Abstract
Understanding the fracturing mechanisms of rock on both macro- and micro-scale is important for properly designing rock engineering applications. However, there is still a lack of understanding of why macro and micro-scale fracturing mechanisms differ. In this study, acoustic emission (AE) and digital image correlation (DIC) techniques were employed to track the microcracking processes in granite specimens subjected to indirect (Brazilian) and direct tensile loadings. The moment tensor inversion of the AE waveforms and the DIC strain field data revealed that the ultimate so-called tensile macro-fracture was predominantly composed of shear microcracks in Brazilian tests and tensile microcracks in the direct tension tests. The different contributions of shear and tensile microcracks to the formation of the macro-fracture explain the difference between direct and indirect tensile strengths. Our results showed that the compressive stress in the Brazilian test due to its biaxial stress field and the grain size are the two critical factors affecting the microcracking mechanisms in the tested coarse-grained granite. Characterizing the surface of the generated macro-fractures and the results of a series of complementary tensile tests performed on fine-grained mortar specimens suggested that reducing the compressive stress and grain size decreases the contribution of shear microcracks. The results of this study can be used in rock fracture applications in granitic rocks such as hydraulic fracturing for geothermal energy extraction, where the knowledge of the cracking location and mechanisms is critical for enhancing the reservoir's productivity.
Highlights
-
So-called tensile macro-fractures are composed of both shear and tensile cracks at the microscale.
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The ratio of shear-to-tensile microcracks depends on the grain size and stress states.
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Microcracks are predominantly shear in Brazilian and tensile in the direct tensile loading.
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Data availability
The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.
Abbreviations
- \({\sigma }_{Bt}\) :
-
Brazilian tensile strength
- \({\sigma }_{Dt}\) :
-
Direct tensile strength
- \({F}_{p}\) :
-
Applied external load at failure
- D:
-
Brazilian disc diameter
- T:
-
Brazilian disc thickness
- A:
-
Nominal cross-sectional area of prismatic specimens
- A0 :
-
Average focal amplitude of acoustic emissions
- Ai :
-
Maximum signal amplitude received by the ith sensor
- ri :
-
Signal source distance to the ith sensor
- n:
-
Number of sensors receiving the same AE signal
- \({\varepsilon }^{e}\) :
-
Elastic strain component
- \({\varepsilon }^{p}\) :
-
Plastic strain component
- \({\varepsilon }^{t}\) :
-
Total strain
References
Akaike H (1998) Information theory and an extension of the maximum likelihood principle. In: Din M (ed) Selected papers of hirotugu akaike. Springer, Newyork
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Contr 19:716–723
Alehossein H, Boland JN (2004) Strength, toughness, damage and fatigue of rock. Struct Integr Fract. 19:716
ASTM (2008) D2936-08 Standard Test Method for Direct Tensile Strength of Intact Rock Core Specimens. ASTM Int 9–11. 10.1520/D2936-20.2
ASTM (2016) D3967-16 Standard test method for splitting tensile strength of intact rock core specimens. ASTM International, West Conshohocken, USA.
Bieniawski ZT (1967) Mechanism of brittle fracture of rock: Part I—theory of the fracture process. Int J Rock Mech Min Sci Geomech Abstr 4:395–406. https://doi.org/10.1016/0148-9062(67)90030-7
Bieniawski ZT, Bernede MJ (1979) Suggested methods for determining the uniaxial compressive strength and deformability of rock materials. In: Bieniawski ZT (ed) International journal of rock mechanics and mining sciences & geomechanics abstracts. Elsevier
Bieniawski ZT, Hawkes I (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci 15:99–103. https://doi.org/10.1016/0148-9062(78)91494-8
Bobet A, Einstein HH (1998) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci 35:863–888. https://doi.org/10.1016/S0148-9062(98)00005-9
Boyd OS, Dreger DS, Lai VH, Gritto R (2015) A systematic analysis of seismic moment tensor at The Geysers geothermal field, California. Bull Seismol Soc Am 105:2969–2986
Brace WF, Paulding BW, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71:3939–3953. https://doi.org/10.1029/jz071i016p03939
Cacciari PP, Futai MM (2018) Assessing the tensile strength of rocks and geological discontinuities via pull-off tests. Int J Rock Mech Min Sci 105:44–52. https://doi.org/10.1016/j.ijrmms.2018.03.011
Cheng Y, Wong LNY (2018) Microscopic characterization of tensile and shear fracturing in progressive failure in marble. J Geophys Res Solid Earth 123:204–225. https://doi.org/10.1002/2017JB014581
CorelatedSolutions (2020) Vic-2D 2020 Reference Manual. Colum- bia, SC, USA. www.CorrelatedSolutions.com. Accessed 2 Jun 2021
Davidsen J, Goebel T, Kwiatek G et al (2021) What controls the presence and characteristics of aftershocks in rock fracture in the lab? J Geophys Res Solid Earth 126:1–25. https://doi.org/10.1029/2021JB022539
E976-15 Standard guide for determining the reproducibility of acoustic emission sensor response. ASTM International, West Conshohocken, USA
Efe T, Demirdag S, Tufekci K et al (2021) Estimating the direct tensile strength of rocks from indirect tests. Arab J Geosci. https://doi.org/10.1007/s12517-021-07539-9
Einstein HH (2021) Fractures: tension and shear. Rock Mech Rock Eng 54:3389–3408. https://doi.org/10.1007/s00603-020-02243-8
García VJ, Márquez CO, Zúñiga-Suárez AR et al (2017) Brazilian test of concrete specimens subjected to different loading geometries: review and new insights. Int J Concr Struct Mater 11:343–363. https://doi.org/10.1007/s40069-017-0194-7
Gischig VS, Preisig G (2015) Hydro-fracturing versus hydro-shearing: a critical assessment of two distinct reservoir stimulation mechanisms. In: Gischig VS (ed) 13th ISRM International Congress of Rock Mechanics. OnePetro, Newyork
Goebel THW, Candela T, Sammis CG et al (2014) Seismic event distributions and off-fault damage during frictional sliding of saw-cut surfaces with pre-defined roughness. Geophys J Int 196:612–625. https://doi.org/10.1093/GJI/GGT401
Gonçalves da Silva BM (2016) Fracturing processes and induced seismicity due to the hydraulic fracturing of rocks. Doct Dissert. 32:675
Griffith A (1924) The theory of rupture. First Int. Cong. Appl. Mech. 44:55–63
Grosse CU, Ochtsu M (2008) Acoustic Emission Testing. Basic Res-Appl Civil Eng. 55:5467
Grosse CU, Ohtsu M, Aggelis DG, Shiotani T (2021) Acoustic emission testing: basics for research-applications in engineering. Springer Nature. 278:10567
Guo TY, Wong LNY (2020) Microcracking behavior of three granites under mode I loading: Insights from acoustic emission. Eng Geol 278:105823. https://doi.org/10.1016/j.enggeo.2020.105823
Guo TY, Zhao Q (2022) Acoustic emission characteristics during the microcracking processes of granite, marble and sandstone under mode i loading. Rock Mech Rock Eng 55:5467–5489
Hoek E, Martin CD (2014) Fracture initiation and propagation in intact rock - A review. J Rock Mech Geotech Eng 6:287–300. https://doi.org/10.1016/j.jrmge.2014.06.001
Hondros G (1959) The evaluation of Poisson’s ratio and the modulus of materials of low tensile resistance by the Brazilian (indirect tensile) test with particular reference to concrete. Aust J Appl Sci 10:243–268
Hudson JA, Brown ET, Rummel F (1972) The controlled failure of rock discs and rings loaded in diametral compression. Int J Rock Mech Min Sci 9:241–248. https://doi.org/10.1016/0148-9062(72)90025-3
Iqbal MJ, Mohanty B (2006) Experimental calibration of stress intensity factors of the ISRM suggested cracked chevron-notched Brazilian disc specimen used for determination of mode-I fracture toughness. Int J Rock Mech Min Sci 43:1270–1276. https://doi.org/10.1016/j.ijrmms.2006.04.014
Kabeya KK, Legge TFH (1997) Relationship between grain size and some surface roughness parameters of rock joints. Int J Rock Mech Min Sci Geomech Abstr 34:528. https://doi.org/10.1016/S1365-1609(97)00186-X
Khosravi A, Simon R, Rivard P (2017) The shape effect on the morphology of the fracture surface induced by the Brazilian test. Int J Rock Mech Min Sci 93:201–209. https://doi.org/10.1016/j.ijrmms.2017.01.007
Kranz RL (1983) Microcracks in rocks: A review. Tectonophysics 100:449–480. https://doi.org/10.1016/0040-1951(83)90198-1
Kurz JH, Grosse CU, Reinhardt HW (2005) Strategies for reliable automatic onset time picking of acoustic emissions and of ultrasound signals in concrete. Ultrasonics 43:538–546. https://doi.org/10.1016/j.ultras.2004.12.005
Labuz JF, Shah SP, Dowding CH (1987) The fracture process zone in granite: evidence and effect. Int J Rock Mech Min Sci Geomech Abstr 24:235–246. https://doi.org/10.1016/0148-9062(87)90178-1
Labuz JF, Shah SP, Dowding CH (1985) Experimental analysis of crack propagation in granite. Int J Rock Mech Min Sci 22:85–98. https://doi.org/10.1016/0148-9062(85)92330-7
Lei X, Kusunose K, Satoh T, Nishizawa O (1992) Fractal structure of the hypoceeter distributions and focal mechanism solutions of acoustic emission in two granites of different grain sizes. J Phys Earth 40:617–634. https://doi.org/10.4294/jpe1952.40.617
Li BQ, da Silva BG, Einstein H (2019) Laboratory hydraulic fracturing of granite: Acoustic emission observations and interpretation. Eng Fract Mech 209:200–220
Li BQ, Einstein HH (2019) Direct and microseismic observations of hydraulic fracturing in barre granite and opalinus clayshale. J Geophys Res Solid Earth 124:11900–11916. https://doi.org/10.1029/2019JB018376
Li BQ, Einstein HH (2017) Comparison of visual and acoustic emission observations in a four point bending experiment on barre granite. Rock Mech Rock Eng 50:2277–2296. https://doi.org/10.1007/s00603-017-1233-z
Li D, Wong LNY (2013) The brazilian disc test for rock mechanics applications: Review and new insights. Rock Mech Rock Eng 46:269–287. https://doi.org/10.1007/s00603-012-0257-7
Lin Q, Wan B, Wang Y et al (2019) Unifying acoustic emission and digital imaging observations of quasi-brittle fracture. Theor Appl Fract Mech 103:102301
Liu J, Chen L, Wang C et al (2014) Characterizing the mechanical tensile behavior of Beishan granite with different experimental methods. Int J Rock Mech Min Sci 69:50–58. https://doi.org/10.1016/j.ijrmms.2014.03.007
Liu L, Li H, Li X et al (2021) Underlying mechanisms of crack initiation for granitic rocks containing a single pre-existing flaw: insights from digital image correlation (DIC) analysis. Rock Mech Rock Eng 54:857–873. https://doi.org/10.1007/s00603-020-02286-x
Lockner D (1993) The role of acoustic emission in the study of rock fracture. Int J Rock Mech Min Sci 30:883–899. https://doi.org/10.1016/0148-9062(93)90041-B
Lotidis MA, Nomikos PP, Sofianos AI (2020) Laboratory study of the fracturing process in marble and plaster hollow plates subjected to uniaxial compression by combined acoustic emission and digital image correlation techniques. Rock Mech Rock Eng 53:1953–1971. https://doi.org/10.1007/s00603-019-02025-x
Lu A, Wang S, Cai H (2018) Closed-Form solution for the stresses in brazilian disc tests under vertical uniform loads. Rock Mech Rock Eng 51:3489–3503. https://doi.org/10.1007/s00603-018-1511-4
Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci 31:643–659. https://doi.org/10.1016/0148-9062(94)90005-1
Maxwell SC, Cipolla C (2011) What does microseismicity tell us about hydraulic fracturing? Proc - SPE Annu Tech Conf Exhib 4:3033–3046. https://doi.org/10.2118/146932-MS
Mellor M, Hawkes I (1971) Measurement of tensile strength by diametral compression of discs and annuli. Eng Geol 5:173–225. https://doi.org/10.1016/0013-7952(71)90001-9
Moore DE, Lockner DA (1995) The role of microcracking in shear-fracture propagation in granite. J Struct Geol. https://doi.org/10.1016/0191-8141(94)E0018-T
Moradian Z, Einstein HH, Ballivy G (2016) Detection of cracking levels in brittle rocks by parametric analysis of the acoustic emission signals. Rock Mech Rock Eng 49:785–800. https://doi.org/10.1007/S00603-015-0775-1/FIGURES/17
Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313
Nicco M, Holley EA, Hartlieb P et al (2018) Methods for characterizing cracks induced in rock. Rock Mech Rock Eng 51:2075–2093. https://doi.org/10.1007/s00603-018-1445-x
Nicksiar M, Martin CD (2014) Factors affecting crack initiation in low porosity crystalline rocks. Rock Mech Rock Eng 47:1165–1181. https://doi.org/10.1007/s00603-013-0451-2
Ohno K, Ohtsu M (2010) Crack classification in concrete based on acoustic emission. Constr Build Mater 24:2339–2346. https://doi.org/10.1016/j.conbuildmat.2010.05.004
Ohtsu M (1991) Simplified moment tensor analysis and unified decomposition of acoustic emission source: application to in situ hydrofracturing test. J Geophys Res Solid Earth 96:6211–6221
Ouchterlony F (1982) Review of fracture toughness testing of rock. SM Arch 7:131–211
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
Qi S, Lan H, Martin D, Huang X (2019) Factors controlling the difference in brazilian and direct tensile strengths of the lac du bonnet granite. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-019-01946-x
Ramana YV, Sarma LP (1987) Split-collar, tensile test grips for short rock cores. Eng Geol 23:255–261
Rocco C, Guinea GV, Planas J, Elices M (1998) Experimental analysis of rupture mechanisms in the brazilian test. Fract Mech Concr Struct 1:121–130
Sakamoto Y, Ishiguro M, Kitagawa G (1986) Akaike information criterion statistics. Dordrecht, Netherlands D Reidel 81:26853
Shams G, Rivard P, Moradian O (2022) Observation of fracture process zone and produced fracture surface roughness in granite under Brazilian splitting tests. Theor Appl Fract Mech 21:103680. https://doi.org/10.1016/j.tafmec.2022.103680
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
Sutton MA, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer Sci Bus Media. 10:746
Sutton MA, Yan JH, Tiwari V et al (2008) The effect of out-of-plane motion on 2D and 3D digital image correlation measurements. Opt Lasers Eng 46:746–757. https://doi.org/10.1016/j.optlaseng.2008.05.005
Tapponnier P, Brace WF (1976) Development of stress-induced microcracks in westerly granite. Int J Rock Mech Min Sci Geomech Abstr 13:103–112
Tavallali A, Vervoort A (2010) Effect of layer orientation on the failure of layered sandstone under Brazilian test conditions. Int J Rock Mech Min Sci 47:313–322. https://doi.org/10.1016/j.jrmge.2013.01.004
Tse R, Cruden DM (1979) Estimating joint roughness coefficients. Int J Rock Mech Min Sci 16:303–307. https://doi.org/10.1016/0148-9062(79)90241-9
Vavryčuk V (2015) Moment Tensor Decompositions Revisited. J Seismol 19:231–252. https://doi.org/10.1007/s10950-014-9463-y
Wang YS, Deng JH, Li LR, Zhang ZH (2019) Micro-failure analysis of direct and flat loading brazilian tensile tests. Rock Mech Rock Eng 52:4175–4187. https://doi.org/10.1007/s00603-019-01877-7
Whittaker BN, Singh RN, Sun G (1992) Rock fracture mechanics. Pri Design Appl. 42:475
Wong LNY, Einstein HH (2009a) Crack coalescence in molded gypsum and carrara marble: Part 1. macroscopic observations and interpretation. Rock Mech Rock Eng 42:475–511. https://doi.org/10.1007/s00603-008-0002-4
Wong LNY, Einstein HH (2009b) Crack coalescence in molded gypsum and carrara marble: Part 2 - Microscopic observations and interpretation. Rock Mech Rock Eng 42:513–545. https://doi.org/10.1007/s00603-008-0003-3
Wong LNY, Guo TY (2019) Microcracking behavior of two semi-circular bend specimens in mode I fracture toughness test of granite. Eng Fract Mech 221:106565. https://doi.org/10.1016/j.engfracmech.2019.106565
Yang SQ, Yang DS, Jing HW et al (2012) An experimental study of the fracture coalescence behaviour of brittle sandstone specimens containing three fissures. Rock Mech Rock Eng 45:563–582. https://doi.org/10.1007/s00603-011-0206-x
You M (2015) Strength criterion for rocks under compressive-tensile stresses and its application. J Rock Mech Geotech Eng 7:434–439. https://doi.org/10.1016/j.jrmge.2015.05.002
Yuan R, Shen B (2017) Numerical modelling of the contact condition of a Brazilian disk test and its influence on the tensile strength of rock. Int J Rock Mech Min Sci 93:54–65. https://doi.org/10.1016/j.ijrmms.2017.01.010
Zafar S, Hedayat A, Moradian O (2022) Evolution of tensile and shear cracking in crystalline rocks under compression. Theor Appl Fract Mech 118:103254. https://doi.org/10.1016/j.tafmec.2022.103254
Zang A, Wagner FC, Stanchits S et al (2000) Fracture process zone in granite. J Geophys Res Solid Earth 105:23651–23661. https://doi.org/10.1029/2000JB900239
Zang A, Wagner FC, Stanchits S et al (1998) Source analysis of acoustic emissions in Aue granite cores under symmetric and asymmetric compressive loads. Geophys J Int 135:1113–1130. https://doi.org/10.1046/j.1365-246X.1998.00706.x
Zhang H, Fu D, Song H et al (2015) Damage and Fracture Investigation of Three-Point Bending Notched Sandstone Beams by DIC and AE Techniques. Rock Mech Rock Eng 48:1297–1303. https://doi.org/10.1007/S00603-014-0635-4/FIGURES/6
Zhao P, Kühn D, Oye V, Cesca S (2014) Evidence for tensile faulting deduced from full waveform moment tensor inversion during the stimulation of the Basel enhanced geothermal system. Geothermics 52:74–83. https://doi.org/10.1016/j.geothermics.2014.01.003
Zhao Y, Huang J, Wang R (1993) Real-time SEM observations of the microfracturing process in rock during a compression test. Int J Rock Mech Min Sci 30:643–652. https://doi.org/10.1016/0148-9062(93)91224-7
Zhou XP, Bi J, Qian QH (2015) Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws. Rock Mech Rock Eng 48:1097–1114. https://doi.org/10.1007/s00603-014-0627-4
Zietlow WK, Labuz JF (1998) Measurement of the intrinsic process zone in rock using acoustic emission. Int J Rock Mech Min Sci 35:291–299
Acknowledgements
The first two authors thank the Natural Sciences and Engineering Research Council (NSERC) [Grant no. RGPIN-2020-07109] of Canada for funding this research program and the Fonds the recherche du Québec – Nature et technologies (FRQNT) for financing the research infrastructure. The authors would also like to acknowledge Mr. Danick Charbonneau and Mr. Jean-Christophe Lacasse, technicians at the Rock Mechanics Laboratory of the University of Sherbrooke, for their valuable cooperation. The authors are also grateful for the support by Correlated Solutions, Inc., for kindly providing us with a free license for DIC software. Thanks should also go to Mr. Alex Loignon for his support in setting up the DIC system.
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Shams, G., Rivard, P. & Moradian, O. Micro-scale Fracturing Mechanisms in Rocks During Tensile Failure. Rock Mech Rock Eng 56, 4019–4041 (2023). https://doi.org/10.1007/s00603-023-03275-6
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DOI: https://doi.org/10.1007/s00603-023-03275-6