Abstract
This article aims to investigate the impact of frequency sequence on mechanical responses of sandstone exposed to multi-level compressive cyclic loading. Two modes were used with three levels of low frequencies (0.1, 0.2, and 0.4 Hz) in incremental or decremental sequences. The analysis was made on rock deformation, energy characteristics and stress–strain phase shift. The experimental results show that frequency sequence has a significant effect on various types of mechanical properties. The decremental frequency causes a greater growth in axial strain at maximum cyclic stress than at the minimum stress. The input and elastic energy are enhanced under incremental frequency sequence, while decremental frequency results in a higher occurrence ratio of phase lag, particularly in the radial direction. These experimental findings can help to deepen the understanding of rock fatigue from the view of frequency sequence.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The data supporting the findings of this study can be accessed upon request. Interested researchers are invited to contact the corresponding author.
References
Attewell PB, Farmer IW (1973) Fatigue behaviour of rock. Int J Rock Mech Min Sci 10:1–9. https://doi.org/10.1016/0148-9062(73)90055-7
Bagde MN, Petroš V (2005a) 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
Bagde MN, Petroš V (2005b) The effect of machine behaviour and mechanical properties of intact sandstone under static and dynamic uniaxial cyclic loading. Rock Mech Rock Eng 38:59–67. https://doi.org/10.1007/s00603-004-0038-z
Burdine NT (1963) Rock failure under dynamic loading conditions. Soc Pet Eng J 3:1–8
Cerfontaine B, Collin F (2018) 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, Bu J, Fan X et al (2017) Effect of loading frequency and stress level on low cycle fatigue behavior of plain concrete in direct tension. Constr Build Mater 133:367–375. https://doi.org/10.1016/j.conbuildmat.2016.12.085
Dang W, Konietzky H, Frühwirt T (2016) Direct shear behavior of a plane joint under dynamic normal load (DNL) conditions. Eng Geol 213:133–141. https://doi.org/10.1016/j.enggeo.2016.08.016
Dang W, Konietzky H, Chang L, Frühwirt T (2018) Velocity-frequency-amplitude-dependent frictional resistance of planar joints under dynamic normal load (DNL) conditions. Tunn Undergr Sp Technol 79:27–34. https://doi.org/10.1016/j.tust.2018.04.038
Duan M, Jiang C, Gan Q et al (2020) Experimental investigation on the permeability, acoustic emission and energy dissipation of coal under tiered cyclic unloading. J Nat Gas Sci Eng 73:103054. https://doi.org/10.1016/j.jngse.2019.103054
Fan J, Jiang D, Chen J et al (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
Han Y, Ma H, Cui H, Liu N (2022) The effects of cycle frequency on mechanical behavior of rock salt for energy storage. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-022-03040-1
He M, Huang B, Zhu C et al (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
Heap MJ, Faulkner DR (2008) Quantifying the evolution of static elastic properties as crystalline rock approaches failure. Int J Rock Mech Min Sci 45:564–573. https://doi.org/10.1016/j.ijrmms.2007.07.018
Hernandez EM, Geoff M (2013) Dissipated energy ratio as a feature for earthquake-induced damage detection of instrumented structures. J Eng Mech 139:1521–1529. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000534
Jiang L, Brooks CR, Liaw PK et al (2001) High-frequency metal fatigue: the high-cycle fatigue behavior of ULTIMET® alloy. Mater Sci Eng A 314:162–175. https://doi.org/10.1016/S0921-5093(00)01928-6
Karbhari VM (2007) 1 - Introduction: the use of composites in civil structural applications. In: Karbhari VM (ed) Durability of Composites for Civil Structural Applications. Woodhead Publishing, pp 1–10
Kliman V, Bílý M (1984) Hysteresis energy of cyclic loading. Mater Sci Eng 68:11–18. https://doi.org/10.1016/0025-5416(84)90239-8
Lei D, Zhang P, He J et al (2017) Fatigue life prediction method of concrete based on energy dissipation. Constr Build Mater 145:419–425. https://doi.org/10.1016/j.conbuildmat.2017.04.030
Li J, Hong L, Zhou K et al (2020) Influence of loading rate on the energy evolution characteristics of rocks under cyclic loading and unloading. Energies 13:. https://doi.org/10.3390/en13154003
Li X, Gong F, Tao M et al (2017) Failure mechanism and coupled static-dynamic loading theory in deep hard rock mining: a review. J Rock Mech Geotech Eng 9:767–782. https://doi.org/10.1016/j.jrmge.2017.04.004
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
Lu C-P, Dou L-M, Zhang N et al (2013) Microseismic frequency-spectrum evolutionary rule of rockburst triggered by roof fall. Int J Rock Mech Min Sci 64:6–16. https://doi.org/10.1016/j.ijrmms.2013.08.022
Lu C-P, Liu G-J, Liu Y et al (2015) Microseismic multi-parameter characteristics of rockburst hazard induced by hard roof fall and high stress concentration. Int J Rock Mech Min Sci 76:18–32. https://doi.org/10.1016/j.ijrmms.2015.02.005
Ma L, Liu X, Wang M 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
McKavanagh B, Stacey FD (1974) Mechanical hysteresis in rocks at low strain amplitudes and seismic frequencies. Phys Earth Planet Inter. https://doi.org/10.1016/0031-9201(74)90091-0
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
Peng K, Shi S, Zou Q et al (2020) Characteristics of energy storage and dissipation of coal under one-time cyclic load. Energy Sci Eng 8:3117–3135. https://doi.org/10.1002/ese3.738
Peng K, Zhou J, Zou Q, Song X (2019) Effect of loading frequency on the deformation behaviours of sandstones subjected to cyclic loads and its underlying mechanism. Int J Fatigue 105349. https://doi.org/10.1016/j.ijfatigue.2019.105349
Ray S, Sarkar M, Singh T (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
Scott-Emuakpor OE, George TJ, Cross CJ, Shen M-HH (2011) Analysis of strain energy behavior throughout a fatigue process. Exp Mech 51:1317–1323. https://doi.org/10.1007/s11340-010-9457-9
Shen S, Airey GD, Carpenter SH, Huang H (2006) A dissipated energy approach to fatigue evaluation. Road Mater Pavement Des 7:47–69. https://doi.org/10.3166/rmpd.7.47-69
Shirani Faradonbeh R, Taheri A, Karakus M (2021) Post-peak behaviour of rocks under cyclic loading using a double-criteria damage-controlled test method. Bull Eng Geol Environ 80:1713–1727. https://doi.org/10.1007/s10064-020-02035-y
Sinaie S, Heidarpour A, Zhao XL, Sanjayan JG (2015) Effect of size on the response of cylindrical concrete samples under cyclic loading. Constr Build Mater 84:399–408. https://doi.org/10.1016/j.conbuildmat.2015.03.076
Song Z, Frühwirt T, Konietzky H (2018a) Characteristics of dissipated energy of concrete subjected to cyclic loading. Constr Build Mater 168:47–60. https://doi.org/10.1016/j.conbuildmat.2018.02.076
Song Z, Frühwirt T, Konietzky H (2020) Inhomogeneous mechanical behaviour of concrete subjected to monotonic and cyclic loading. Int J Fatigue 132:105383. https://doi.org/10.1016/j.ijfatigue.2019.105383
Song Z, Konietzky H, Cai X (2021a) Modulus degradation of concrete exposed to compressive fatigue loading: Insights from lab testing. Struct Eng Mech 78:281–296
Song Z, Konietzky H, Frühwirt T (2018b) Hysteresis energy-based failure indicators for concrete and brittle rocks under the condition of fatigue loading. Int J Fatigue 114:298–310. https://doi.org/10.1016/J.IJFATIGUE.2018.06.001
Song Z, Konietzky H, Wu Y et al (2022a) Mechanical behaviour of medium-grained sandstones exposed to differential cyclic loading (DCL) with distinct loading and unloading rates. J Rock Mech Geotech Eng 14
Song Z, Konietzky H, Wu Y, Cai X (2022b) Mechanical and microseismic characteristics of sandstones subject to moderate low-frequency differential cyclic loading (DCL) followed by monotonic loading up to failure. Acta Geotech. https://doi.org/10.1007/s11440-022-01570-0
Song Z, Wang Y, Konietzky H, Cai X (2021b) Mechanical behavior of marble exposed to freeze-thaw-fatigue loading. Int J Rock Mech Min Sci 138:104648. https://doi.org/10.1016/j.ijrmms.2021.104648
Song Z, Wu Y, Konietzky H et al (2022c) Mechanical behaviors of anthracite coal subject to low-cycle compressive differential cyclic loading (DCL) after wetting–drying (WD) treatment: an experimental study. Geomech Geophys Geo-Energy Geo-Resources 8:116. https://doi.org/10.1007/s40948-022-00423-0
Song Z, Wu Y, Yang Z et al (2021c) Mechanical responses of a deeply buried granite exposed to multilevel uniaxial and triaxial cyclic stresses: insights into deformation behavior, energy dissipation, and hysteresis. Adv Mater Sci Eng 2021:3160968. https://doi.org/10.1155/2021/3160968
Sugimoto T, Sasaki Y (2006) Effect of loading frequency on fatigue life and dissipated energy of structural plywood under panel shear load. Wood Sci Technol 40:501–515. https://doi.org/10.1007/s00226-006-0080-y
Tepfers R, Hedberg B, Szczekocki G (1984) Absorption of energy in fatigue loading of plain concrete. Matériaux Constr 17:59–64
Tien YM, Lee DH, Juang CH (1990) Strain, pore pressure and fatigue characteristics of sandstone under various load conditions. Int J Rock Mech Min Sci Geomech Abstr 27:283–289. https://doi.org/10.1016/0148-9062(90)90530-F
Voznesenskii AS, Kutkin YO, Krasilov MN, Komissarov AA (2015) Predicting fatigue strength of rocks by its interrelation with the acoustic quality factor. Int J Fatigue 77:194–198. https://doi.org/10.1016/j.ijfatigue.2015.02.012
Wang Y, Gao SH, Li CH, Han JQ (2021) Energy dissipation and damage evolution for dynamic fracture of marble subjected to freeze-thaw and multiple level compressive fatigue loading. Int J Fatigue 142:105927. https://doi.org/10.1016/j.ijfatigue.2020.105927
Xiao J-Q, Ding D-X, Xu G, Jiang F-L (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
Zhang M, Dou L, Konietzky H et al (2020) Cyclic fatigue characteristics of strong burst-prone coal: Experimental insights from energy dissipation, hysteresis and micro-seismicity. Int J Fatigue 133:105429. https://doi.org/10.1016/j.ijfatigue.2019.105429
Funding
The paper is supported by the Open Fund of State Key Laboratory of Mining-induced Response and Disaster Prevention and Control in Deep Coal Mines (Grant No. SKLMRDPC21KF08), NSFC (Grant No. 52204086), Research Grant of Joint National-local Engineering Research Centre for Safe and Precise Coal Mining (Grant No. EC2021004), and Fundamental Research Funds for the Central Universities (Grant No. 06500182), Grant from Humboldt Research Fellowship, Young Talents International Exchange and Growth Program in USTB (Grant No. QNXM20220007).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Song, Z., Wang, C., Zhao, Y. et al. Effect of frequency on rock’s mechanical responses under multi-level compressive cyclic loading: an experimental investigation. Bull Eng Geol Environ 82, 224 (2023). https://doi.org/10.1007/s10064-023-03263-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10064-023-03263-8