Abstract
Four groups (1 × 10–5/s, 1 × 10–4/s, 1 × 10–3/s and 1 × 10–2/s) of triaxial compression tests at a confining pressure of 30 MPa are carried out to clarify the strain rate effect and damage evolution of siltstone. The elastic modulus, peak stress, strain energy evolution and failure modes of siltstone at different strain rates are analyzed, followed by an interpretation based on statistical damage theory. In the range of the quasi-static strain rate, as the strain rate increases, the elastic modulus, peak stress, total strain energy density and elastic strain energy density at the peak stress of siltstone increase, and the failure mode of the siltstone gradually change from single-plane shear failure to extensile failure. The plastic shear strain is adopted as the random variable of the Weibull distribution to formulate a new statistical damage model, which can better reproduce the post-peak characteristics of the stress–strain curve and interpret the damage evolution process of siltstone; this also reveals that the nonlinear evolution of random variables with axial strain should be considered to capture the post-peak stress–strain curve. The damage variable evolution curves are similar to the dissipated strain energy density curves, which are ‘L-shaped’. Finally, a simplified method for determining the influence of strain rate on damage at peak stress Dcr is proposed and discussed.
Highlights
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In the range of the quasi-static strain rate, four groups of triaxial compression tests are carried out to reveal the strain rate effect of siltstone.
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Incorporating the plastic shear strain, a statistical damage model is proposed to better interpret the mechanical behaviour of siltstone.
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Based on the damage theory, a simplified method for determining the influence of strain rate on damage at peak stress Dcr is proposed.
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References
Bian K, Liu J, Zhang W et al (2019) Mechanical behavior and damage constitutive model of rock subjected to water-weakening effect and uniaxial loading. Rock Mech Rock Eng 52:97–106. https://doi.org/10.1007/s00603-018-1580-4
Cao A, Jing G, Ding Y et al (2019) Mining-induced static and dynamic loading rate effect on rock damage and acoustic emission characteristic under uniaxial compression. Saf Sci 116:86–96. https://doi.org/10.1016/j.ssci.2019.03.003
Cao W, Zhao H, Li X et al (2012) A statistical damage simulation method for rock full deformation process with consideration of the deformation characteristics of residual strength phase. Chin Civil Eng J 45(6):139–145. https://doi.org/10.15951/j.tmgcxb.2012.06.001
Chen X, Yu J, Tang C et al (2017) Experimental and numerical investigation of permeability evolution with damage of sandstone under triaxial compression. Rock Mech Rock Eng 50(6):1529–1549. https://doi.org/10.1007/s00603-017-1169-3
Chen H, Zhu H, Zhang L (2021) Analytical solution for deep circular tunnels in rock with consideration of disturbed zone, 3D strength and large Strain. Rock Mech Rock Eng 54(3):1391–1410. https://doi.org/10.1007/s00603-020-02339-1
Geng J, Sun Q, Zhang Y et al (2017) Studying the dynamic damage failure of concrete based on acoustic emission. Constr Build Mater 149:9–16. https://doi.org/10.1016/j.conbuildmat.2017.05.054
Gu Q, Ma Q, Tan Y et al (2019) Acoustic emission characteristics and damage model of cement mortar under uniaxial compression. Constr Build Mater 23:377–385. https://doi.org/10.1016/j.conbuildmat.2019.04.090
He M (2010) Physical modeling of an underground roadway excavation in geologically 45° inclined rock using infrared thermography. Eng Geol 121(3–4):165–176. https://doi.org/10.1016/j.enggeo.2010.12.001
He J, Afolagboye L, Zheng B et al (2022a) Effect of strain rate on anisotropic mechanical behavior of the shale under uniaxial compression conditions. Rock Mech Rock Eng 55:5297–5305. https://doi.org/10.1007/s00603-022-02892-x
He M, Cheng T, Qiao Y et al (2022b) A review of rockburst: Experiments, theories, and simulations. J Rock Mech Geotech Eng 15(5):1312–1353. https://doi.org/10.1016/j.jrmge.2022.07.014
Ju M, Li J, Li X et al (2019a) 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 J, Yao Q et al (2019b) Rate effect on crack propagation measurement results with crack propagation gauge, digital image correlation, and visual methods. Eng Fract Mech 219:106537. https://doi.org/10.1016/j.engfracmech.2019.106537
Ju M, Li J, Li J et al (2020) Loading rate effects on anisotropy and crack propagation of weak bedding plane-rich rocks. Eng Fract Mech 203:106983. https://doi.org/10.1016/j.engfracmech.2020.106983
Ju M, Li X, Li X et al (2022) A review of the effects of weak interfaces on crack propagation in rock: from phenomenon to mechanism. Eng Fract Mech 263:108297. https://doi.org/10.1016/j.engfracmech.2022.108297
Lemaitre J (1984) How to use damage mechanics. Nucl Eng Des 80(2):233–245. https://doi.org/10.1016/0029-5493(84)90169-9
Li Y, Huang D, Li X et al (2014) Strain rate dependency of coarse crystal marble under uniaxial compression: strength, deformation and strain energy. Rock Mech Rock Eng 47(4):1153–1164. https://doi.org/10.1007/s00603-013-0472-x
Li D, Ren G, Ke B, Zhang C et al (2020a) Loading rate effect and energy dissipation mechanism of dihydrate gypsum under confining pressure. Chin J Rock Mech Eng 39(9): 1883–1892. https://doi.org/10.13722/j.cnki.jrme.2020.0031
Li S, Wu Y, Huo R et al (2020b) Mechanical properties of acid-corroded sandstone under uniaxial compression. Rock Mech Rock Eng 54(01):289–302. https://doi.org/10.1007/s00603-020-02262-5
Li X, Li H, Zhang G et al (2021a) Rate dependency mechanism of crystalline rocks induced by impacts: insights from grain-scale fracturing and micro heterogeneity. Int J Impact Eng 155:103855. https://doi.org/10.1016/j.ijimpeng.2021.103855
Li H, Qiao Y, Shen X et al (2021b) Effect of water on mechanical behavior and acoustic emission response of sandstone during loading process: phenomenon and mechanism. Eng Geol 294:106386. https://doi.org/10.1016/j.enggeo.2021.106386
Li H, Qiao Y, He M et al (2023) Effect of water saturation on dynamic behavior of sandstone after wetting-drying cycles. Eng Geol 319:107105. https://doi.org/10.1016/j.enggeo.2023.107105
Liang C, Zhang Q, Li X et al (2016) The effect of specimen shape and strain rate on uniaxial compressive behavior of rock material. Bull Eng Geol Environ 75(4):1669–1681. https://doi.org/10.1007/s10064-015-0811-0
Liu X, Hao Q, Wu S, et al (2019) Nonlinear mechanical properties of coal rock under quasi-static strain rate. J Chin Coal Soc 44(5):1437–1445. https://doi.org/10.13225/j.cnki.jccs.2019.6008
Liu W, Yan E, Dai H, Du Y et al (2020) Study on characteristic strength and energy evolution law of Badong formation mudstone under water effect. Chin. J Rock Mech Eng 39(2):311–326
Martin C, Chandler N (1994) The progressive failure of Lac du Bonnet granite. Int J Rock Mech Min Sci 31(6):643–659
Meng Q, Han L, Pu H et al (2016) Effect of the size and strain rate on the mechanical behavior of rock specimens. J Chin Univ Min Technol 45(2): 233–243. https://doi.org/10.13247/j.cnki.jcumt.000477
Perras M, Diederichs M (2016) Predicting excavation damage zone depths in brittle rocks. J Rock Mech Geotech Eng 8(1):60–74. https://doi.org/10.1016/j.jrmge.2015.11.004
Qiao Y, Xiao Y, Ding W et al (2023) Effect of rock nonlinear mechanical behavior on plastic zone around deeply buried tunnel: a numerical investigation. Comput Geotech 161:105532. https://doi.org/10.1016/j.compgeo.2023.105532
Ren C, Jin Y, Cai Y et al (2021) A novel constitutive model with plastic internal and damage variables for brittle rocks. Eng Fract Mech 248:10773. https://doi.org/10.1016/j.engfracmech.2021.107731
Sun X, Peng S, Zhao C et al (2018) Physical modeling experimental study on failure mechanism of surrounding rock of deep-buried soft tunnel based on digital image correlation technology. Arab J Geosci 11(20):624. https://doi.org/10.1007/s12517-018-3979-3
Wang Q, Jiang B, Pan R et al (2018) Failure mechanism of surrounding rock with high stress and confined concrete support system. Int J Rock Mech Min Sci 102:89–102. https://doi.org/10.1016/j.ijrmms.2018.01.020
Wu X, Jiang Y, Guan Z (2018) A modified strain-softening model with multi-post-peak behaviours and its application in circular tunnel. Eng Geol 240:21–33. https://doi.org/10.1016/j.enggeo.2018.03.031
Xiao Y, He M, Qiao Y et al (2023) A novel semi-analytical solution to ground reactions of deeply buried tunnels considering the nonlinear behavior of rocks. Comput Geotech 159:105429. https://doi.org/10.1016/j.compgeo.2023.105429
Xie H, Li L, Peng R et al (2009) Energy analysis and criteria for structural failure of rocks. J Rock Mech Geotech 1(1):11–20. https://doi.org/10.3724/SP.J.1235.2009.00011
Xie L, Zhao G, Meng X (2013) Research on damage viscoelastic dynamic constitutive model of soft rock and concrete materials. Chin J Rock Mech Eng 32(4):857–864
Xie H, Zhu J, Zhou T, Zhang K et al (2020) Conceptualization and preliminary study of engineering disturbed rock dynamics. Geomech Geophys Geo-energ Geo-resour 6:51. https://doi.org/10.1007/s40948-020-00174-w
Xu X, Karakus M (2018) A coupled thermo-mechanical damage model for granite. Int J Rock Mech Min Sci 103:195–204. https://doi.org/10.1016/j.ijrmms.2018.01.030
Yang S, Zeng S, Wang H (2005) Experimental analysis on mechanical effects of loading rates on limestone. Chin J Geotech Eng 27(7):786–788
Yin X, Ge X, Li C et al (2010) Influence of loading rates on mechanical behaviors of rock materials. Chin J Rock Mech Eng 29(S1):2610–2615
Zhang Y, Li B, Jiang X et al (2021) Study on triaxial compression damage evolution characteristics of coal based on energy dissipation. Chin J Rock Mech Eng 40(8):1614–1627. https://doi.org/10.13722/j.cnki.jrme.2020.1133
Zhang Q, Zhao J (2014) A review of dynamic experimental techniques and mechanical behaviour of rock materials. Rock Mech Rock Eng 47(4):1411–1478. https://doi.org/10.1007/s00603-013-0463-y
Zhao K, Yu X, Zhou Y et al (2020) Energy evolution of brittle granite under different loading rates. Int J Rock Mech Min Sci 132:104392. https://doi.org/10.1016/j.ijrmms.2020.104392
Zhou Y, Sheng Q, Li N et al (2020) The influence of strain rate on the energy characteristics and damage evolution of rock materials under dynamic uniaxial compression. Rock Mech Rock Eng 53(8):3823–3834. https://doi.org/10.1007/s00603-020-02128-w
Acknowledgements
This research is financed by the National Natural Science Foundation of China (No. 42007255, No. 41941018), and Key Technology Research on Water Diversion Project for Central Area of Yunnan Province.
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Xiao, Y., Qiao, Y., He, M. et al. Strain Rate Effect of Siltstone Under Triaxial Compression and Its Interpretation from Damage Mechanics. Rock Mech Rock Eng 56, 8643–8656 (2023). https://doi.org/10.1007/s00603-023-03528-4
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DOI: https://doi.org/10.1007/s00603-023-03528-4