Abstract
A large amount of slates is distributed along Kangding No. 2 tunnel of Sichuan–Tibet Railway (China). The bedding of the Kangding slate is rich, showing apparent anisotropy of strength. For underground tunnels excavated in the anisotropic rock mass, the rock material is vulnerable to damage in tension because of its low tensile strength. Therefore, the tensile strength and fracture modes are important for the support design of layered surrounding-rock tunnel. In this study, first, a series of direct tensile tests were carried out on slate samples with five kinds of bedding dip angles. Second, the effect of bedding dip angle on the slate's tensile strength, failure modes, and acoustic emission characteristics was analyzed. Third, based on the Nova–Zaninetti criterion and the experiment results, a new phenomenological anisotropic criterion was proposed by introducing anisotropic coefficient, which could describe the nonlinear variation trend of tensile strength with foliation angles. Compared with four typical tensile strength criteria, the accuracy and universality of the new criterion were verified. Finally, the new criterion was implemented into the combined finite-discrete element method (FDEM) to conduct direct tensile simulation of slate with different foliation angles. The results indicated that the direct tensile strength followed an S-shaped increasing trend with the variation of foliation angles. The direct tensile failure modes of slate samples with different foliation angles could be divided into layer activation failure, mixed failure, and rock matrix failure. The acoustic emission process of slate with different bedding inclination under direct tension could be roughly divided into the following three stages: quiet period—stepped saltatory increase—drastic increase. The fitting effect of the new criterion was the highest among Kangding slate and other six typical layered rocks, which showed that the new criterion was suitable for predicting its Brazilian strength and direct tensile strength. At the same time, the numerical simulation results were in good agreement with the experimental results, which further verified the accuracy of the new criterion.
Highlights
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The acoustic emission characteristic parameters helped to reveal the direct tensile failure characteristics of layered rocks.
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A new phenomenological anisotropic tensile failure criterion was proposed.
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The direct tensile test data and the Brazilian splitting test data were used to study the accuracy and universality of the new anisotropic tensile failure criterion.
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FDEM was used to study the accuracy of the new anisotropic tensile failure criterion.
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References
ASTM D5607-08 (2008) Standard test method for performing laboratory direct shear strength tests of rock specimens under constant normal force. ASTM International, West Conshohocken
Barla G, Goffi L (1974) Direct tensile testing of anisotropic rocks. In: Proceedings of the 3rd congress of the international society for rock mechanics, Denver, Colorado, USA. Int J Rock Mech Min 12(11):152–153
Capurso M, Sacchi G (1970) Una condizione di plasticità per solidi anisotropi. Istituto di Scienza e Tecnica delle Costruzioni del Politecnico di Milano
Cen D, Huang D, Song Y et al (2020) Direct tensile behavior of limestone and sandstone with bedding planes at different strain rates. Rock Mech Rock Eng 53(6):2643–2651. https://doi.org/10.1007/s00603-020-02070-x
Chen MX (2007) Elasticity and plasticity. Science Press
Chen J (2019) Study on brittle fracture mechanism and brittle characterization method of hard rock under high stress. Institute of Rock & Soil Mechanics Chinese Academy of Sciences
Chen J, Zhou H, Zeng Z et al (2019) Macro- and microstructural characteristics of the tension–shear and compression-shear fracture of granite. Rock Mech Rock Eng 53:201–209. https://doi.org/10.1007/s00603-019-01896-4
Dan DQ, Konietzky H, Herbst M (2013) Brazilian tensile strength tests on some anisotropic rocks. Int J Rock Mech Min 58:1–7. https://doi.org/10.1016/j.ijrmms.2012.08.010
Ding C, Zhang Y, Hu D et al (2020) Foliation effects on mechanical and failure characteristics of slate in 3D space under Brazilian test conditions. Rock Mech Rock Eng 53:3919–3936. https://doi.org/10.1007/s00603-020-02146-8
Feng G, Kang Y, Wang X et al (2020) Investigation on the failure characteristics 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
Guo CB, Wang BD, Liu JK et al (2007) Main progress and achievements of the geological survey project of Sichuan-Tibet Railway traffic corridor. Geol Survey China 7(6):1–12. https://doi.org/10.19388/j.zgdzdc.2020.06.01
Herbert H, Einstein WSD (1990) Tensile and shear fracturing in predominantly compressive stress fields-a review. Eng Geol 29:149–172. https://doi.org/10.1016/0013-7952(90)90004-K
Huang X, Liu QS, Liu B et al (2017) Experimental study on the dilatancy and fracturing behavior of soft rock under unloading conditions. Int J Civ Eng 15(6):921–948. https://doi.org/10.1007/s40999-016-0144-9
Huang X, Liu QS, Peng XX et al (2019) Mechanism and forecasting model for shield jamming during TBM tunnelling through deep soft ground. Eur J Environ Civ En 23(9):1035–1068. https://doi.org/10.1080/19648189.2017.1327895
ISRM (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr 15(3):99–103
Jaeger JC, Cook NGW, Zimmerman RW (2009) Fundamentals of rock mechanics, 4th edn. Blackwell Publishing, Malden
Jensen SS (2016) Experimental study of direct tensile strength in sedimentary rocks. Norwegian University of Science and Technology
Jiang Q, Feng XT, Hatzor YH et al (2014) Mechanical anisotropy of columnar jointed basalts: an example from the Baihetan hydropower station, China. Eng Geol 175:35–45. https://doi.org/10.1016/j.enggeo.2014.03.019
Khanlari G, Rafiei B, Abdilor Y (2014) An experimental investigation of the Brazilian tensile strength and failure patterns of laminated sandstones. Rock Mech Rock Eng 48:843–852. https://doi.org/10.1007/s00603-014-0576-y
Labiouse V, Vietor T (2013) Laboratory and in situ simulation tests of the excavation damaged zone around galleries in opalinus clay. Rock Mech Rock Eng 47:57–70. https://doi.org/10.1007/s00603-013-0389-4
Lee YK, Pietruszczak S (2015) Tensile failure criterion for transversely isotropic rocks. Int J Rock Mech Min 79:205–215. https://doi.org/10.1016/j.ijrmms.2015.08.019
Li JB (2020) Study on large deformation law of surrounding rock of Zheduoshan tunnel on Sichuan-Tibet line. Master. Chengdu University of Technology
Li L, Aubertin M (2000) Un critere de rupture multiaxial pour les roches avec une anisotropie planaire. In: Proceedings of the 53rd Canadian geotechnical conference, vol 1. pp 357–364
Li K, Cheng Y, Yin ZY et al (2020) Size effects in a transversely isotropic rock under Brazilian tests: laboratory testing. Rock Mech Rock Eng 53(6):2623–2642. https://doi.org/10.1007/s00603-020-02058-7
Li C, Zou B, Zhou H et al (2021) Experimental investigation on failure behaviors and mechanism of an anisotropic shale in direct tension. Geomech Geophys Geol. https://doi.org/10.1007/s40948-021-00294-x
Li SC, Hu J, Amann F et al (2022) A multifunctional rock testing system for rock failure analysis under different stress states: Development and application. J Rock Mech Geotech. https://doi.org/10.1016/j.jrmge.2021.12.017
Liao JJ, Yang MT, Hsieh HY (1997) Direct tensile behavior of a transversely isotropic rock. Int J Rock Mech Min 34:837–849. https://doi.org/10.1016/S1365-1609(96)00065-4
Lisjak A, Tatone BSA, Grasselli G et al (2012) Numerical modelling of the anisotropic mechanical behaviour of opalinus clay at the laboratory-scale using fem/dem. Rock Mech Rock Eng 47:187–206. https://doi.org/10.1007/s00603-012-0354-7
Lisjak A, Grasselli G, Vietor T (2014) Continuum–discontinuum analysis of failure mechanisms around unsupported circular excavations in anisotropic clay shales. Int J Rock Mech Min 65:96–115. https://doi.org/10.1016/j.ijrmms.2013.10.006
Lisjak A, Garitte B, Grasselli G et al (2015) The excavation of a circular tunnel in a bedded argillaceous rock (Opalinus Clay): Short-term rock mass response and FDEM numerical analysis. Tunn Undergr Space Technol 45(1):227–248. https://doi.org/10.1016/j.tust.2014.09.014
Lisjak A, Tatone BSA, Mahabadi OK et al (2016) Hybrid finite-discrete element simulation of the EDZ formation and mechanical sealing process around a microtunnel in opalinus clay. Rock Mech Rock Eng 49:1849–1873. https://doi.org/10.1007/s00603-015-0847-2
Lo CM, Feng ZY (2014) Deformation characteristics of slate slopes associated with morphology and creep. Eng Geol 178:132–154. https://doi.org/10.1016/j.enggeo.2014.06.011
Luo YB, Chen JX, Wang LB et al (2018) Mechanical model calculations of tunnel roof with horizontal stratified rock mass tunneling considering the interlayer cohesion. China J Highw Transp 31(10):230–237 (265)
Ma T, Wu B, Fu J et al (2017a) Fracture pressure prediction for layered formations with anisotropic rock strengths. J Nat Gas Sci Eng 38:485–503. https://doi.org/10.1016/j.jngse.2017.01.002
Ma T, Zhang QB, Chen P et al (2017b) Fracture pressure model for inclined wells in layered formations with anisotropic rock strengths. J Petrol Sci Eng 149:393–408. https://doi.org/10.1016/j.petrol.2016.10.050
Mahendra S, Samadhiya NK, Kumar A et al (2015) A nonlinear criterion for triaxial strength of inherently anisotropic rocks. Rock Mech Rock Eng 48:1387–1405. https://doi.org/10.1007/s00603-015-0708-z
Marschall P, Distinguin M, Shao H et al (2006) Creation and evolution of damage zones around a microtunnel in a claystone formation of the Swiss Jura Mountains. In: Proceedings of the international symposium and exhibition on formation damage control. Society of Petroleum Engineers, Lafayette, Louisiana, USA SPE-98537-MS
Meng Y, Jing H, Liu X et al (2021) Experimental and numerical investigation on the effects of bedding plane properties on the mechanical and acoustic emission characteristics of sandy mudstone. Eng Fract Mech 245:107582. https://doi.org/10.1016/j.engfracmech.2021.107582
Molinda G, Mark C (2010) Ground failures in coal mines with weak roof. Electron J Geotech Eng (f. Bund) 15:547–588
Munjiza A (2004) The combined finite-discrete element method. Wiley, London
Munjiza A, Owen DRJ, Bicanic N (1995) A combined finite-discrete element method in transient dynamics of fracturing solids. Eng Comput 12:145–174. https://doi.org/10.1108/02644409510799532
Munjiza A, Knight EE, Rougier E (2011) Computational mechanics of discontinua. Wiley, Chichester
Nova R, Zaninetti A (1990) An investigation into the tensile behaviour of a schistose rock. Int J Rock Mech Min 27:231–242. https://doi.org/10.1016/0148-9062(90)90526-8
Perras MA, Diederichs MS (2014) A review of the tensile strength of rock: concepts and testing. Geotech Geol Eng 32:525–546. https://doi.org/10.1007/s10706-014-9732-0
Ramamurthy T, Rao GV, Singh J (1993) Engineering behaviour of phyllites. Eng Geol 33(3):209–225. https://doi.org/10.1016/0013-7952(93)90059-L
Shen J, Jimenez R, Karakus M et al (2013) A simplified failure criterion for intact rocks based on rock type and uniaxial compressive strength. Rock Mech Rock Eng 47:357–369. https://doi.org/10.1007/s00603-013-0408-5
Stockton E, Leshchinsky BA, Olsen MJ et al (2019) Influence of both anisotropic friction and cohesion on the formation of tension cracks and stability of slopes. Eng Geol 249:31–44. https://doi.org/10.1016/j.enggeo.2018.12.016
Sunay B, Ahmet Ö (2015) Investigating the anisotropy of rocks depending on the indirect tensile strength. In: Proceedins of the ISRM regional symposium-Eurock, Isrm-Eurock-2015-2088
Tatone BSA, Grasselli G (2015) A calibration procedure for two-dimensional laboratory-scale hybrid finite–discrete element simulations. Int J Rock Mech Min 75:56–72. https://doi.org/10.1016/j.ijrmms.2015.01.011
Tavallali A, Vervoort A (2010) Effect of layer orientation on the failure of layered sandstone under Brazilian test conditions. Int J Rock Mech Min 47:313–322. https://doi.org/10.1016/j.ijrmms.2010.01.001
Tsidzi KEN (1990) The influence of foliation on point load strength anisotropy of foliated rocks. Eng Geol 29:49–58. https://doi.org/10.1016/0013-7952(90)90081-B
Vervoort A, Min KB, Konietzky H et al (2014) Failure of transversely isotropic rock under Brazilian test conditions. Int J Rock Mech Min 70:343–352. https://doi.org/10.1016/j.ijrmms.2014.04.006
Wang JJ, Zhu JG, Chiu CF et al (2007) Experimental study on fracture toughness and tensile strength of a clay. Eng Geol 94:65–75. https://doi.org/10.1016/j.enggeo.2007.06.005
Xue YG, Kong FM, Yang WM et al (2020) Main unfavorable geological conditions and engineering geological problems along Sichuan-Tibet railway. Chin J Rock Mech Eng 39(3):445–468
Yan CZ, Jiao YY (2019) FDEM-TH3D: a three-dimensional coupled hydrothermal model for fractured rock. Int J Numer Anal Methods Geo Mech 43(1):415–440. https://doi.org/10.1002/nag.2869
Yan CZ, Zheng H (2017) A coupled thermo-mechanical model based on the combined finite-discrete element method for simulating thermal cracking of rock. Int J Rock Mech Min Sci 91:170–178. https://doi.org/10.1016/j.ijrmms.2016.11.023
Yan CZ, Zheng H, Sun GH, Ge XR (2016) Combined finite-discrete element method for simulation of hydraulic fracturing. Rock Mech Rock Eng 49:1389–1410. https://doi.org/10.1007/s00603-015-0816-9
Yan CZ, Jiao YY, Zheng H (2018) A fully coupled three-dimensional hydro-mechanical finite discrete element approach with real porous seepage for simulating 3D hydraulic fracturing. Comput Geotech 96:73–89. https://doi.org/10.1016/j.compgeo.2017.10.008
Yan CZ, Wang T, Ke WH, Wang G (2021a) A 2D FDEM-based moisture diffusion–fracture coupling model for simulating soil desiccation cracking. Acta Geotech 16:2609–2628. https://doi.org/10.1007/s11440-021-01297-4
Yan CZ, Wang X, Huang DR, Wang G (2021b) A new 3D continuous-discontinuous heat conduction model and coupled thermomechanical model for simulating the thermal cracking of brittle materials. Int J Solids Struct 229:111123. https://doi.org/10.1016/j.ijsolstr.2021.111123
Yan CZ, Zheng YC, Huang DR, Wang G (2021c) A coupled contact heat transfer and thermal cracking model for discontinuous and granular media. Comput Methods Appl Mech Eng 375(1):113587. https://doi.org/10.1016/j.cma.2020.113587
Yan CZ, Zheng YC, Ke WH, Wang G (2021d) A FDEM 3D moisture migration-fracture model for simulation of soil shrinkage and desiccation cracking. Comput Geotech 140:104425. https://doi.org/10.1016/j.compgeo.2021.104425
Yan CZ, Xie X, Ren YH, Ke WH, Wang G (2022) A FDEM-based 2D coupled thermal-hydro-mechanical model for multiphysical simulation of rock fracturing. Int J Rock Mech Min Sci 149:104964. https://doi.org/10.1016/j.ijrmms.2021.104964
Yang ZP, Bai HE, Xie LZ et al (2015) Strength and failure modes of shale based on Brazilian test. Rock Soil Mech 36:3447–3464. https://doi.org/10.16285/j.rsm.2015.12.015
Yang SQ, Yin PF, Huang YH (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
Youash YY (1966) Experimental deformation of layered rocks. In: First international society for rock mechanics congress. Lisbon, Portugal, vol 3, pp 787–795
Zhang HJ, Cui DD, Cheng PF (2019) Height nonlinear velocity field and variance fluctuation model construction method for CORS stations. Acta Geodaet Cartogr Sin 48(9):1096–1106 (in Chinese)
Zhang Q, Fan X, Chen P et al (2020) Geomechanical behaviors of shale after water absorption considering the combined effect of anisotropy and hydration. Eng Geol 269:105547. https://doi.org/10.1016/j.enggeo.2020.105547
Zhong S, Zuo SY, Mao L et al (2020) Mechanism of anisotropic characteristics of layered limestone and a constitutive model for different bedding angles based on a Brazilian tensile test. Arab J Geosci. https://doi.org/10.1007/s12517-020-06222
Zhou H, Chen J, Lu JJ et al (2018) Development of a multi-functional shear test system for rock. Rock Soil Mech 39(03):1115–1122 (in Chinese)
Zhou W, Shi G, Wang J et al (2022) The influence of bedding planes on tensile fracture propagation in shale and tight sandstone. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-021-02742-2
Acknowledgements
The work of this paper is based on the Y-Code of Munjiza et al. and the Y-Geo and Y-GUI of Grasselli’s Geomechanics Group (http://www.geogroup.utoronto.ca/). This research received support from the Natural Science Foundation of China (Grant Nos. U21A20153, 41941018, 52074258), Key Research and Development Project of Hubei Province (Grant Nos. 2021BCA133, 2020BCB073).
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PL: Experiment, Data curation, Software, Writing the original draft. Q-sL: Conceptualization, Methodology, Funding acquisition. XH: Investigation, Validation, Review & Editing. M-mH: Visualization, Formal analysis. YB: Validation. DY: Validation. XqX: Visualization, Validation.
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Liu, P., Liu, Q., Huang, X. et al. Direct Tensile Test and FDEM Numerical Study on Anisotropic Tensile Strength of Kangding Slate. Rock Mech Rock Eng 55, 7765–7789 (2022). https://doi.org/10.1007/s00603-022-03036-x
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DOI: https://doi.org/10.1007/s00603-022-03036-x