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Energy Analysis of the Deformation and Failure Process of Sandstone and Damage Constitutive Model

  • Geotechnical Engineering
  • Published:
KSCE Journal of Civil Engineering Aims and scope

Abstract

The damage theory was introduced to clarify and simulate the strain softening property of rocks. On the basis of the theory, an energy method was utilized to portray the rock mechanical properties from microscopic perspective. Firstly, from the perspective of rock microstructure, damage variable (expressed as D) was redefined by dividing the rock into three portions: undamaged materials, damaged materials and micro-defects, and an impact factor was introduced as the connection between the damaged material and the micro-defects. Meanwhile, the method for determining the impact factor was presented. Secondly, the damage variable was redefined in light of energy dissipation, then damage evolution analysis was conducted based on triaxial tests. An improved rock damage constitutive model was further obtained in another expression to reflect the energy change law. Subsequently, the relationship between D and the deformation and failure process of rocks was analyzed on account of the damage evolution equation formularized by fitting to a logistic function, which can measure the influence of energy dissipation on the propagation of micro-defects. By comparing between experimental results and theoretical results of illustrative examples, the effectiveness of the improved model was validated, and the its application was also discussed.

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References

  • Alonso, E. E., Zandarín, M. T., and Olivella, S. (2013). “Joints in unsaturated rocks: Thermo-hydro-mechanical formulation and constitutive behaviour.” Journal of Rock Mechanics and Geotechnical Engineering, Vol. 5, No. 3, pp. 200–213, DOI: 10.1016/j.jrmge.2013.05.004.

    Article  Google Scholar 

  • Cao, W. G., Zhang, S., and Zhao, M. H. (2006). “Study on statistical damage constitutive model of rock based on new definition of damage.” Rock and Soil Mechanics, Vol. 27, No. 1, pp. 41–46.

    Google Scholar 

  • Cao, W. G., Zhao, H., Li, X., and Zhang, Y. J. (2010). “Statistical damage model with strain softening and hardening for rocks under the influence of voids and volume changes.” Canadian Geotechnical Journal, Vol. 47, No. 8, pp. 857–871, DOI:10.1139/T09-148.

    Article  Google Scholar 

  • Cao, W. G., Zhao, M. H., and Tang, X. J. (2003). “Study on simulation of statistical damage in the full process of rock failure.” Chinese Journal of Geotechnical Engineering, Vol. 25, No. 2, pp. 184–187.

    Google Scholar 

  • Chen, X. D., Xu, L. Y., and Bu, J. W. (2016a). “Experimental study and constitutive model on complete stress-strain relations of plain concrete in uniaxial cyclic tension.” KSCE Journal of Civil Engineering, Vol. 21, No. 5, pp. 1829–1835, DOI: 10.1007/s12205-016-0802-0.

    Article  Google Scholar 

  • Chen, X. D., Xu, L. Y., and Zhu, Q. (2016b). “Mechanical behavior and damage evolution for concrete subjected to multiple impact loading.” KSCE Journal of Civil Engineering, Vol. 21, No. 6, pp. 2351–2359, DOI: 10.1007/s12205-016-1143-8.

    Article  Google Scholar 

  • Deng, J. and Gu, D. S. (2011). “On a statistical damage constitutive model for rock materials.” Computers & Geosciences, Vol. 37, No. 2, pp. 122–128, DOI: 10.1016/j.cageo.2010.05.018.

    Article  Google Scholar 

  • Duriez, J., Darve, F., and Donzé, F. V. (2011). “A discrete modelingbased constitutive relation for infilled rock joints.” International Journal of Rock Mechanics and Mining Sciences, Vol. 48, No. 3, pp. 458–468, DOI: 10.1016/j.ijrmms.2010.09.008.

    Article  Google Scholar 

  • Gaziev, E. (2001). “Rupture energy evaluation for brittle materials.” International Journal of Solids and Structures, Vol. 38, No. 42, pp. 7681–7690, DOI: 10.1016/S0020-7683(01)00037-3.

    Article  MATH  Google Scholar 

  • Gosar, A. and Nagode, M. (2013). “Energy dissipation under multiaxial thermomechanical fatigue loading.” International Journal of Fatigue, Vol. 48, pp. 223–230, DOI: 10.1016/j.ijfatigue.2012.10.021.

    Article  Google Scholar 

  • Hayhurst, D. R. (1972). “Creep rupture under multi-axial states of stress.” Journal of the Mechanics and Physics of Solids, Vol. 20, No. 6, pp. 381–390, DOI: 10.1016/0022-5096(72)90015-4.

    Article  Google Scholar 

  • He, M. C., Miao, J. L., and Feng, J. L. (2010). “Rock burst process of limestone and its acoustic emission characteristics under true-triaxial unloading conditions.” International Journal of Rock Mechanics and Mining Sciences, Vol. 47, No. 2, pp. 286–298, DOI: 10.1016/j.ijrmms.2009.09.003.

    Article  Google Scholar 

  • **, F. N., Jiang, M. R., and Gao, X. L. (2004). “Defining damage variable based on energy dissipation.” Chinese Journal of Rock Mechanics and Engineering, Vol. 23, No. 12, pp. 1976–1980.

    Google Scholar 

  • Kachanov, L. M. (1967). The theory of creep, National Lending Library for Science and Technology, Boston Spa, Yorkshire, England.

    Google Scholar 

  • Lee, S. (2005). “Application of logistic regression model and its validation for landslide susceptibility map** using GIS and remote sensing data.” International Journal of Remote Sensing, Vol. 26, No. 7, pp. 1477–1491, DOI: 10.1080/01431160412331331012.

    Article  Google Scholar 

  • Lee, H. and Haimson, B. C. (2011). “True triaxial strength, deformability, and brittle failure of granodiorite from the San Andreas Fault Observatory at Depth.” International Journal of Rock Mechanics and Mining Sciences, Vol. 48, No. 7, pp. 1199–1207, DOI: 10.1016/j.ijrmms.2011.08.003.

    Article  Google Scholar 

  • Lee, S. and Pradhan, B. (2007). “Landslide hazard map** at Selangor, Malaysia using frequency ratio and logistic regression models.” Landslides, Vol. 4, No. 1, pp. 33–41, DOI: 10.1007/s10346-006-0047-y.

    Article  Google Scholar 

  • Lemaitre, J. (1985). “A continuous damage mechanics model for ductile fracture.” Journal of Engineering Materials and Technology, Vol. 107, No. 1, pp. 83–89, DOI: 10.1115/1.3225775.

    Article  Google Scholar 

  • Li, X., Cao, W. G., and Su, Y. H. (2012). “A statistical damage constitutive model for softening behavior of rocks.” Engineering Geology, Vols. 143–144, pp. 1–17, DOI: 10.1016/j.enggeo.2012.05.005.

    Article  Google Scholar 

  • Liu, X. S., Ning, J. G., Tan, Y. L., and Gu, Q. H. (2016). “Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading.” International Journal of Rock Mechanics and Mining Sciences, Vol. 85, pp. 27–32, DOI: 10.1016/j.ijrmms.2016.03.003.

    Article  Google Scholar 

  • Long, Y., Chen, J. H., and Zhang, J. S. (2017). “Introduction and analysis of a strain-softening damage model for soil–structure interfaces considering shear thickness.” KSCE Journal of Civil Engineering, Vol. 21, No. 7, pp. 2634–2640, DOI: 10.1007/s12205-017-0476-2.

    Article  Google Scholar 

  • Ma, T. S., Yang, C. H., Chen, P., Wang, X. D., and Guo, Y. T. (2016). “On the damage constitutive model for hydrated shale using CT scanning technology.” Journal of Natural Gas Science and Engineering, Vol. 28, pp. 204–214, DOI: 10.1016/j.jngse.2015.11.025.

    Article  Google Scholar 

  • Mathew, J., Jha, V. K., and Rawat, G.S. (2009). “Landslide susceptibility zonation map** and its validation in part of Garhwal Lesser Himalaya, India, using binary logistic regression analysis and receiver operating characteristic curve method.” Landslides, Vol. 6, No. 1, pp. 17–26, DOI: 10.1007/s10346-008-0138-z.

    Article  Google Scholar 

  • Mazars, J. and Pijaudier-Cabot, G. (1989). “Continuum damage theoryapplication to concrete.” Journal of Engineering Mechanics, Vol. 115, No. 2, pp. 345–365, DOI: 10.1061/(ASCE)0733-9399(1989)115:2(345).

    Article  Google Scholar 

  • Pourhosseini, O. and Shabanimashcool, M. (2014). “Development of an elasto-plastic constitutive model for intact rocks.” International Journal of Rock Mechanics and Mining Sciences, Vol. 66, pp. 1–12, DOI: 10.1016/j.ijrmms.2013.11.010.

    Article  Google Scholar 

  • Shojaei, A., Dahi Taleghani, A., and Li, G. (2014). “A continuum damage failure model for hydraulic fracturing of porous rocks.” International Journal of Plasticity, Vol. 59, pp. 199–212, DOI: 10.1016/j.ijplas.2014.03.003.

    Article  Google Scholar 

  • Singh, M., Raj, A., and Singh, B. (2011). “Modified Mohr-Coulomb criterion for non-linear triaxial and polyaxial strength of intact rocks.” International Journal of Rock Mechanics and Mining Sciences, Vol. 48, No. 4, pp. 546–555, DOI: 10.1016/j.ijrmms.2011.02.004.

    Article  Google Scholar 

  • Sloan, J. A., Filz, G. M., and Collin, J. G. (2013). “Field-scale columnsupported embankment test facility.” Geotechnical Testing Journal, Vol. 36, No. 6, pp. 891–902, DOI: 10.1520/GTJ20120229.

    Article  Google Scholar 

  • Song, D., Wang, E., and Liu, J. (2012). “Relationship between EMR and dissipated energy of coal rock mass during cyclic loading process.” Safety Science, Vol. 50, No. 4, pp. 751–760, DOI: 10.1016/j.ssci.2011.08.039.

    Article  Google Scholar 

  • Stead, D., Eberhardt, E., and Coggan, J.S. (2006). “Developments in the characterization of complex rock slope deformation and failure using numerical modelling techniques.” Engineering Geology, Vol. 83, No. 1, pp. 217–235, DOI: 10.1016/j.enggeo.2005.06.033.

    Article  Google Scholar 

  • Taheri, A. and Tatsuoka, F. (2013). “A new method to simulate stressstrain relations from multiple-step loading triaxial compression test results.” Geotechnical Testing Journal, Vol. 36, No. 6, pp. 799–810, DOI: 10.1520/GTJ20130005.

    Article  Google Scholar 

  • 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.” Geomechanics and Engineering, Vol. 11, No.1, pp. 77–94, DOI: 10.12989/gae.2016.11.1.077.

    Article  Google Scholar 

  • Wang, Z., Li, Y., and Wang, J. G. (2007). “A damage-softening statistical constitutive model considering rock residual strength.” Computers & Geosciences, Vol. 33, No. 1, pp. 1–9, DOI: 10.1016/j.cageo.2006.02.011.

    Article  Google Scholar 

  • Wen, T., Liu, Y. R., Yang, C. G., and Yi, X. L. (2018a). “A rock damage constitutive model and damage energy dissipation rate analysis for characterising the crack closure effect.” Geomechanics and Geoengineering: An International Journal, Vol. 13, No. 1, pp. 54–63, DOI: 10.1080/17486025.2017.1330969.

    Article  Google Scholar 

  • Wen, T., Tang, H. M., Liu, Y. R., Wang, K., and Yang, C. G. (2016). “Energy and damage analysis of slate during triaxial compression under different confining pressures.” Coal Geology and Exploration, Vol. 44, No. 3, pp. 80–86.

    Google Scholar 

  • Wen, T., Tang, H. M., Ma, J. W., and Wang, Y. K. (2018b). “Evaluation of methods for determining crack initiation stress under compression.” Engineering Geology, Vol. 235, pp. 81–97, DOI: 10.1016/j.enggeo.2018.01.018.

    Article  Google Scholar 

  • Xu, X., Dong, Y., and Fan, C. (2015). “Laboratory investigation on energy dissipation and damage characteristics of frozen loess during deformation process.” Cold Regions Science and Technology, Vol. 109, pp. 1–8, DOI: 10.1016/j.coldregions.2014.09.006.

    Article  Google Scholar 

  • Ye, D. Y. and Wang, Z. L. (2001). “A new approach to low-cycle fatigue damage based on exhaustion of static toughness and dissipation of cyclic plastic strain energy during fatigue.” International Journal of Fatigue, Vol. 23, No. 8, pp. 679–687, DOI: 10.1016/S0142-1123(01)00027-5.

    Article  Google Scholar 

  • Zhang, L. M., Gao, S., Wang, Z. Q., and Cong, Y. (2013). “Analysis of marble failure energy evolution under loading and unloading conditions.” Chinese Journal of Rock Mechanics and Engineering, Vol. 32, No. 8, pp. 1572–1578.

    Google Scholar 

  • Zhang, G. C., Tang, H. M., **ang, X., Karakus, M., and Wu, J. P. (2015). “Theoretical study of rockfall impacts based on logistic curves.” International Journal of Rock Mechanics and Mining Sciences, Vol. 78, pp. 133–143, DOI: 10.1016/j.ijrmms.2015.06.001.

    Article  Google Scholar 

  • Zhang, J. W., Zhang, Y. S., and Li, X. Z. (2015). “Study on damage constitutive model of rock considering progressive failure.” Chinese Journal of Underground Space and Engineering, Vol. 11, No. 6, 1528–1532.

    Google Scholar 

  • Zhou, J. W., Xu, W. Y., and Yang, X. G. (2010). “A microcrack damage model for brittle rocks under uniaxial compression.” Mechanics Research Communications, Vol.37, No. 4, pp. 399–405, DOI: 10.1016/j.mechrescom.2010.05.001.

    Article  MATH  Google Scholar 

  • Zhou, C. Y. and Zhu, F. X. (2010). “An elasto-plastic damage constitutive model with double yield surfaces for saturated soft rock.” International Journal of Rock Mechanics and Mining Sciences, Vol. 47, No. 3, pp. 385–395, DOI: 10.1016/j.ijrmms.2010.01.002.

    Article  Google Scholar 

  • Zhu, J. M., Cheng, H. F., and Yao, Y. P. (2013). “Statistical damage softening model of fractured rock based on SMP failure criterion and its application.” Chinese Journal of Rock Mechanics and Engineering, Vol. 32, No. S2, pp. 3160–3168.

    Google Scholar 

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Authors and Affiliations

  1. School of Geosciences, Yangtze University, Wuhan, 430100, China

    Tao Wen

  2. Faculty of Engineering, China University of Geosciences, Wuhan, 430074, China

    Tao Wen, Huiming Tang & Yourong Liu

  3. Three Gorges Research Center for Geo-hazards of Ministry of Education, China University of Geosciences, Wuhan, 430074, China

    Huiming Tang & Junwei Ma

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  1. Tao Wen
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Correspondence to Huiming Tang.

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Wen, T., Tang, H., Ma, J. et al. Energy Analysis of the Deformation and Failure Process of Sandstone and Damage Constitutive Model. KSCE J Civ Eng 23, 513–524 (2019). https://doi.org/10.1007/s12205-018-0789-9

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  • DOI: https://doi.org/10.1007/s12205-018-0789-9

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