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Analytical and numerical analysis for frost heaving stress distribution within rock joints under freezing and thawing cycles

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Abstract

Water-bearing joints within rock engineering in cold areas are often subjected to frost heaving force in cold season due to water–ice phase transition. To evaluate the damage and stability of rock mass in cold regions, a 3D model that considers moisture migration loss during freezing and thawing was established to study the characteristics of frost heaving force within joints. Then, the numerical simulation of cyclic freeze-thawing of water-bearing joints was carried out through equivalent expansion coefficient and particle flow calculation methods. The distribution of frost heaving force in and around the joints was obtained. According to the results of the numerical tests and theoretical calculations, the frost heaving force in joints is basically stable, the tensile stress concentration area appears at the joint tip, and the frost heaving force decreases gradually away from the jointed rock mass area. The frost heaving force decreases considerably with increasing cycle number and moisture migration loss but it increases with increasing mechanical strength and joint geometric size of rock and ice. The comparison between the numerical solution of the equivalent expansion coefficient method and the theoretical solution shows that the force size and distribution law of frost heaving for the two methods are consistent.

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References

  • AlirezaAgharazi DC, Tannant D (2012) A three-dimensional equivalent continuum constitutive model for jointed rock masses containing up to three random joint sets. Geomechan Geoeng 7:227–238

    Article  Google Scholar 

  • Altindag R, Alyildiz IS, Onargan T (2004) Mechanical property degradation of ignimbrite subjected to recurrent freeze–thaw cycles. Int J Rock Mech Min Sci 41:1023–1028

    Article  Google Scholar 

  • Antes H (1985) A boundary element procedure for transient wave propagations in two-dimensional isotropic elastic media. Finite Elem Anal Des 1:313–322

    Article  Google Scholar 

  • Arosio D, Longoni L, Mazza F (2013) Freeze-thaw cycle and rockfall monitoring. Landslide science and practice:385–390

  • Binal A (2009) A new laboratory rock test based on freeze-thaw using a steel chamber. Q J Eng GeolHydrogeol 42:179–198

    Article  Google Scholar 

  • Bost M, Pouya A (2017) Stress generated by the freeze–thaw process in open cracks of rock walls: empirical model for tight limestone. Bull Eng Geol Env 76:1491–1505. https://doi.org/10.1007/s10064-016-0955-6

    Article  Google Scholar 

  • Bouchat A, Tremblay B (2017) Using sea-ice deformation fields to constrain the mechanical strength parameters of geophysical sea ice. J Geophys Res 122:5802–5825

    Article  Google Scholar 

  • Cao R-h, Cao P, Lin H (2018) Failure characteristics of intermittent fissures under a compressive-shear test: Experimental and numerical analyses. Theoret Appl Fract Mech 96:740–757. https://doi.org/10.1016/j.tafmec.2017.11.002

    Article  Google Scholar 

  • Chen H, Fan X, Lai H, Xie Y, He Z (2019) Experimental and numerical study of granite blocks containing two side flaws and a tunnel-shaped opening. Theoret Appl Fract Mech 104:102394. https://doi.org/10.1016/j.tafmec.2019.102394

    Article  Google Scholar 

  • Chen Y, Yang YG, Gao F, Zhang XX (2018) Researches on damage evolution and acoustic emission characteristics of rocks. Advan Civil Eng. https://doi.org/10.1155/2018/3108065

    Article  Google Scholar 

  • Davidson GP, Nye JF (1985) A photoelastic study of ice pressure in rock cracks. Cold Reg Sci Technol 11:141–153

    Article  Google Scholar 

  • Fan X, Li K, Lai H, Xie Y, Cao R, Zheng J (2018a) Internal stress distribution and cracking around flaws and openings of rock block under uniaxial compression: A particle mechanics approach. Computers & Geotechnics

  • Fan X, Li K, Lai H, Zhao Q, Sun Z (2018) Experimental and numerical study of the failure behavior of intermittent rock joints subjected to direct shear load. Advan Civil Eng 2018:19. https://doi.org/10.1155/2018/4294501

    Article  Google Scholar 

  • Hetnarski RB, Ignaczak J (2006) Mathematical theory of elasticity. MCGRAW-HILL

  • Hori M, Morihiro H (1998) Micromechanical analysis on deterioration due to freezing and thawing in porous brittle materials. Int J Eng Sci 36:511–522

    Article  Google Scholar 

  • Huang S, Liu Q, Cheng A, Liu Y (2018) A statistical damage constitutive model under freeze-thaw and loading for rock and its engineering application. Cold Reg Sci Technol 145:142–150. https://doi.org/10.1016/j.coldregions.2017.10.015

    Article  Google Scholar 

  • Huang S, Liu Q, Cheng A, Liu Y, Liu G (2018) A fully coupled thermo-hydro-mechanical model including the determination of coupling parameters for freezing rock. Int J Rock Mech Min Sci 103:205–214

    Article  Google Scholar 

  • Huang SB, Liu QS, Cheng AP, Liu YZ (2018) A coupled hydro-thermal model of fractured rock mass under low temperature and its numerical analysis. Rock Soil Mechan 39:735–744

    Google Scholar 

  • Jiang C, Zhang Z, He J (2020) Nonlinear analysis of combined loaded rigid piles in cohesionless soil slope. Comput Geotech 117: https://doi.org/10.1016/j.compgeo.2019.103225

    Article  Google Scholar 

  • Kang Y, Liu Q, Huang S (2013) A fully coupled thermo-hydro-mechanical model for rock mass under freezing/thawing condition. Cold Reg Sci Technol 95:19–26

    Article  Google Scholar 

  • Krautblatter M, Funk D, Günzel FK (2013) Why permafrost rocks become unstable: a rock–ice-mechanical model in time and space. Earth Surf Proc Land 38:876–887

    Article  Google Scholar 

  • Lei D, Lin H, Chen Y, Cao R, Wen Z (2019) Effect of cyclic freezing-thawing on the shear mechanical characteristics of nonpersistent joints. Advan Materials Sci Eng 2019:14. https://doi.org/10.1155/2019/9867681

    Article  Google Scholar 

  • Li JL, Zhou KP, Liu WJ, Deng HW (2016) NMR research on deterioration characteristics of microscopic structure of sandstones in freeze–thaw cycles. Transac Nonferrous Metals Soc China 26:2997–3003

    Article  Google Scholar 

  • Li K, Cheng Y, Yin ZY, Han DY, Meng JJ (2020) Size effects in a transversely isotropic rock under brazilian tests: laboratory testing. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-020-02058-7

    Article  Google Scholar 

  • Li QL, Ling XZ, Hu JJ, Xu XT (2018) Experimental investigation on dilatancy behavior of frozen silty clay subjected to long-term cyclic loading. Cold Reg Sci Technol 153:156–163. https://doi.org/10.1016/j.coldregions.2018.05.008

    Article  Google Scholar 

  • Lin H, Yang H, Wang Y, Zhao Y, Cao R (2019) Determination of the stress field and crack initiation angle of an open flaw tip under uniaxial compression. Theoret Appl Fract Mech 104:102358. https://doi.org/10.1016/j.tafmec.2019.102358

    Article  Google Scholar 

  • Lin H, Zhang X, Cao R, Wen Z (2020) Improved nonlinear Burgers shear creep model based on the time-dependent shear strength for rock. Environm Earth Sci 79:149. https://doi.org/10.1007/s12665-020-8896-6

    Article  Google Scholar 

  • Lin H, Zhu Y, Yang J, Wen ZJ (2020) Anchor stress and deformation of the bolted joint under shearing. Advan Civil Eng 2020:3696489. https://doi.org/10.1155/2020/3696489

    Article  Google Scholar 

  • Liu J, Wang J, Wan W (2018) Numerical study of crack propagation in an indented rock specimen. Comput Geotech 96:1–11. https://doi.org/10.1016/j.compgeo.2017.10.014

    Article  Google Scholar 

  • Liu QS, Huang SB, Kang YS, Yang P, Cui XZ (2015) Numerical and theoretical studies on frost heaving pressure in a single fracture of frozen rock mass under low temperature. Chinese J Geotech Eng 37:1572–1580

    Google Scholar 

  • Matsuoka N (2010) Direct observation of frost wedging in alpine bedrock. Earth Surf Proc Land 26:601–614

    Article  Google Scholar 

  • Matsuoka N, Sakai H (1999) Rockfall activity from an alpine cliff during thawing periods. Geomorphology 28:309–328

    Article  Google Scholar 

  • Mu JQ, Pei XJ, Huang RQ, Rengers N, Zou XQ (2017) Degradation characteristics of shear strength of joints in three rock types due to cyclic freezing and thawing. Cold Reg Sci Technol 138:91–97

    Article  Google Scholar 

  • Naderloo M, Moosavi M, Ahmadi M (2019) Using acoustic emission technique to monitor damage progress around joints in brittle materials. Theoret Appl Fract Mech 104:102368. https://doi.org/10.1016/j.tafmec.2019.102368

    Article  Google Scholar 

  • Neaupane KM, Yamabe T, Yoshinaka R (1999) Simulation of a fully coupled thermo–hydro–mechanical system in freezing and thawing rock. Int J Rock Mech Min Sci 36:563–580

    Article  Google Scholar 

  • Ng KLA, Small JC (1997) Behavior of joints and interfaces subjected to water pressure. Comput Geotech 20:71–93

    Article  Google Scholar 

  • Ping M, Li Y (2017) Estimating the three-dimensional joint roughness coefficient value of rock fractures. Bulletin of Engineering Geology & the Environment:857–866

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

    Article  Google Scholar 

  • Shen Y, Yang H, Xi J, Yang Y, Yongzhi W, Wei X (2019) A novel shearing fracture morphology method to assess the influence of freeze–thaw actions on concrete–granite interface. Cold Reg Sci Technol 169:102900. https://doi.org/10.1016/j.coldregions.2019.102900

    Article  Google Scholar 

  • Shen YJ, Yang GS, Huang HW, Rong TL, Jia HL (2018) The impact of environmental temperature change on the interior temperature of quasi-sandstone in cold region: Experiment and numerical simulation. Eng Geol 239:241–253

    Article  Google Scholar 

  • Štefane P, Naib S, Hertelé S, De Waele W, Gubeljak N (2019) Crack tip constraint analysis in welded joints with pronounced strength and toughness heterogeneity. Theoret Appl Fract Mech 103:102293. https://doi.org/10.1016/j.tafmec.2019.102293

    Article  Google Scholar 

  • Wang M, Cao P, Chen Y (2017) Anisotropy of rock profile JRC values and its empirical formula: a case study on yellow rust granite. Geotech Geol Eng 35:1645–1655. https://doi.org/10.1007/s10706-017-0199-7

    Article  Google Scholar 

  • Wang Y, Lin H, Zhao Y, Li X, Guo P, Liu Y (2019) Analysis of fracturing characteristics of unconfined rock plate under edge-on impact loading. Eur J Environ Civil Eng 23:1–16. https://doi.org/10.1080/19648189.2018.1509021

    Article  Google Scholar 

  • Wang Y, Zhang H, Lin H, Zhao Y, Liu Y (2020) Fracture behaviour of central-flawed rock plate under uniaxial compression. Theoret Appl Fract Mech 106:102503. https://doi.org/10.1016/j.tafmec.2020.102503

    Article  Google Scholar 

  • Winkler EM (1968) Frost damage to stone and concrete: geological considerations. Eng Geol 2:315–323

    Article  Google Scholar 

  • Xie S, Lin H, Chen Y, Yong R, Xiong W, Du S (2020) A damage constitutive model for shear behavior of joints based on determination of the yield point. Int J Rock Mech Min Sci 128:104269. https://doi.org/10.1016/j.ijrmms.2020.104269

    Article  Google Scholar 

  • Xie S, Lin H, Wang Y, Chen Y, Xiong W, Zhao Y, Du S (2020) A statistical damage constitutive model considering whole joint shear deformation. Int J Damage Mech 29:1056789519900778. https://doi.org/10.1177/1056789519900778

    Article  Google Scholar 

  • Xing K, Zhou Z, Yang H, Liu B (2018) Macro–meso freeze–thaw damage mechanism of soil–rock mixtures with different rock contents. International Journal of Pavement Engineering:1–11

  • Yong R, Ye J, Li B, Du SG (2018) Determining the maximum sampling interval in rock joint roughness measurements using Fourier series. Int J Rock Mech Min Sci 101:78–88

    Article  Google Scholar 

  • Zhang C, Zou P, Wang Y, Jiang T, Lin H, Cao P (2020) An elasto-visco-plastic model based on stress functions for deformation and damage of water-saturated rocks during the freeze-thaw process. Constr Build Mater 250:118862. https://doi.org/10.1016/j.conbuildmat.2020.118862

    Article  Google Scholar 

  • Zhang CY, Lin H, Qiu CM, Jiang TT, Zhang JH (2020) The effect of cross-section shape on deformation, damage and failure of rock-like materials under uniaxial compression from both a macro and micro viewpoint. Int J Damage Mech 20:1–20. https://doi.org/10.1177/1056789520904119

    Article  Google Scholar 

  • Zhao Y, Tang J, Chen Y, Zhang L, Wang W, Wan W, Liao J (2017) Hydromechanical coupling tests for mechanical and permeability characteristics of fractured limestone in complete stress-strain process. Environm Earth Sci 76:24. https://doi.org/10.1007/s12665-016-6322-x

    Article  Google Scholar 

  • Zhao Y, Wang Y, Wang W, Tang L, Liu Q, Cheng G (2019) Modeling of rheological fracture behavior of rock cracks subjected to hydraulic pressure and far field stresses. Theoret Appl Fract Mech 101:59–66

    Article  Google Scholar 

  • Zhou KP, Li B, Li J-L, Deng HW, Feng B (2015) Microscopic damage and dynamic mechanical properties of rock under freeze–thaw environment. Trans Nonferrous Metals Soc China 25:1254–1261

    Article  Google Scholar 

  • Zhu HG, Jiang YD, Yi C, Xie HP (2014) A new geometrical model of fluid flow in rockfractures for valid application of the cubic law. Appl Mechan Materials 580–583:6

    Google Scholar 

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Acknowledgement

This paper gets its funding from project (51774322) supported by National Natural Science Foundation of China; Project (2018JJ2500) supported by Hunan Provincial Natural Science Foundation of China. Project (2018zzts209) supported by the fundamental Research Funds for the Central Universities of Central South University. The authors wish to acknowledge these supports. The anonymous reviewer are gratefully acknowledged for his valuable comments on the manuscript.

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Authors and Affiliations

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

    Hang Lin, Daxing Lei & Chong Jiang

  2. School of Civil and Environmental Engineering, Ningbo University, Ningbo, 315211, Zhejiang, China

    Rui Yong & Shigui Du

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  1. Hang Lin
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  2. Daxing Lei
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Correspondence to Hang Lin or Chong Jiang.

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Lin, H., Lei, D., Yong, R. et al. Analytical and numerical analysis for frost heaving stress distribution within rock joints under freezing and thawing cycles. Environ Earth Sci 79, 305 (2020). https://doi.org/10.1007/s12665-020-09051-x

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