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Fatigue fracture behaviour and constitutive model of freeze-thaw sandstone under multilevel fatigue loads

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Abstract

The fatigue fracture behaviour and a constitutive model of the freeze-thaw (F-T) sandstone are studied to investigate the failure mechanism of engineering rock in cold regions. First, the fatigue properties of the samples are analysed in terms of stress-strain, deformation characteristics, and pore structure. Second, the types of hysteresis curves are analysed using the load-unload response ratio (LURR) method. Scanning electron microscopy (SEM) and acoustic emission (AE) techniques are then used to investigate the structural damage, crack evolution, and spectral characteristics of the samples. Based on the Lemaitre strain equivalence hypothesis, the improved Harris distribution is used to propose a new constitutive model of rock that underwent F-T cycles under multilevel fatigue loading. Finally, based on the strain difference model, the nonlinear stage of the model is corrected by defining new compaction coefficients using the Weibull distribution. Research shows that the deformation modulus of the F-T rock mass under fatigue loading has degradation behaviour and F-T cycles enhance the fatigue softening of samples. The dominant frequency range of samples under coupling is 70–330 kHz, showing multiband coexistence. As fatigue loading progresses, the hysteresis curve changes from stress hysteresis to strain hysteresis, and the frequency band gradually widens and develops towards low frequencies. The occurrence of a 0 kHz dominant frequency or LURR = 1 can be used as an early warning index of rock fatigue failure. As the number of F-T cycles progresses, the porosity composition curve shifts to the right, and the distribution of AE counts and the dominant frequency shift to the early loading stage.

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Abbreviations

A d :

Damage area

A e :

Effective bearing area

D :

Damage variable

D FL :

Fatigue damage

D FT :

Freeze-thaw damage

D FTFL :

Coupled damage

E :

Elastic modulus

E + :

Loading modulus

E − :

Unloading modulus

E d :

Deformation modulus

E v :

Initial elastic modulus

F a :

Micro-scale rock unit strength

K :

Compaction coefficient

m :

The mth freeze-thaw cycle

n :

The nth cycle

P :

Porosity

U :

Number of micro-scale units

X :

Response rate

ε :

Strain

ε c :

Crack closure point strain

ε m :

Maximum cyclic strain

ε p :

Peak strain

ε s :

Yield strain

ε v :

Initial cyclic strain

σ :

Stress

σ c :

Crack closure point stress

σ i :

Crack initiation stress

σ m :

Maximum cyclic stress

σ max :

Upper limit stress

σ min :

Lower limit stress

σ p :

Peak stress

σ s :

Yield stress

References

  • Ahmadi S, Ghasemzadeh H, Changizi F (2021a) Effects of A low-carbon emission additive on mechanical properties of fine-grained soil under freeze-thaw cycles. J Cleaner Prod 304:127157

    Article  Google Scholar 

  • Ahmadi S, Ghasemzadeh H, Changizi F (2021b) Effects of thermal cycles on microstructural and functional properties of nano treated clayey soil. Eng Geol 280:105929

    Article  Google Scholar 

  • Amiri SAG, Grimstad G, Kadivar M et al (2016) Constitutive model for rate-independent behavior of saturated frozen soils. Can Geotech J 53(10):1646–1657

    Article  Google Scholar 

  • Bagde MN, Petroš V (2005) Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading. Int J Rock Mech Min Sci 42(2):237–250

    Article  Google Scholar 

  • Cao D-F, Zhu H-H, Wu B et al (2021) Investigating temperature and moisture profiles of seasonally frozen soil under different land covers using actively heated fiber Bragg grating sensors. Eng Geol 290:106197

    Article  Google Scholar 

  • Cerfontaine B, Collin F (2018) Cyclic and fatigue behaviour of rock materials: review, interpretation and research perspectives. Rock Mech Rock Eng 51(2):391–414

    Article  Google Scholar 

  • Changizi F, Ghasemzadeh H, Ahmadi S (2022) Evaluation of strength properties of clay treated by nano-SiO2 subjected to freeze-thaw cycles. Road Mater Pavement Des 23(6):1221–1238

    Article  Google Scholar 

  • Council CE (2013) Standard for test methods of engineering rock mass, Ministry of Housing and Urban-Rural Development of the People’s Republic of China. GB/T 50266–2013:132

    Google Scholar 

  • Culshaw MG (2015) The ISRM suggested methods for rock characterization, testing and monitoring: 2007–2014. Ulusay, R (ed.). Bull Eng Geol Environ 74(4):14992–1500

  • Deryagin B, Churaev N (1976) Definition of disjoining pressure and its importance in equilibrium and flow of thin-films. Colloid Journal of the USSR 38(3):402–410

    Google Scholar 

  • Everett D (1961) The thermodynamics of frost damage to porous solids. Trans Faraday Soc 57:1541–1551

    Article  Google Scholar 

  • Frigo M, Johnson SG (1998) FFTW: an adaptive software architecture for the FFT. Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP’98 (Cat. No. 98CH36181). IEEE

  • Gao F, Xiong X, Xu C et al (2021) Mechanical property deterioration characteristics and a new constitutive model for rocks subjected to freeze-thaw weathering process. Int J Rock Mech Min Sci 140:104642

    Article  Google Scholar 

  • Ghasemzadeh H, Ghoreishian Amiri SA (2013) A hydro-mechanical elastoplastic model for unsaturated soils under isotropic loading conditions. Comput Geotech 51:91–100

    Article  Google Scholar 

  • Ghasemzadeh H, Sojoudi MH, Ghoreishian Amiri SA et al (2017) Elastoplastic model for hydro-mechanical behavior of unsaturated soils. Soils Found 57(3):371–383

    Article  Google Scholar 

  • Ghoreishian Amiri SA, Grimstad G, Kadivar M (2022) An elastic-viscoplastic model for saturated frozen soils. Eur J Environ Civ Eng 26(7):2537–2553

    Article  Google Scholar 

  • Huang H, Ju N, Li L et al (2018a) Improved Harris function based statistical damage softening model for rocks. J Eng Geol 26(02):520–527

    Google Scholar 

  • Huang S, Liu Q, Cheng A et al (2018b) A statistical damage constitutive model under freeze-thaw and loading for rock and its engineering application. Cold Reg Sci Technol 145:142–150

    Article  Google Scholar 

  • Jafari M, Hosseini KA, Pellet F et al (2003) Evaluation of shear strength of rock joints subjected to cyclic loading. Soil Dyn Earthquake Eng 23(7):619–630

    Article  Google Scholar 

  • Jin J, Li S, Song C et al (2019) Ageing deformation of tailings dams in seasonally frozen soil areas under freeze-thaw cycles. Sci Rep 9(1):15033

    Article  Google Scholar 

  • Kjelstrup S, Ghoreishian Amiri SA, Loranger B et al (2021) Transport coefficients and pressure conditions for growth of ice lens in frozen soil. Acta Geotech 16(7):2231–2239

    Article  Google Scholar 

  • Konrad J-M, Morgenstern NR (1980) A mechanistic theory of ice lens formation in fine-grained soils. Can Geotech J 17(4):473–486

    Article  Google Scholar 

  • Konrad J-M, Morgenstern NR (1981) The segregation potential of a freezing soil. Can Geotech J 18(4):482–491

    Article  Google Scholar 

  • Lemaitre J (1984) How to use damage mechanics. Nucl Eng Des 80(2):233–245

    Article  Google Scholar 

  • Li J, Zhou K, Liu W et al (2018) Analysis of the effect of freeze-thaw cycles on the degradation of mechanical parameters and slope stability. Bull Eng Geol Environ 77(2):573–580

    Article  Google Scholar 

  • Lin Y, Zhou K, Gao F et al (2019) Damage evolution behavior and constitutive model of sandstone subjected to chemical corrosion. Bull Eng Geol Environ 78(8):5991–6002

    Article  Google Scholar 

  • Liu Q, Huang S, Kang Y et al (2015a) A prediction model for uniaxial compressive strength of deteriorated rocks due to freeze-thaw. Cold Reg Sci Technol 120:96–107

    Article  Google Scholar 

  • Liu Q, Huang S, Tang Y et al (2015b) Advance and review on freezing-thawing damage of fractured rock. Chin J Rock Mech Eng 34(03):452–471

    Google Scholar 

  • Liu T, Zhang C, Li J et al (2021) Detecting freeze-thaw damage degradation of sandstone with initial damage using NMR technology. Bull Eng Geol Environ 80(6):4529–4545

    Article  Google Scholar 

  • Liu XS, Ning JG, Tan YL et al (2016) Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading. Int J Rock Mech Min Sci 85:27–32

    Article  Google Scholar 

  • Liu Y, Dai F (2018) A damage constitutive model for intermittent jointed rocks under cyclic uniaxial compression. Int J Rock Mech Min Sci 103:289–301

    Article  Google Scholar 

  • 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(5):1203–1230

    Article  Google Scholar 

  • Liu Y, Dai F, Dong L et al (2018) Experimental investigation on the fatigue mechanical properties of intermittently jointed rock models under cyclic uniaxial compression with different loading parameters. Rock Mech Rock Eng 51(1):47–68

    Article  Google Scholar 

  • Miller R (1972) Freezing and heaving of saturated and unsaturated soils. Highway Res Rec 393(1):1–11

    Google Scholar 

  • Nejati HR, Ghazvinian A (2014) Brittleness effect on rock fatigue damage evolution. Rock Mech Rock Eng 47:1839–1848

    Article  Google Scholar 

  • 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(4):543–549

    Article  Google Scholar 

  • Sass O (2004) Rock moisture fluctuations during freeze-thaw cycles: preliminary results from electrical resistivity measurements. Polar Geogr 28(1):13–31

    Article  Google Scholar 

  • Shi Z, Li J, Wang J (2022a) Effect of creep load on fatigue behavior and acoustic emission characteristics of sandstone containing pre-existing crack during fatigue loading. Theor Appl Fract Mech 119:103296

  • Shi Z, Li J, Wang J (2022b) Energy evolution and fracture behavior of sandstone under the coupling action of freeze- thaw cycles and fatigue load. Rock Mech Rock Eng 56(2):1321–1341

  • Shi Z, Li J, Wang J (2022c) Research on the fracture mode and damage evolution model of sandstone containing pre-existing crack under different stress paths. Eng Fract Mech 264:108299

  • Shi Z, Li J, Wang J et al (2023a) Fracture behavior and damage evolution model of sandstone containing a single pre-existing flaw under discontinuous fatigue loading. Int J Damage Mech 32(1):3–27

    Article  Google Scholar 

  • Shi Z, Li J, Wang J et al (2023b) Experimental and numerical study on fracture characteristics and constitutive model of sandstone under freeze-thaw-fatigue. Int J Fatigue 166:107236

    Article  Google Scholar 

  • Singh S (1989) Fatigue and strain hardening behaviour of graywacke from the flagstaff formation. New South Wales Eng Geol 26(2):171–179

    Google Scholar 

  • Song Z, Wang Y, Konietzky H et al (2021) Mechanical behavior of marble exposed to freeze-thaw-fatigue loading. Int J Rock Mech Min Sci 138:104648

    Article  Google Scholar 

  • Suresh S (1998) Fatigue of materials. Cambridge University Press

    Book  Google Scholar 

  • Taber S (1929) Frost heaving. J Geol 37(5):428–461

    Article  Google Scholar 

  • Vutukuri VS, Lama RD, Saluja S (1974) Handbook on mechanical properties of rocks. Publications, Clausthal, Germany Trans Tech

    Google Scholar 

  • Wang Y, Gao SH, Li CH et al (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

    Article  Google Scholar 

  • Yang S-Q, Huang Y-H, Tang J-Z (2020) Mechanical, acoustic, and fracture behaviors of yellow sandstone specimens under triaxial monotonic and cyclic loading. Int J Rock Mech Min Sci 130:104268

    Article  Google Scholar 

  • Yin XC, Wang YC, Peng KY et al (2000) Development of a new approach to earthquake prediction: load/unload response ratio (LURR) theory. Pure Appl Geophys 157(11):2365–2383

    Article  Google Scholar 

  • Zhang J, Deng H, Deng J et al (2020a) Influence of freeze-thaw cycles on the degradation of sandstone after loading and unloading. Bull Eng Geol Environ 79(4):1967–1977

    Article  Google Scholar 

  • Zhang M, Dou L, Konietzky H et al (2020b) Cyclic fatigue characteristics of strong burst-prone coal: experimental insights from energy dissipation, hysteresis and micro-seismicity. Int J Fatigue 133:105429

    Article  Google Scholar 

  • Zhang Q, Liu Y, Dai F et al (2022) Experimental assessment on the fatigue mechanical properties and fracturing mechanism of sandstone exposed to freeze-thaw treatment and cyclic uniaxial compression. Eng Geol 306:106724

    Article  Google Scholar 

  • Zhou X-P, Zhang J-Z, Qian Q-H et al (2019) Experimental investigation of progressive cracking processes in granite under uniaxial loading using digital imaging and AE techniques. J Struct Geol 126:129–145

    Article  Google Scholar 

  • Zhou X, Fu Y, Wang Y et al (2022) Experimental study on the fracture and fatigue behaviors of flawed sandstone under coupled freeze-thaw and cyclic loads. Theor Appl Fract Mech 119:103299

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank the journal editors and reviewers for their valuable comments.

Funding

This study was supported by the National Natural Science Foundation of China [grant number 51979293], Hunan Provincial Key Research and Development Program [grant number 2022SK2082], Science and Technology Project of Hunan Natural Resources Department [grant number 2021-52], Hunan Civil Air Defence Research Project [grant number HNRFKJ-2021-07], and Postgraduate Innovative Project of Central South University [grant number 2021XQLH154].

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Authors and Affiliations

  1. School of Resources and Safety Engineering, Central South University, Changsha, 410083, China

    Zhanming Shi, Jiangteng Li, Mengxiang Wang, Jinci Chen, Hang Lin & Ping Cao

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  1. Zhanming Shi
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Correspondence to Jiangteng Li.

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Shi, Z., Li, J., Wang, M. et al. Fatigue fracture behaviour and constitutive model of freeze-thaw sandstone under multilevel fatigue loads. Bull Eng Geol Environ 82, 319 (2023). https://doi.org/10.1007/s10064-023-03338-6

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