Technical Papers
Jun 8, 2022

Statistical Damage Constitutive Model for Anhydrite Rock under Freeze–Thaw Cycles Considering the Residual Strength and Postpeak Stress Dropping Rate

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Publication: International Journal of Geomechanics
Volume 22, Issue 8

Abstract

The stability of rock engineering in cold regions is deteriorated by the day–night and seasonal freeze–thaw environments. Therefore, it is crucial to develop a damage constitutive model that can effectively describe the damage evolution and deformation characteristics of rock under freeze–thaw cycles. In this work, a series of laboratory tests were performed to acquire the physical and mechanical evolution characteristics of anhydrite rock subjected to freeze–thaw processes. Experimental results show that as the number of freeze–thaw cycles increases, the triaxial compression strength and elastic modulus of anhydrite rock decrease exponentially, but the mass variation, ductility deformation characteristics, and micropores’ area increase. A new statistical constitutive damage model for anhydrite rock under freeze–thaw cycles considering the residual strength and postpeak stress dropping rate was proposed based on the theory of continuous damage mechanics and Lemaitre’s strain-equivalent principle. The physical meaning of the model parameters m, f0, and n represent the brittleness, ductility, and postpeak stress dropping rate of rock, respectively. Compared with the reference model, the proposed model can effectively reflect the postpeak stress dropping rate and the residual strength of the stress–strain behavior for rock with a minor error. Moreover, it is proved that the proposed model is applicable for other types of rocks with similar damage mechanisms.

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Acknowledgments

This study was financially supported by the Key Technologies Research and Development Program of China (Grant No. 2021YFB3901402) and the National Nature Science Foundation of China (Grant No. 51578091). This support is gratefully acknowledged.

References

Al-Omari, A., K. Beck, X. Brunetaud, A. Torok, and M. Al-Mukhtar. 2015. “Critical degree of saturation: A control factor of freeze–thaw damage of porous limestones at castle of Chambord, France.” Eng. Geol. 185: 71–80. https://doi.org/10.1016/j.enggeo.2014.11.018.
Bao, T., J. Burghardt, V. Gupta, E. Edelman, B. McPherson, and M. White. 2021. “Experimental workflow to estimate model parameters for evaluating long term viscoelastic response of CO2 storage caprocks.” Int. J. Rock Mech. Min. Sci. 146: 104796. https://doi.org/10.1016/j.ijrmms.2021.104796.
Chen, G., Y. Wan, Y. Li, X. J. Pei, and D. Huang. 2021. “Time-dependent damage mechanism of rock deterioration under freeze–thaw cycles linked to alpine hazards.” Nat. Hazard. 108 (1): 635–660. https://doi.org/10.1007/s11069-021-04699-5.
Eslami, J., C. Walbert, A.-L. Beaucour, A. Bourges, and A. Noumowe. 2018. “Influence of physical and mechanical properties on the durability of limestone subjected to freeze–thaw cycles.” Constr. Build. Mater. 162: 420–429. https://doi.org/10.1016/j.conbuildmat.2017.12.031.
Fan, X., J. Xu, and P. Wang. 2018. “Compressive failure characteristics of yellow sandstone subjected to the coupling effects of chemical corrosion and repeated freezing and thawing.” Eng. Geol. 233: 160–171. https://doi.org/10.1016/j.enggeo.2017.12.014.
Freire-Lista, D. M., R. Fort, and M. J. Varas-Muriel. 2015. “Freeze–thaw fracturing in building granites.” Cold Reg. Sci. Technol. 113: 40–51. https://doi.org/10.1016/j.coldregions.2015.01.008.
Fu, H., J. Zhang, Z. Huang, Y. Shi, and W. Chen. 2018. “A statistical model for predicting the triaxial compressive strength of transversely isotropic rocks subjected to freeze–thaw cycling.” Cold Reg. Sci. Technol. 145: 237–248. https://doi.org/10.1016/j.coldregions.2017.11.003.
Gao, F., X. Xiong, C. Xu, and K. Zhou. 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. https://doi.org/10.1016/j.ijrmms.2021.104642.
Ghobadi, M. H., and R. Babazadeh. 2015. “Experimental studies on the effects of cyclic freezing–thawing, salt crystallization, and thermal shock on the physical and mechanical characteristics of selected sandstones.” Rock Mech. Rock Eng. 48: 1001–1016. https://doi.org/10.1007/s00603-014-0609-6.
Grossi, C. M., P. Brimblecombe, and I. Harris. 2007. “Predicting long term freeze–thaw risks on Europe built heritage and archaeological sites in a changing climate.” Sci. Total Environ. 377: 273–281. https://doi.org/10.1016/j.scitotenv.2007.02.014.
Hallet, B. 2006. “Why do freezing rocks break?” Science 314: 1092–1093. https://doi.org/10.1126/science.1135200.
Han, T., Z. Li, and Y. Chen. 2021. “Sulfate attack induced dry–wet failure modes and a constitutive model for mortar specimens with a single intermittent fracture.” Int. J. Geomech. 21 (2): 04020249. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001909.
Hori, M., and H. Morihiro. 1998. “Micromechanical analysis on deterioration due to freezing and thawing in porous brittle materials.” Int. J. Eng. Sci. 36 (4): 511–522. https://doi.org/10.1016/S0020-7225(97)00080-3.
Huang, S., Q. Liu, A. Cheng, and Y. Liu. 2018a. “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.
Huang, S., Q. Liu, A. Cheng, Y. Liu, and G. Liu. 2018b. “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. https://doi.org/10.1016/j.ijrmms.2018.01.029.
Huang, S., Z. Lu, Z. Ye, and Z. Xin. 2020. “An elastoplastic model of frost deformation for the porous rock under freeze–thaw.” Eng. Geol. 278: 105820. https://doi.org/10.1016/j.enggeo.2020.105820.
Ke, B., K. P. Zhou, H. W. Deng, and F. Bin. 2017. “NMR pore structure and dynamic characteristics of sandstone caused by ambient freeze–thaw action.” Shock Vib. 4: 1–10.
Ke, B., K. Zhou, C. Xu, H. Deng, J. Li, and F. Bin. 2018. “Dynamic mechanical property deterioration model of sandstone caused by freeze–thaw weathering.” Rock Mech. Rock Eng. 51 (9): 2791–2804. https://doi.org/10.1007/s00603-018-1495-0.
Khanlari, G., and Y. Abdilor. 2015. “Influence of wet–dry, freeze–thaw, and heat–cool cycles on the physical and mechanical properties of upper Red sandstones in central Iran.” Bull. Eng. Geol. Environ. 74: 1287–1300. https://doi.org/10.1007/s10064-014-0691-8.
Kim, K., J. A. Franklin, A. J. Bowling, P. Lecomte, and H. Grob. 1999. “International society for rock mechanics commission on testing methods.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 24 (1): 53–73.
Lazzarin, P., F. Berto, and M. R. Ayatollahi. 2013. “Brittle failure of inclined key-hole notches in isostatic graphite under in-plane mixed mode loading.” Fatigue Fract. Eng. Mater. Struct. 36: 942–955. https://doi.org/10.1111/ffe.12057.
Lemaitre, J. 2012. A course on damage mechanics. New York: Springer.
Li, J., K. Zhou, W. Liu, and Y. Zhang. 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. https://doi.org/10.1007/s10064-017-1013-8.
Li, M., X. Liu, Y. Li, Z. Hou, and S. Qiao. 2022. “Effect of contact areas on seepage behavior in rough fractures under normal stress.” Int. J. Geomech. 22 (4): 04022019. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002330.
Li, X., W.-G. Cao, and Y.-H. Su. 2012. “A statistical damage constitutive model for softening behavior of rocks.” Eng. Geol. 143-144: 1–17. https://doi.org/10.1016/j.enggeo.2012.05.005.
Liu, Q., Z. Qian, and Z. Wu. 2019. “Micro/macro physical and mechanical variation of red sandstone subjected to cyclic heating and cooling: An experimental study.” Bull. Eng. Geol. Environ. 78: 1485–1499. https://doi.org/10.1007/s10064-017-1196-z.
Luo, X., N. Jiang, C. Zuo, Z. Dai, and S. Yan. 2014. “Damage characteristics of altered and unaltered diabases subjected to extremely cold freeze–thaw cycles.” Rock Mech. Rock Eng. 47: 1997–2004. https://doi.org/10.1007/s00603-013-0516-2.
Momeni, A., Y. Abdilor, G. R. Khanlari, M. Heidari, and A. A. Sepahi. 2016. “The effect of freeze–thaw cycles on physical and mechanical properties of granitoid hard rocks.” Bull. Eng. Geol. Environ. 75 (4): 1649–1656. https://doi.org/10.1007/s10064-015-0787-9.
Mousavi, S. Z. S., H. Tavakoli, P. Moarefvand, and M. Rezaei. 2019. “Assessing the effect of freezing–thawing cycles on the results of the triaxial compressive strength test for calc-schist rock.” Int. J. Rock Mech. Min. Sci. 123: 104090. https://doi.org/10.1016/j.ijrmms.2019.104090.
Mousavi, S. Z. S., H. Tavakoli, P. Moarefvand, and M. Rezaei. 2020. “Micro-structural, petro-graphical and mechanical studies of schist rocks under the freezing–thawing cycles.” Cold Reg. Sci. Technol. 174: 103039. https://doi.org/10.1016/j.coldregions.2020.103039.
Nicholson, D. T., and F. H. Nicholson. 2000. “Physical deterioration of sedimentary rocks subjected to experimental freeze–thaw weathering.” Earth Surf. Processes Landforms 25 (12): 1295–1307. https://doi.org/10.1002/1096-9837(200011)25:12%3C1295::AID-ESP138%3E3.0.CO;2-E.
Park, E.-S., Y.-B. Jung, W.-K. Song, D.-H. Lee, and S.-K. Chung. 2010. “Pilot study on the underground lined rock cavern for LNG storage.” Eng. Geol. 116 (1): 44–52. https://doi.org/10.1016/j.enggeo.2010.07.006.
Park, J., C.-U. Hyun, and H.-D. Park. 2014. “Changes in microstructure and physical properties of rocks caused by artificial freeze–thaw action.” Bull. Eng. Geol. Environ. 74 (2): 555–565. https://doi.org/10.1007/s10064-014-0630-8.
Sabatakakis, N., G. Koukis, G. Tsiambaos, and S. Papanakli. 2008. “Index properties and strength variation controlled by microstructure for sedimentary rocks.” Eng. Geol. 97 (1-2): 80–90. https://doi.org/10.1016/j.enggeo.2007.12.004.
Serafeimidis, K., and G. Anagnostou. 2015. “The solubilities and thermodynamic equilibrium of anhydrite and gypsum.” Rock Mech. Rock Eng. 48 (1): 15–31. https://doi.org/10.1007/s00603-014-0557-1.
Shen, P., H. Tang, Y. Ning, and D. Xia. 2019. “A damage mechanics based on the constitutive model for strain-softening rocks.” Eng. Fract. Mech. 216: 106521. https://doi.org/10.1016/j.engfracmech.2019.106521.
Sun, Y., C. Zhai, J. Xu, Y. Cong, L. Qin, and C. Zhao. 2020. “Characterisation and evolution of the full size range of pores and fractures in rocks under freeze–thaw conditions using nuclear magnetic resonance and three-dimensional X-ray microscopy.” Eng. Geol. 271: 105616. https://doi.org/10.1016/j.enggeo.2020.105616.
Tan, X., W. Chen, D. Yang, Y. Dai, G. Wu, J. Yang, H. Yu, H. Tian, and W. Zhao. 2014. “Study on the influence of airflow on the temperature of the surrounding rock in a cold region tunnel and its application to insulation layer design.” Appl. Therm. Eng. 67 (1): 320–334. https://doi.org/10.1016/j.applthermaleng.2014.03.016.
Tan, X., W. Chen, J. Yang, and J. Gao. 2011. “Laboratory investigations on the mechanical properties degradation of granite under freeze–thaw cycles.” Cold Reg. Sci. Technol. 68 (3): 130–138. https://doi.org/10.1016/j.coldregions.2011.05.007.
Wang, P., J. Xu, S. Liu, and H. Wang. 2016. “Dynamic mechanical properties and deterioration of red-sandstone subjected to repeated thermal shocks.” Eng. Geol. 212: 44–52. https://doi.org/10.1016/j.enggeo.2016.07.015.
Wang, Y., S. H. Gao, C. H. Li, and J. Q. Han. 2020. “Investigation on fracture behaviors and damage evolution modeling of freeze-thawed marble subjected to increasing-amplitude cyclic loads.” Theor. Appl. Fract. Mech. 109 (2): 102679. https://doi.org/10.1016/j.tafmec.2020.102679.
Xu, J., H. Pu, and Z. Sha. 2021. “Mechanical behavior and decay model of the sandstone in Urumqi under coupling of freeze–thaw and dynamic loading.” Bull. Eng. Geol. Environ. 80 (4): 2963–2978. https://doi.org/10.1007/s10064-021-02133-5.
YRSRI (Yangtze River Scientific Research Institute). 2001. Specifications for rock tests in water conservancy and hydroelectric engineering. [In Chinese.]. SL264-2001. Beijing: China Water Power Press.
Zhang, C., and Y. Bai. 2020. “Research on the establishment and application of parameter oriented geometric damage model for rocks.” [In Chinese.]. Rock Soil Mech. 41 (12): 3899–3909.
Zhang, H. M., X. Z. Meng, C. Peng, G. S. Yang, W. J. Ye, Y. J. Shen, and H. Liu. 2018. “Freeze–thaw damage model and parameters of rock deformation in whole process.” [In Chinese.]. J. Xi’an Univ. Sci. Tech. 38 (2): 260–265.
Zhang, H., X. Meng, and G. Yang. 2020. “A study on mechanical properties and damage model of rock subjected to freeze–thaw cycles and confining pressure.” Cold Reg. Sci. Technol. 174: 103056. https://doi.org/10.1016/j.coldregions.2020.103056.
Zhang, H. M., X. Z. Meng, C. Peng, G. S. Yang, W. J. Ye, Y. J. Shen, and H. Liu. 2019a. “Rock damage constitutive model based on residual intensity characteristics under freeze–thaw and load.” [In Chinese.]. J. China Coal Soci. 44 (11): 3404–3411.
Zhang, H. M., and G. S. Yang. 2010. “Research on damage model of rock under coupling action of freeze–thaw and load.” Chin. J. Rock Mech. Eng. 29 (3): 471–476.
Zhang, H. M., C. Yuan, G. S. Yang, L. Y. Wu, and C. Peng. 2019b. “A novel constitutive modeling approach measured under simulated freeze–thaw cycles for the rock failure.” Eng. Comput. 35 (3): 1–14.
Zhou, S. T., N. Jiang, X. D. Luo, W. Fang, and X. He. 2020. “Uniaxial compression fractal damage constitutive model of rock subjected to freezing and thawing.” Period. Polytech., Civ. Eng. 64 (2): 500.
Zhu, Z.-n., H. Tian, G.-s. Jiang, and W. Cheng. 2018. “Effects of high temperature on the mechanical properties of Chinese marble.” Rock Mech. Rock Eng. 51: 1937–1942. https://doi.org/10.1007/s00603-018-1426-0.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 22Issue 8August 2022

History

Received: Dec 14, 2021
Accepted: Apr 24, 2022
Published online: Jun 8, 2022
Published in print: Aug 1, 2022
Discussion open until: Nov 8, 2022

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Ph.D. Student, School of Civil Engineering, Chongqing Univ., Chongqing 400044, PR China. Email: [email protected]
Xiaoguang Jin [email protected]
Professor, School of Civil Engineering, Chongqing Univ., Chongqing 400044, PR China; Key Laboratory of New Technology for Construction of Cities in Mountain Area of the Ministry of Education, Chongqing Univ., Chongqing 400044, PR China; State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing Univ., Chongqing 400044, PR China (corresponding author). Email: [email protected]
Ph.D. Student, School of Civil Engineering, Chongqing Univ., Chongqing 400044, PR China. Email: [email protected]
Ph.D. Student, School of Civil Engineering, Chongqing Univ., Chongqing 400044, PR China. Email: [email protected]

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  • Experimental Investigation on Fracture Behavior and Mechanical Properties of Red Sandstone Subjected to Freeze–Thaw Cycles, Sustainability, 10.3390/su142114155, 14, 21, (14155), (2022).

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