Document Type: Case Study

Authors

Rock Mechanics Department, School of Engineering, Tarbiat Modares University, Tehran, Iran

Abstract

Assessment of the correlation between rock brittleness and rock fracture toughness has been the subject of extensive research works in the recent years. Unfortunately, the brittleness measurement methods have not yet been standardized, and rock fracture toughness cannot be estimated satisfactorily by the proposed indices. In the present study, statistical analyses are performed on some data collected from the literature to develop two equations for estimation of modes I and II fracture toughness. Then a probabilistic sensitivity analysis is performed to determine the impact of the input parameters on the output ones. Based on the results obtained for the probabilistic analysis, a new empirical brittleness index including tensile strength, uniaxial compressive strength, and elastic modulus is suggested for estimating modes I and II fracture toughness. The analyses results reveal that the proposed index is capable of estimating rock fracture toughness with more satisfactory correlation compared to the previous indices.

Keywords

[1]. Sun, Z. and Ouchterlony, F. (1986). Fracture toughness of Stripa granite cores. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 23 (6): 399-409.

[2]. Whittaker, B.N., Singh, R.N. and Sun, G. (1992). Rock fracture mechanics principles, design and applications, developments in geotechnical engineering. Elsevier, Amsterdam.

[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 Eng. 41 (4): 509-538.

[4]. Ghazvinian, A., Nejati, H.R., Sarfarazi, V. and Hadei, M.R. (2013). Mixed mode crack propagation in low brittle rock-like materials. Arab J Geosci. 6: 4435–4444. doi:10.1007/s12517-012-0681-8.

[5]. Kahraman, S. and Altindag, R. (2004). A brittleness index to estimate fracture toughness. International Journal of Rock Mechanics & Mining Sciences. 41: 343-348.

[6]. Zhixi, C., Mian, C., Yan, J. and Rongzun, H. (1997). Determination of rock fracture toughness and its relationship with acoustic velocity. International Journal of Rock Mechanics & Mining Sciences. 34 (3-4).

[7]. Brown, G.J. and Reddish, D.J. (1997). Experimental relations between rock fracture toughness and density. Int. J. Rock Mech. Min. Sci. 34(1): 153-155.

[8]. Zhang, Z.X. (2002). An empirical relation between mode I fracture toughness and the tensile strength of rock. International Journal of Rock Mechanics & Mining Sciences. 39: 401-406.

[9]. Chang, S.H., Lee, C.I. and Jeon, S. (2002). Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimens. Engineering Geology. 66: 79-97.

[10]. Wang, J.J., Zhu, J.G., Chiu, C.F. and Zhang, H. (2007). Experimental study on fracture toughness and tensile strength of a clay. Engineering Geology. 94: 65-75.

[11]. Broek, D. (1986). Elementary Engineering Fracture Mechanics. 4th edition. Martinus Nijhoff Publishers, Dordrecht.

[12]. Nejati, H.R. and Ghazvinian, A. (2014). Brittleness effect on rock fatigue damage evolution. Rock Mech Rock Eng. 47(5): 1839-1848

[13]. Evans, I. and Pomeroy, C.D. (1996). The strength, Fracture and workability of coal, Pergamon Press.

[14]. Hucka, V. and Das, B. (1974). Brittleness determination of rocks by different methods. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1: 389-392.

[15]. Mcfeat-Smith, I. (1977). Rock property testing for the assessment of tunneling machine performance. Tunnels and Tunnelling. pp. 23–33.

[16]. Singh, P.S. (1986). Brittleness and the mechanical winning of coal. Min. Sci. and Tech. 3: 173-180.

[17]. Göktan, R.M. (1991). Brittleness and micro-scale rock cutting efficiency. Mining Science and Technology, 13: 237-241.

[18]. Altindag, R. (2000). The role of rock brittleness on analysis of percussive drilling performance, (in Turkish). Proc. of 5th National Rock Mech. Symp., Turkey. pp. 105-112.

[19]. Yarali, O. and Soyer, E. (2011). The effect of mechanical rock properties and brittleness on drillability. Scientific Research and Essays. 6 (5): 1077-1088.

[20]. Tarasov, B. and Potvin, Y. (2013). Universal criteria for rock brittleness estimation under triaxial compression International Journal of Rock Mechanics & Mining Sciences. 59: 57-69.

[21]. Meng, F., Zhou, H., Zhang, C., Xu, R. and Lu, J. (2015). Evaluation Methodology of Brittleness of Rock Based on Post-Peak Stress–Strain Curves. Rock Mech Rock Eng. 48:1787-1805.

[22]. Singh, R.N. and Sun, G.X. (1989). Relationships between fracture toughness, hardness indices and mechanical properties of rocks. Mining Department Magazine, department of mining engineering, University of Nottingham, Englan, pp. 49-62.

[23]. Al-Shayea, N.A., Khan, K. and Abduljauwad, S.N. (2000). Effects of confining pressure and temperature on mixed-mode (I-II) fracture toughness of a limestone rock. Int. J. Rock Mech. Min. Sci. 37: 629-643.

[24]. Rao, Q., Sun, Z., Stephansson, O., Li, C. and Stillborg, B. (2003). Shear fracture (Mode II) of brittle rock. International Journal of Rock Mechanics & Mining Sciences. 40: 355-375.

[25]. Backers, T. (2004). Fracture toughness determination and micromechanics of rock under mode i and mode II loading. PhD Dissertation, University of Potsdam, Germany.

[26]. Christer, A. (2007). Rock Mass Response to Coupled Mechanical Thermal Loading: Äspö Pillar Stability Experiment, Sweden. Doctoral thesis, KTH, School of Architecture and the Built Environment, Sweden.

[27]. Stephansson, O., Shen, B., Amemiya, K., Yamashi, R. and Toguri, S. (2008). FRACOD Modeling of Rock Fracturing and Permeability Change in Excavation Damaged Zones. The 12th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG). Goa, India.

[28]. Rinne, M. (2008). Fracture mechanics and subcritical crack growth approach to model time-dependent failure in brittle rock, Doctoral Dissertation, Helsinki University of Technology, Sweden.

[29]. Siren, T. (2011). Fracture Mechanics Prediction for Posiva’s Olkiluoto Spalling Experiment (POSE). Working Report, POSIVA OY finland.

[30]. Rubinstein, R.Y. and Kroese, D.P. (2007). Simulation and the Monte Carlo Method. A John Wiley & Sons, Inc., Publication.

[31]. Irwin, G.R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate. ASME Journal of Applied Mechanics. 24: 361-364.

[32]. Grasselli, G. (2001). Shear strength of rock joints based on quantified surface description. Ph.D. thesis n. 2404, Civil Engineering Department, EPFL, Lausanne, Switzerland.

[33]. Zhang, H.Q., Zhao, Z.Y., Tang, C.A. and Song, L. (2006). Numerical study of shear behavior of intermittent rock joints with different geometrical parameters. Int J Rock Mech Min Sci. 43: 802-816.

[34]. Ghazvinian, A., Azinfar, M.J. and Geranmayeh Vaneghi, R. (2012). Importance of Tensile Strength on the Shear Behavior of Discontinuities. Rock Mech Rock Eng. 45: 349-359.

[35]. Sarfarazi, V., Ghazvinian, A., Schubert, W., Blumel, M. and Nejati, H.R. (2014). Numerical Simulation of the Process of Fracture of Echelon Rock Joints. Rock Mech Rock Eng. 47 (4): 1355-1371.

[36]. Park, J.W. and Song, J.J. (2009). Numerical simulation of a direct shear test on a rock joint using a bonded-particle model International Journal of Rock Mechanics & Mining Sciences. 46: 1315-1328.