Abstract
After excavation, the rock mass often fails in the state of triaxial extension. To explore the fracture mechanism of sandstone under triaxial extension at different loading rates, the triaxial extension tests under confining pressure of 10 MPa and 30 MPa with different loading rates (range from 1 × 10–4 to 1 mm/s) were carried out on sandstone. Scanning electron microscopy and 3D optical scanning were used to obtain fracture characteristics. The results show that failure strength and elastic modulus increase with the increasing loading rate. Based on the analysis of asperity height, slope angle, aspect direction, fractal dimension, and fracture pattern, the fracture mechanism of sandstone at different loading rates was obtained: at a lower loading rate, microcracks propagate along weak structures. Microcracks grow into tensile cracks under lower confining pressure; grow into shear cracks under higher confining pressure. At a higher loading rate, more grains are damaged. Microcracks grow into tensile cracks under lower confining pressure; microcracks grow into tensile–shear cracks under higher confining pressure.
Highlights
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Triaxial extension tests at different loading rates were carried out on sandstone under confining pressure of 10 MPa and 30 MPa.
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The fracture patterns at different loading rates were determined.
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The 3D morphological characteristics of fracture surfaces were obtained by using 3D optical scanner, and asperity height, slope angle, aspect direction, and fractal dimension were calculated.
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The influence of confining pressure and loading rate on fracture behavior was determined.
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References
Ai T, Zhang R, Zhou H, Pei J (2014) Box-counting methods to directly estimate the fractal dimension of a rock surface. Appl Surf Sci 314:610–621. https://doi.org/10.1016/j.apsusc.2014.06.152
Babadagli T, Develi K (2003) Fractal characteristics of rocks fractured under tension. Theoret Appl Fract Mech 39(1):73–88. https://doi.org/10.1016/S0167-8442(02)00139-8
Backers T, Fardin N, Dresen G, Stephansson O (2003) Effect of loading rate on mode I fracture toughness, roughness and micromechanics of sandstone. Int J Rock Mech Min Sci 40(3):425–433. https://doi.org/10.1016/S1365-1609(03)00015-7
Bae D-s, Kim K-s, Koh Y-k, Kim J-y (2011) Characterization of joint roughness in granite by applying the scan circle technique to images from a borehole televiewer. Rock Mech Rock Eng 44(4):497–504. https://doi.org/10.1007/s00603-011-0134-9
Bao H, Zhang G, Lan H, Yan C, Xu J, Xu W (2020) Geometrical heterogeneity of the joint roughness coefficient revealed by 3D laser scanning. Eng Geol 265:105415. https://doi.org/10.1016/j.enggeo.2019.105415
Bobich J K.2005. Experimental analysis of the extension to shear fracture transition in Berea Sandstone, Texas A&M University.
Cadoni E (2010) Dynamic characterization of orthogneiss rock subjected to intermediate and high strain rates in tension. Rock Mech Rock Eng 43(6):667–676. https://doi.org/10.1007/s00603-010-0101-x
Cai M (2008) Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries—insight from numerical modeling. Int J Rock Mech Min Sci 45(5):763–772. https://doi.org/10.1016/j.ijrmms.2007.07.026
Cai M, Kaiser P, Tasaka Y, Maejima T, Morioka H, Minami M (2004) Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations. Int J Rock Mech Min Sci 41(5):833–847. https://doi.org/10.1016/j.ijrmms.2004.02.001
Cao Rh, Wang C, Yao R, Hu T, Lei D, Lin H, Zhao Y (2020) Effects of cyclic freeze-thaw treatments on the fracture characteristics of sandstone under different fracture modes: laboratory testing. Theor Appl Fract Mech 109:102738. https://doi.org/10.1016/j.tafmec.2020.102738
Cao R-h, Wang C, Hu T, Yao R, Li T, Lin Q (2022) Experimental investigation of plane shear fracture characteristics of sandstone after cyclic freeze–thaw treatments. Theor Appl Fract Mech 118:103214. https://doi.org/10.1016/j.tafmec.2021.103214
Chen Y, Lin G, Mao R, Li M, Mao X, Zhang K (2020) Strain rate effect on the mechanical properties and fracture surface roughness of sandstone subjected to dynamic direct tension. IEEE Access 8:107977–107992. https://doi.org/10.1109/ACCESS.2020.3001066
Cui Z, Qian S, Zhang G, Maochu Z (2021) An experimental investigation of the influence of loading rate on rock tensile strength and split fracture surface morphology. Rock Mech Rock Eng 54(4):1969–1983. https://doi.org/10.1007/s00603-021-02368-4
Dai F, Xia K, Tang L (2010) Rate dependence of the flexural tensile strength of Laurentian granite. Int J Rock Mech Min Sci 47(3):469–475. https://doi.org/10.1016/j.ijrmms.2009.05.001
Demirdag S, Tufekci K, Sengun N, Efe T, Altindag R (2019) Determination of the direct tensile strength of granite rock by using a new dumbbell shape and its relationship with Brazilian tensile strength. In: World Multidisciplinary Earth Sciences Symposium. IOP Conference Series: Earth and Environmental Science. https://doi.org/10.1088/1755-1315/221/1/012094
Feng X-T, Xu H, Qiu S-L, Li S-J, Yang C-X, Guo H-S, Cheng Y, Gao Y-H (2018) In situ observation of rock spalling in the deep tunnels of the China Jinping underground laboratory (2400 m depth). Rock Mech Rock Eng 51(4):1193–1213. https://doi.org/10.1007/s00603-017-1387-8
Feng F, Chen S, Wang Y, Huang W, Han Z (2021) Cracking mechanism and strength criteria evaluation of granite affected by intermediate principal stresses subjected to unloading stress state. Int J Rock Mech Min Sci 143:104783. https://doi.org/10.1016/j.ijrmms.2021.104783
Golshani A, Oda M, Okui Y, Takemura T, Munkhtogoo E (2007) Numerical simulation of the excavation damaged zone around an opening in brittle rock. Int J Rock Mech Min Sci 44(6):835–845. https://doi.org/10.1016/j.ijrmms.2006.12.005
Gong F-Q, Zhao G-F (2014) Dynamic indirect tensile strength of sandstone under different loading rates. Rock Mech Rock Eng 47(6):2271–2278. https://doi.org/10.1007/s00603-013-0503-7
Gong F, Zhang L, Wang S (2019) Loading rate effect of rock material with the direct tensile and three Brazilian disc tests. Adv Civil Eng. https://doi.org/10.1155/2019/6260351
Hallbauer D, Wagner H, Cook N (1973) Some observations concerning the microscopic and mechanical behaviour of quartzite specimens in stiff, triaxial compression tests. Int J Rock Mech Min Sci Geomech Abst. https://doi.org/10.1016/0148-9062(73)90015-6
Huang R, Huang D (2014) Evolution of rock cracks under unloading condition. Rock Mech Rock Eng 47(2):453–466. https://doi.org/10.1007/s00603-013-0429-0
Huang D, Liu Y, Cen D, Zeng B, Wu Z, Yang Y (2022) Effect of confining pressure on deformation and strength of granite in confined direct tension tests. Bull Eng Geol Env 81(3):1–20. https://doi.org/10.1007/s10064-022-02609-y
ISRM (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr 15(3):99–103. https://doi.org/10.1016/0148-9062(78)90003-7
Jiang Q, Feng X, Gong Y, Song L, Ran S, Cui J (2016) Reverse modelling of natural rock joints using 3D scanning and 3D printing. Comput Geotech 73:210–220. https://doi.org/10.1016/j.compgeo.2015.11.020
Ju M, Li J, Li X, Zhao J (2019) Fracture surface morphology of brittle geomaterials influenced by loading rate and grain size. Int J Impact Eng 133:103363. https://doi.org/10.1016/j.ijimpeng.2019.103363
Ju M, Li X, Li X, Zhang G (2022) A review of the effects of weak interfaces on crack propagation in rock: From phenomenon to mechanism. Eng Fract Mech. https://doi.org/10.1016/j.engfracmech.2022.108297
Kranz RL (1979) Crack growth and development during creep of Barre granite. Int J Rock Mech Min Sci Geomech Abst. https://doi.org/10.1016/0148-9062(79)90772-1
Lan H, Chen J, Macciotta R (2019) Universal confined tensile strength of intact rock. Sci Rep 9(1):1–9. https://doi.org/10.1038/s41598-019-42698-6
Li H, Li J, Liu B, Li J, Li S, Xia X (2013) Direct tension test for rock material under different strain rates at quasi-static loads. Rock Mech Rock Eng 46(5):1247–1254. https://doi.org/10.1007/s00603-013-0406-7
Li X, Li H, Zhao J (2019) The role of transgranular capability in grain-based modelling of crystalline rocks. Comput Geotech 110:161–183. https://doi.org/10.1016/j.compgeo.2019.02.018
Li C, Xie H, Wang J (2020) Anisotropic characteristics of crack initiation and crack damage thresholds for shale. Int J Rock Mech Min Sci 126:104178. https://doi.org/10.1016/j.ijrmms.2019.104178
Li Z, Xu G, Dai Y, Zhao X, Fu Y (2021) Effects of foliation on deformation and failure mechanism of silty slates. Int J Rock Mech Min Sci 141:104703. https://doi.org/10.1016/j.ijrmms.2021.104703
Li X, Lan Y, Zou J (1983) A study of rock fractures. In: Balkema AA, Rotterdam N (eds) 5th ISRM Congress, Melbourne, VIC, Australia, April 1983. International Society for Rock Mechanics and Rock Engineering, pp A261-A263
Liu Z, Zhou H, Zhang W, Xie S, Shao J (2019) A new experimental method for tensile property study of quartz sandstone under confining pressure. Int J Rock Mech Min Sci 123:104091. https://doi.org/10.1016/j.ijrmms.2019.104091
Liu Y, Huang D, Cen D, Zhong Z, Gong F, Wu Z, Yang Y (2021a) Tensile strength and fracture surface morphology of granite under confined direct tension test. Rock Mech Rock Eng 54(9):4755–4769. https://doi.org/10.1007/s00603-021-02543-7
Liu Z, Ma C, Xie W (2021b) Experimental study on mechanical properties and failure modes of pre-existing cracks in sandstone during uniaxial tension/compression testing. Eng Fract Mech 255:107966. https://doi.org/10.1016/j.engfracmech.2021b.107966
Liu S, Lan H, Martin CD (2022a) Progressive transition from extension fracture to shear fracture of altered granite during uniaxial tensile tests. Rock Mech Rock Eng 55(9):5355–5375. https://doi.org/10.1007/s00603-022-02897-6
Liu Z, Ma C, Wei X-a (2022b) Electron scanning characteristics of rock materials under different loading methods: A review. Geomech Geophys Geo-Energy Geo-Res 8(2):1–27. https://doi.org/10.1007/s40948-022-00392-4
Liu Z, Ma C, Wei X, a, Xie W, (2022c) Experimental study of rock subjected to triaxial extension. Rock Mech Rock Eng 55(2):1069–1077. https://doi.org/10.1007/s00603-021-02660-3
Liu Z, Ma C, Wei X, a, Xie W, (2022d) Experimental study on the mechanical characteristics of single-fissure sandstone under triaxial extension. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-022-02876-x
Ramsey JM, Chester FM (2004) Hybrid fracture and the transition from extension fracture to shear fracture. Nature 428(6978):63–66. https://doi.org/10.1038/nature02333
Rao Q, Liu Z, Ma C, Yi W, Xie W (2021) A New flattened cylinder specimen for direct tensile test of rock. Sensors 21(12):4157. https://doi.org/10.3390/s21124157
Shuzui H (2001) Process of slip-surface development and formation of slip-surface clay in landslides in Tertiary volcanic rocks. Jpn Eng Geol 61(4):199–220. https://doi.org/10.1016/S0013-7952(01)00025-4
Song L, Jiang Q, Zhong Z, Dai F, Wang G, Wang X, Han G, Zhang D (2022) Technical path of model reconstruction and shear wear analysis for natural joint based on 3D scanning technology. Measurement 188:110584. https://doi.org/10.1016/j.measurement.2021.110584
Wang H, Dyskin A, Pasternak E (2019) Comparative analysis of mechanisms of 3-D brittle crack growth in compression. Eng Fract Mech 220:106656. https://doi.org/10.1016/j.engfracmech.2019.106656
Wong T-F (1982) Micromechanics of faulting in Westerly granite. Int J Rock Mech Min Sci Geomech Abstr. https://doi.org/10.1016/0148-9062(82)91631-X
Wu XY, Baud P, Wong T-f (2000) Micromechanics of compressive failure and spatial evolution of anisotropic damage in Darley Dale sandstone. Int J Rock Mech Min Sci 37(1–2):143–160. https://doi.org/10.1016/S1365-1609(99)00093-3
Xie J, Gao M, Zhang R, Peng G, Lu T, Wang F (2020) Experimental investigation on the anisotropic fractal characteristics of the rock fracture surface and its application on the fluid flow description. J Pet Sci Eng 191:107190. https://doi.org/10.1016/j.petrol.2020.107190
Zeng B, Huang D, Ye S, Chen F, Zhu T, Tu Y (2019) Triaxial extension tests on sandstone using a simple auxiliary apparatus. Int J Rock Mech Min Sci 120:29–40. https://doi.org/10.1016/j.ijrmms.2019.06.006
Zhang Z, Yu J, Kou S, Lindqvist P-A (2001) On study of influences of loading rate on fractal dimensions of fracture surfaces in gabbro. Rock Mech Rock Eng. https://doi.org/10.1007/s006030170011
Zhao J, Li H (2000) Experimental determination of dynamic tensile properties of a granite. Int J Rock Mech Min Sci 37(5):861–866. https://doi.org/10.1016/S1365-1609(00)00015-0
Zhong J, Shengxin L, Yinsheng M, Chengming Y, Chenglin L, Zongxing L, Xuan L, Yong L (2015) Macro-fracture mode and micro-fracture mechanism of shale. Pet Explor Dev 42(2):269–276. https://doi.org/10.1016/S1876-3804(15)30016-1
Zhou H, Xie H (2003) Direct estimation of the fractal dimensions of a fracture surface of rock. Surf Rev Lett 10(05):751–762. https://doi.org/10.1142/S0218625X03005591
Zhu W, Niu L, Li S, Xu Z (2015) Dynamic Brazilian test of rock under intermediate strain rate: pendulum hammer-driven SHPB test and numerical simulation. Rock Mech Rock Eng 48(5):1867–1881. https://doi.org/10.1007/s00603-014-0677-7
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This work was funded by the National Natural Science Foundation of China (Grant No. 52074352)
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Ma, C., Tan, G., Lv, Z. et al. Fracture Mechanism of Sandstone Under Triaxial Extension at Different Loading Rates. Rock Mech Rock Eng 56, 3429–3450 (2023). https://doi.org/10.1007/s00603-023-03246-x
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DOI: https://doi.org/10.1007/s00603-023-03246-x