Document Type: Original Research Paper

Author

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

10.22044/jme.2020.9581.1872

Abstract

In this work, the interaction between the semi-circular space and the neighboring joint with and without the presence of rock bolts was investigated using the particle flow code (PFC) approach. For this purpose, firstly, the calibration of PFC was performed using both the Brazilian experimental test and the uniaxial compression test. Secondly, a numerical model with the dimension of 100 mm * 100 mm was prepared. A semi-circular space with a radius of 25 mm was situated below the model. A joint with a length of 40 mm was situated above the space. The joint opening was 2 mm. The joint angles related to the horizontal direction were 0°, 15°, 30°, 45°, 60°, and 75°. Totally, 6 different configurations of the semi-circular space and neighboring joint were prepared. These models were tested with and without the presence of vertical rock bolts by the biaxial test. The rock bolt length was 50 mm. The value of the lateral force was fixed at 2 MPa. An axial force was applied to the model till the final failure occurred. The results obtained showed that the presence of rock bolts changed the failure pattern of the numerical model. In the absence of rock bolts, two tensile wing cracks initiated from the joint tip and propagated diagonally till coalescence from the model boundary. Also several shear bands were initiated in the left and right sides of the tunnel. In the presence of rock bolts, several shear bands were initiated in the left and right sides of the tunnel. The compressive strength with the presence of rock bolts was more than that without the presence of rock bolts. The failure stress had a minimum value when the joint angle was 45°.

Keywords

[1]. Indraratna, B. and Kaiser, P.K. (1990) Analytical model for the design of grouted rock bolts". International Journal for Numerical and Analytical Methods in Geomechanics. 14 (4): 227–251. 

[2]. Li, C. and Stillborg, B. (1999) Analytical models for rock bolts. International Journal of Rock Mechanics and Mining Sciences, 36(8):1013–1029.

[3]. Li, C.C. (2017) Principles of rockbolting design. Journal of Rock Mechanics and Geotechnical Engineering, 9(3), pp. 396–414. 2017.

[4]. Zhao, H., Ru, Z. and Zhu, C. (2018) Reliability-based Support Optimization of Rockbolt Reinforcement around Tunnels in Rock Masses. Periodica Polytechnica Civil Engineering. 62 (1): 250–258. 

[5]. Oreste, P. (2005) A probabilistic design approach for tunnel supports. Computers and Geotechnics, 32(7): 520–534.

[6]. Sharan, S.K. (2005) Exact and approximate solutions for displacements around circular openings in elastic-brittle-plastic Hoek-Brown rock. International Journal of Rock Mechanics and Mining Sciences. 42 (4) 542– 549.

[7]. Sharan, S.K. (2008) Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock. International Journal of Rock Mechanics and Mining Sciences. 45 (1):  78–85.

[8]. Hoek, E. and Brown, E.T. (1980) Underground Excavations in Rock. The Institution of Mining and Metallurgy, London.

[9]. Brown, E.T., Bray, J.W., Ladanyi, B. and Hoek, E. (1983) Ground reponse curves for rock tunnel. Journal of Geotechnical Engineering. 109 (1): 15– 39.

[10]. Cai, Y., Esaki, T. and Jiang, Y. (2004) An analytical model to predict axial loading routed rock bolt for soft rock tunneling. Tunnelling and Underground Space Technology. 19 (6): 607–618. 

[11]. Guan, Zh., Jiang, Y., Tanabasi, Y. and Huang, H.W. (2007) Reinforcement mechanics of passive bolts in conventional tunnelling. International Journal of Rock Mechanics and Mining Sciences: 44 (4). pp. 625–636.

[12]. Oreste, P. (2008) Distinct analysis of fully grouted bolts around a circular tunnel considering the congruence of displacements between the bar and the rock. International Journal of Rock Mechanics and Mining Sciences, 45(7): 1052–1067.

[13]. Indraratna, B. and Kaiser, P.K. (1990) Design for grouted rock bolts based on the convergence control method. International Journal of Rock Mechanics and Mining Sciences. 27 (4): 269–281.

[14]. Fahimifar, A. and Soroush, H. (2005) A theoretical approach for analysis of the interaction between grouted rockbolts and rock masses. Tunnelling and Underground Space Technology. 20 (4):333–343.

[15]. Carranza-Torres, C. (2009) Analytical and numerical study of the mechanics of rockbolt reinforcement around tunnels in rock masses. Rock Mechanics and Rock Engineering. 42 (2): 175–228.

[16]. Bobet, A. and Einstein, H.H. (2011) Tunnel reinforcement with rockbolts. Tunnelling and Underground Space Technology. 26 (1):100–123.

[17]. Mollon, G., Daniel, D. and Abdul, H.S. (2009) Probabilistic analysis of circular tunnels in homogeneous soil using response surface methodology. Journal of Geotechnical and Geoenvironmental Engineering. 135 (9):1314–1325.

[18]. Li, H. Z. and Low, B.K. (2010) Reliability analysis of circular tunnel under hydrostatic stress field. Computers and Geotechnics. 37 (1–2): 50–58.

[19]. Lu, Q. and Low, B.K. (2011) Probabilistic analysis of underground rock excavations using response surface method and SORM. Computers and Geotechnics. 38 (8):1008–1021.

[20]. Su, Y.H., Li, X. and Xie, Z.Y. (2011) Probabilistic evaluation for the implicit limitstate function of stability of a highway tunnel in China. Tunnel and Underground Space Technology. 26 (2), pp. 422–434.

[21]. Zhao, H., Ru, Z., Chang, X., Yin, S. and Li, S. (2014) Reliability analysis of tunnel using least square support vector machine. Tunnel and Underground Space Technology, 41:14–23.

[22]. Hoek, E. (1998) Reliability of Hoek-Brown estimates of rock mass properties and their impact on design. International Journal of Rock Mechanics and Mining Sciences. 35 (1): 63–68.

[23]. Zhang, W. and Goh, A.T.C. (2012) Reliability assessment on ultimate and serviceability limit states and determination of critical factor of safety for underground rock caverns. Tunnel and Underground Space Technology, 32: 221–230.

[24]. Itasca Consulting Group Inc, (2008) PFC2D (Particle Flow Code in 2D) Theory and Background,” Minneapolis, Minn, USA.

[25]. Potyondy, D.O. and Cundall, P.A. (2004) A bonded-particle model for rock, International Journal of Rock Mechanics and Mining Sciences, Vol. 41, No. 8, pp.1329–1364, 2004.

[26]. Donze, F.V., Richefeu, V. and Magnier S.A. (2009) Advances in discrete element method applied to soil rock and concrete mechanics. Electronic Journal of Geological Engineering 8: 1-44.