Document Type : Original Research Paper


1 Department of mining Engineering, Bafgh Branch, Islamic Azad University, Bafgh, Iran

2 State Key Laboratory for Deep GeoMechanics and Underground Engineering, Beijing, China

3 Department of Mining Engineering, Hamedan University of Technology, Hamedan, Iran

4 Mine Exploitation Engineering Department, Faculty of Mining and Metallurgy, Institution of Engineering, Yazd University, Yazd, Iran


The propagation mechanism of cracks emanating from two holes within the concrete specimens is studied by considering the effects of different lateral compressive stresses. The experimental part of this research work is carried out on some specially prepared pre-cracked specimens with two neighbouring holes under only a uniaxial compression in the laboratory. The numerical modeling part is performed under both the uniaxial compresion and the lateral confinment by the 2D particle flow code (PFC2D). It is shown that the lateral confinement may change the path of crack propagation in a specimen compared to that of the uniaxially-loaded one. Various senarios of the mixed mode radial crack propagation around the holes are obtained, and both the wing (induced tensile) cracks and secondary (shear) cracks are produced and propagated in various paths due to a change in the confining pressure. The fracturing pattern changes from a single tensile crack to that of the several shear bands by increasing the confining pressure. Also the number of shear cracks is increased by increasing the lateral confinement.On the other hand, as the confining pressure increases, the wing cracks start their growth from the walls and reach the center of the cracks under high confinements.


[1]. Huang, D., Gu, D. and Yang, C. (2016). Investigation on Mechanical Behaviors of Sandstone with Two Pre-existing Flaws under Triaxial Compression. Rock Mech Rock Eng. 49: 375–399.
[2]. Tian, J., Xu, D. and Liu, T. (2020). An experimental investigation of the fracturing behavior of rock-like materials containing two V-shaped parallelogram aws. International Journal of Mining Science and Technology. (06): 777-783.
[3]. Ke, C.C, Chen, C.S., and Tu, C.H. (2008). Determination of fracture toughness of anisotropic rocks by boundary element method. Rock Mech. Rock. Engin. 41: 509–538.
[4]. Yang, S.Q. (2011). Crack coalescence behavior of brittle sandstone samples containing two coplanar assures in the process of deformation failure. Engineering Fracture Mechanics. 78 (17): 3059-3081.
[5]. Shen, W., Yan, R.J., Barltrop, N., and Song, M. (2016). Fatigue crack growth analysis of T junction under biaxial compressive-compressive loading. Engineering Fracture Mechanics. 154: 207–224.
[6]. Bobet, A. and Einstein, H.H. (1998a). Fracture coalescence in rock-type materials under uniaxial and biaxial compressions. Int. J. Rock Mech Min, Sci. 35:863–888.
[7]. Bobet, A. and Einstein, H.H. (1998b). Numerical modeling of fracture coalescence in a model rock material. Int. J. Fracture 92:221–252.

[8]. Pu, C.Z. and Cao, P. (2012). Failure characteristics and its influencing factors of rock-like material with multi-fissures under uniaxial compression. Transactions of Non-ferrous Metals Society of China. 22 (1): 185-191.

[9]. Wong, L.N.Y. and Einstein, H.H. (2009). Systematic evaluation of cracking behavior in specimens containing single aws under uniaxial compression. Int J Rock Mech Min Sci. 46 (2): 239–249.
[10]. Lee, S. and Ravichandran, G. (2003). Crack initiation in brittle solids under multi-axial compression. Engin. Fract. Mech. 70:1645–1658.
[11]. Li, Y.P., Chen, L.Z., and Wang, Y.H. (2005). Experimental research on pre-cracked marble under compression. Int. J. Solids and Structures 42: 2505–2516.
[12]. Yang, Q., Dai, Y.H., Han, L.J., and Jin, Z.Q. (2009). Experimental study on mechanical behavior of brittle marble samples containing different flaws under uniaxial compression. Engin. Fract. Mech. 76:1833-1845S.
[13]. Park, C.H. and Bobet, A. (2010). Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Engin Fract Mech 77: 2727–2748.
[14]. Zhao, Y., Zhang, L., and Wang, W. (2016). Cracking and Stress–Strain Behavior of Rock-Like Material Containing Two Flaws under Uniaxial Compression. Rock Mech Rock Eng. 49: 2665–2687.
[15]. Yang, S.Q. (2011). Crack coalescence behavior of brittle sandstone samples containing two coplanar fissures in the process of deformation failure. Engin. Fract. Mech. 78:3059-3081.
[16]. Lee, H. and Jeon, S. (2011). An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. Int. J. of Solids and Structures 48:979-999.
[17]. Wei, C., Li, Y., Zhu, W., Li, S., Wang, S., and Wang, H., (2020). Experimental observation and numerical investigation on propagation and coalescence process of multiple flaws in rock-like materials subjected to hydraulic pressure and far-field stress. Theoretical and Applied Fracture Mechanics,
[18]. Reis, J.M.L. and Nunes, L.C.S. (2014). Experimental investigation of mixed-mode-I/II fracture in polymer mortars using digital image correlation method. Latin American journal of solids and structures. 11: 330–343.
[19]. Tang, C.A., Lin, P., Wong, R.H.C., and Chau, K.T. (2001). Analysis of crack coalescence in rock-like materials containing three flaws—Part II: Numerical approach. Int. J. Rock Mech. Min. Sci. 38: 925–939.
[20]. Iturrioz, I., Miguel, L.F.F, and Riera, J. D. (2009). Dynamic fracture analysis of concrete or rock plates by means of the Discrete Element Method. Latin American journal of solids and structures 6:229–245.
[21]. Marji, M.F., Hosseinin_Nasab, H, and Kohsary, A.H. (2006). On the uses of special crack tip elements in numerical rock fracture mechanics. Int. j. Solids and Structures 43: 1669-1692.
[22]. Marji, M.F., Hosseini-nasab, H., and Hossein morshedy, A. (2009). Numerical modeling of the mechanism of crack propagation in rocks under TBM disc cutters. J. Mech. Mater. Struct. 2: 439-457.
[23]. Marji, M.F. (2013). On the Use of Power Series Solution Method in the Crack Analysis of Brittle Materials by Indirect Boundary Element Method. Engin Fract Mech 98: 365–382.
[24]. Haeri, H., Shahriar, K., Marji, M.F., and Moaref Vand, P. (2014). On the HDD analysis of micro cracks initiation, propagation and coalescence in brittle substances. Arab. J. geosc. doi:10.1007/s12517-014-1290-5.
[25]. Haeri, H. (2015). Propagation Mechanism of Neighboring Cracks in Rock-like Cylindrical Specimens under Uniaxial Compression, Journal of Mining Science, No. 3.
[26]. Zhang, L. and Zhu, J. (2020). Analysis of Mechanical Strength and Failure Morphology of Prefabricated Closed Cracked Rock Mass under Uniaxial Compression. Geotech Geol Eng. 38: 4905–4915.
[27]. Hao, X.A., Yqa, B., Gang, W., Cheng, F.A., Mw, E. and Rui, W.F. (2020). Discrete element study on mesomechanical behavior of crack propagation in coal samples with two prefabricated ssures under biaxial compression. Powder Technology. 375: 42-59.
[28]. Haeri, H., Sarfarazi, V., Zhu, Z., and Nejati, H.R. (2019). Numerical simulations of fracture shear test in anisotropy rocks with bedding layers. Advances in Concrete Construction: 7 (4): 241-247.
[30] Zhao W, Huang R, and Yan M (2015) Mechanical and fracture behavior of rock mass with parallel concentrated joints with different dip angle and number based on pfc simulation. Geomechanics and Engineering. 8 (6): 757-767.
[31] Li, H. and Wong, L. (2012). Influence of flaw inclination angle and loading condition on crack initiation and propagation. International Journal of Solids and Structures. 49 (18): 2482-2499.
[32] Hazzard, J.F., Young R.P., and Maxwell S.C. (2000) Micro-mechanical modeling of cracking and failure in brittle rocks Journal of Geophysical Research. 105 (B7): 16683-16697.
[33] Park,  E.S. (2004) Simulation of the mechanical behavior of discontinuous rock masses using a bonded-particle model Proceedings from gulf rocks 2004, the 6th North America rock mechanics symposium (NARMS), American Rock Mechanics Association (ARMA) 55-60.
[34] Holt, R.M. and Kjølaas, J. (2005) Comparison between controlled laboratory experiments and discrete particle simulations of the mechanical behavior of rock International Journal of Rock Mechanics and Mining Sciences. 42 (7–8): 985-995.
[35] Yoon J. (2007) Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation International Journal of Rock Mechanics and Mining Sciences. 44 (6): 871-889.
[36] Cho N. and Martin, C.D. (2007) A clumped particle model for rock International Journal of Rock Mechanics and Mining Sciences. 44 (7): 997-1010.