Abstract
Shear strength is an important mechanical index of rock. The adjustment and reorganization of rock structure can be reflected by the variation of shear strength. During rock rheology, the shear strength decreases with time due to rock damage. Therefore, from the point of difference of shear strength, the mechanical properties of rock can be effectively studied. In this paper, for the state of direct shear test, the Kachanov creep damage law was adopted to describe the time characteristics of the rock shear strength during the accelerated creep stage. A nonlinear viscoplastic element on the basis of time-dependent shear strength was established by connecting the plastic element representing shear strength with the viscous element in parallel. After introducing the nonlinear viscoplastic element into the classic Burgers model, the rationality of the model was verified by the shear creep test results of rock discontinuity. Results showed that the modified Burgers model can reflect the mechanical properties of rock in three creep stages. In addition, the model parameter δ can also reflect the evolution of internal cracks in rock during creep.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ban L, Qi C, Lu C (2018) A direction-dependent shear strength criterion for rock joints with two new roughness parameters. Arab J Geosci 11:466. https://doi.org/10.1007/s12517-018-3818-6
Cao P, Wen Y, Wang Y, Yuan H, Yuan B (2016) Study on nonlinear damage creep constitutive model for high-stress soft rock. Environ Earth Sci 75:900
Casagrande D, Buzzi O, Giacomini A, Lambert C, Fenton G (2017) A new stochastic approach to predict peak and residual shear strength of natural rock discontinuities. Rock Mech Rock Eng 51:69–99
Challamel N, Lamos C, Casandjian C (2005) Creep damage modelling for quasi-brittle materials. Eur J Mech 24:593–613
Chen YF, Lin H (2019) Consistency analysis of Hoek-Brown and equivalent Mohr-coulomb parameters in calculating slope safety factor. Bull Eng Geol Environ 78:4349–4361. https://doi.org/10.1007/s10064-018-1418-z
Dai F, Xu Y, Zhao T, Xu NW, Liu Y (2016) Loading-rate-dependent progressive fracturing of cracked chevron-notched Brazilian disc specimens in split Hopkinson pressure bar tests. Int J Rock Mech Min Sci 88:49–60
Deng QL, Zhu ZY, Cui ZQ, Wang XP (2000) Mass rock creep and landsliding on the Huangtupo slope in the reservoir area of the Three Gorges Project, Yangtze River, China. Eng Geol 58:67–83
Fahimifar A, Karami M, Fahimifar A (2015) Modifications to an elasto-visco-plastic constitutive model for prediction of creep deformation of rock samples. Soils Found 55:1364–1371
Hao T, Wang D, Huang R, Pei X, Chen W (2018) A new rock creep model based on variable-order fractional derivatives and continuum damage mechanics. Bull Eng Geol Environ 77:375–383
Hedayat A, Pyrak-Nolte LJ, Bobet A (2015) Precursors to the shear failure of rock discontinuities. Geophys Res Lett 41:5467–5475
Hu K, Qian F, Li H, Hu Q (2017) Study on creep characteristics and constitutive model for thalam rock mass with fracture in tunnel. Geotech Geol Eng 36:827–834
Jia CJ, Xu WY, Wang RB, Wang SS, Lin ZN (2018) Experimental investigation on shear creep properties of undisturbed rock discontinuity in Baihetan Hydropower Station. Int J Rock Mech Min Sci 104:27–33. https://doi.org/10.1016/j.ijrmms.2018.02.011
Lei D, Lin H, Chen Y, Cao R, Wen Z (2019) Effect of cyclic freezing-thawing on the shear mechanical characteristics of nonpersistent joints. Adv Mater Sci Eng 2019:14. https://doi.org/10.1155/2019/9867681
Li X, Qi C, Shao Z (2018) A microcrack growth-based constitutive model for evaluating transient shear properties during brittle creep of rocks. Eng Fract Mech 194:9–23. https://doi.org/10.1016/j.engfracmech.2018.02.034
Lin H, Ding X, Yong R, Xu W, Du S (2019a) Effect of non-persistent joints distribution on shear behavior. CR Méc 347:477–489. https://doi.org/10.1016/j.crme.2019.05.001
Lin H, Xie SJ, Yong R, Chen YF, Du SG (2019b) An empirical statistical constitutive relationship for rock joint shearing considering scale effect. CR Mec 347:561–575. https://doi.org/10.1016/j.crme.2019.08.001
Lin H, Yang H, Wang Y, Zhao Y, Cao R (2019c) Determination of the stress field and crack initiation angle of an open flaw tip under uniaxial compression. Theoret Appl Fract Mech 104:102358. https://doi.org/10.1016/j.tafmec.2019.102358
Lin H, Zhu Y, Yang J, Wen ZJ (2020) Anchor stress and deformation of the bolted joint under shearing. Adv Civil Eng. https://doi.org/10.1155/2020/3696489
Liu J, Chen Y, Wan W, Wang J, Fan X (2018) The influence of bedding plane orientation on rock breakages in biaxial states. Theoret Appl Fract Mech 95:186–193. https://doi.org/10.1016/j.tafmec.2018.03.005
Liu L, Wang GM, Chen JH (2013) Creep experiment and rheological model of deep saturated rock. Trans Nonferrous Met Soc China 23:478–483
Ma L, Wang M, Ning Z, Fan P, Jie L (2017) A variable-parameter creep damage model incorporating the effects of loading frequency for rock salt and its application in a Bedded Storage Cavern. Rock Mech Rock Eng 50:1–15
Naderloo M, Moosavi M, Ahmadi M (2019) Using acoustic emission technique to monitor damage progress around joints in brittle materials. Theoret Appl Fract Mech 104:102368. https://doi.org/10.1016/j.tafmec.2019.102368
Shen Y, Wang Y, Yang Y, Sun Q, Luo T, Zhang H (2019) Influence of surface roughness and hydrophilicity on bonding strength of concrete-rock interface. Constr Build Mater 213:156–166
Wang G, Zhang L, Zhang Y, Ding G (2014a) Experimental investigations of the creep-damage-rupture behaviour of rock salt. Int J Rock Mech Min Sci 66:181–187
Wang J, Liu J, Cao P, Liang Q, Duan J (2017) Coupled creep characteristics of anchor structures and soils under chemical corrosion. Indian Geotech J 47:521–528. https://doi.org/10.1007/s40098-017-0244-8
Wang J, Liu X, Liu X, Huang M (2014b) Creep properties and damage model for salt rock under low-frequency cyclic loading. Geomech Eng 7:569–587
Wang X, Qu Z, Dou Y, Ma W (2015) Loads of casing and cement sheath in the compressive viscoelastic salt rock. J Petrol Sci Eng 135:146–151. https://doi.org/10.1016/j.petrol.2015.08.020
Wang Y, Guo P, Li X, Lin H, Liu Y, Yuan H (2019a) Behavior of fiber-reinforced and lime-stabilized clayey soil in triaxial tests. Appl Sci 9:900
Wang Y, Lin H, Zhao Y, Li X, Guo P, Liu Y (2019b) Analysis of fracturing characteristics of unconfined rock plate under edge-on impact loading. Eur J Environ Civ Eng. https://doi.org/10.1080/19648189.2018.1509021
Wang Y, Zhang H, Lin H, Zhao Y, Liu Y (2020) Fracture behaviour of central-flawed rock plate under uniaxial compression. Theoret Appl Fract Mech 106:102503. https://doi.org/10.1016/j.tafmec.2020.102503
Xie S, Lin H, Wang Y, Chen Y, Xiong W, Zhao Y, Du S (2020) A statistical damage constitutive model considering whole joint shear deformation. Int J Damage Mech. https://doi.org/10.1177/1056789519900778
Yang L, Li Z-d (2018) Nonlinear variation parameters creep model of rock and parametric inversion. Geotech Geol Eng 36:2985–2993. https://doi.org/10.1007/s10706-018-0517-8
Zhang C, Pu C, Cao R, Jiang T, Huang G (2019a) The stability and roof-support optimization of roadways passing through unfavorable geological bodies using advanced detection and monitoring methods, among others, in the Sanmenxia Bauxite Mine in China’s Henan Province. Bull Eng Geol Environ 78:5087–5099. https://doi.org/10.1007/s10064-018-01439-1
Zhang CY, Lin H, Qiu CM, Jiang TT, Zhang JH (2020) The effect of cross-section shape on deformation, damage and failure of rock-like materials under uniaxial compression from both a macro and micro viewpoint. Int J Damage Mech 20:1–20. https://doi.org/10.1177/1056789520904119
Zhang J-Z, Zhou X-P, Yin P (2019b) Visco-plastic deformation analysis of rock tunnels based on fractional derivatives. Tunn Undergr Space Technol 85:209–219. https://doi.org/10.1016/j.tust.2018.12.019
Zhang QZ, Shen MR, Bo AJ, Ding WQ (2016) Creep behavior of rocks with rough surfaces. J Mater Civ Eng 28:04016063
Zhao Y, Zhang L, Wang W, Wen W, Li S, Ma W, Wang Y (2017a) Creep behavior of intact and cracked limestone under multi-level loading and unloading cycles. Rock Mech Rock Eng 50:1–16
Zhao YL, Wang YX, Wang WJ, Wan W, Tang JZ (2017b) Modeling of non-linear rheological behavior of hard rock using triaxial rheological experiment. Int J Rock Mech Min Sci 93:66–75. https://doi.org/10.1016/j.ijrmms.2017.01.004
Zhou H, Wang C, Han B, Duan Z (2011a) A creep constitutive model for salt rock based on fractional derivatives. Int J Rock Mech Min Sci 48:116–121
Zhu S, Yin Y, Li B, Wei Y (2019) Shear creep characteristics of weak carbonaceous shale in thick layered Permian limestone, southwestern China. J Earth Syst Sci. https://doi.org/10.1007/s12040-018-1051-z
Acknowledgements
This paper gets its funding from Project (51774322) supported by National Natural Science Foundation of China; Project (2018JJ2500) supported by Hunan Provincial Natural Science Foundation of China; Project (MDPC201814) supported by Open Fund of State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science, Shandong University of Science and Technology. The authors wish to acknowledge these supports.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Lin, H., Zhang, X., Cao, R. et al. Improved nonlinear Burgers shear creep model based on the time-dependent shear strength for rock. Environ Earth Sci 79, 149 (2020). https://doi.org/10.1007/s12665-020-8896-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12665-020-8896-6