Abstract
During the operation of a CAES (compressed air energy storage) system, the rock surrounding a salt cavern suffers cyclic loading with high-stress intervals (HSIs). To investigate the effect of HSIs on the fatigue of rock salt, fatigue tests with constant stress intervals at different stress levels and interval durations were conducted. Results show that the axial stress–strain curves with HSIs present three stages of “sparse–dense–sparse”. The hysteresis loops in a single cycle consist of seven phases (crack compaction, elastic deformation, plastic deformation, creep deformation, cease, elastic recovery and pore restore). The irreversible deformation per cycle and fatigue life with HSIs present an upward and downward trend, respectively, compared to cases without intervals. The surface of fractured specimens shows a mix of shear and tensile cracks, and the salt crystals present the interaction of intra-grain and inter-grain cracks.
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Abbreviations
- CAES:
-
Compressed air energy storage
- HSIs:
-
High-stress intervals
- UCS:
-
Uniaxial compression strength
- SEM:
-
Scanning electron microscope
- \({t}_{H}\) :
-
Hold time per cycle
- \({\sigma }_{max}\) :
-
Maximum cyclic stress
- \({\sigma }_{min}\) :
-
Minimum cyclic stress
- \(R\) :
-
Stress ratio
- \({A}_{1},\) \({A}_{2}\) :
-
Fitting constants
- \({\varepsilon }_{p}\) :
-
Axial plastic strain per cycle
- \({F}_{r}\) :
-
Life reduction ratio
- \({N}_{cf}\) :
-
Fatigue life with stress intervals
- \({N}_{f}\) :
-
Fatigue life without stress intervals
- \(N\) :
-
Cycle number to failure
- \(A\), \(p\) :
-
Constants
- \(\gamma\) :
-
Sensitivity parameter of mean stress
- \(n\) :
-
Norton creep exponent
References
Allen R, Doherty T, Fossum AF (1982) Geotechnical issues and guidelines for storage of compressed air in excavated hard rock caverns. Pacific Northwest Lab, Richland. https://doi.org/10.2172/5437632
Bordenave S, Chatterjee I, Voordouw G (2013) Microbial community structure and microbial activities related to CO2 storage capacities of a salt cavern. Int Biodeterior Biodegrad 81:82–87. https://doi.org/10.1016/j.ibiod.2012.08.001
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
Caglayan DG, Weber N, Heinrichs HU, Linßen J, Robinius M, Kukla PA, Stolten D (2020) Technical potential of salt caverns for hydrogen storage in Europe. Int J Hydrogen Energy 45:6793–6805. https://doi.org/10.1016/j.ijhydene.2019.12.161
Carter NL, Hansen FD (1983) Creep of rocksalt. Tectonophysics 92:275–333. https://doi.org/10.1016/0040-1951(83)90200-7
Carter NL, Horseman ST, Russell JE, Handin J (1993) Rheology of rocksalt. J Struct Geol 15:1257–1271. https://doi.org/10.1016/0191-8141(93)90168-A
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 G, Zhang Y, Xu DK, Lin YC, Chen X (2016) Low cycle fatigue and creep-fatigue interaction behavior of nickel-base superalloy GH4169 at elevated temperature of 650 °C. Mater Sci Eng, A 655:175–182. https://doi.org/10.1016/j.msea.2015.12.096
Comte PL (1965) Creep in rock salt. J Geol 73:469–484. https://doi.org/10.1086/627078
Deng GJ, Tu ST, Wang QQ, Zhang XC, Xuan FZ (2014) Small fatigue crack growth mechanisms of 304 stainless steel under different stress levels. Int J Fatigue 64:14–21. https://doi.org/10.1016/j.ijfatigue.2014.01.027
Dowling NE, Calhoun CA, Arcari A (2009) Mean stress effects in stress-life fatigue and the Walker equation. Fatigue Fract Eng Mater Struct 32:163–179. https://doi.org/10.1111/j.1460-2695.2008.01322.x
Dusseault MB, Bachu S, Rothenburg L (2004) Sequestration of CO2 in salt caverns. J Can Pet Technol. https://doi.org/10.2118/04-11-04
Erarslan N, Williams DJ (2012a) The damage mechanism of rock fatigue and its relationship to the fracture toughness of rocks. Int J Rock Mech Min Sci. 56:15-–26. https://doi.org/10.1016/j.ijrmms.2012.07.015
Erarslan N, Williams DJ (2012b) Mechanism of rock fatigue damage in terms of fracturing modes. Int J Fatigue 43:76–89. https://doi.org/10.1016/j.ijfatigue.2012.02.008
Fan J, Chen J, Jiang D, Ren S, Wu J (2016) Fatigue properties of rock salt subjected to interval cyclic pressure. Int J Fatigue 90:109–115. https://doi.org/10.1016/j.ijfatigue.2016.04.021
Fan J, Jiang D, Chen J, Liu W, Tiedeu Ngaha W, Chen J (2018) Fatigue performance of ordinary concrete under discontinuous cyclic loading. Constr Build Mater 166:974–981. https://doi.org/10.1016/j.conbuildmat.2018.01.115
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
Fomin F, Horstmann M, Huber N, Kashaev N (2018) Probabilistic fatigue-life assessment model for laser-welded Ti-6Al-4V butt joints in the high-cycle fatigue regime. Int J Fatigue 116:22–35. https://doi.org/10.1016/j.ijfatigue.2018.06.012
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 135–136:10–23. https://doi.org/10.1016/j.enggeo.2012.02.012
Gao L, Lin W, Sun D, Wang H (2013) Experimental anelastic strain recovery compliance of three typical rocks. Rock Mech Rock Eng 47:1987–1995. https://doi.org/10.1007/s00603-013-0526-0
Goulart MBR, Costa PVMd, Costa AMd, Miranda ACO, Mendes AB, Ebecken NFF, Meneghini JR, Nishimoto K, Assi GRS (2020) Technology readiness assessment of ultra-deep salt caverns for carbon capture and storage in Brazil. Int J Greenhouse Gas Control 99:103083. https://doi.org/10.1016/j.ijggc.2020.103083
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
Guo C, Pan L, Zhang K, Oldenburg CM, Li C, Li Y (2016) Comparison of compressed air energy storage process in aquifers and caverns based on the Huntorf CAES plant. Appl Energy 181:342–356. https://doi.org/10.1016/j.apenergy.2016.08.105
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
Han Y, Ma H, Yang C, Zhang N, Daemen JJK (2020) 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. https://doi.org/10.1007/s00603-020-02097-0
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
He M, Li N, Zhu C, Chen Y, Wu H (2019) Experimental investigation and damage modeling of salt rock subjected to fatigue loading. Int J Rock Mech Min Sci 114:17–23. https://doi.org/10.1016/j.ijrmms.2018.12.015
Hunsche U, Hampel A (1999) Rock salt-the mechanical properties of the host rock material for a radioactive waste repository. Eng Geol 52:271–291. https://doi.org/10.1016/S0013-7952(99)00011-3
Jaeger JC, Cook NG, Zimmerman R (2009) Fundamentals of rock mechanics. John Wiley & Sons
Johnston WG, Gilman JJ (1959) Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals. J Appl Phys 30:129–144. https://doi.org/10.1063/1.1735121
Khaledi K, Mahmoudi E, Datcheva M, Schanz T (2016) Analysis of compressed air storage caverns in rock salt considering thermo-mechanical cyclic loading. Environ Earth Sci 75:1149. https://doi.org/10.1007/s12665-016-5970-1
Kushnir R, Dayan A, Ullmann A (2012) Temperature and pressure variations within compressed air energy storage caverns. Int J Heat Mass Transf 55:5616–5630. https://doi.org/10.1016/j.ijheatmasstransfer.2012.05.055
Kwofie S (2001) An exponential stress function for predicting fatigue strength and life due to mean stresses. Int J Fatigue 23:829–836. https://doi.org/10.1016/S0142-1123(01)00044-5
Lall A, Sarkar S, Ding R, Bowen P, Rabiei A (2019) Performance of Alloy 709 under creep-fatigue at various dwell times. Mater Sci Eng, A 761:138028. https://doi.org/10.1016/j.msea.2019.138028
Langer M (1993) Use of solution-mined caverns in salt for oil and gas storage and toxic waste disposal in Germany. Eng Geol 35:183–190. https://doi.org/10.1016/0013-7952(93)90005-W
Li L, Sun S, Wang J, Yang W, Song S, Fang Z (2020) Experimental study of the precursor information of the water inrush in shield tunnels due to the proximity of a water-filled cave. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2020.104320
Liu Y, Dai F (2021) A review of experimental and theoretical research on the deformation and failure behavior of rocks subjected to cyclic loading. J Rock Mech Geotech Eng 13:1203–1230. https://doi.org/10.1016/j.jrmge.2021.03.012
Lux K-H (2009) Design of salt caverns for the storage of natural gas, crude oil and compressed air: geomechanical aspects of construction, operation and abandonment. Geol Soc Lond Special Publ 313:93–128. https://doi.org/10.1144/SP313.7
Lyu C, Liu J, Ren Y, Liang C, Liao Y (2021) Study on very long-term creep tests and nonlinear creep-damage constitutive model of salt rock. Int J Rock Mech Min Sci 146:104873. https://doi.org/10.1016/j.ijrmms.2021.104873
Ma L-j, Liu X-y, Wang M-y, Xu H-f, Hua R-p, Fan P-x, Jiang S-r, Wang G-a, Yi Q-k (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
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
Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstracts 31:643–659. https://doi.org/10.1016/0148-9062(94)90005-1
Niesłony A, Böhm M (2013) Mean stress effect correction using constant stress ratio S-N curves. Int J Fatigue 52:49–56. https://doi.org/10.1016/j.ijfatigue.2013.02.019
Nihei M, Heuler P, Boller C, Seeger T (1986) Evaluation of mean stress effect on fatigue life by use of damage parameters. Int J Fatigue 8:119–126. https://doi.org/10.1016/0142-1123(86)90002-2
Norton FH (1929) The creep of steel at high temperatures. McGraw-Hill Book Company, New York
Özşen H, Özkan İ, Şensöğüt C (2014) Measurement and mathematical modelling of the creep behaviour of Tuzköy rock salt. Int J Rock Mech Min Sci 66:128–135. https://doi.org/10.1016/j.ijrmms.2014.01.005
Payten WM, Dean DW, Snowden KU (2010) A strain energy density method for the prediction of creep–fatigue damage in high temperature components. Mater Sci Eng, A 527:1920–1925. https://doi.org/10.1016/j.msea.2009.11.028
Peng H, Fan J, Zhang X, Chen J, Li Z, Jiang D, Liu C (2020) Computed tomography analysis on cyclic fatigue and damage properties of rock salt under gas pressure. Int J Fatigue. https://doi.org/10.1016/j.ijfatigue.2020.105523
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.mechmat.2015.10.009
Prasad K, Sarkar R, Ghosal P, Kumar V (2013) Simultaneous creep-fatigue damage accumulation of forged turbine disc of IN 718 superalloy. Mater Sci Eng, A 572:1–7. https://doi.org/10.1016/j.msea.2013.02.003
Qiu Y, Zhou S, Wang J, Chou J, Fang Y, Pan G, Gu W (2020) Feasibility analysis of utilising underground hydrogen storage facilities in integrated energy system: case studies in China. Appl Energy. https://doi.org/10.1016/j.apenergy.2020.115140
Quast P, Crotogino F (1979) Initial experience with the compressed-air energy storage (CAES) project of Nordwestdeutsche Kraftwerke AG (NWK) at Huntorf/West Germany. Erdoel-Erdgas z 95(9):310–314
Raju M, Kumar Khaitan S (2012) Modeling and simulation of compressed air storage in caverns: a case study of the Huntorf plant. Appl Energy 89:474–481. https://doi.org/10.1016/j.apenergy.2011.08.019
Ray SK, Sarkar M, Singh TN (1999) Effect of cyclic loading and strain rate on the mechanical behaviour of sandstone. Int J Rock Mech Min Sci 36:543–549. https://doi.org/10.1016/S0148-9062(99)00016-9
Ren S, Bai Y-m, Zhang J-P, Jiang D-y, Yang C-h (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
Roberts LA, Buchholz SA, Mellegard KD, Düsterloh U (2015) Cyclic loading effects on the creep and dilation of salt rock. Rock Mech Rock Eng 48:2581–2590. https://doi.org/10.1007/s00603-015-0845-4
Schulze O, Popp T, Kern H (2001) Development of damage and permeability in deforming rock salt. Eng Geol 61:163–180. https://doi.org/10.1016/S0013-7952(01)00051-5
Senseny PE, Hansen FD, Russell JE, Carter NL, Handin JW (1992) Mechanical behaviour of rock salt: phenomenology and micromechanisms. Int J Rock Mech Mining Sci Geomech Abstracts 29:363–378. https://doi.org/10.1016/0148-9062(92)90513-Y
Shankar V, Mariappan K, Sandhya R, Laha K (2016) Understanding low cycle fatigue and creep–fatigue interaction behavior of 316 L(N) stainless steel weld joint. Int J Fatigue 82:487–496. https://doi.org/10.1016/j.ijfatigue.2015.09.003
Ulusay R (2014) The ISRM suggested methods for rock characterization, testing and monitoring: 2007–2014. Springer
Urai JL, Spiers CJ, Zwart HJ, Lister GS (1986) Weakening of rock salt by water during long-term creep. Nature 324:554–557. https://doi.org/10.1038/324554a0
Venkataramani G, Parankusam P, Ramalingam V, Wang J (2016) A review on compressed air energy storage-A pathway for smart grid and polygeneration. Renew Sustain Energy Rev 62:895–907. https://doi.org/10.1016/j.rser.2016.05.002
Walker K, Pendleberry S, McElwee R, 1970. Effects of environment and complex load history on fatigue life. ASTM STP. 462,
Wang R-Z, Bo C, Zhang X-C, Tu S-T, Ji W, Zhang C-C (2017) The effects of inhomogeneous microstructure and loading waveform on creep-fatigue behaviour in a forged and precipitation hardened nickel-based superalloy. Int J Fatigue 97:190–201. https://doi.org/10.1016/j.ijfatigue.2017.01.002
Wang Y, Hu YZ, Gao SH (2020) Dynamic mechanical behaviors of interbedded marble subjected to multi-level uniaxial compressive cyclic loading conditions: an insight into fracture evolution analysis. Eng Fract Mech. https://doi.org/10.1016/j.engfracmech.2020.107410
Wang J, Zhang Q, Song Z, Zhang Y (2021) Experimental study on creep properties of salt rock under long-period cyclic loading. Int J Fatigue 143:106009. https://doi.org/10.1016/j.ijfatigue.2020.106009
Warren JK (2006) Evaporites: sediments, resources and hydrocarbons. Springer Science & Business Media, Berlin
Wisetsaen S, Walsri C, Fuenkajorn K (2015) Effects of loading rate and temperature on tensile strength and deformation of rock salt. Int J Rock Mech Min Sci 73:10–14. https://doi.org/10.1016/j.ijrmms.2014.10.005
Yang C, Daemen JJK, Yin J-H (1999) Experimental investigation of creep behavior of salt rock. Int J Rock Mech Min Sci 36:233–242. https://doi.org/10.1016/S0148-9062(98)00187-9
Yin H, Yang C, Ma H, Shi X, Chen X, Zhang N, Ge X, Liu W (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
Yu D, Liu E, Sun P, Xiang B, Zheng Q (2020) Mechanical properties and binary-medium constitutive model for semi-through jointed mudstone samples. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2020.104376
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 Y, Niu S, Du Z, Hao J, Yang J (2020) Dynamic fracture evolution of tight sandstone under uniaxial compression in high resolution 3D X-ray microscopy. J Petrol Sci Eng 195:107585. https://doi.org/10.1016/j.petrol.2020.107585
Zhao K, Liu Y, Li Y, Ma H, Hou W, Yu C, Liu H, Feng C, Yang C (2021a) Feasibility analysis of salt cavern gas storage in extremely deep formation: a case study in China. J Energy Storage. https://doi.org/10.1016/j.est.2021.103649
Zhao K, Ma H, Yang C, Chen X, Liu Y, Liang X, Cai R (2021b) Damage evolution and deformation of rock salt under creep-fatigue loading. Rock Mech Rock Eng 54:1985–1997. https://doi.org/10.1007/s00603-020-02342-6
Zhao Y, Bi J, Wang C, Liu P (2021c) Effect of unloading rate on the mechanical behavior and fracture characteristics of sandstones under complex triaxial stress conditions. Rock Mech Rock Eng 54:4851–4866. https://doi.org/10.1007/s00603-021-02515-x
Zhu SP, Huang HZ, Liu Y, Yuan R, He L (2012) An efficient life prediction methodology for low cycle fatigue-creep based on ductility exhaustion theory. Int J Damage Mech 22:556–571
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. http://hdl.handle.net/1853/53776.
Acknowledgements
The authors are sincerely grateful to Professor J. J. K. Daemen (University of Nevada, USA) for his language help of this article. The authors would gratefully like to acknowledge the financial support from the National Natural Science Foundation of China (Nos. 51874273, 51874274), National Science Foundation for Excellent Young Scholars (No. 52122403), Youth Innovation Promotion Association CAS (Grant No. 2019324), Special Fund for Strategic Pilot Technology of Chinese Academy of Sciences (Grant No. XDPB21) and Major Research Development Program of Hebei province (Grant No. 21374101D). The authors would like to thank the anonymous reviewers and Editors for their constructive suggestions which greatly improve the quality of the manuscript.
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Zhao, K., Ma, H., Zhou, J. et al. Rock Salt Under Cyclic Loading with High-Stress Intervals. Rock Mech Rock Eng 55, 4031–4049 (2022). https://doi.org/10.1007/s00603-022-02848-1
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DOI: https://doi.org/10.1007/s00603-022-02848-1