Abstract
To ensure the safe and effective application of deep geotechnical engineering, it is necessary to establish a suitable constitutive model of the rocks in thermal environment, including geothermal energy mining, and deep geological treatment of nuclear waste and tunnel fire. A strain-softening damage model of the rocks with defect growth is established based on damage evolution. According to the change in the tangent modulus from the compression phase to the elastic stage, we established a constitutive model reflecting the nonlinearity characteristics of the compression phase. According to the change in the energy conversion, the energy consumption coefficient is introduced to describe the deformation characteristics of the rocks when the residual stress is reached. The specific physical meaning and the calculation method of the energy consumption coefficient are given to correct the shortcomings of the evolution of the damage variable. We then analyzed the relationship between parameters in the constitutive model of the rocks at high temperature and normal temperature. Based on the constitutive model of the rocks at normal temperature, we established a constitutive model reflecting the influence of high temperature. Finally, the established model fit the stress-strain curves of several kinds of the rocks at different temperatures and generated desired results. The established model can be used to describe the stress-strain curve characteristics of the rocks at different temperatures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ai C, Zhang J, Li YW et al (2016) Estimation criteria for rock brittleness based on energy analysis during the rupturing process. Rock Mech Rock Eng 49:4681–4698. https://doi.org/10.1007/s00603-016-1078-x
Cai M, Kaiser PK, Tasaka Y et al (2004) Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations. Int J Rock Mech Min Sci 41:833–847. https://doi.org/10.1016/j.ijrmms.2004.02.001
Chaki S, Takarli M, Agbodjan WP (2008) Influence of thermal damage on physical properties of a granite rock: porosity, permeability and ultrasonic wave evolutions. Constr Build Mater 22:1456–1461. https://doi.org/10.1016/j.conbuildmat.2007.04.002
Chen GQ, Li TB, Guo F, Wang YK (2017) Brittle mechanical characteristics of hard rock exposed to moisture. Bull Eng Geol Environ (2017) 76:219–230. https://doi.org/10.1007/s10064-016-0857-7
Christian EL, Patricia MP, Clarisa B et al (2017) Mechanical mandible competence in rats with nutritional growth retardation. Arch Oral Biol 80:10–17. https://doi.org/10.1016/j.archoralbio.2017.03.009
David L, Marian M, Isik Y et al (2016) Geodetic monitoring of roads as a tool for determination of hazard zones in areas influenced by deep coal mining. Bull Eng Geol Environ 75:1033–1044. https://doi.org/10.1007/s10064-015-0769-y
Deng J, Gu DS (2011) On a statistical damage constitutive model for rock materials. Comput Geosci 37:122–128. https://doi.org/10.1016/j.cageo.2010.05.018
Dimitriyev AP, Kusyayev LS, Protasov YI, Yamschichikov VS (1969) Physical properties of rocks at high temperature (translated from Russian). Nedra, Moskva
Feng WL, Qiao CS, Niu SJ (2019a) Study on sandstone creep properties of Jushan Mine affected by degree of damage and confining pressure. Bull Eng Geol Environ 79:869–888. https://doi.org/10.1007/s10064-019-01615-x
Feng WL, Qiao CS, Niu SJ et al (2019b) Macro-mechanical properties of saturated sandstone of Jushan Mine under post-peak cyclic loading: an experimental study. Arab J Geosci 12:702. https://doi.org/10.1007/s12517-019-4904-0
Giacomo P, Andrea C, Laura G, Riccardo B (2017) Variability of intact rock mechanical properties for some metamorphic rock types and its implications on the number of test specimens. Bull Eng Geol Environ 76:629–644. https://doi.org/10.1007/s10064-016-0912-4
Giacomo P, Simone M, Giovanna P, Andrea C (2018) Relation between crack initiation-damage stress thresholds and failure strength of intact rock. Bull Eng Geol Environ 77:709–724. https://doi.org/10.1007/s10064-017-1172-7
José JCL, Antenor BP (2004) Linear thermal expansion of granitic rocks: influence of apparent porosity, grain size and quartz content. Bull Eng Geol Environ 63:215–220. https://doi.org/10.1007/s10064-004-0233-x
Kachanov LM (1999) Rupture process under creep conditions. Int J Fract 97:26–31. https://doi.org/10.1023/a:1018671022008
Legendre D, Mazars J (1984) Damage and fracture mechanics for concrete. Fracture 4-10(11):2841–2848. https://doi.org/10.1016/B978-1-4832-8440-8.50301-X
Lemaitre J (1984) How to use damage mechanics. Nucl Eng Des 80:233–245. https://doi.org/10.1016/0029-5493(84)90169-9
Lemaitre J (1985) A continuous damage mechanics model for ductile fracture. J Eng Mater Technol 107:83–89. https://doi.org/10.1115/1.3225775
Li CB, Xie LZ, Ren L, Wang J (2015) Progressive failure constitutive model for softening behavior of rocks based on maximum entropy theory. Environ Earth Sci 73:5905–5915. https://doi.org/10.1007/s12665-015-4228-7
Li DY, Sun Z, Xie T et al (2017) Energy evolution characteristics of hard rock during triaxial failure with different loading and unloading paths. Eng Geol 228:270–281. https://doi.org/10.1016/j.enggeo.2017.08.006
Lin Y, Zhou KP, Gao F, Li JL (2019) Damage evolution behavior and constitutive model of sandstone subjected to chemical corrosion. Bull Eng Geol Environ 3:1–12. https://doi.org/10.1007/s10064-019-01500-7
Lisetta G, Roberto S (2012) History of the exploitation of thermo-mineral resources in Campi Flegrei and Ischia, Italy. J Volcanol Geotherm Res 209-210:19–32. https://doi.org/10.1016/j.jvolgeores.2011.10.004
Liu DQ, Li D, Zhang XY (2017a) A new strain softening damage constitutive model for rocks based on defects growth. Chin J Rock Mech Eng 36:3902–3909. https://doi.org/10.13722/j.cnki.jrme.2017.0934
Liu DQ, Wang Z, Zhang XY (2017b) Characteristics of strain softening of rocks and its damage constitutive model. Rock Soil Mech 38:2901–2908. https://doi.org/10.16285/j.rsm.2017.10.017
Liu DQ, He MC, Cai M (2017c) A damage model for modeling the complete stress–strain relations of brittle rocks under uniaxial compression. Int J Damage Mech:1–20. https://doi.org/10.1177/1056789517720804
Liu DF, Liu CW, Kang YM et al (2018) Mechanical behavior of Benxi Formation limestone under triaxial compression: a new post-peak constitutive model and experimental validation. Bull Eng Geol Environ 77:1701–1715. https://doi.org/10.1007/s10064-017-1193-2
Lu GM, Li YH, Ferri H, Zhang XW (2017) The influence of microwave irradiation on thermal properties of main rock-forming minerals. Appl Therm Eng 112:1523–1532. https://doi.org/10.1016/j.applthermaleng.2016.11.015
Makedon T, Chatzigogos N (2012) Failure mechanism of overhanging slopes in sedimentary rocks with dissimilar mechanical properties. Bull Eng Geol Environ 71:703–708. https://doi.org/10.1007/s10064-012-0441-8
Manish KJ, Verma VK, Sachin M, Ankur C (2016) Study of temperature effect on thermal conductivity of Jhiri shale from Upper Vindhyan, India. Bull Eng Geol Environ 75:1657–1668. https://doi.org/10.1007/s10064-015-0829-3
Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Geomech Abstr 31:643–659. https://doi.org/10.1016/0148-9062(94)90005-1
Mostafa S, Mohsen S, Mohammad SD (2010) Back analysis of an excavated slope failure in highly fractured rock mass: the case study of Kargar slope failure (Iran). Environ Earth Sci 60:183–192. https://doi.org/10.1007/s12665-009-0178-2
Qin BD, He J, Chen LJ (2009) Experimental research on mechanical properties of limestone and sandstone under high temperature. J Geomech 15:254–261 (in Chinese). 1006–6616(2009) 03–0253-09
Rabotnov YN (1960) The theory of creep and its applications. Plasticity 8:338–346. https://doi.org/10.1016/B978-0-08-009459-5.50022-3
Rabotnov YN (1963) On the equations of state for creep. Prog Appl Mech 68:307–315. https://doi.org/10.1243/PIME_CONF_1963_178_030_02
Randi KR, Kirsti M, Heiko TL et al (2015) Thermal conductivity map of the Oslo region based on thermal diffusivity measurements of rock core samples. Bull Eng Geol Environ (2015) 74:1275–1286. https://doi.org/10.1007/s10064-014-0701-x
Stepanov IA (2013) The first law of thermodynamics for auxetic materials. J Non-Cryst Solids 367:51–52. https://doi.org/10.1016/j.jnoncrysol.2013.02.017
Stuart DCW, Ilya NL (2013) Micromechanical modeling of thermal spallation in granitic rock. Int J Heat Mass Transf 65:366–373. https://doi.org/10.1016/j.ijheatmasstransfer.2013.05.043
Sygała A, Bukowska M, Janoszek T (2013) High temperature versus geomechanical parameters of selected rocks – the present state of research. J Sustain Min 12:45–51. https://doi.org/10.7424/jsm130407
Tang FR, Wang LG, Lu YL (2015) Thermophysical properties of coal measure strata under high temperature. Environ Earth Sci 73:6009–6018. https://doi.org/10.1007/s12665-015-4364-0
Tian HM, Chen WZ, Yang DS, Dai YH, Yang JP (2016) Application of the orthogonal design method in geotechnical parameter back analysis for underground structures. Bull Eng Geol Environ 75:239–249. https://doi.org/10.1007/s10064-015-0730-0
Tiskatine R, Eddemani A, Gourdo L et al (2016) Experimental evaluation of thermo-mechanical performances of candidate rocks for use in high temperature thermal storage. Appl Energy 172:243–255. https://doi.org/10.1016/j.apenergy.2016.03.061
Tolga Y, Alexander K, Ozan Y, Metin A, Faruk Y (2018) Second law of thermodynamics is ingrained within quantum mechanics. Results Phys 10:818–821. https://doi.org/10.1016/j.rinp.2018.06.058
Wang ZL, Li YC, Wang JG (2007) A damage-softening statistical constitutive model considering rock residual strength. Comput Geosci 33:1–9. https://doi.org/10.1016/j.cageo.2006.02.011
Winton JG (2018) A review of energy associated with coal bursts. Int J Min Sci Technol 28:755–761. https://doi.org/10.1016/j.ijmst.2018.08.004
Wu G, Wang DY, Zhao ST et al (2012) Test research on mechanical properties of marble under high temperature. Chin J Rock Mech Eng 31(6):1237–1244 (in Chinese)
Wu G, Sun H, Zhai ST (2016) A disturbed state constitution model of rock under high temperature. J Glaciol Geocryol 38:875–879(in Chinese). https://doi.org/10.7522/j.issn.1000-0240.2016.0098
Xu YH, Xu XL (2017) Study on damage constitutive model of rock under high temperature. J Guangxi Univ (Nat Sci Ed) 42:226–236 (in Chinese). https://doi.org/10.13624/j.cnki.issn.1001-7445.2017.0226
You MQ (2011) Strength and damage of marble in ductile failure. J Rock Mech Geotech Eng 3:161–166. https://doi.org/10.3724/SP.J.1235.2011.00161
Zhang CQ, Feng XT, Zhou H, Qiu S, Wu WP (2013) Rockmass damage development following two extremely intense rockbursts in deep tunnels at Jinping II hydropower station, southwestern China. Bull Eng Geol Environ 72:237–247. https://doi.org/10.1007/s10064-013-0470-y
Zhao H, Zhang C, Cao WG et al (2016) Statistical meso-damage model for quasi-brittle rocks to account for damage tolerance principle. Environ Earth Sci 75:862. https://doi.org/10.1007/s12665-016-5681-7
Zhao Y, Yang TH, Yu QL, Zhang PH (2019) Dynamic reduction of rock mass mechanical parameters based on numerical simulation and microseismic data – a case study. Tunn Undergr Space Technol 83:437–451. https://doi.org/10.1016/j.tust.2018.09.018
Acknowledgments
Thanks to Dr. Wang Tan, School of Civil Engineering, University of Birmingham, for the modification of the language of this paper. Thanks to Beijing Jiaotong University’s International Academic Communication Writing Center for the modification of the language of this paper. The authors are grateful to the editors and reviewers for discerning comments on this paper.
Funding
The work presented in this paper was funded by the National Natural Science Foundation of China (No. 51278046, No. 51304068, and No. 51478031).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Feng, Wl., Qiao, Cs., Wang, T. et al. Strain-softening composite damage model of rock under thermal environment. Bull Eng Geol Environ 79, 4321–4333 (2020). https://doi.org/10.1007/s10064-020-01808-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10064-020-01808-9