Abstract
In order to evaluate the damage deterioration degree of freeze–thaw rock under in-situ stress in cold area engineering, it is necessary to establish the triaxial compression damage constitutive model and study on meso-failure characteristics of freeze–thaw rock. The triaxial compression tests under confining pressure of 3 MPa, 5 MPa, and 10 MPa were carried out on saturated sandstone after 0, 20, 40, and 60 freeze–thaw cycles. The results show that with the increase of freezing–thawing times, the peak deviatoric stress and elastic modulus under the same confining pressure decrease gradually, and increase gradually with the increase of confining pressure. The triaxial compression damage constitutive model of freeze–thaw rock was established based on the dissipation energy ratio and the principle of minimum energy dissipation. Based on this model, the evolution law of energy ratio in different stages of compression process was studied, and the influence characteristics of confining pressure and freeze–thaw on rock failure were analyzed. PFC2D was used to establish the numerical method on triaxial compression of frozen-thawed rock and determine the calculation parameters. The energy evolution law and the number growth law of different cracks in the triaxial compression process of frozen-thawed rock were studied. It is found that the energy value at the peak and the ratio of tensile crack to shear crack decrease with the number of freezing–thawing cycles. Meanwhile, the characteristics of freezing–thawing cycles promoting the shear failure of rock were clarified.
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References
Chen W, Konietzky H, Tan X, Frühwirt T (2016) Pre-failure damage analysis for brittle rocks under triaxial compression. Comput Geotech 74:45–55. https://doi.org/10.1016/j.compgeo.2015.11.018
Chen Z, He C, Ma G, Xu G, Ma C (2019) Energy damage evolution mechanism of rock and its application to brittleness evaluation. Rock Mech Rock Eng 52(4):1265–1274. https://doi.org/10.1007/s00603-018-1681-0
Feng Q, Jin J, Zhang S, Liu W, Yang X, Li W (2022) Study on a damage model and uniaxial compression simulation method of frozen-thawed rock. Rock Mech Rock Eng 55(1):187–211. https://doi.org/10.1007/s00603-021-02645-2
Guo T and Du Z (2021) Meso-numerical simulation of rock triaxial compression based on the damage model. In: Proceedings of the 3rd International Conference on Environmental Prevention and Pollution Control Technologies, Zhuhai, China, 687(1): 012134. (in Chinese)
Huang D, Li Y (2014) Conversion of strain energy in triaxial unloading tests on marble. Int J Min Sci Technol 66:160–168. https://doi.org/10.1016/j.ijrmms.2013.12.001
Krajcinovic D, Silva MAG (1982) Statistical aspects of the continuous damage theory. Int J Solids Struct 18(7):551–562. https://doi.org/10.1016/0020-7683(82)90039-7
Krautblatter M, Funk D, Günzel FK (2013) Why permafrost rocks become unstable: a rock-ice-mechanical model in time and space. Earth Surf Process Landf 38(8):876–887. https://doi.org/10.1002/esp.3374
Li T, Pei X, Wang D, Huang R, Tang H (2019) Nonlinear behavior and damage model for fractured rock under cyclic loading based on energy dissipation principle. Eng Fract Mech 206:330–341. https://doi.org/10.1016/j.engfracmech.2018.12.010
Liu XS, Ning JG, Tan YL, Gu QH (2016) Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading. Int J Rock Mech Min Sci 85:27–32. https://doi.org/10.1016/j.ijrmms.2016.03.003
Luo X, Jiang N, Fan X, Mei N, Luo H (2015) Effects of freeze-thaw on the determination and application of parameters of slope rock mass in cold regions. Cold Reg Sci Technol 110:32–37. https://doi.org/10.1016/j.coldregions.2014.11.002
Meng Q, Zhang M, Zhang Z, Han L, Pu H (2019) Research on non-linear characteristics of rock energy evolution under uniaxial cyclic loading and unloading conditions. Environ Earth Sci 78(23):1–20. https://doi.org/10.1007/s12665-019-8638-9
Ning J, Wang J, Jiang J, Hu S, Jiang L, Liu X (2018) Estimation of crack initiation and propagation thresholds of confined brittle coal specimens based on energy dissipation theory. Rock Mech Rock Eng 51(1):119–134. https://doi.org/10.1007/s00603-017-1317-9
Pan Y, Zhao Z, He L, Wu G (2020) A nonlinear statistical damage constitutive model for porous rocks. Adv Civ Eng 2020:8851914. https://doi.org/10.1155/2020/8851914
Pudasaini SP, Krautblatter M (2014) A two-phase mechanical model for rock-ice avalanches. J Geophys Res Earth Surf 119(10):2272–2290. https://doi.org/10.1002/2014JF003183
Qiu WL, Teng F, Pan SS (2020) Damage constitutive model of concrete under repeated load after seawater freeze-thaw cycles. J Constr Build Mater 236:117560. https://doi.org/10.1016/j.conbuildmat.2019.117560
Qu D, Li D, Li X, Luo Y, Xu K (2018) Damage evolution mechanism and constitutive model of freeze-thaw yellow sandstone in acidic environment. Cold Reg Sci Technol 155:174–183. https://doi.org/10.1016/j.coldregions.2018.07.012
Rakhimzhanova AK, Thornton C, Minh NH, Fok SC, Zhao Y (2019) Numerical simulations of triaxial compression tests of cemented sandstone. Comput Geotech 113:103068. https://doi.org/10.1016/j.compgeo.2019.04.013
Tian ZY, Wang W, Li XH, Xu WY (2014) A statistical damage constitutive model for brittle rocks based on the Lade-Duncan failure criterion. Adv Mater Res 919:632–636. https://doi.org/10.4028/www.scientific.net/AMR.919-921.632
Wang Z, Li Y, Wang JG (2007) A damage-softening statistical constitutive model considering rock residual strength. Comput Geosci 33(1):1–9. https://doi.org/10.1016/j.cageo.2006.02.011
Wang Y, Tan WH, Liu DQ, Hou ZQ, Li CH (2019) On anisotropic fracture evolution and energy mechanism during marble failure under uniaxial deformation. Rock Mech Rock Eng 52(10):3567–3583. https://doi.org/10.1007/s00603-019-01829-1
Wang J G, Anand S, Ye F J (2008) A statistical damage constitutive model of brittle rocks based on Weibull distribution. In: Proceedings of the first southern hemisphere international rock mechanics Symposium, Perth, Australia, pp 121–134. https://doi.org/10.36487/ACG_repo/808_167
Wen T, Liu Y, Yang C, Yi X (2018) A rock damage constitutive model and damage energy dissipation rate analysis for characterising the crack closure effect. Geomech Geoengin Int J 13(1):54–63. https://doi.org/10.1080/17486025.2017.1330969
Xie HP, Ju Y, Li LY (2005) Criteria for strength and structural failure of rocks based on energy dissipation and energy release principles. Chin J Rock Mech Eng 24(17):3003–3010
Xie HP, Li LY, Peng RD, Ju Y (2009) Energy analysis and criteria for structural failure of rocks. J Rock Mech Geotech Eng 1(1):11–20. https://doi.org/10.3724/SP.J.1235.2009.00011
Zhang K, Zhou H, Shao J (2013) An experimental investigation and an elastoplastic constitutive model for a porous rock. Rock Mech Rock Eng 46(6):1499–1511. https://doi.org/10.1007/s00603-012-0364-5
Zhang S, Chen L, Lu P, Zhang Y (2021) Analysis of the energy and damage evolution rule for sandstone based on the particle flow method. Mech Time Depend Mater, 1–16. https://doi.org/10.1007/s11043-021-09499-9
Zhao H, Zhang C, Cao W, Zhao M (2016) Statistical meso-damage model for quasi-brittle rocks to account for damage tolerance principle. Environ Earth Sci 75(10):862. https://doi.org/10.1007/s12665-016-5681-7
Zhou ZB (2001) Principle of minimum energy consumption and its application. Science Press, Beijing ((in Chinese))
Zhu T, Chen J, Huang D, Luo Y, Li Y, Xu L (2021) A DEM-based approach for modeling the damage of rock under freeze-thaw cycles. Rock Mech Rock Eng 54(6):2843–2858. https://doi.org/10.1007/s00603-021-02465-4
Funding
This work was supported by the Natural Science Foundation of Shandong Province (ZR2022QE066, ZR2023MD099), Research and Innovation Team Project of College of Civil Engineering and Architecture, Shandong University of Science and Technology (2019TJKYTD02), and Project of Shandong Province Higher Educational Young Innovative Talent Introduction and Cultivation Team (Disaster prevention and control team of underground engineering involved in sea).
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Feng, Q., Xu, J., Cai, C. et al. Damage constitutive model and meso-failure characteristics of freeze–thaw rock under triaxial compression. Bull Eng Geol Environ 83, 112 (2024). https://doi.org/10.1007/s10064-024-03594-0
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DOI: https://doi.org/10.1007/s10064-024-03594-0