Document Type : Original Research Paper
Authors
Mining Engineering Department, Hamedan University of Technology, Hamedan, Iran
Abstract
This work presents the Semi-Circular Bend (SCB) test and Notched Brazilian Disc (NBD) test of shotcrete using experimental test and Particle Flow Code in two-dimensions (PFC2D) in order to determine a relation between mode I fracture toughness and the tensile strength of shotcrete. Firstly, the micro-parameters of flat joint model are calibrated using the results of shotcrete experimental test (uniaxial compressive strength and splitting tensile test). Secondly, numerical models with edge notch (SCB model) and internal notch (NBD model) with diameter of 150 mm are prepared. Notch lengths are 20 mm, 30 mm, and 40 mm. The tests are performed by the loading rate of 0.016 mm/s. Tensile strength of shotcrete is 3.25 MPa. The results obtained show that by using the flat joint model, it is possible to determine the crack growth path and crack initiation stress similar to the experimental one. Mode I fracture toughness is constant by increasing the notch length. Mode I fracture toughness and tensile strength of shotcrete can be related to each other by the equation, σt = 6.78 KIC. The SCB test yields the lowest fracture toughness due to pure tensile stress distribution on failure surface.
Keywords
[1]. Chen, X., Li, W., and Li, H. (2009). Evaluation of fracture properties of epoxy asphalt mix- tures by SCB test. J. Southeast Univ. 25 (4): 527–530.
[2]. Huang, B., Li, G., and Mohammad, L.N. (2003). Analytical modeling and experimental study of tensile strength of asphalt concrete composite at low temperatures. Comput. Part B Eng. 34 (8): 705–714.
[3]. Bearman R.A. (1999). The use of the point load test for the rapid estimation of mode I fracture toughness. Int J Rock Mech Min Sci; 36:257–63.
[4]. Ouchterlony F. (1982) A review of fracture toughness testing of rocks. Solid Mech Arch 7:131– 211.
[5]. Cui ZD, Liu D.A., An G.M., Sun B., Zhou M., and Cao F.Q. (2010). A comparison of two ISRM suggested chevron notched specimens for testing Mode-I rock fracture toughness. Int J rock Mech Min Sci 47:871–876.
[6]. Guo H., Aziz N.I., and Schmidt L.C. (1993). Rock fracture toughness determination by the Brazilian test. Eng Geol. 33 (3): 177–188.
[7]. Awaji. H., and Sato. S. (1978). Combined mode fracture toughness measurement by disk test. J Eng Mater Technol. 100 (2):175–182.
[8]. Atkinson. C., Smelser. R.E., and Sanchez. J. (1982). Combined mode fracture via the cracked Brazilian disk test. Int J Fract. 18 (4): 279–291.
[9]. Aliha. M.R.M., Ayatollahi. M.R., Smith. D.J., and Pavier. M.J. (2010). Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Eng Fract Mech. 77 (11): 2200–2212.
[10]. Aliha. M.R.M., Ayatollahi. M.R., and Akbardoost. J. (2012). Typical upper bound-lower bound mixed mode fracture resistance envelopes for rock material. Rock Mech Rock Eng. 45 (1): 65–74.
[11]. Aliha. M.R.M., Sistaninia. M., Smith. D.J., Pavier. M.J., and Ayatollahi. M.R. (2012b) Geometry effects and statistical analysis of mode I fracture in guiting limestone. Int J Rock Mech Min Sci 51:128– 135.
[12]. Chen. C.H., Chen. C.S., and Wu. J.H. (2008) Fracture toughness analysis on cracked ring disks of anisotropic rock. Rock Mech Rock Eng. 41 (4): 539–562.
[13]. Wang. Q.Z. and Xing. L. (1999) Determination of fracture toughness KIc by using the flattened Brazilian disc specimen for rocks. Eng Fract Mech 64 (2):193–201.
[14]. Keles. C., and Tutluoglu. L. (2011). Investigation of proper specimen geometry for mode I fracture toughness testing with flattened Brazilian disc method. Int J Fract. 169 (1):61–75.
[15]. Amrollahi. H., Baghbanan A., and Hashemolhosseini. H. (2011). Measuring fracture toughness of crystalline marbles under modes I and II and mixed mode I-II loading conditions using CCNBD and HCCD specimens. Int J Rock Mech Min Sci 48(7):1123–1134.
[16]. Tang. T., Bazˇ ant. Z.P., Yang S., and Zollinger D. (1996). Variable-notch one-size test method for fracture energy and process zone length. Eng Fract Mech. 55 (3):383–404.
[17]. Yang. S., Tang. T.X., Zollinger. D., and Gurjar A. (1997). Splitting tension tests to determine rock fracture parameters by peak-load method. Adv Cem Based Mater 5:18–28.
[18]. Thiercelin. M., and Roegiers. J.C. (1986). Fracture toughness determination with the modified ring test. In: Proceedings of the International Symposium on Engineering in Complex Rock Formations, Beijing, China, pp 1–8.
[19]. Thiercelin. M. (1989). Fracture toughness and hydraulic fracturing. Int J Rock Mech Min Sci Geomech Abstr 26:177–183.
[20]. Tutluoglu. L., and Keles. C. (2011). Mode I fracture toughness determination with straight notched disk bending method. Int J Rock Mech Min Sci. 48. (8): 1248–1261.
[21]. Shiryaev. A.M., and Kotkis. A.M. (1982). Methods for determining fracture-toughness of brittle porous materials. Ind Lab. 48 (9): 917–918.
[22]. Wang. Q.Z., Jia. X.M., Kou. S.Q., Zhang. Z.X., and Lindqvist. P.A. (2003). More accurate stress intensity factor derived by finite element analysis for the ISRM suggested rock fracture toughness specimen-CCNBD. Int J Rock Mech Min Sci. 4 (2): 233–241.
[23]. Iqbal MJ and Mohanty B (2007). Experimental calibration of isrm suggested fracture toughness measurement techniques in selected brittle rocks. Rock Mech. Rock Eng. 40 (5): 453–475.
[24]. Dai. F., Chen. R., Iqbal. M.J., and Xia. K. (2010). Dynamic cracked chevron notched Brazilian disc method for measuring rock fracture parameters. Int J Rock Mech Min Sci. 47 (4): 606–613.
[25]. Dai. F., Chen. R., and Xia. K. (2010). A semi-circular bend technique for determining dynamic fracture toughness. Exp Mech. 50 (6): 783–791.
[26]. Dai. F., and Xia. K. (2013). Laboratory measurements of the rate dependence of the fracture toughness anisotropy of Barre granite. Int J Rock Mech Min Sci 60: 57–65.
[27]. Kuruppu, M.D. (2014a) ISRM-suggested method for determining the mode I static fracture toughness using semi-circular bend specimen. Rock Mech. Rock Eng. 47: 267–274.
[28]. Kuruppu M.D., Obara. Y., Ayatollahi. M.R., Chong. K.P., and Funatsu. T. (2014). ISRM-Suggested method for determining the mode I static fracture toughness using semi-circular bend specimen. Rock Mech Rock Eng. 47 (1): 267–274.
[29]. 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. Eng Geol. 66 (1): 79–97.
[30]. Dai. F., Wei. M.D., Xu. N.W., Ma. Y., and Yang. D.S. (2015) Numerical assessment of the progressive rock fracture mechanism of cracked chevron notched Brazilian disc specimens. Rock Mech Rock Eng. 48 (2):463–479.
[31]. Berto, F., Cendon, D.A., Lazzarin, P., Elices, M. (2013). Fracture behavior of notched round bars made of PMMA subjected to torsion at −60 °C. Eng. Fract. Mech. 102, 271–287.
[32]. Baek, S.H., Hong, J.P., Kim, S.U., Choi, J.S., and Kim, K.W. (2011). Evaluation of fracture toughness of semi-rigid asphalt concretes at low temperatures. Transp. Res. Rec. 2210, 30–36.
[33]. Xu. N.W., Dai. F., Wei. M.D., Xu. Y., and Zhao. T. (2015). Numerical observation of three dimensional wing-cracking of cracked chevron notched Brazilian disc rock specimen subjected to mixed mode loading. Rock Mech Rock Eng. 32(2):33-44.
[34]. Yaylaci. M., and Birinci. A. (2013). The receding contact problem of two elastic layers supported by two elastic quarter planes. Structural Engineering and Mechanics, 48(2): 241-255.
[35]. Yaylaci. M., Öner. E., and Birinci. A. (2014). Comparison between Analytical and ANSYS Calculations for a Receding
[36]. Yaylacı M and Avcar M (2020). Finite element modeling of contact between an elastic layer and two elastic quarter planes. Computers and Concrete, Vol. 26, No. 2 (2020) 107-114.
[37]. Yaylacı M, Terzi C, and Avcar M. (2019). Numerical analysis of the receding contact problem of two bonded layers resting on an elastic half plane. Structural Engineering and Mechanics, 72 (6).
[38]. Akbulut, H and Aslantas, K (2004). Finite element analysis of stress distribution on bitu- minous pavement and failure mechanism. Mater. Des. 26, 383–387.
[39]. Potyondy, D.O. (2012). A flat-jointed bonded-particle material for hard rock. Paper presented at the 46th U.S. Rock Mechanics/Geomechanics Symposium, Chicago, USA.
[40]. Potyondy, D.O. (2015). The bonded-particle model as a tool for rock mechanics research and application: Current trends and future directions. Geosystem Engineering, 18(1): 1–28.
[41]. Potyondy, D.O. (2017). Simulating perforation damage with a flat-jointed bonded-particle material. Paper presented at the 51st US Rock Mechanics/Geomechanics Symposium, San Francisco, California, USA.
)