[1] Esterhuizen GS, Dolinar DR, Ellenberger JL. Pillar strength in underground stone mines in the United States. Int J Rock Mech Min Sci. 2011;48(1):42-50.
[2] Esterhuizen GS, Tyrna PL, Murphy MM. A case study of the collapse of slender pillars affected by through-going discontinuities at a limestone mine in Pennsylvania. Rock Mech Rock Eng. 2019;52(12):4941- 4952.
[3] Yang SQ, Jing HW, Huang YH, Ranjith PG, Jiao YY. Fracture mechanical behavior of red sandstone containing a single fissure and two parallel fissures after exposure to different high temperature treatments. J Struct Geol. 2014;69:245-264.
[4] Cao RH, Cao P, Lin H, Fan X, Zhang CY, Liu TY. Crack initiation, propagation, and failure characteristics of jointed rock or rock-like specimens: a review. Adv Civ Eng. 2019;6975751.
[5] Xie HP, Zhu JB, Zhou T, Zhang K, Zhou CT. Conceptualization and preliminary study of engineering disturbed rock dynamics. Geomech Geophys Geo-energ Geo-resour. 2020;6(2):34.
[6] Zhou X-P, Zhang J-Z, Yang S-Q, Berto F. Compression-induced crack initiation and growth in flawed rocks: A review. Fatigue Fract Eng Mater Struct. 2021;1–27.
[7] Bobet A, Einstein HH. Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci. 1998;35(7):863- 889.
[8] Yang SQ, Jing HH. Evaluation on strength and deformation behavior of red sandstone under simple and complex loading paths. Eng Geol. 2013;164:1-17.
[9] Yang SQ, Tian WL, Huang YH, Ranjith PG, Yu Y. An experimental and numerical study on cracking behavior of brittle sandstone containing two non-coplanar fissures under uniaxial compression. Rock Mech Rock Eng. 2016;49(4):1497-1515.
[10] Wong LNY, Xiong Q. A method for multiscale interpretation of fracture processes in Carrara marble specimen containing a single flaw under uniaxial compression. J Geophys Res–Sol Ea. 2018;123(8):6459- 6490.
[11] Liu XW, Liu QS, Liu B, Zhu YG, Zhang PL. Failure behavior for rocklike material with cross crack under biaxial compression. J Mater Civ Eng. 2019;31(2):06018025.
[12] Du K, Yang CZ, Su R, Tao M, Wang SF. Failure properties of cubic granite, marble, and sandstone specimens under true triaxial stress. Int J Rock Mech Min Sci. 2020;130:104309.
[13] Liu K, Zhao J, Wu G, Maksimenko A, Haque A, Zhang QB. Dynamic strength and failure modes of sandstone under biaxial compression. Int J Rock Mech Min Sci. 2020;128:104260.
[14] Wang HY, Dyskin A, Pasternak E, Dight P. 3D crack growth in biaxial compression: influence of shape and inclination of initial cracks. Rock Mech Rock Eng. 2020;53(7):3161-3183.
[15] Wang HY, Dyskin A, Pasternak E, Dight P, Sarmadivaleh M. Experimental and numerical study into 3D crack growth from a spherical pore in biaxial compression. Rock Mech Rock Eng. 2020;53(1):77-102.
[16] Mughieda O, Karasneh I. Coalescence of offset rock joints under biaxial loading. Geotech Geo Eng. 2006;24(4):985-999.
[17] Prudencio M, Van Sint Jan M. Strength and failure modes of rock mass models with non-persistent joints. Int J Rock Mech Min Sci. 2007;44(6):890-902.
[18] Yang SQ, Huang YH, Ranjith PG. Failure mechanical and acoustic behavior of brine saturated sandstone containing two pre-existing flaws under different confining pressures. Eng Fract Mech. 2018;193:108-121.
[19] Huang D, Gu D, Yang C, Huang R, Fu G. Investigation on mechanical behaviors of sandstone with two preexisting flaws under triaxial compression. Rock Mech Rock Eng. 2015;49: 375-399.
[20] Ghazvinian, A., Sarfarazi, V., Schubert, W., Blumel, M., 2012. A study of the failure mechanism of planar non-persistent open joints using PFC2D. Rock Mech. Rock. Eng. 45 (5), 677–693.
[21] SARFARAZI V, HAERI H, SHEMIRANI A B, HEDAYAT A, HOSSEINI S S. Investigation of ratio of TBM disc spacing to penetration depth in rocks with different tensile strengths using PFC2D [J]. Computers and Concrete, 2017, 20(4): 429−437. DOI: 10.12989/cac.2017.20.4.429.
[22] CHEN S J, YIN D W, JIANG N, WANG F, GUO W J. Simulation study on effects of loading rate on uniaxial compression failure of composite rock-coal layer [J]. Geomechanics and Engineering, 2019, 17(4): 333−342. DOI: 10.12989/gae.2019.17.4.333.
[23] LIU Guang, SUN Wai-ching, LOWINGER S M, ZHANG Zhen-hua, HUANG Ming, PENG Jun. Coupled flow network and discrete element modeling of injectioninduced crack propagation and coalescence in brittle rock [J]. Acta Geotechnica, 2019, 14(13): 843−868. DOI: 10.1007/s11440- 018-0682-1.
[24] YIN Peng-fei, YANG Sheng-qi. Discrete element modeling of strength and failure behavior of transversely isotropic rock under uniaxial compression [J]. Journal of the Geological Society of India, 2019, 93(2): 235−246. DOI: 10.1007/s12594-019-1158-0.
[25] CAO R H, CAO P, LIN H, PU C Z, OU K. Mechanical behavior of brittle rock-like specimens with pre-existing fissures under uniaxial loading: Experimental studies and particle mechanics approach [J]. Rock Mechanics and Rock Engineering, 2016, 49(3): 763−783. DOI: 10.1007/s00603-015-0779-x.
[26] WU Shun-chuan, XU Xue-liang. A study of three intrinsic problems of the classic discrete element method using flat-joint model [J]. Rock Mechanics and Rock Engineering, 2016, 49(5): 1813−1830. DOI: 10.1007/s00603-015-0890-z.
[27] POTYONDY D O. The bonded-particle model as a tool for rock mechanics research and application: Current trends and future directions [J]. Geosystem Engineering, 2015, 18(1):1−28. DOI: 10.1080/12269328.2014. 998346.
[28] Cheng, C., Chen, X., & Zhang, S. (2016). Multipeak deformation behavior of jointed rock mass under uniaxial compression: insight from particle flow modeling. Engineering Geology, 213, 25-45.
[29] Itasca Consulting Group, Inc. (2014a). PFC (particle flow code in 2 and 3 dimensions), version 5.0 [User’s manual]. Minneapolis, MN: IC