Statistical Damage Constitutive Model for Rocks Considering Residual Strength
Publication: International Journal of Geomechanics
Volume 17, Issue 1
Abstract
Statistical damage constitutive models (SDCMs) have been widely employed to describe the mechanical response of strain-softening rock, especially in brittle failure under moderate confining pressure. The residual strength, referring to the strength of strain-softening rock in the postpeak region, has not been accurately considered in present works. In this study, an extended definition of damage was proposed based on the fact that the intact material gradually evolves into another damaged material, and these two parts are mixed together to carry external loads. Accordingly, a modified damage mechanical model was established. Then, the evolution equation of the damage variable was formulated based on the well-known Weibull distribution. Furthermore, a modified SDCM reflecting strain-softening and residual strength behavior for rocks loaded in conventional triaxial compression (CTC) was developed. The model parameters were estimated based on the extremum method. Finally, validation indicated that the calculated results from the modified SDCM had good agreement with the experimental observation and were much better than the calculated results from other models. Issues related to the lateral deformation of this model were also examined.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was fully supported by the National Natural Science Foundation of China under Contract 51478178.
References
Barbero, E. J., and De Vivo, L. (2001). “A constitutive model for elastic damage in fiber-reinforced PMC laminae.” Int. J. Damage Mech., 10(1), 73–93.
Cai, M., Kaiser, P. K., Tasaka, Y., and Minami M. (2007). “Determination of residual strength parameters of jointed rock masses using the GSI system.” Int. J. Rock Mech. Min. Sci., 44(2), 247–265.
Cao, W. G., Fang, Z. L., and Tang, X. J. (1998). “A study of statistical constitutive model for softening and damage rocks.” Chin. J. Rock Mech. Eng., 17(6), 628–633 (in Chinese with English abstract).
Cao, W. G., and Zhang, S. (2005). “Study on random statistical method of damage for softening hardening constitutive model of rock.” Proc., 2nd China-Japan Geotechnical Symp., Tongji University Press, Shanghai, China, 269–273.
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.” Can. Geotech. J., 47(8), 857–871.
Cividini, A., Contini, A., Locatelli, L., and Gioda, G. (2012). “Investigation on the cause of damages of a deep tunnel.” Int. J. Geomech., 722–731.
Deng, J., and Gu, D. S. (2011). “On a statistical damage constitutive model for rock materials.” Comput. Geosci., 37(2), 122–128.
Dragon, A., and Mróz, Z. (1979). “A continuum model for plastic-brittle behaviour of rock and concrete.” Int. J. Eng. Sci., 17(2), 121–137.
Drucker, D., and Prager, W. (1952). “Soil mechanics and plastic analysis or limit design.” Q. Appl. Math., 10(2), 157–165.
Fang, Z., and Harrison, J. P. (2002). “Application of a local degradation model to the analysis of brittle fracture of laboratory scale rock specimens under triaxial conditions.” Int. J. Rock Mech. Min. Sci., 39(4), 459–476.
Hajiabdolmajid, V., Kaiser, P. K., and Martin, C. D. (2002). “Modelling brittle failure of rock.” Int. J. Rock Mech. Min. Sci., 39(6), 731–741.
Hoonil, S., Sangseom, J., and Yongmin, K. (2009). “Load transfer analysis of rock-socketed drilled shafts by coupled soil resistance.” Comp. Geotech., 36(3), 446–453.
Jiang, T., Shao, J. F., Xu, W. Y., and Zhou, C. B. (2010). “Experimental investigation and micromechanical analysis of damage and permeability variation in brittle rocks.” Int. J. Rock Mech. Min. Sci., 47(5), 703–713.
Kachanov, L. M. (1986). Introduction to continuum damage mechanics, Martinus Nijhoft, Dordrecht, Netherlands.
Krajcinovic, D. (2000). “Damage mechanics: Accomplishments, trends and needs. Int. J. Solids Struct., 37(1–2), 267–267.
Krajcinovic, D., and Silva, M. A. D. (1982). “Statistical aspects of the continuous damage theory.” Int. J. Solids Struct., 18(7), 551–562.
Kumar, R., Sharma, K. G., and Varadarajan, A. (2010). “Post-peak response of some metamorphic rocks of India under high confining pressures.” Int. J. Rock Mech. Min. Sci., 47(8), 1357–1362.
Lemaitre, J., and Chaboche, J. L. (1990). Mechanics of solid materials, Cambridge University Press, Cambridge, U.K.
Li, C. (1995). “Micromechanics modelling for stress-strain behavior of brittle rocks.” Int. J. Numer. Anal. Methods Geomech., 19(5), 331–344.
Li, G., and Tang, C. A. (2015). “A statistical meso-damage mechanical method for modeling trans-scale progressive failure process of rock.” Int. J. Rock Mech. Min. Sci., 74, 133–150.
Li, L., and Aubertin, M. (2009). “Numerical investigation of the stress state in inclined backfilled stopes.” Int. J. Geomech., 52–62.
Li, X., Cao, W. G., and Su, Y. H. (2012). “A statistical damage constitutive model for softening behavior of rocks.” Eng. Geol., 143/144, 1–17.
Menéndez, B., Zhu, W., and Wong, T. (1996). “Micromechanics of brittle faulting and cataclastic flow in Berea sandstone.” J. Struct. Geol., 18(1), 1–16.
Moradian, Z., and Behnia, M. (2009). “Predicting the uniaxial compressive strength and static Young’s modulus of intact sedimentary rocks using the ultrasonic test.” Int. J. Geomech., 14–19.
Pariseau, W. G. (2007). “Fitting failure criteria to laboratory strength tests.” Int. J. Rock Mech. Min. Sci., 44(4), 637–646.
Shao, J. F., and Khazraei, R. (1996). “A continuum damage mechanics approach for time independent and dependent behaviour of brittle rock.” Mech. Res. Commun., 23(3), 257–265.
Wang, Z. L., Li, Y. C., and Wang, J. G. (2007). “A damage-softening statistical constitutive model considering rock residual strength.” Comp. Geosci., 33(1), 1–9.
Weibull, W. (1951). “A statistical distribution function of wide applicability.” J. Appl. Mech., 18, 293–297.
Xu, W. Y., and Wei, L. D. (2002). “Study on statistical damage constitutive mode of rock.” Chin. J. Mech. Eng., 21(6), 787–791 (in Chinese with English abstract).
Yang, S. Q., Jiang, Y. Z., Xu, W. Y., and Chen, X. Q. (2008). “Experimental investigation on strength and failure behavior of pre-cracked marble under conventional triaxial compression.” Int. J. Solids Struct., 45(17), 4796–4819.
Yumlu, M., and Ozbay, M. U. (1995). “Study of the behaviour of brittle rocks under plane strain and triaxial loading conditions.” Int. J. Rock Mech. Min. Sci., 32(7), 725–733.
Zareifard, M., and Fahimifar, A. (2014). “Elastic–brittle–plastic analysis of circular deep underwater cavities in a Mohr-Coulomb rock mass considering seepage forces.” Int. J. Geomech., 04014077.
Zhang, P., Li, N., Li, X. B., and Nordlund, E. (2009). “Compressive failure model for brittle rocks by shear faulting and its evolution of strength components.” Int. J. Rock Mech. Min. Sci., 46(5), 830–841.
Zhou, G. L., Tham, L. G., Lee, P. K. K., and Tsui Y. (2001). “A phenomenological constitutive model for rocks with shear failure mode.” Int. J. Numer. Anal. Methods Geomech., 25(4), 39l–414.
Zhu, Q. Z., and Shao J. F. (2015). “A refined micromechanical damage-friction model with strength prediction for rock-like materials under compression.” Int. J. Solids Struct., 60–61, 75–83.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 17 • Issue 1 • January 2017
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Mar 16, 2015
Accepted: Feb 23, 2016
Published online: Apr 4, 2016
Discussion open until: Sep 4, 2016
Published in print: Jan 1, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.