Abstract
It is known that time-dependent rheological deformation of rocks is influenced by cyclic disturbance loads. However, the stress relaxation behavior after cyclic disturbance is still poorly understood. To study such effects, a dynamic disturbance electrohydraulic servo triaxial test system was developed. A series of disturbance relaxation tests with different disturbance numbers and amplitudes were carried out on marble at several strain levels. The influence of cyclic disturbance parameters on the relaxation magnitude, relaxation rate, and peak stress was analyzed. Relaxation magnitude and relaxation rate after cyclic disturbance loads are larger than those of conventional relaxation. In addition, sensitivity analysis reveals that the relaxation magnitude is more sensitive to the disturbance amplitude. Damage variables defined by the plastic strain method can well reflect the evolution law of relaxation damage under different disturbance conditions. It is believed that the damage model constructed by Harris function can better describe the relaxation damage evolution law at various strain levels.
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References
Areias, P., Reinoso, J., Camanho, P.P., et al.: Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation. Eng. Fract. Mech. 189, 339–360 (2018). https://doi.org/10.1016/j.engfracmech.2017.11.017
Aydan, Ö., Ito, T., Özbay, U., et al.: ISRM suggested methods for determining the creep characteristics of rock. In: The ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 2007–2014, pp. 115–130. Springer, Cham (2013)
Cao, A., Jing, G., Ding, Y., et al.: Mining-induced static and dynamic loading rate effect on rock damage and acoustic emission characteristic under uniaxial compression. Saf. Sci. 116, 86–96 (2019). https://doi.org/10.1016/j.ssci.2019.03.003
Chen, X., Tang, C. Kong, X.: Study on progressive damage and failure of sandstone samples subjected to cyclic disturbance loads using a modified triaxial test system. KSCE J. Civ. Eng. 23(5), 2371–2383 (2019). https://doi.org/10.1007/s12205-019-2047-1
Feng, X., Chen, B., Li, S., et al.: Studies on the evolution process of rockbursts in deep tunnels. J. Rock Mech. Geotech. Eng. 4(4), 289–295 (2012). https://doi.org/10.3724/SP.J.1235.2012.00289
Feng, X.T., Yu, Y., Feng, G.L., et al.: Fractal behaviour of the microseismic energy associated with immediate rockbursts in deep, hard rock tunnels. Tunn. Undergr. Space Technol. 51, 98–107 (2016). https://doi.org/10.1016/j.tust.2015.10.002
Fuenkajorn, K., Phueakphum, D.: Effects of cyclic loading on mechanical properties of Maha Sarakham salt. Eng. Geol. 112(1–4), 43–52 (2010). https://doi.org/10.1016/j.enggeo.2010.01.002
Gao, Y., Huang, W., Qu, G., et al.: Perturbation effect of rock rheology under uniaxial compression. J. Cent. South Univ. 24(7), 1684–1695 (2017). https://doi.org/10.1007/s11771-017-3575-9
Hu, X., Su, G., Chen, G., et al.: Experiment on rockburst process of borehole and its acoustic emission characteristics. Rock Mech. Rock Eng. 52(3), 783–802 (2019). https://doi.org/10.1007/s00603-018-1613-z
Jiang, Q., Li, J., Luo, Z., et al.: Study on the time-lag failure of sandstone with different degrees of unloading damage. Periodica Polytechnica Civil Engineering, 63(1), 206–214 (2019). https://doi.org/10.3311/PPci.13260
Ko, T.Y., Kemeny, J.: Determination of the subcritical crack growth parameters in rocks using the constant stress-rate test. Int. J. Rock Mech. Min. Sci. 59, 166–178 (2013). https://doi.org/10.1016/j.ijrmms.2012.11.006
Li, Y., Xia, C.: Time-dependent tests on intact rocks in uniaxial compression. Int. J. Rock Mech. Min. Sci. 37(3), 467–475 (2000). https://doi.org/10.1016/S1365-1609(99)00073-8
Li, H., Zhong, Z., Eshiet, K.I.I., et al.: Experimental investigation of the permeability and mechanical behaviours of chemically corroded limestone under different unloading conditions Rock Mech. Rock Eng. 53, 1–17 (2019a). https://doi.org/10.1007/s00603-019-01961-y
Li, S., Zhu, W.C., Xu, T., et al.: Time-frequency distribution analysis of the stress relaxation of sandstones affected by dynamic disturbance. Exp. Tech. 43(4), 415–428 (2019b). https://doi.org/10.1007/s40799-018-0295-5
Liu, E., He, S.: Effects of cyclic dynamic loading on the mechanical properties of intact rock samples under confining pressure conditions. Eng. Geol. 125, 81–91 (2012). https://doi.org/10.1016/j.enggeo.2011.11.007
Liu, Y., Liu, C., Kang, Y., et al.: Experimental research on creep properties of limestone under fluid–solid coupling. Environ. Earth Sci. 73(11), 7011–7018 (2015). https://doi.org/10.1007/s12665-015-4022-6
Liu, J., Yang, H., Xiao, Y., et al.: Macro-mesoscopic fracture and strength character of pre-cracked granite under stress relaxation condition. Rock Mech. Rock Eng. 51(5), 1401–1412 (2018). https://doi.org/10.1007/s00603-018-1399-z
Lv, S., Xia, C., Liu, C., et al.: Fatigue equation for asphalt mixture under low temperature and low loading frequency conditions. Constr. Build. Mater. 211, 1085–1093 (2019). https://doi.org/10.1016/j.conbuildmat.2019.03.312.
Ma, L., Liu, X., Wang, M., et al.: Experimental investigation of the mechanical properties of rock salt under triaxial cyclic loading. Int. J. Rock Mech. Min. Sci. 62, 34–41 (2013). https://doi.org/10.1016/j.ijrmms.2013.04.003
Mishra, B., Verma, P.: Uniaxial and triaxial single and multistage creep tests on coal-measure shale rocks. Int. J. Coal Geol. 137, 55–65 (2015). https://doi.org/10.1016/j.coal.2014.11.005
Miura, K., Okui, Y., Horii, H.: Micromechanics-based prediction of creep failure of hard rock for long-term safety of high-level radioactive waste disposal system. Mech. Mater. 35(3/6), 587–601 (2003). https://doi.org/10.1016/S0167-6636(02)00286-7.
Niu, S., Feng, W., Yu, J., et al.: Experimental study on the mechanical properties of short-term creep in post-peak rupture damaged sandstone. Mechanics of Time-Dependent Materials 1–23 (2019). https://doi.org/10.1007/s11043-019-09431-2
Özsen, H., Özkan, İ., Sensögüt, C.: Measurement and mathematical modelling of the creep behaviour of Tuzköy rock salt. Int. J. Rock Mech. Min. Sci. 66(1997), 128–135 (2014). https://doi.org/10.1016/j.ijrmms.2014.01.005
Peng, K., Zhou, J., Zou, Q., et al.: Effect of loading frequency on the deformation behaviours of sandstones subjected to cyclic loads and its underlying mechanism. Int. J. Fatigue 131, 105349 (2020). https://doi.org/10.1016/j.ijfatigue.2019.105349
Peng, K., Zhou, J., Zou, Q., et al.: Deformation characteristics of sandstones during cyclic loading and unloading with varying lower limits of stress under different confining pressures. Int. J. Fatigue 127, 82–100 (2019). https://doi.org/10.1016/j.ijfatigue.2019.06.007
Rabczuk, T., Ren, H.: A peridynamics formulation for quasi-static fracture and contact in rock. Eng. Geol. 225, 42–48 (2017). https://doi.org/10.1016/j.enggeo.2017.05.001
Ren, H., Zhuang, X., Cai, Y., et al.: Dual-horizon peridynamics. Int. J. Numer. Methods Eng. 108(12), 1451–1476 (2016). https://doi.org/10.1002/nme.5257
Ren, H., Zhuang, X., Rabczuk, T.: Dual-horizon peridynamics: a stable solution to varying horizons. Comput. Methods Appl. Mech. Eng. 318, 762–782 (2017). https://doi.org/10.1016/j.cma.2016.12.031
Schulze, O.: Strengthening and stress relaxation of opalinus clay Phys. Chem. Earth Parts A/B/C 36(17–18), 1891–1897 (2011). https://doi.org/10.1016/j.pce.2011.07.090
Shelly, D.R., Gregory, C., et al.: Non-volcanic tremor and low-frequency earthquake swarms. Nature 446(7133), 305–307 (2007). https://doi.org/10.1038/nature05666
Song, D., Wang, E., Liu, J.: Relationship between EMR and dissipated energy of coal rock mass during cyclic loading process. Saf. Sci. 50(4), 751–760 (2012). https://doi.org/10.1016/j.ssci.2011.08.039
Sun, Q., Indraratna, B., Nimbalkar, S.: Effect of cyclic loading frequency on the permanent deformation and degradation of railway ballast. Geotechnique 64(9), 746–751 (2014). https://doi.org/10.1680/geot.14.T.015
Taheri, A., Tani, K.: Use of down-hole triaxial apparatus to estimate the mechanical properties of heterogeneous mudstone(CT) experiments on limestone damage evolution during unloading. Int. J. Rock Mech. Min. Sci. 45(8), 1390–1402 (2008). https://doi.org/10.1016/j.ijrmms.2008.01.017
Tian, H., Chen, W., Yang, D., et al.: Relaxation behavior of argillaceous sandstone under high confining pressure. Int. J. Rock Mech. Min. Sci. 88, 151–156 (2016). https://doi.org/10.1016/j.ijrmms.2016.07.016
Xiao, J., Ding, D.X., Jiang, F.L., et al.: Fatigue damage variable and evolution of rock subjected to cyclic loading. Int. J. Rock Mech. Min. Sci. 47, 461–468 (2010). https://doi.org/10.1016/j.ijrmms.2009.11.003
Yang, X.J.: New general fractional-order rheological models with kernels of Mittag-Leffler functions. Rom. Rep. Phys. 69(4), 118 (2017)
Yang, X.J.: New rheological problems involving general fractional derivatives with nonsingular power-law kernels. Proc. Rom. Acad., Ser. A: Math. Phys. Tech. Sci. Inf. Sci. 19(1), 45–52 (2018)
Yang, X.J.: New general calculi with respect to another functions applied to describe the Newton-like dashpot models in anomalous viscoelasticity. Therm. Sci. 23(6B), 3751–3757 (2019a). https://doi.org/10.2298/TSCI180921260Y
Yang, X.J.: New non-conventional methods for quantitative concepts of anomalous rheology. Therm. Sci. 23(6B), 4117–4127 (2019b). https://doi.org/10.2298/TSCI191028427Y
Yang, X.J., Gao, F., Srivastava, H.M.: New rheological models within local fractional derivative. Rom. Rep. Phys. 69(3), 113 (2017a)
Yang, H., Liu, J., Zhou, X.: Effects of the loading and unloading conditions on the stress relaxation behavior of pre-cracked granite. Rock Mech. Rock Eng. 50(5), 1157–1169 (2017b). https://doi.org/10.1007/s00603-016-1161-3
Yang, X.J., Gao, F., Jing, H.W.: New mathematical models in anomalous viscoelasticity from the derivative with respect to another function view point. Therm. Sci. 23(3A), 1555–1561 (2019). https://doi.org/10.2298/TSCI190220277Y
Yang, X.J., Gao, F., Ju, Y.: General Fractional Derivatives with Applications in Viscoelasticity. Academic Press, San Diego (2020)
Yao, W., Cai, Y., Yu, J., et al.: Experimental and numerical study on mechanical and cracking behaviors of flawed granite under triaxial compression. Measurement 145, 573–582 (2019). https://doi.org/10.1016/j.measurement.2019.03.035
Yao, W., Yu, J., Liu, X., et al.: Study on acoustic emission characteristics and failure prediction of post-high-temperature granite. J. Test. Eval. 48(3), 2459–2473 (2020). https://doi.org/10.1520/JTE20190575
Yong, R., Ye, J., Li, B., et al.: Determining the maximum sampling interval in rock joint roughness measurements using Fourier series. Int. J. Rock Mech. Min. Sci. 101, 78–88 (2018). https://doi.org/10.1016/j.ijrmms.2017.11.008
Yu, J., Li, T., Zhang, J., et al.: Stress characteristics of surrounding rocks for inner water exosmosis in high-pressure hydraulic tunnels. J. Cent. South Univ. 21(7), 2970–2976 (2014). https://doi.org/10.1007/s11771-014-2264-1
Yu, J., Chen, S., Chen, X., et al.: Experimental investigation on mechanical properties and permeability evolution of red sandstone after heat treatments. J. Zhejiang Univ. Sci. A 16, 749–759 (2015a). https://doi.org/10.1631/jzus.A1400362
Yu, J., Chen, X., Li, H., et al.: Effect of freeze-thaw cycles on mechanical properties and permeability of red sandstone under triaxial compression. J. Mt. Sci. 12(1), 218–231 (2015b). https://doi.org/10.1007/s11629-013-2946-4
Yu, J., Chen, X., Cai, Y., et al.: Triaxial test research on mechanical properties and permeability of sandstone with a single joint filled with gypsum. KSCE J. Civ. Eng. 20(6), 2243–2252 (2016a). https://doi.org/10.1007/s12205-015-1663-7
Yu, H., Zhang, X., Liu, H., et al.: Stress relaxation behavior of silty mudstone considering the effect of confining pressure. Environ. Earth Sci. 75(12), 1001 (2016b). https://doi.org/10.1007/s12665-016-5771-6
Yu, J., Liu, G., Cai, Y., et al.: Time-dependent deformation mechanism for swelling soft-rock tunnels in coal mines and its mathematical deduction. Int. J. Geomech. 20(3), 04019186 (2020a). https://doi.org/10.1061/(ASCE)GM.1943-5622.0001594
Yu, J., Liu, Z., He, Z., et al.: Fluctuation characteristic test of oblique stress waves in infilled jointed rock and study of the analytic method. Adv. Civ. Eng. 2020, 7924742 (2020b). https://doi.org/10.1155/2020/7924742
Zhang, Y., Xu, W., Gu, J., et al.: Triaxial creep tests of weak sandstone from fracture zone of high dam foundation. J. Cent. South Univ. 20(9), 2528–2536 (2013). https://doi.org/10.1007/s11771-013-1765-7
Zhang, Y., Zhang, Z., Xue, S., et al.: Stability analysis of a typical landslide mass in the three gorges reservoir under varying reservoir water levels. Environ. Earth Sci. 79(1), 42 (2020). https://doi.org/10.1007/s12665-019-8779-x
Zhou, X.P., Zhang, J.Z., Qian, Q.H., et al.: Experimental investigation of progressive cracking processes in granite under uniaxial loading using digital imaging and AE techniques. J. Struct. Geol. 126, 129–145 (2019). https://doi.org/10.1016/j.jsg.2019.06.003
Zhu, W., Li, S., Niu, L., et al.: Experimental and numerical study on stress relaxation of sandstones disturbed by dynamic loading. Rock Mech. Rock Eng. 49(10), 3963–3982 (2016a). https://doi.org/10.1007/s00603-016-1049-2
Zhu, H., Zhou, S., Yan, Z., et al.: A two-dimensional micromechanical damage–healing model on microcrack-induced damage for microcapsule-enabled self-healing cementitious composites under compressive loading. Int. J. Damage Mech. 25(5), 727–749 (2016b). https://doi.org/10.1177/1056789516641593
Acknowledgements
This study was supported by National Natural Science Foundation of China (No. 51874144, No. 51679093), National Natural Science Foundation of Fujian province (No. 2018J01630), and Scientific and Technology Plan Projects in Xiamen (No. 3502z20193040)
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Zhu, Y., Yu, J., Zhou, X. et al. Uniaxial stress relaxation behavior of marble after cyclic disturbance loads. Mech Time-Depend Mater 25, 513–537 (2021). https://doi.org/10.1007/s11043-020-09458-w
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DOI: https://doi.org/10.1007/s11043-020-09458-w