Tensile strength is one of the most important characteristics of rock masses that could govern the stability of rock structures. Due to difficulties in its direct measurements, indirect methods such as the Brazilian test have been developed to assess the tensile strength of laboratory-scale rock material. This study considers the effect of loading contact angle on the indirect tensile strength of rock-like disks by adopting experimental and discrete element methods. Several experimental specimens made of synthetic materials were examined under diametrical loading, and consequently, a numerical model using PFC3D was calibrated accordingly. Then, the impacts of the loading contact angle (θ) on the tensile strength, failure pattern, and contact force chain were investigated in detail. The results indicated that as θ increases from 0°, suggested by ASTM, to 90°, the tensile state is dominated at the specimen center, whereas for angles greater than 90°, the dominant stress state changed to compression. Also, while σxx (tensile stress) at the center of the disk did not change for θ below 40°, the σyy (compressive stress) and σzz (out-of-plan normal stress) increased after θ =30°. The analysis of developed cracks suggested that when θ is lower than 30°, the percentage of tensile and shear cracks were constant (80% and 20%, respectively). As the loading contact angle increased, tensile cracks decreased, whereas the other increased. By analyzing the failed specimens, three categories of crack patterns and two categories of contact force chains were identified.
Asadizadeh, M.; Khosravi, S.; Abbasssalimi, N.; Babanouri, N.; Rezaei, M.; Alipour, A.; Lapčević, V.; Hedayat, A.; Sherizadeh, T. The effect of loading contact angle on the tensile behavior of rock disks. Rock Mechanics Letters, 2025, 2, 23. doi:10.70425/rml.202503.23
AMA Style
Asadizadeh M, Khosravi S, Abbasssalimi N et al.. The effect of loading contact angle on the tensile behavior of rock disks. Rock Mechanics Letters; 2025, 2(3):23. doi:10.70425/rml.202503.23
Chicago/Turabian Style
Asadizadeh, Mostafa; Khosravi, Saeed; Abbasssalimi, Nasrin; Babanouri, Nima; Rezaei, Mohammad; Alipour, Aref; Lapčević, Veljko, and et al. 2025. "The effect of loading contact angle on the tensile behavior of rock disks" Rock Mechanics Letters 2, no.3:23. doi:10.70425/rml.202503.23
APA Style
Asadizadeh, M., Khosravi, S., Abbasssalimi, N., Babanouri, N., Rezaei, M., Alipour, A., Lapčević, V., Hedayat, A., & Sherizadeh, T. (2025). The effect of loading contact angle on the tensile behavior of rock disks. Rock Mechanics Letters, 2(3), 23. doi:10.70425/rml.202503.23
Article Metrics
Article Access Statistics
References
Pros A, Díez P, Molins C (2011) Numerical modeling of the double punch test for plain concrete. Int J Solids Struct. 48: 1229–1238. https://doi.org/10.1016/j.ijsolstr.2011.01.006
ASTM-D3697-16 (2016) Standard test method for splitting tensile strength of intact rock core specimens. In: In Annual book of ASTM standards. West Conshohocken PA: ASTM International. pp 1–3
Yu Y, Yin J, Zhong Z (2006) Shape effects in the Brazilian tensile strength test and a 3D FEM correction. Int J Rock Mech Min Sci. 43: 623–627
Yu Y, Zhang J, Zhang J (2009) A modified Brazilian disk tension test. Int J Rock Mech Min Sci. 46: 421–425. https://doi.org/10.1016/j.ijrmms.2008.04.008
Chen S, Yue ZQ, Tham LG (2004a) Digital image-based numerical modeling method for prediction of inhomogeneous rock failure. Int J Rock Mech Min Sci. 41: 939–957. https://doi.org/10.1016/J.IJRMMS.2004.03.002
Chen S, Yue ZQ, Tham LG, Lee PKK (2004b) Modeling Of The Indirect Tensile Test For Inhomogeneous Granite Using A Digital Image-Based Numerical Method. Int J Rock Mech Min Sci. 41: 466–471. https://doi.org/10.1016/J.IJRMMS.2004.03.084
Zhu WC, Tang CA (2006) Numerical simulation of Brazilian disk rock failure under static and dynamic loading. Int J Rock Mech Min Sci. 43: 236–252. https://doi.org/10.1016/J.IJRMMS.2005.06.008
Tavallali A, Vervoort A (2013) Behaviour of layered sandstone under Brazilian test conditions: Layer orientation and shape effects. J Rock Mech Geotech Eng. 5: 366–377. https://doi.org/10.1016/j.jrmge.2013.01.004
Vervoort A, Min K-B, Konietzky H, et al (2014) Failure of transversely isotropic rock under Brazilian test conditions. Int J Rock Mech Min Sci. 70: 343–352. https://doi.org/10.1016/j.ijrmms.2014.04.006
Khanlari G, Rafiei B, Abdilor Y (2015) Evaluation of strength anisotropy and failure modes of laminated sandstones. Arab J Geosci. 8: 3089–3102. https://doi.org/10.1007/s12517-014-1411-1
Tan X, Konietzky H, Frühwirt T, Dan DQ (2015) Brazilian Tests on Trans-versely Isotropic Rocks: Laboratory Testing and Numerical Simulations. Rock Mech Rock Eng. 48: 1341–1351. https://doi.org/10.1007/s00603-014-0629-2
Mokhtari M, Tutuncu AN (2016) Impact of laminations and natural fractures on rock failure in Brazilian experiments: A case study on Green River and Niobrara formations. J Nat Gas Sci Eng. 36: 79–86. https://doi.org/10.1016/j.jngse.2016.10.015
Wang P, Cai M, Ren F (2018) Anisotropy and directionality of tensile be-haviours of a jointed rock mass subjected to numerical Brazilian tests. Tunn Undergr Sp Technol. 73: 139–153. https://doi.org/10.1016/j.tust.2017.12.018
Feng G, Kang Y, Wang X, et al (2020) Investigation on the Failure Charac-teristics and Fracture Classification of Shale Under Brazilian Test Conditions. Rock Mech Rock Eng. 53: 3325–3340. https://doi.org/10.1007/s00603-020-02110-6
Zhao NN, Feng JL (2021) Investigation on fracture mechanism of layered slate: experiment and beam-particle method. Environ Earth Sci. 80: 788. https://doi.org/10.1007/s12665-021-10106-w
Lavrov A, Vervoort A (2002) Theoretical treatment of tangential loading effects on the Brazilian test stress distribution. Int J Rock Mech Min Sci. 39: 275–283. https://doi.org/10.1016/S1365-1609(02)00010-2
Dorogoy A, Banks-Sills L (2005) Effect of crack face contact and friction on Brazilian disk specimens—A finite difference solution. Eng Fract Mech. 72: 2758–2773. https://doi.org/10.1016/J.ENGFRACMECH.2005.05.005
Markides CF, Pazis DN, Kourkoulis SK (2010) Influence of Friction on the Stress Field of the Brazilian Tensile Test. Rock Mech Rock Eng. 441:113–119. https://doi.org/10.1007/S00603-010-0115-4
Serati M, Bahaaddini M, Roshan H, et al (2021) On assessing the tensile cracking pattern in brittle rocks and solids. Bull Eng Geol Environ. 80:.5867–5879. https://doi.org/10.1007/s10064-021-02249-8
Serati M, Masoumi H, Williams DJ, Alehossein H (2017) Modified Brazilian Test for Indirect Measurement of Tensile Strength of Brittle Materials. 51st U.S. Rock Mech. Symp. ARMA-2017-0834
Wang Z, Yang S, Tang Y (2020) Mechanical behavior of different sedimentary rocks in the Brazilian test. Bull Eng Geol Environ. 79: 5415–5432. https://doi.org/10.1007/s10064-020-01906-8
ISRM (2007) The Complete ISRM Suggested Methods for Rock Characteri-zation, Testing and Monitoring; 1974-2006
Fairhurst C (1964) On the validity of the “Brazilian” test for brittle materials. Int J Rock Mech Min Sci. 1: 535–546. https://doi.org/10.1016/0148-9062(64)90060-9
Lanaro F, Sato T, Stephansson O (2009) Microcrack modelling of Brazilian tensile tests with the boundary element method. Int J Rock Mech Min Sci. 46: 450–461. https://doi.org/10.1016/j.ijrmms.2008.11.007
Lin H, Xiong W, Zhong W, Xia C (2014) Location of the Crack Initiation Points in the Brazilian Disc Test. Geotech Geol Eng. 32: 1339–1345. https://doi.org/10.1007/s10706-014-9800-5
Wang SY, Sloan SW, Tang CA (2014) Three-Dimensional Numerical Inves-tigations of the Failure Mechanism of a Rock Disc with a Central or Eccentric Hole. Rock Mech Rock Eng. 47: 2117–2137. https://doi.org/10.1007/s00603-013-0512-6
Komurlu E, Kesimal A, Demir S (2016) Experimental and numerical study on determination of indirect (splitting) tensile strength of rocks under various load apparatus. Can Geotech J. 53: 360–372. https://doi.org/10.1139/cgj-2014-0356
Markides CF, Kourkoulis SK (2012) The stress field in a standardized Brazilian disc: The influence of the loading type acting on the actual contact length. Rock Mech Rock Eng. 45:.145–158. https://doi.org/10.1007/s00603-011-0201-2
Markides CF, Kourkoulis SK (2016) The influence of jaw’s curvature on the results of the Brazilian disc test. J Rock Mech Geotech Eng. 8: 127–146. https://doi.org/10.1016/j.jrmge.2015.09.008
Gutiérrez-Moizant R, Ramírez-Berasategui M, Santos-Cuadros S, Gar-cía-Fernández C (2018) Computational Verification of the Optimum Boundary Condition of the Brazilian Tensile Test. Rock Mech Rock Eng. 51: 3505–3519. https://doi.org/10.1007/s00603-018-1553-7
Gutiérrez-Moizant R, Ramírez-Berasategui M, Santos-Cuadros S, Gar-cía-Fernández CC (2020) A Novel Analytical Solution for the Brazilian Test with Loading Arcs. Math Probl Eng. 2020: 1–19. https://doi.org/10.1155/2020/2935812
Erarslan N, Williams DJ (2012) Experimental, numerical and analytical studies on tensile strength of rocks. Int J Rock Mech Min Sci. 49: 21–30. https://doi.org/10.1016/j.ijrmms.2011.11.007
Komurlu E, Kesimal A (2015) Evaluation of Indirect Tensile Strength of Rocks Using Different Types of Jaws. Rock Mech Rock Eng. 48: 1723–1730. https://doi.org/10.1007/s00603-014-0644-3
Erarslan N, Liang ZZ, Williams DJ (2012) Experimental and Numerical Studies on Determination of Indirect Tensile Strength of Rocks. Rock Mech Rock Eng. 45: 739–751. https://doi.org/10.1007/s00603-011-0205-y
Bahaaddini M, Serati M, Masoumi H, Rahimi E (2019) Numerical assessment of rupture mechanisms in Brazilian test of brittle materials. Int J Solids Struct. 180–181: 1–12. https://doi.org/10.1016/j.ijsolstr.2019.07.004
Abdullah R, Tsutsumi T, Amin MFM, et al (2020) Evolution on deformation behaviour of brazilian test under different contact area using particle image velocimetry and finite element modelling. Measurement. 159: 107796. https://doi.org/10.1016/j.measurement.2020.107796
Imani M, Nejati HR, Goshtasbi K, Nazerigivi A (2022) Effect of brittleness on the micromechanical damage and failure pattern of rock specimens. Smart Struct Syst. 29: 535–547. https://doi.org/10.12989/SSS.2022.29.4.535
Asadizadeh M, Khosravi S, Abharian S, et al (2023a) Tensile behavior of layered rock disks under diametral loading: experimental and numerical investigations. Granul Matter. 25: 21. https://doi.org/10.1007/s10035-023-01311-4
Asadizadeh M, Moosavi M, Hossaini MF, et al. (2023b) Numerical Modeling of Rock Blocks with Nonpersistent Rough Joints Subjected to Uniaxial Com-pressive and Shear Loadings. Int J Geomech. 23: 1–26. https://doi.org/10.1061/ijgnai.gmeng-7858
Ma Y, Huang H (2018) DEM analysis of failure mechanisms in the intact Brazilian test. Int J Rock Mech Min Sci. 102: 109–119. https://doi.org/10.1016/j.ijrmms.2017.11.010
He J, Afolagboye LO (2018) Influence of layer orientation and interlayer bonding force on the mechanical behavior of shale under Brazilian test conditions. Acta Mech Sin. 34: 349–358. https://doi.org/10.1007/s10409-017-0666-7
Yang SQ, Yin P-F, Huang Y-H (2019) Experiment and Discrete Element Modelling on Strength, Deformation and Failure Behaviour of Shale Under Brazilian Compression. Rock Mech Rock Eng. 52: 4339–4359. https://doi.org/10.1007/s00603-019-01847-z
Wu S, Ma J, Cheng Y, et al (2018) Numerical analysis of the flattened Brazilian test: Failure process, recommended geometric parameters and loading conditions. Eng Fract Mech. 204: 288–305. https://doi.org/10.1016/j.engfracmech.2018.09.024
Sun W, Wu S (2021) A study of crack initiation and source mechanism in the Brazilian test based on moment tensor. Eng Fract Mech. 246: 107622. https://doi.org/10.1016/j.engfracmech.2021.107622
Asadizadeh M, Hossaini MF, Moosavi M, et al (2019) Mechanical characteri-sation of jointed rock-like material with non-persistent rough joints subjected to uniaxial compression. Eng Geol. 260: 105224. https://doi.org/10.1016/j.enggeo.2019.105224
Asadizadeh M, Hossaini MF, Moosavi M, Mohammadi S (2016) A laboratory study on mix design to properly resemble a jointed brittle rock. Int J Min Geo-Engineering. 50: 201–210. https://doi.org/10.22059/ijmge.2016.59830
Asadizadeh M, Moosavi M, Hossaini MF, Masoumi H (2018) Shear Strength and Cracking Process of Non-persistent Jointed Rocks: An Extensive Experi-mental Investigation. Rock Mech Rock Eng. 51: 415–428. https://doi.org/10.1007/s00603-017-1328-6
Asadizadeh M, Khosravi S, Karimi J, et al. (2022) Mechanical behavior of single-flawed cylindrical specimens subjected to axial loading: a numerical investigation. Bull Eng Geol Environ. 81: 442. https://doi.org/10.1007/s10064-022-02940-4
Amir Hosseini M, Kamrava S, Sahimi M, Tahmasebi P (2023) Effect of Wettability on Two-Phase Flow Through Granular Porous Media: Fluid Rupture and Mechanics of the Media. Chem Eng Sci. 269: 118446. https://doi.org/10.1016/J.CES.2023.118446
Potyondy DO (2012) A flat-jointed bonded-particle material for hard rock. 46th US Rock Mech Symp 10.
Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci. 41: 1329–1364. https://doi.org/10.1016/j.ijrmms.2004.09.011
Bahaaddini M, Sharrock G, Hebblewhite BK (2013a) Numerical direct shear tests to model the shear behaviour of rock joints. Comput Geotech. 51: 101–115. https://doi.org/10.1016/j.compgeo.2013.02.003
Bahaaddini M, Sharrock G, Hebblewhite BK (2013b) Numerical investigation of the effect of joint geometrical parameters on the mechanical properties of a non-persistent jointed rock mass under uniaxial compression. Comput Geotech. 49: 206–225. https://doi.org/10.1016/j.compgeo.2012.10.012