Abstract
The fluctuation of the operation pressure during injection and withdrawal is a key factor affecting the long-term stability of surrounding rock in a compressed air energy storage (CAES) cavern. To assess the mechanical behavior of rock salt under different pressure fluctuations and to optimize the operating parameters of CAES caverns, uniaxial cyclic loading tests under the sine condition were carried out by changing three cycle parameters, namely the mean stress, half-amplitude and cycle period. The test results show that the deformation behavior during cyclic loading tests can be divided into transient, steady, and accelerated stages, which is similar to that of creep tests. The strain and steady strain rates increase with increasing cycle parameters, showing a nonlinear deformation property of rock salt under cyclic loading. To describe the nonlinear response that cannot be captured by the Burgers model, a stiffness scaling factor is proposed based on the test results. A modified cyclic creep model of rock salt is established by introducing this stiffness scaling factor into the conventional Burgers creep model. The agreement with the experimental data indicates that the modified cyclic creep model can accurately reflect the influence of the three cyclic parameters on the deformation properties of rock salt.
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Abbreviations
- \(\sigma_{1}\) :
-
Axial stress
- \(a\) :
-
Mean stress
- \(b\) :
-
Half-amplitude
- \(T\) :
-
Cycle period
- \(G_{1}\) :
-
Shear modulus of the Maxwell body
- \(\eta_{1}\) :
-
Viscous coefficient of the Maxwell body
- \(G_{2}\) :
-
Shear modulus of the Kelvin body
- \(\eta_{2}\) :
-
Viscous coefficient of the Kelvin body
- \(K\) :
-
Bulk modulus of the Burgers model
- \(\varepsilon_{11}\) :
-
Axial strain
- \(\sigma_{ \text{max} }\) :
-
The maximum stress
- \(\sigma_{\text{min} }\) :
-
The minimum stress
References
Aeran A, Siriwardane SC, Mikkelsen O, Langen I (2017) A new nonlinear fatigue damage model based only on S-N curve parameters. Int J Fatigue 103:327–341. https://doi.org/10.1016/j.ijfatigue.2017.06.017
Akinyele DO, Rayudu RK (2014) Review of energy storage technologies for sustainable power networks. Sustain Energy Technol Assess 8:74–91. https://doi.org/10.1016/j.seta.2014.07.004
Bagde MN, Petros V (2009) Fatigue and dynamic energy behaviour of rock subjected to cyclical loading. Int J Rock Mech Min Sci (1997) 46:200–209. https://doi.org/10.1016/j.ijrmms.2008.05.002
Bagde MN, Petroš V (2005) Waveform effect on fatigue properties of intact sandstone in uniaxial cyclical loading. Rock Mech Rock Eng 38:169–196. https://doi.org/10.1007/s00603-005-0045-8
Bilgili M, Ozbek A, Sahin B, Kahraman A (2015) An overview of renewable electric power capacity and progress in new technologies in the world. Renew Sustain Energy Rev 49:323–334. https://doi.org/10.1016/j.rser.2015.04.148
Budt M, Wolf D, Span R, Yan J (2016) A review on compressed air energy storage: basic principles, past milestones and recent developments. Appl Energy 170:250–268. https://doi.org/10.1016/j.apenergy.2016.02.108
Cavallo A (2007) Controllable and affordable utility-scale electricity from intermittent wind resources and compressed air energy storage (CAES). Energy 32:120–127. https://doi.org/10.1016/j.energy.2006.03.018
Cerfontaine B, Collin F (2017) Cyclic and Fatigue Behaviour of Rock Materials: review, Interpretation and Research Perspectives. Rock Mech Rock Eng 51:391–414. https://doi.org/10.1007/s00603-017-1337-5
Chen X, Li Y, Liu W, Ma H, Ma J, Shi X, Yang C (2018) Study on sealing failure of wellbore in bedded salt cavern gas storage. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-018-1571-5
Chen J, Lu D, Liu W, Fan J, Jiang D, Yi L, Kang Y (2020) Stability study and optimization design of small-spacing two-well (SSTW) salt caverns for natural gas storages. Journal of Energy Storage 27:101131. https://doi.org/10.1016/j.est.20-19.101131
Cristescu NA (1993) general constitutive equation for transient and stationary creep of rock salt. Int J Rock Mech Min Sci Geomech Abstr 2:125–140
Crotogino F, Mohmeyer K U, Scharf R (2001). Huntorf CAES: more than 20 years of successful operation. In: SMRI Spring meeting
David E, Brantut N, Schubnel A, Zimmerman RW (2012) Sliding crack model for nonlinearity and hysteresis in the uniaxial stress–strain curve of rock. Int J Rock Mech Min Sci 52:9–17. https://doi.org/10.1016/j.ijrmms.2012.02.001
Erarslan N (2016) Microstructural investigation of subcritical crack propagation and Fracture Process Zone (FPZ) by the reduction of rock fracture toughness under cyclic loading. Eng Geol 208:181–190. https://doi.org/10.1016/j.eng-geo.2016.04.035
Fan J, Jiang D, Liu W, Wu F, Chen J, Daemen J (2019) Discontinuous fatigue of salt rock with low-stress intervals. Int J Rock Mech Min Sci 115:77–86. https://doi.org/10.1016/j.ijrmms.2019.01.013
Fuenkajorn K, Phueakphum D (2010) Effects of cyclic loading on mechanical properties of Maha Sarakham salt. Eng Geol 112:43–52. https://doi.org/10.1016/j.enggeo.2010.01.002
Fuenkajorn K, Sriapai T, Samsri P (2012) Effects of loading rate on strength and deformability of Maha Sarakham salt. Eng Geol 135:10–23. https://doi.org/10.1016/j.enggeo.2012.02.012
Guo Y, Yang C, Mao H (2012) Mechanical properties of Jintan mine rock salt under complex stress paths. Int J Rock Mech Min Sci 56:54–61. https://doi.org/10.1016/j.ijrmms.2012.07.025
Haghgouei H, Baghbanan A, Hashemolhosseini H (2018) Fatigue life prediction of rocks based on a new Bi-linear damage model. Int J Rock Mech Min Sci 106:20–29. https://doi.org/10.1016/j.ijrmms.2018.04.009
He M, Huang B, Zhu C, Chen Y, Li N (2018) Energy dissipation-based method for fatigue life prediction of rock salt. Rock Mech Rock Eng 51:1447–1455. https://doi.org/10.1007/s00603-018-1402-8
Khaledi K, Mahmoudi E, Datcheva M, Schanz T (2016) Stability and serviceability of underground energy storage caverns in rock salt subjected to mechanical cyclic loading. Int J Rock Mech Min Sci 86:115–131. https://doi.org/10.1016/j.ijrmms.2016.04.010
Li H, Yang J, Han Y, Yang C, Daemen J, Li P (2019a) Weibull grain-based model (W-GBM) for simulating heterogeneous mechanical characteristics of salt rock. Eng Anal Bound Elem 108:227–243. https://doi.org/10.1016/j.e-nganabound.2019.09.001
Li J, Tang Y, Shi X, Xu W, Yang C (2019b) Modeling the construction of energy storage salt caverns in bedded salt. Appl Energy 255:113866. https://doi.org/10.1016/j.apener-gy.2019.113866
Li T, Pei X, Wang D, Huang R, Tang H (2019c) 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.engfracme-ch.2018.12.010
Li H, Yang C, Ma H, Shi X, Zhang H, Dong Z (2020) A 3D grain-based creep model (3D-GBCM) for simulating long-term mechanical characteristic of rock salt. J Pet Sci Eng 185:106672. https://doi.org/10.1016/j.petr-ol.2019.106672
Liang W, Zhang C, Gao H, Yang X, Xu S, Zhao Y (2012) Experiments on mechanical properties of salt rocks under cyclic loading. J Rock Mech Geotech En 4:54–61. https://doi.org/10.3724/SP.J.1235.2012.00054
Liu J, Xie H, Hou Z, Yang C, Chen L (2013) Damage evolution of rock salt under cyclic loading in unixial tests. Acta Geotech 9:153–160. https://doi.org/10.1007/s11440-013-0236-5
Liu W, Zhang Z, Chen J, Fan J, Jiang D, Jjk D, Li Y (2019) Physical simulation of construction and control of two butted-well horizontal cavern energy storage using large molded rock salt specimens. Energy 185:682–694
Ma L et al (2013) Experimental investigation of the mechanical properties of rock salt under triaxial cyclic loading. Int J Rock Mech Min Sci 62:34–41. https://doi.org/10.1016/j.ijrmms.2013.04.003
Ma L, Wang M, Zhang N, Fan P, Li J (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 50:2495–2509. https://doi.org/10.1007/s00603-017-1236-9
Mansouri H, Ajalloeian R (2018) Mechanical behavior of salt rock under uniaxial compression and creep tests. Int J Rock Mech Min Sci 110:19–27. https://doi.org/10.1016/j.ijrmms.2018.07.006
Momeni A, Karakus M, Khanlari GR, Heidari M (2015) Effects of cyclic loading on the mechanical properties of a granite. Int J Rock Mech Min Sci 77:89–96. https://doi.org/10.1016/j.ijrmms.2015.03.029
Nakhamkin M, Andersson L, Swensen E, Howard J, Mehta B (1992) AEC 110 mw CAES plant; Status of project. J Eng Gas Turbines Power 114:695–700
Pollak R (1994). History of first US compressed-air energy storage (CAES) Plant (110 MW 26h) volume 2: Construction. Electric Power Research Institute (EPRI), Palo Alto, CA, p 202
Pouya A, Zhu C, Arson C (2016) Micro–macro approach of salt viscous fatigue under cyclic loading. Mech Mater 93:13–31. https://doi.org/10.1016/j.mech-mat.2015.10.009
Song R, Yue-ming B, Jing-Peng Z, De-yi J, Chun-he Y (2013) Experimental investigation of the fatigue properties of salt rock. Int J Rock Mech Min Sci 64:68–72. https://doi.org/10.1016/j.ijrmms.2013.08.023
Ulusay R (2015) The ISRM suggested methods for rock characterization, testing and monitoring: 2007-2014. https://doi.org/10.1007/978-3-319-07713-0
Wang T, Yang C, Ma H, Li Y, Shi X, Li J, Daemen JJK (2016) Safety evaluation of salt cavern gas storage close to an old cavern. Int J Rock Mech Min Sci 83:95–106. https://doi.org/10.1016/j.ijrmms.2016.01.005
Wang T, Yang C, Chen J, Daemen JJK (2018) Geomechanical investigation of roof failure of China’s first gas storage salt cavern. Eng Geol 243:59–69. https://doi.org/10.1016/j.enggeo.2018.06.013
Xiao J, Ding D, Xu G, Jiang F (2009) Inverted S-shaped model for nonlinear fatigue damage of rock. Int J Rock Mech Min Sci 46:643–648. https://doi.org/10.1016/j.ijrmms.2008.11.002
Xiao J, Ding D, Jiang F, Xu G (2010) Fatigue damage variable and evolution of rock subjected to cyclic loading. Int J Rock Mech Min Sci 47:461–468. https://doi.org/10.1016/j.ijrmms.2009.11.003
Xu H, Wang C, Ma L, Dong L (2015) Volumetric strain of rock salt under triaxial low-frequency cyclic loading. Chin J Geotech Eng 37:741–746
Yin H et al (2018) Study on damage and repair mechanical characteristics of rock salt under uniaxial compression. Rock Mech Rock Eng 52:659–671. https://doi.org/10.1007/s00603-018-1604-0
Yucekaya A (2013) The operational economics of compressed air energy storage systems under uncertainty. Renew Sustain Energy Rev 22:298–305. https://doi.org/10.1016/j.rser.2013.01.047
Zhang H, Wang Z, Zheng Y, Duan P, Ding S (2012) Study on tri-axial creep experiment and constitutive relation of different rock salt. Saf Sci 50:801–805. https://doi.org/10.1016/j.ssci.2011.08.030
Zhang G, Li Y, Daemen JJK, Yang C, Wu Y, Zhang K, Chen Y (2014) Geotechnical feasibility analysis of compressed air energy storage (CAES) in bedded salt formations: a case study in Huai’an City, China. Rock Mech Rock Eng 48:2111–2127. https://doi.org/10.1007/s00603-014-0672-z
Zhang N, Yang C, Shi X, Wang T, Yin H, Daemen JJK (2018) Analysis of mechanical and permeability properties of mudstone interlayers around a strategic petroleum reserve cavern in bedded rock salt. Int J Rock Mech Min Sci 112:1–10. https://doi.org/10.1016/j.ijrmms.2018.10.014
Zhang N, Shi X, Zhang Y, Shan P (2020) Tightness analysis of underground natural gas and oil storage caverns with limit pillar widths in bedded rock salt. IEEE Access. https://doi.org/10.1109/ACCESS.2020.2966006
Zhu Q, Kondo D, Shao J, Pensee V (2008) Micromechanical modelling of anisotropic damage in brittle rocks and application. Int J Rock Mech Min Sci 45:467–477. https://doi.org/10.1016/j.ijrmms.2007.07.014
Zhu C, Pouya A, Arson C (2015) Micro-macro analysis and phenomenological modelling of salt viscous damage and application to salt caverns. Rock Mech Rock Eng 48:2567–2580. https://doi.org/10.1007/s00603-015-0832-9
Zoback MD, Byerlee JD (1975) The effect of cyclic differential stress on dilatancy in westerly granite under uniaxial and triaxial conditions. J Geophys Res 80:1526–1530
Acknowledgements
This research has been financed and fully supported by the National Natural Science Foundation of China (Grant No. 5187041724), for which the authors would like to express their sincere gratitude.
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Han, Y., Ma, H., Yang, C. et al. A Modified Creep Model for Cyclic Characterization of Rock Salt Considering the Effects of the Mean Stress, Half-Amplitude and Cycle Period. Rock Mech Rock Eng 53, 3223–3236 (2020). https://doi.org/10.1007/s00603-020-02097-0
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DOI: https://doi.org/10.1007/s00603-020-02097-0