Skip to main content

Advertisement

SpringerLink
Log in

Energy Evolution and Fracture Behavior of Sandstone Under the Coupling Action of Freeze–Thaw Cycles and Fatigue Load

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

A series of freeze–thaw (F–T) cycle and multilevel fatigue loading tests are carried out on sandstone samples to explore rock mass's fracture behavior and energy evolution characteristics under the coupling action of F–T cycles and fatigue loads. First, the energy evolution characteristics of the sample are analyzed by the image integration method, and the law of energy storage and energy dissipation of the sample are further discussed. Subsequently, a coupled damage model is established based on the Lemaitre strain equivalence hypothesis. Finally, based on the b value and AF-RA waveform theory, the sample's crack evolution process and failure mode are analyzed using acoustic emission (AE) technology. The results show that the specimen's elastic energy and total energy density under the coupling action increase step-like with increasing the upper limit stress. The dissipated energy density decreases rapidly and stabilizes after the first cycle of each stage. The energy evolution process of the sample obeys the linear energy storage law and the two-stage energy dissipation law, in which the energy dissipation law is transformed from linear to exponential in the accelerated energy release stage. The coupling damage of the sample increases exponentially with the number of cycles, and the damage growth rate is slow at first and then fast. In addition, the crack propagation process of the specimen exhibits a 3-stage characteristic. As the number of F–T cycles increases, the proportion of shear cracks in the sample increases significantly, the failure mode transitions from X-conjugate failure to shear failure with a single oblique section, and the fatigue-softening effect is enhanced.

Highlights

  • Freeze-thaw sandstone sample is tested under multi-level fatigue loads.

  • The linear energy storage law and two-stage energy dissipation law are proposed.

  • The sample has obvious accelerated energy release before failure.

  • A coupling damage model under F–T cycles and fatigue load is established.

  • Facture behavior of the sample is analyzed by b value and AF-RA waveform theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Abbreviations

A dB :

AE Amplitude

b :

b Value

C AE :

AE count

D :

Damage variable

E d :

Dynamic elastic modulus

M :

AE threshold

N :

Total number of cycles

m :

Number of freeze–thaw cycles

n :

Number of cycle loading

Q :

Growth factor

Q U :

Total energy density growth factor

Q Ud :

Dissipated energy density growth factor

Q Ue :

Elastic energy density growth factor

T C :

AE duration time

T S :

The rise time of AE

U :

Total energy density

U d :

Dissipated energy density

U e :

Elastic energy density

V :

Sample volume

v p :

P-wave speed

AF :

AE count/Duration time

RA :

Rise time/Amplitude

σ :

Stress

σ max :

Upper limit stress

σ min :

Lower limit stress

ε :

Strain

ρ :

Rock density

μ :

Poisson's ratio

References

  • Abdolghanizadeh K, Hosseini M, Saghafiyazdi M (2020) Effect of freezing temperature and number of freeze-thaw cycles on mode I and mode II fracture toughness of sandstone. Theor Appl Fract Mech 105:102428

    Google Scholar 

  • Cao R, Lin H, Cao P (2018) Strength and failure characteristics of brittle jointed rock-like specimens under uniaxial compression: digital speckle technology and a particle mechanics approach. Int J Min Sci Technol 28(4):669–677

    Google Scholar 

  • Cao R, Yao R, Meng J, Lin Q, Lin H, Li S (2020a) Failure mechanism of non-persistent jointed rock-like specimens under uniaxial loading: laboratory testing. Int J Rock Mech Min Sci 132:104341

    Google Scholar 

  • Cao RH, Wang CS, Yao RB, Hu T, Lei DX, Lin H, Zhao YL (2020b) Effects of cyclic freeze-thaw treatments on the fracture characteristics of sandstone under different fracture modes: laboratory testing. Theor Appl Fract Mech 109:102738

    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

    Google Scholar 

  • Chang X, Zhang X, Dang FN, Zhang BF, Chang FQ (2022) Failure behavior of sandstone specimens containing a single flaw under true triaxial compression. Rock Mech Rock Eng 55(4):2111–2127

    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

  • Culshaw MG (2015) The ISRM suggested methods for rock characterization, testing and monitoring. Bull Eng Geol Environ 74(4):1499–1500

    Google Scholar 

  • Du K, Li X, Tao M, Wang S (2020) Experimental study on acoustic emission (AE) characteristics and crack classification during rock fracture in several basic lab tests. Int J Rock Mech Min Sci 133:104411

    Google Scholar 

  • Feng Q, Jin J, Zhang S, Liu W, Yang X, Li W (2022) Study on a damage model and uniaxial compression simulation method of frozen-thawed rock. Rock Mech Rock Eng 55(1):187–211

    Google Scholar 

  • Gao F, Wang Q, Deng H, Zhang J, Tian W, Ke B (2017) Coupled effects of chemical environments and freeze-thaw cycles on damage characteristics of red sandstone. Bull Eng Geol Environ 76(4):1481–1490

    Google Scholar 

  • Gao F, Xiong X, Xu C, Zhou K (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

    Google Scholar 

  • Gong F, Yan J, Luo S, Li X (2019) Investigation on the linear energy storage and dissipation laws of rock materials under uniaxial compression. Rock Mech Rock Eng 52(11):4237–4255

    Google Scholar 

  • Gutenberg B, Richter CF (1955) Magnitude and energy of earthquakes. Nature 176(4486):795–795

    Google Scholar 

  • Hashemi M, Bashiri Goudarzi M, Jamshidi A (2018) Experimental investigation on the performance of Schmidt hammer test in durability assessment of carbonate building stones against freeze–thaw weathering. Environ Earth Sci 77(19):684

    Google Scholar 

  • Huang S, Cai Y, Liu Y, Liu G (2021) Experimental and theoretical study on frost deformation and damage of red sandstones with different water contents. Rock Mech Rock Eng 54(8):4163–4181

    Google Scholar 

  • Jamshidi A (2021) Predicting the strength of granitic stones after freeze-thaw cycles: considering the petrographic characteristics and a new approach using petro-mechanical parameter. Rock Mech Rock Eng 54(6):2829–2841

    Google Scholar 

  • Ke B, Zhou K, Xu C, Deng H, Li J, Bin F (2018) Dynamic mechanical property deterioration model of sandstone caused by freeze-thaw weathering. Rock Mech Rock Eng 51(9):2791–2804

    Google Scholar 

  • Lei XL, Kusunose K, Rao M, Nishizawa O, Satoh T (2000) Quasi-static fault growth and cracking in homogeneous brittle rock under triaxial compression using acoustic emission monitoring. J Geophys Res-Solid Earth 105(B3):6127–6139

    Google Scholar 

  • Lemaitre J (1985) A continuous damage mechanics model for ductile fracture. J Eng Mater Technol 107(1):83–89

    Google Scholar 

  • Li JL, Zhou KP, Liu WJ, Zhang YM (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

    Google Scholar 

  • Lin Q, Cao P, Mao S, Ou C, Cao R (2020) Fatigue behaviour and constitutive model of yellow sandstone containing pre-existing surface crack under uniaxial cyclic loading. Theor Appl Fract Mech 109:102776

    Google Scholar 

  • Lin Q, Cao P, Wen G, Meng J, Cao R, Zhao Z (2021) Crack coalescence in rock-like specimens with two dissimilar layers and pre-existing double parallel joints under uniaxial compression. Int J Rock Mech Min Sci 139:104621

    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

    Google Scholar 

  • Liu Q, Huang S, Tang Y, Huang X (2015) Fatigue damage model and evaluation index for rock mass under freezing-thawing cycles. Chin J Rock Mech Eng 34(06):1116–1127

    Google Scholar 

  • Liu Y, Dai F, Dong L, Xu N, Feng P (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

    Google Scholar 

  • Liu C, Deng H, Chen X, Xiao D, Li B (2020) Impact of rock samples size on the microstructural changes induced by freeze-thaw cycles. Rock Mech Rock Eng 53(11):5293–5300

    Google Scholar 

  • Lv Z, Luo S, Xia C, Zeng X (2022) A thermal-mechanical coupling elastoplastic model of freeze-thaw deformation for porous rocks. Rock Mech Rock Eng 55(6):3195–3212

    Google Scholar 

  • Meng Q, Zhang M, Han L, Pu H, Nie T (2016) Effects of acoustic emission and energy evolution of rock specimens under the uniaxial cyclic loading and unloading compression. Rock Mech Rock Eng 49(10):3873–3886

    Google Scholar 

  • Qiao C, Song ZY, Wang Y, Tannant D, Li CH (2022) Fractures and acoustic emission features of non-persistent jointed rocks subjected to freeze-thaw-compression load: experimental insights. Rock Mech Rock Eng 55(1):109–123

    Google Scholar 

  • Shi Z, Li J, Zhao Y (2021) Study on damage evolution and constitutive model of sandstone under the coupled effects of wetting-drying cycles and cyclic loading. Eng Fract Mech 253:107883

    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

    Google Scholar 

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

    Google Scholar 

  • Shi Z, Li J, Wang J, Chen J, Lin H, Cao P (2022c) Experimental and numerical study on fracture characteristics and constitutive model of sandstone under freeze-thaw-fatigue. Int J Fatigue 166:107236

    Google Scholar 

  • Solecki R, Conant RJ (2003) Advanced mechanics of materials. Oxford University Press, Oxford

    Google Scholar 

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

    Google Scholar 

  • Tan XJ, Chen WZ, Yang JP, Cao JJ (2011) Laboratory investigations on the mechanical properties degradation of granite under freeze-thaw cycles. Cold Reg Sci Technol 68(3):130–138

    Google Scholar 

  • Wang T-l, Liu Y-j, Yan H, Xu L (2015) An experimental study on the mechanical properties of silty soils under repeated freeze–thaw cycles. Cold Reg Sci Technol 112:51–65

    Google Scholar 

  • Wang F, Cao P, Wang Y, Hao R, Meng J, Shang J (2020) Combined effects of cyclic load and temperature fluctuation on the mechanical behavior of porous sandstones. Eng Geol 266:105466

    Google Scholar 

  • Wang Y-Q, Peng K, Shang X-Y, Li L-P, Liu Z-P, Wu Y, Long K (2021a) Experimental and numerical simulation study of crack coalescence modes and microcrack propagation law of fissured sandstone under uniaxial compression. Theor Appl Fract Mech 115:103060

    Google Scholar 

  • Wang Y, Gao SH, Li CH, Han JQ (2021b) 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

    Google Scholar 

  • Wang Y, Zhang B, Gao SH, Li CH (2021c) Investigation on the effect of freeze-thaw on fracture mode classification in marble subjected to multi-level cyclic loads. Theor Appl Fract Mech 111:102847

    Google Scholar 

  • Wang Y, Zhang B, Li B, Li CH (2021d) A strain-based fatigue damage model for naturally fractured marble subjected to freeze-thaw and uniaxial cyclic loads. Int J Damage Mech 30(10):1594–1616

    Google Scholar 

  • Wang J, Li J, Shi Z (2022a) Deformation damage and acoustic emission characteristics of red sandstone under fatigue–creep interaction. Theor Appl Fract Mech 117:103192

    Google Scholar 

  • Wang Y, Song Z, Mao T, Zhu C (2022b) Macro-meso fracture and instability behaviors of hollow-cylinder granite containing fissures subjected to freeze–thaw–fatigue loads. Rock Mech Rock Eng 55(7):4051–4071

    Google Scholar 

  • Xie H, Li L, Ju Y, Peng R, Yang Y (2011) Energy analysis for damage and catastrophic failure of rocks. Sci China Technol Sci 54(1):199–209

    Google Scholar 

  • Zhou K-p, Li B, Li J-l, H-w D, Bin F (2015) Microscopic damage and dynamic mechanical properties of rock under freeze-thaw environment. Trans Nonferrous Metals Soc China 25(4):1254–1261

    Google Scholar 

  • Zhou X-P, Niu Y, Zhang J-Z, Shen X-C, Zheng Y, Berto F (2019a) Experimental study on effects of freeze-thaw fatigue damage on the cracking behaviors of sandstone containing two unparallel fissures. Fatigue Fract Eng Mater Struct 42(6):1322–1340

    Google Scholar 

  • Zhou X-P, Wang Y-T, Zhang J-Z, Liu F-N (2019b) Fracturing behavior study of three-flawed specimens by uniaxial compression and 3D digital image correlation: sensitivity to brittleness. Rock Mech Rock Eng 52(3):691–718

    Google Scholar 

  • Zhou X-P, Zhang J-Z, Yang S-Q, Berto F (2021a) Compression-induced crack initiation and growth in flawed rocks: a review. Fatigue Fract Eng Mater Struct 44(7):1681–1707

    Google Scholar 

  • Zhou Y, Zhao D, Li B, Wang H, Tang Q, Zhang Z (2021b) Fatigue damage mechanism and deformation behaviour of granite under ultrahigh-frequency cyclic loading conditions. Rock Mech Rock Eng 54(9):4723–4739

    Google Scholar 

  • Zhou XP, Fu YH, Wang Y, Zhou JN (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

    Google Scholar 

  • Zhu T, Chen J, Huang D, Luo Y, Li Y, Xu L (2021) A DEM-based approach for modeling the damage of rock under freeze-thaw cycles. Rock Mech Rock Eng 54(6):2843–2858

    Google Scholar 

Download references

Funding

This work is supported by the National Natural Science Foundation of China [grant number 51979293]; Postgraduate Innovative Project of Central South University [grant number 2021XQLH154]. We also thank the journal editors and reviewers for their valuable comments.

Author information

Authors and Affiliations

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

    Zhanming Shi, Jiangteng Li & Ju Wang

Authors
  1. Zhanming Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiangteng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ju Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiangteng Li.

Ethics declarations

Conflict of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, Z., Li, J. & Wang, J. Energy Evolution and Fracture Behavior of Sandstone Under the Coupling Action of Freeze–Thaw Cycles and Fatigue Load. Rock Mech Rock Eng 56, 1321–1341 (2023). https://doi.org/10.1007/s00603-022-03138-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-022-03138-6

Keywords

Search

Navigation