 206-225. https://doi.org/10.1016/j.compgeo.2012.10.012.
- Baynes, F.J. (2010), "Sources of geotechnical risk", Q. J. Eng. Geol. Hydroge., 43(3), 321-331. https://doi.org/10.1144/1470-9236/08-003.
- Cai, M., Kaiser, P.K., Tasaka, Y., Maejima, T., Morioka, H. and Minami, M. (2004), "Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations", Int. J. Rock Mech. Min. Sci., 41(5), 833-847. https://doi.org/10.1016/j.ijrmms.2004.02.001.
- Diederichs, M.S., Kaiser, P.K, and Eberhardt, E. (2004), "Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation", Int. J. Rock Mech. Min. Sci., 41(5), 785-812. https://doi.org/10.1016/j.ijrmms.2004.02.003.
- Erarslan, N. (2016), "Microstructural investigation of subcritical crack propagation and Fracture Process Zone (FPZ) by the reduction of rock fracture toughness under cyclic loading", Eng. Geol., 208, 181-190. https://doi.org/10.1016/j.enggeo.2016.04.035.
- Gu H.L., Tao M., Li X.B., Cao W.Z. and Li Q.Y. (2020), "Dynamic response and meso-deterioration mechanism of water-saturated sandstone under different porosities", Measurement, 167,1-12. https://doi.org/10.1016/j.measurement.2020.108275.
- Guo, X.F., Zhao, Z.Q., Gao, X., Xu, X.Y. and Ma, N.J. (2019), "Analytical solutions for characteristic radii of circular roadway surrounding rock plastic zone and their application", Int. J. Min. Sci. Technol., 29(2), 263-272. https://doi.org/10.1016/j.ijmst.2018.10.002.
- Han, C.R., Bai, S.W., and Zhang, B. (2007), "Analysis of stress distribution near borehole in orthotropic rockmass with stress calculus of variations", Rock Soil Mech., 28(12), 2593-2597. https://doi.org/10.1007/s11747-006-0011-3.
- Han, G.S., Jing, H.W, Su, H.J, Zhu, T.T., Du, M.R., Xiong, F. and Wu, J.Y. (2017), "Experimental study on compressive strength and fracture characteristics of sandstone containing double circular cavities", J. China Coal Soc., 42(4), 871-878. https://doi.org/10.13225/j.cnki.jccs.2016.0792.
- Huang, Y. H., Yang, S.Q., Ranjith, P.G. and Zhao, J. (2017), "Strength failure behavior and crack evolution mechanism of granite containing pre-existing non-coplanar holes: Experimental study and particle flow modeling", Comput. Geotech., 88,182-198. https://doi.org/10.1016/j.compgeo.2017.03.015.
- Inglis, C.E. (1913), "Stresses in a plate due to the presence of cracks and sharp corners". Inst. Naval Architect. London, 55, 219-230.
- Jia, C.Y., Wang, H.L., Sun, X.Z., Yu, X.B. and Luan, H.J. (2020), "Study on rockburst prevention technology of isolated working face with thick-hard roof", Geomech. Eng., 20(5), 447-459. https://doi.org/10.12989/gae.2020.20.5.447.
- Kong, R., Feng, X.T, Zhang, X.W, and Yang, C.X. (2018), "Study on crack initiation and damage stress in sandstone under true triaxial compression", Int. J. Rock Mech. Min. Sci., 106, 117-123. https://doi.org/10.1016/j.ijrmms.2018.04.019.
- Kong, P., Jiang, L.S., Shu, J.M., Sainoki, A. and Wang, Q.B. (2019), "Effect of fracture heterogeneity on rock mass stability in a highly heterogeneous underground roadway", Rock Mech. Rock Eng., 52(2), 1-18. https://doi.org/10.1007/s00603-019-01887-5.
- Leith, K., Moore, J.R., Amann, F., and Loew, S. (2014), "In situ stress control on microcrack generation and macroscopic extensional fracture in exhuming bedrock", J. Geophys. Res., 119(1), 594-615. https://doi.org/10.1002/2012JB009801.
- Li, D.Y., Zhu, Q.Q., Zhou, Z.L., Li, X.B. and Ranjith, P.G. (2017), "Fracture analysis of marble specimens with a hole under uniaxial compression by digital image correlation", Eng. Fract. Mech., 183, 109-124. https://doi.org/10.1016/j.engfracmech.2017.05.035.
- Li, D.Y., Gao, F.H., Han, Z.Y. and Zhu, Q.Q. (2020), "Full- and local-field strain evolution and fracture behavior of precracked granite under coupled static and dynamic loads", Shock Vib., (8), 1-15. https://doi.org/10.1155/2020/8866673.
- Li, M.T., Li, S.C., Yang. L. and Zhang, N. (2009), "Experimental study of the surface crack propagation mode in rock-like materials", J. Exp. Mech., 24(1), 21-26. https://doi.org/10.1360/972009-754.
- Lin, P., Wong, R.H., and Tang, C.A. (2015), "Experimental study of coalescence mechanisms and failure under uniaxial compression of granite containing multiple holes", Int. J. Rock Mech. Min. Sci., 77, 313-327. https://doi.org/10.1016/j.ijrmms.2015.04.017.
- Lin, P., Zhou, Y.N., Liu, H.Y. and Wang, C. (2013), "Reinforcement design and stability analysis for large-span tailrace bifurcated tunnels with irregular geometry", Tunn. Undergr. Sp. Technol., 38(9),189-204. https://doi.org/10.1016/j.tust.2013.07.011.
- Liu, S.H. (2014), "The study on the mechanism and prevention of dynamic-loading rockburs", Ph.D. Dissertation, Coal Science Research Institute, Beijing, China.
- Lv, A., Masoumi, H., Walsh, S.D., and Roshan, H. (2019), "Elastic-softening-plasticity around a borehole: An analytical and experimental study", Rock Mech. Rock Eng., 52(4), 1149-1164. https://doi.org/10.1007/s00603-018-1650-7.
- Meng, F.B, Wen, Z.J., Shen, B.T., Jiang, Y.J., Shi, S.S. and Zhao, R.L. (2019), "A pplicability of yielding-resisting sand column and three-dimensional coordination support in stopes", Materials, 12(16), 2635. https://doi.org/10.3390/ma12162635.
- Monnier, T., Seydou, D., Godin, N. and Zhang, F. (2012), "Primary calibration of acoustic emission sensors by the method of reciprocity, theoretical and experimental considerations", J. Acoust. Emission, 152-166. https://doi.org/10.1016/0042-207X(66)90610-5.
- Olsson, W.A. and Holcomb, D.J. (2000), "Compaction localization in porous rock", Geophys. Res. Lett., 27(21), 3537-3540. https://doi.org/10.1029/2000GL011723.
- Rongkun, P., Fu, D., Yu, M.G. and Lei, C. (2017), "Directivity effect of unloading bedding coal induced fracture evolution and its application", Int. J. Min. Sci. Technol., 27(5), 825-829. https://doi.org/CNKI:SUN:ZHKD.0.2017-05-016. https://doi.org/10.1016/j.ijmst.2017.07.022
- Shen, B.T. (1993), "Mechanics of fractures and intervening bridges in hard rocks", Ph.D. Dissertation, Royal Institute of Technology, Stockholm, Sweden.
- Shen, B.T, Stephansson, O., Einstein, H.H., and Ghahreman, B. (1995), "Coalescence of fractures under shear stresses in experiments", J. Geophys. Res., 100(6), 5975-5990. https://doi.org/10.1029/95JB00040.
- Sun, W.B., Du, H.Q., Zhou, F. and Shao, J.L. (2019), "Experimental study of crack propagation of rock-like specimens containing conjugate fractures", Geomech. Eng., 17(4), 323-331.https://doi.org/10.12989/gae.2019.17.4.323.
- Sun, X.Z, Zhang B.L., Yin, D.W. and Shen, B.T. (2018), "Experimental study of three-dimensional cracks propagation characteristics under uniaxial compression", J. Basic Sci. Eng., 27(04), 890-905. https://doi.org/10.16058/j.issn.1005-0930.2019.04.017.
- Tsangouri, E., Remy, O., Boulpaep, F., Verbruggen, S., Livitsanos, G. and Aggelis, D.G. (2019), "Structural health assessment of prefabricated concrete elements using acoustic emission: Towards an optimized damage sensing tool", Constr. Build. Mater., 206, 261-269. https://doi.org/10.1016/j.conbuildmat.2019.02.035.
- Wang, C.X., Shen, B.T., Chen, J.T., Tong, W.X., Jiang, Z., Liu, Y. and Li, Y.Y. (2020), "Compression characteristics of filling gangue and simulation of mining with gangue backfilling: An experimental investigation", Geomech. Eng., 20(6), 485-495. https://doi.org//10.12989/gae.2020.20.6.485.
- Wang, J., Ning, J.G., Jiang, L., Jiang, L.S. and Bu, T. (2018), "Structural characteristics of strata overlying of a fully mechanized longwall face: A case study", J. S. Afr. I. Min. Metall., 118(11),1195-1204. https://doi.org/10.17159/2411-9717/2018/v118n11a10.
- Wang, X. and Tian L.G. (2018), "Mechanical and crack evolution characteristics of coal-rock under different fracture-hole conditions: A numerical study based on particle flow code", Environ. Earth. Sci., 77(8), 1-10. https://doi.org/10.1007/s12665-018-7486-3.
- Wang, X., Wen, Z.J., Jiang, Y.J. and Huang, H. (2018), "Experimental study on mechanical and acoustic emission characteristics of rock-like material under non-uniformly distributed loads", Rock Mech. Rock Eng., 51(3), 1-17. https://doi.org/10.1007/s00603-017-1363-3.
- Wong, L.N.Y. and Einstein, H.H. (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 Einstein, H.H. (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.
- Xi, X., Yang, S.T. and Li, C.Q. (2018), "A non-uniform corrosion model and meso-scale fracture modelling of concrete", Cement Concrete Res., 108, 87-102. https://doi.org/10.1016/j.cemconres.2018.03.009.
- Yang, S.Q. and Huang, Y.H. (2014), "Experiment and particle flow simulation on crack coalescence behavior of sandstone specimens containing double holes and a single fissure", J. Basic Sci. Eng., 22(3), 584-597. https://doi.org/10.3969/j.issn.1005-0930.2014.03.017.
- Yang, S.Q., Yin, P.F., Zhang, Y.C., Chen, M., Zhou, X.P. and Jing, H.W. (2019), "Failure behavior and crack evolution mechanism of a non-persistent jointed rock mass containing a circular hole", Int. J. Rock Mech. Min. Sci., 114, 101-121. https://doi.org/10.1016/j.ijrmms.2018.12.017.
- Yang, S.Q., Yang, Z., Zhang, P.C. and Tian, W.L. (2020), "Experiment and peridynamic simulation on cracking behavior of red sandstone containing a single non-straight fissure under uniaxial compression - sciencedirect", Theor Appl Fract Mec , 108, 1-19. https://doi.org/ 10.1016/j.tafmec.2020.102637.
- Yang, S.Q., Tian, W.L., Liu, X.R., Huang, Y.H. and Yang. J. (2021), "An experimental study on failure mechanical behavior and cracking mechanism of rectangular solid sandstone containing two non-coplanar fissures under conventional triaxial compression", Theor. Appl. Fract. Mec., 114, 1-17. https://doi.org/10.1016/j.tafmec.2021.102975.
- Zhang, G.L., Ranjith, P.G., Li, D.Y., Wanniarachchi, W.A.M. and Zhang, B.N. (2020), "In situ synchrotron x-ray microtomography observations of fracture network evolution of coal due to waterflooding", Geophys. Res. Lett., 47(10). https://doi.org/10.1029/2020GL087375.
- Zhang, S.C., Li, Y.Y., Shen, B.T., Sun, X.Z. and Gao, L.Q. (2019), "Effective evaluation of pressure relief drilling for reducing rock bursts and its application in underground coal mines", Int. J. Rock Mech. Min. Sci., 114, 7-16. https://doi.org/10.1016/j.ijrmms.2018.12.010.
- Zhang, X.F. and Bar-Ziv, E. (1996), "A 3D position controller for a charged particle suspended in a modified electrodynamic chamber", Rev. Sci. Instrum., 67(10), 3483-3490. https://doi.org/10.1063/1.1147163.
- Zhao, X.D., Zhang, X.H. and Zhu, W.C. (2014), "Fracture evolution around pre-existing cylindrical cavities in brittle rocks under uniaxial compression", T. Nonferr. Metals Soc., 24(3), 806-815. https://doi.org/10.1016/S1003-6326(14)63129-0.
- Zhou, Y., Liu, B., Wang, L., Li, X. and Ding, G.P. (2017), "Mesoscopic mechanical properties of rock-like material containing two circular holes under uniaxial compression", Chin. J. Rock Mech. Eng., 36(11), 2662-2671. https://doi.org/10.13722/j.cnki.jrme.2017.0501.
- Zhu, T.T, Jing, H.W., Su, H.J., Yin, Q. and Du, M.R. (2015), "Mechanical behavior of sandstone containing double circular avities under uniaxial compression", Chin. J. Geo. Eng., 37(6), 1047-1056.https://doi.org/10.11779/CJGE201506011.