Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Mechanical damage evolution and a statistical damage constitutive model for water-weak sandstone and mudstone

  • Lu yuan Wu (School of Civil Engineering and Architecture, Henan University) ;
  • Fei Ding (School of Civil Engineering and Architecture, Henan University) ;
  • Jian hui Li (School of Civil Engineering and Architecture, Henan University) ;
  • Wei Qiao (School of Resources and Earth Sciences, China University of Mining and Technology)
  • Received : 2023.09.05
  • Accepted : 2024.06.26
  • Published : 2024.07.10
⟨ Previous Next ⟩

Abstract

The weakening effect of water on rocks is one of the main factors inducing deformation and failure in rock engineering. To clarify this weakening effect, immersion tests and post-immersion triaxial compression tests were conducted on sandstone and mudstone. The results showed that the strength of water-immersed sandstone decreases with increasing immersion time, exhibiting an exponential relationship. Similarly, the strength of water-immersed mudstone decreases with increasing environmental humidity, also following an exponential relationship. Subsequently, a statistical damage model for water-weakened rocks was proposed, changes in elastic modulus to describe the weakening effect of water. The model effectively simulated the stress-strain relationships of water-affected sandstone and mudstone under compression. The R2 values between the theoretical and experimental peak values ranged from 0.962 to 0.996, and the MAPE values fell between 3.589% and 9.166%, demonstrating the model's effectiveness and reliability. The damage process of water-saturated rocks corresponds to five stages: compaction stage - no damage, elastic stage - minor damage, crack development stage - rapid damage increase, post-peak residual stage - continuous damage increase, and sliding stage - damage completion. This study provides a foundational reference for researching the fracture characteristics of overlying strata during coal mining under complex hydrogeological conditions.

Keywords

Acknowledgement

All authors contributed to the study conception and design. This work is supported by Henan Natural Science Foundation Youth Fund Project (No.232300421331),Key Scientific Research Projects of Colleges and Universities in Henan Province (No.23A440005) and Postdoctoral Research Grant in Henan Province (No.202103049), China Postdoctoral Science Foundation (2023M741009).

References

  1. Bian, K., Liu, J., Zhang, W., Zheng, X., Ni, S. and Liu, Z. (2019), "Mechanical behavior and damage constitutive model of rock subjected to water-weakening effect and uniaxial loading", Rock Mech. Rock Eng., 52(1), 97-106. https://doi.org/10.1007/s00603-018-1580-4.
  2. Cai, X., Zhou, Z., Liu, K., Du, X. and Zang, H. (2019), "Water-weakening effects the on mechanical behavior of different rock types:Phenomena and mechanisms", Appl. Sci., 9(20). https://doi.org/10.3390/app9204450.
  3. Cao, W.G., Fang, Z.L. and Tang, X.J. (1998), "Research on statistical constitutive models for rock damage and softening", J. Rock Mech. Eng., 17(6):628-633.
  4. Chen,Y., Xiao, P., Du, X., Wang, S., Fernandez-Steeger, T.M. and Azzam, R. (2021), "Study on damage constitutive model of rock under freeze-thaw-confining pressureacid erosion", Appl. Sci., 11(20), 9431. https://doi.org/10.3390/APP11209431
  5. Deng, H., Hu, A., Li, J., Zhang, X., Hu, Y., Chang, D. and Zhu, D. (2017), "Statistical constitutive model for sandstone degradation and damage under water rock interaction", Geotech. Mech., 38(3), 631-639. https://doi.org/10.16285/j.rsm.2017.03.003.
  6. Dyke, C.G. and Dobereiner, L. (1991), "Evaluating the strength and deformability of sandstones", Int. J. Rock Mech. Min. Sci. Geomech. Abstracts, 28(1), 123-134. https://doi.org/10.1144/GSL.QJEG.1991.024.01.13.
  7. Feng, X.T., Chen, S. and Li, S. (2001), "Effects of water chemistry on microcracking and compressive strength of granite - sciencedirect", Int. J. Rock Mech. Min. Sci.s, 38(4), 557-568. https://doi.org/10.1016/S1365-1609(01)00016-8.
  8. He, Z., Zhu, Z., Ruan, H. and Dai, B. (2019), "Research on statistical damage constitutive model of rock under water pressure", J. Yangtze River Academy Sci., 36(6), 6. https://doi.org/10.11988/ckyyb.20171328.
  9. Huang, X., Yang, C., Liu, J., He, X., Chen, J. and Duan, X. (2008), "Creep tests of mudstone under different water content conditions and their impact on casing damage in oil fields", J. Rock Mech. Eng., 27(2), 3477-3482. https://doi.org/10.3321/j.issn:1000-6915.2008.z2.026.
  10. Jean Lemaitre, T.B.N.J. and Chunhu, T. (1996), Damage mechanics Course, Science Press, Beijing, China.
  11. Jiang, J., Hou, Z.M., Hou, K.P., Lu, Y.F., Sun, H.F. and Niu, X.D. (2009), "The damage constitutive model of sandstone under water-rock coupling", J. Rock Mech. Eng., 28(1), 2637-2643. https://doi.org/10.3321/j.issn:1000-6915.2009.z1.007.
  12. Kim, E., Stine, M.A., de Oliveira, D.B.M. and Changani, H. (2017), "Correlations between the physical and mechanical properties of sandstones with changes of water content and loading rates", Int. J. Rock Mech. Min. Sci., 100, 255-262. https://doi.org/10.1016/j.ijrmms.2017.11.00595.
  13. Krajcinovic, D. and Silva, M.A.G. (1982), "Statistical aspects of the continuous damage theory", Int. J. Solids Struct., 18(7): 551-562. https://doi.org/10.1016/0020-7683(82)90039-7.
  14. Li, T., Chen, Z., Chen, G., Ma, C., Tang, O. and Wang, M. (2015), "Research on the energy mechanism of sandstone under different water content effects", Geotech. Mech., 36(2), 229-236. https://doi.org/10.16285/j.rsm.2015.S2.030.
  15. Li, X., Che, X., Li, H. and Qi, C. (2023), "A meso-macro method of evaluating water content effect on direct tensile fracture in brittle rocks", KSCE J. Civil Eng., 28(4), 1513-1521. https://doi.org/10.1007/S12205-023-0255-1.
  16. Li, Z., Liu. S., Ren. W., Fang, J., Zhu, Q. and Dun, Z. (2020), "Multiscale laboratory study and numerical analysis of water-weakening effect on shale", Adv. Mater. Sci. Eng., 2020(7), 1-14. https://doi.org/10.1155/2020/5263431.
  17. Liu, B., Yu, M., Sun, J., Huang, R. and Deng, T. (2023), "Study on mechanical properties and damage constitutive model of shale under water force coupling cooperation", J. Rock Mech. Eng., 42, 1-14. https://doi.org/10.13722/j.cnki.jrme.2022.0655.
  18. Liu, J., Zhu, X., Xu, L. and Zhang, S. (2021), "Study on the damage evolution law of granite after high temperature cooling", Coal Technology, 40(2), 30-33. https://doi.org/10.13301/ j. cnki.ct.2021.02.009.
  19. Ma, D., Cai, X., Li, Q. and Duan, H. (2018), "In-situ and numerical investigation of groundwater inrush hazard from grouted karst collapse pillar in longwall mining", Water, 10(9): 1187-1187. https://doi.org/10.3390/w10091187.
  20. Ma, T., Yang, C., Chen, P., Wang, X. and Guo, Y. (2016), "On the damage constitutive model for hydrated shale using ct scanning technology", J. Natural Gas Sci. Eng., 28, 204-214. https://doi.org/10.1016/j.jngse.2015.11.025.
  21. Meng, Z., Pan, J., Liu, L., Meng, G. and Zhao, Z. (2009), "The influence of water content on the mechanical properties and impact tendency of sedimentary rocks", J. Rock Mech. Eng., 28(1), 2637-2643. https://doi.org/10.3321/j.issn:1000-6915.2009.z1.007.
  22. Miao, F., Wu, Y .,Akos T , Li, L. and Xue, Y. (2022), "Centrifugal model test on a riverine landslide in the Three Gorges Reservoir induced by rainfall and water level fluctuation", Geosci. Front., 13(3), 101378. https://doi.org/10.1016/j.gsf.2022.101378.
  23. Mousavi S, Tavakoli H, Moarefvand P. and Rezaei, M. (2020a), "Evaluating the effect of freezing-thawing cycles on the compressional wavevelocity and dry density of schist rock (case study: Angouran mine)", Appl. Geol., 10(2020), 15-30. https://doi.org/10.22055/AAG.2019.28197.1922.
  24. Mousavi, S.Z.S. and Rezaei, M. (2022), "Correlation assessment between degradation ratios of ucs and non-destructive properties of rock under freezingthawing cycles", Geoderma, 428(116209). https://doi.org/10.1016/j.geoderma.2022.116209.
  25. Mousavi, S.Z.S., Tavakoli, H., Moarefvand, P. and Rezaei, M. (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.
  26. Mousavi S.Z.S., Tavakoli, H., Moarefvand, P. and Rezaei, M. (2020b), "Micro-structural, petro- graphical and mechanical studies of schist rocks under the freezingthawing cycles", Cold Reg. Sci. Technol., 174(103039). https://doi.org/10.1016/j.coldregions.2020.103039.
  27. Olena S. (2019), "Water effect on the rocks and mine roadways stability" E3S Web of Conferences, 109, 1-7. https://doi.org/10.1051/e3sconf/201910900092.
  28. Pan, J.L., Cai, M.f., Li, P. and Guo, Q. (2022), "A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression", J. Central South Univ., 29, 1-13. https://doi.org/10.1007/S11771-022-4949-1.
  29. Peng, Y. (2018), "Research on statistical constitutive model of rock damage under triaxial compression", Technol. Innov. Appl., (24), 2. https://doi.org/CNKI:SUN:CXYY.0.2018-24-017.
  30. Qi, X., Tian, A., Luo, X., and Tang, Q. (2022), "Chemical damage constitutive model establishment and the energy analysis of rocks under water-rock interaction", Energies, 15(24), 9386-9386. https://doi.org/10.3390/EN15249386.
  31. Qin, Y. (2001), "Discussion on damage mechanics model of rock and its constitutive equation", J. Rock Nech. Eng., 20(4), 3. https://doi.org/10.3321/j.issn:1000-6915.2001.04.028.
  32. Rabotnov, Y.N. (1963), "On the equations of state for creep", Progress Appl. Mech., 178, 307-315.
  33. Seyed Mousavi, S.Z., Tavakoli, H., Moarefvand, P. and Rezaei, M. (2020), "Evaluating the variations of density and durability index of schist rock under the effect of freezing-thawing cycles", Iranian Soc. Min. Eng., 14(45), 1-12. https://doi.org/10.22034/IJME.2020.37382.
  34. Shi, W., Cai, W., Meng, Y., Li, G., Wnn, K. and Zhang, Y. (2016), "Weakening laws of rock uniaxial compressive strength with consideration of water content and rock porosity", Arabian J. Geosci., 9(5), 369-369. https://doi.org/10.1007/s12517-016-2426-6.
  35. Song, H., Li, S., Zhang, Q., Guo, Y. and Xu, G. (2024), "A study on the characteristics of acoustic emission stage and damage evolution of cement containing sandstone", J. Undergr. Sp. Eng., 20(1), 72-81.
  36. Sun, B., Yang, H., Zeng, S., Yin, Y. and Fan, J. (2023), "Crack initiation mechanism and meso- crack evolution of pre-fabricated cracked sandstone specimens under uniaxial loading", Geomech. Eng., 33(6), 597-609. https://doi.org/10.12989/gae.2023.33.6.597.
  37. Sun, Z., Zhang, Q., Ju, Z., Zhang, Y. and Wang, P. (2023b), "A study of constitutive model of rock damage under the joint effect of load and moisture", Appl. Sci., 13(2). https://doi.org/10.3390/APP13021224.
  38. Wang, S., Qi, X., Fu, P., et al. (2022), "Study on constitutive relationship of composite rock considering temperature damage", Min. Res. Development, 42(12), 8. https://doi.org/10.13827/j.cnki.kyyk.2022.12.012.
  39. Wang, Y., Liu, X., Liang,, L. and Ziong, J. (2020), "Experimental study on the damage of organic-rich shale during water-shale interaction", J. Natural Gas Sci. Eng., 74, 103103. https://doi.org/10.1016/j.jngse.2019.103103.
  40. Wasantha, P. and Ranjith, P. (2014), "Water-weakening behavior of hawkesbury sandstone in brittle regime", Eng. Geol., 178, 91-101. https://doi.org/10.1016/j.enggeo.2014.05.015.
  41. Wong, F. (2013), "Research on rock statistical damage constitutive model based on triaxial compression test", MS, Tsinghua University, Beijing.
  42. Wu, L. (2020), "Research on the evolution mechanism of water inrush disasters in coal seam overlying strata", PhD thesis, China University of Mining and Technology, Xuzhou. 10.27623/d.cnki.gzkyu.2020.001832.
  43. Wu, Z., Ji, X., Liu, Q. and Fan, L. (2020), "Study of microstructure effect on the nonlinear mechanical behavior and failure process of rock using an image-based-fdem model", Comput. Geotech., 121, 103480. https://doi.org/10.1016/j.compgeo.2020.103480.
  44. Xie, H., Li, X., Shan, C., Xia, Z. and Yu, L. (2022), "Study on the damage mechanism and energy evolution characteristics of water-bearing coal samples under cyclic loading", Rock Mech. Rock Eng., 56(2), 1367-1385. https://doi.org/10.1007/S00603-022-03136-8
  45. Xu, W. and Wei, L. (2002), "Research on statistical constitutive models for rock damage", J. Rock Mech. Eng., 21(6), 5. https://doi.org/10.3321/j.issn:1000-6915.2002.06.006.
  46. Yang, X. and Jiang, A. (2022), "Study on the coupled mechanism of seep-age-stress damage and damage constitutive model of rock after freezing and thawing", Int. J. Geomech., 22(11). https://doi.org/10.1061/(ASCE)GM.1943-5622.0002402.
  47. Yang, Y. (2011), "Critical warning characteristics of water inrush geological hazards in karst tunnels", PhD thesis, Beijing Jiaotong University, Beijing.
  48. Zhai, Y., Meng, F., Li, Y., Zhao, R. and Zhang, Y. (2022), "Research on dynamic compression failure characteristics and damage constitutive model of sandstone after freeze-thaw cycles", Eng. Fail. Anal., 140, 106577. https://doi.org/10.1016/j.engfailanal.2022.106577.
  49. Zhang, C., Cao, P., Wang, Y. and Ning, G. (2013), "Creep characteristics of deep amphibolite under natural and saturated conditions", J. Central South Univ. (Natural Science Edition), 44(4), 1587-1595. https://doi.org/CNKI:SUN:ZNGD.0.2013-04-043.
  50. Zhang, C., Bai, Q., Han, P., Wnag, L., Wang, X. and Wnag, F. (2023), "Strength weakening and its micromech- anism in water-rock interaction, a short review in laboratory tests", Int. J. Coal Sci. Tech., 10(1). https://doi.org/10.1007/S40789-023-00569-6.
  51. Zhang, Y., Wu, X., Guo, Q., Wang, L., Wang, X. and Wang, F. (2022), "Research on the mechanical properties and damage constitutive model of multi-shape fractured sandstone under hydro-mechanical coupling", Minerals, 12. https://doi.org/10.3390/min12040436.
  52. Zhou, J., Lou, J., Wei, J., Dai, F., Chen, J. and Zhang, M. (2023), "A 3d microseismic data-driven damage model for jointed rock mass under hydro-mechanical coupling conditions and its application", J. Rock Mech. Geotech. Eng., 15(4), 911-925. https://doi.org/10.1016/J.JRMGE.2022.10.002.