Geomechanics and Engineering

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Damage constitutive model of brittle rock considering the compaction of crack

  • Gu, Qingheng (School of Mining and Safety Engineering, Shandong University of Science and Technology) ;
  • Ning, Jianguo (Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology) ;
  • Tan, Yunliang (Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology) ;
  • Liu, Xuesheng (Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology) ;
  • Ma, Qing (School of Mining and Safety Engineering, Shandong University of Science and Technology) ;
  • Xu, Qiang (School of Mining and Safety Engineering, Shandong University of Science and Technology)
  • Received : 2017.08.28
  • Accepted : 2018.02.09
  • Published : 2018.08.10
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Abstract

The deformation and strength of brittle rocks are significantly influenced by the crack closure behavior. The relationship between the strength and deformation of rocks under uniaxial loading is the foundation for design and assessment of such scenarios. The concept of relative crack closure strain was proposed to describe the influence of the crack closure behavior on the deformation and strength of rocks. Considering the crack compaction effect, a new damage constitutive model was developed based on accumulated AE counts. First, a damage variable based on the accumulated AE counts was introduced, and the damage evolution equations for the four types of brittle rocks were then derived. Second, a compaction coefficient was proposed to describe the compaction degree and a correction factor was proposed to correct the error in the effective elastic modulus instead of the elastic modulus of the rock without new damage. Finally, the compaction coefficient and correction factor were used to modify the damage constitutive model obtained using the Lemaitre strain equivalence hypothesis. The fitted results of the models were then compared with the experimental data. The results showed that the uniaxial compressive strength and effective elastic modulus decrease with an increase in the relative crack closure strain. The values of the damage variables increase exponentially with strains. The modified damage constitutive equation can be used to more accurately describe the compressive deformation (particularly the compaction stage) of the four types of brittle rocks, with a coefficient of determination greater than 0.9.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China, Shandong University of Science and Technology, Shandong Province Natural Science Fund

References

  1. Ai, T., Zhang, R., Liu, J.F. and Ren, L. (2012), "Space-time evolution rules of acoustic emission location of unloaded coal sample at different loading rates", J. Min. Sci. Technol., 22(6), 847-854. https://doi.org/10.1016/j.ijmst.2012.12.001
  2. Cerfontaine, B., Charlier, R., Collin, F. and Taiebat, M. (2017), "Validation of a new elastoplastic constitutive model dedicated to the cyclic behaviour of brittle rock materials", Rock Mech. Rock Eng., 50(10), 2677-2694. https://doi.org/10.1007/s00603-017-1258-3
  3. Daniela, C., Neil, D., Gary, J.F. and Gianluca, M. (2017), "Analysis of acoustic emission patterns for monitoring of rock slope deformation mechanisms", Eng. Geol., 219, 21-31. https://doi.org/10.1016/j.enggeo.2016.11.021
  4. David, E.C., Brantut, N., Schubnel, A. and Zimmerman, R.W. (2012), "Sliding crack model for nonlinearity and hysteresis in the uniaxial stress-strain curve of rock", J. Rock Mech. Min. Sci., 52, 9 -17. https://doi.org/10.1016/j.ijrmms.2012.02.001
  5. Diederichs, M.S. and Martin, C.D. (2010), "Measurement of spalling parameters from laboratory testing", Proceedings of the European Rock Mechanics Symposium, EUROCK, Lausanne, Switzerland, June.
  6. Fairhurst, C.E. and Hudson, J.A. (1999), "Draft ISRM suggested method for the complete stress-strain curve for the intact rock in uniaxial compression", J. Rock Mech. Min. Sci., 36(3), 279-289. https://doi.org/10.1016/S0148-9062(99)00006-6
  7. Hu, S.C., Tan, Y.L., Zhou, H., Guo, W.Y., Hu, D.W., Meng, F.Z. and Liu, Z.G. (2017), "Impact of bedding planes on mechanical properties of sandstone", Rock Mech. Rock Eng., 50(8), 2243-2251. https://doi.org/10.1007/s00603-017-1239-6
  8. Huang, W.P., Yuan, Q., Tan, Y.L., Wang, J., Liu, G.L., Qu, G.L. and Li, C. (2018), "An innovative support technology employing a concrete-filled steel tubular structure for a 1000-mdeep roadway in a high in situ stress field", Tunn. Undergr. Sp. Technol., 73, 26-36. https://doi.org/10.1016/j.tust.2017.11.007
  9. Jiang, C.B., Duan, M.K., Yin, G.Z., Wang, J.G., Lu, T.Y., Xu, J., Zhang, D.M. and Huang, G. (2017), "Experimental study on seepage properties, AE characteristics and energy dissipation of coal under tiered cyclic loading", Eng. Geol., 221, 114-123. https://doi.org/10.1016/j.enggeo.2017.03.005
  10. Jin, W.C. and Chloe, A. (2017), "Discrete equivalent wing crack based damage model for brittle solids", J. Solid. Struct., 110, 279-293.
  11. Kachanov, L.M. (1958), "Time rupture process under creep conditions", Izy. Akad. Nauk SSSR Otd. Tech. Nauk, 8, 26-31.
  12. Li, Y.W., Jia, D., Rui, Z.H., Peng, J.Y., Fu, C.K. and Zhang, J. (2017), "Evaluation method of rock brittleness based on statistical constitutive relations for rock damage", J. Petrol. Sci. Eng., 153, 123-132. https://doi.org/10.1016/j.petrol.2017.03.041
  13. Liu, B.X., Huang, J.L., Wang, Z.Y. and Liu, L. (2009), "Study on damage evolution and acoustic emission character of coal-rock under uniaxial compression", Chin. J. Rock Mech. Eng., 28(S1), 3234-3238 (in Chinese).
  14. Liu, D. (2014), "Study on rock damage constitutive model and chaos characterstics in the process of deformation and failure", Ph.D. Dissertation, University of Mining and Technology, Beijing, China (in Chinese).
  15. Liu, X.S., Ning, J.G., Tan, Y.L. and Gu, Q.H. (2016b), "Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading", J. Rock Mech. Min. Sci., 85, 27-32. https://doi.org/10.1016/j.ijrmms.2016.03.003
  16. Lockner, D. (1993), "The role of acoustic emission in the study of rock fracture", J. Rock Mech. Min. Sci. Geomech. Abstr., 30(7), 883-899. https://doi.org/10.1016/0148-9062(93)90041-B
  17. Ning, J.G., Wang, J., Jiang, J.Q., Hu, S.C., Jiang, L.S. and Liu, X.S. (2017), "Estimation of crack initiation and propagation thresholds of confined brittle coal specimens based on energy dissipation theory", Rock Mech. Rock Eng., 51(1), 119-134.
  18. Panaghi, K., Golshani, A. and Takemura, T. (2015), "Rock failure assessment based on crack density and anisotropy index variations during triaxial loading tests", Geomech. Eng., 9(6), 793-813. https://doi.org/10.12989/gae.2015.9.6.793
  19. Peng, J., Rong, G., Cai, M. and Zhou, C.B. (2015a), "A model for characterizing crack closure effect of rocks", Eng. Geol., 189, 48-57. https://doi.org/10.1016/j.enggeo.2015.02.004
  20. Peng, J., Cai, M., Liu, D.Q., He, M.C. and Zhou, C.B. (2015b), "A phenomenological model of brittle rocks under uniaxial compression", J. Geohazards Environ., 1(2), 53-62.
  21. Pourhosseini, O. and Shabanimashcool, M. (2014), "Development of an elasto-plastic constitutive model for intact rocks", J. Rock Mech. Min. Sci., 66, 1-12. https://doi.org/10.1016/j.ijrmms.2013.11.010
  22. Tan, Y.L., Yu, F.H., Ning, J.G. and Zhao, T.B. (2015), "Design and construction of entry retaining wall along a gob side under hard roof stratum", J. Rock Mech. Min. Sci., (77), 115-121.
  23. Tan, Y.L., Liu, X.S., Ning, J.G. and Lu, Y.W. (2017), "In situ investigations on failure evolution of overlying strata induced by mining multiple coal seams", Geotech. Test. J., 40(2), 1-14.
  24. Wang, H.P., Li, Y., Li, S.C., Zhang, Q.S. and Liu, J. (2016), "An elasto-plastic damage constitutive model for jointed rock mass with an application", Geomech. Eng., 11(1), 77-94. https://doi.org/10.12989/gae.2016.11.1.077
  25. Wang, P., Jiang, L.S., Jiang, J.Q., Zheng, P.Q. and Li, W. (2018), "Strata behaviors and rock burst-inducing mechanism under the coupling effect of a hard, thick stratum and a normal fault", J. Geomech., 18(2), 04017135. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001044
  26. Xiao, Y.Q., Wan, Y.P. and Liu, B.X. (2013), Research on Landscape Limestone Damage and Deformation under Uniaxial Compression based on Acoustic Emission, in Applied Mechanics and Materials, Trans Tech Publications, 914-919.
  27. Zhang, G.C., He, F.L., Jia, H.G. and Lai, Y.H. (2017), "Analysis of gateroad stability in relation to yield pillar size: A case study", Rock Mech. Rock Eng., 50(5), 1-16. https://doi.org/10.1007/s00603-016-1095-9
  28. Zhang, J.C., Xu, W.Y., Wang, H.L., Wang, R.B., Meng, Q.X. and Du, S.W. (2016), "A coupled elastoplastic damage model for brittle rocks and its application in modelling underground excavation", J. Rock Mech. Min. Sci., 84, 130-141. https://doi.org/10.1016/j.ijrmms.2015.11.011
  29. Zhao, T.B., Guo, W.Y., Tan, Y.L., Lu, C.P., and Wang, C.W. (2017), "Case histories of rock bursts under complicated geological conditions", Bull. Eng. Geol. Environ., 1-17.

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