Separation of Elastoviscoplastic Strains of Rock and a Nonlinear Creep Model
Publication: International Journal of Geomechanics
Volume 18, Issue 1
Abstract
A series of triaxial creep tests were carried out on fractured limestone specimens under multilevel loading and unloading cycles to capture elastoviscoplastic strain components. A new data processing algorithm was proposed to analyze the experimental data, determine the instantaneous elastic and instantaneous plastic strain components and the viscoelastic and viscoplastic strain components from the total strain, and separate the viscoelastic and viscoplastic strain curves from the total creep strain curve. The instantaneous elastic strain, instantaneous plastic strain, viscoelastic strain, and viscoplastic strain versus deviatoric stress relationships are highly nonlinear. The proportion of the viscoplastic strain component in the total creep strain increases with increased deviatoric stress. On the basis of the experimental results, a nonlinear elastoviscoplastic (EVP) creep constitutive model was proposed by connecting a Hooke body, a parallel combination of Hooke and St. Venant bodies, a Kelvin body, and a generalized Bingham body. The proposed EVP creep model can describe both the loading and unloading creep behavior precisely. The creep model curves agree very well with the experimental results and give a precise description of the full stages of creep, especially the tertiary creep stage. Moreover, the variation law of the creep parameters is also supported by the experimental observations. So the validity and great practical potential of the proposed EVP creep model are shown well.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was supported by the National Natural Science Foundation of China (51774131, 51434006, and 51404309), the Natural Science Foundation of Hunan province (2015JJ2067), the Open Projects of State Key Laboratory of Coal Resources and Safe Mining, CUMT (SKLCRSM16KF12), and the CRSRI Open Research Program (CKWV2017508/KY).
References
ASTM. (2005a). “Creep of rock core under constant stress and temperature.” ASTM D7070-08,West Conshohocken, PA.
ASTM. (2005b). “Standard test methods for compressive strength and elastic moduli of intact rock core specimens under varying states of stress and temperatures.” ASTM D7012-14,West Conshohocken, PA.
Aydan, Ö., et al. (2014). “ISRM suggested methods for determining the creep characteristics of rock.” Rock Mech. Rock Eng.,47(1), 275–290.
Aydan, Ö., and Nawrocki, P. (1998). “Rate-dependent deformability and strength characteristics of rocks.” Proc., 2nd Int. Symp., Hard soils: The geotechnics of hard soils—Soft rocks, A. Evangelista and L. Picarelli, eds., Vol.1,A. A. Balkema,Rotterdam, Netherlands, 403–411.
Aydan, Ö., and Ulusay, R. (2013). “Geomechanical evaluation of Derinkuyu antique underground city and its implications in geo-engineering.” Rock Mech. Rock Eng.,46(4), 731–754.
Bai, F., Yang, X. H., and Zeng, G. W. (2014). “Creep and recovery behavior characterization of asphalt mixture in compression.” Constr. Build. Mater.,54, 504–511.
Barla, G., Debernardi, D., and Sterpi, D. (2012). “Time-dependent modeling of tunnels in squeezing conditions.” Int. J. Geomech., 697–710.
Bérest, P. (1987). “Viscoplasticité en mécanique des roches.” Manuel de rhéologie des géomatériaux,Presses des Ponts,Paris, 235–257.
Bonini, M., Debernardi, D., Barla, M., and Barla, G. (2009). “The mechanical behaviour of clay shales and implications on the design of tunnels.” Rock Mech. Rock Eng.,42(Apr), 361–388.
Brantut, N., Heap, M. J., Meredith, P. G., and Baud, P. (2013). “Time-dependent cracking and brittle creep in crustal rocks: A review.” J. Struct. Geol.,52(Jul), 17–43.
Chen, B.-R., Zhao, X.-J., Feng, X.-T., Zhao, H.-B., and Wang, S.-Y. (2014). “Time dependent damage constitutive model for the marble in the Jinping II Hydropower Station in China.” Bull. Eng. Geol. Environ.,73(2), 499–515.
Cristescu, N. D., and Gioda, G. (1994). Visco-plastic behaviour of geomaterials,Springer,New York.
Cruden, D. M. (1974). “The static fatigue of brittle rock under uniaxial compression.” Int. J. Rock Mech. Min. Sci.,11(2), 67–73.
Cruden, D. M. (1983). “Long term behaviour in compression of Lac du Bonnet Granite.” Technical Record 211,Dept. of Civil Engineering, Univ. of Alberta,Edmonton, AB, Canada.
Debernardi, D., and Barla, G. (2009). “New viscoplastic model for design analysis of tunnels in squeezing conditions.” Rock Mech. Rock Eng.,42(Apr), 259–288.
Feng, J., Chuhan, Z., Gang, W., and Guanglun, W. (2003). “Creep modeling in excavation analysis of a high rock slope.” Geotech. Geoenviron. Eng., 849–857.
FLAC3D [Computer software].Itasca Consulting Group,Minneapolis.
Gatelier, N., Pellet, F., and Loret, B. (2002). “Mechanical damage of an anisotropic porous rock in cyclic triaxial tests.” Int. J. Rock Mech. Min. Sci.,39(3), 335–354.
Kachanov, L. M. (1967). “The theory of creep.” Nat. Lend. Lib. Sci. Tech., 160–176.
Li, Y., and Xia, C. (2000). “Time-dependent tests on intact rocks in uniaxial compression.” Int. J. Rock Mech. Min. Sci.,37(3), 467–475.
Liu, Y., Liu, C., Kang, Y., Wang, D., and Ye, D. (2015). “Experimental research on creep properties of limestone under fluid–solid coupling.” Environ. Earth Sci.,73(11), 7011–7018.
Malan, D. F. (1999). “Time-dependent behaviour of deep level tabular excavations in hard rock.” Rock Mech. Rock Eng.,32(2), 123–155.
Malan, D. F. (2002). “Manuel Rocha medal recipient simulating the time-dependent behaviour of excavations in hard rock.” Rock Mech. Rock Eng.,35(4), 225–254.
Maranini, E., and Brignoli, M. (1999). “Creep behaviour of a weak rock: experimental characterization.” Int. J. Rock Mech. Min. Sci.,36(1), 127–138.
Maranini, E., and Yamaguchi, T. (2001). “A non-associated viscoplastic model for the behaviour of granite in triaxial compression.” Mech. Mater.,33(5), 283–293.
Martin, C. D. (1997). “Seventeenth Canadian Geotechnical Colloquium: The effect of cohesion loss and stress path on brittle rock strength.” Can. Geotech. J.,34(5), 698–725.
Mishra, B., and Verma, P. (2015). “Uniaxial and triaxial single and multistage creep tests on coal-measure shale rocks.” Int. J. Coal Geol.,137, 55–65.
Miura, K., Okui, Y., and Horii, H. (2003). “Micromechanics-based prediction of creep failure of hard rock for long-term safety of high-level radioactive waste disposal system.” Mech. Mater.,35, 587–601.
Ottosen, N. S. (1986). “Viscoelastic-viscoplastic formulas for analysis of cavities in rock salt.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr.,23(3), 201–212.
Pellet, F., Hajdu, A., Deleruyelle, F., and Besnus, F. A. (2005). “A viscoplastic model including anisotropic damage for the time dependent behaviour of rock.” Int. J. Numer. Anal. Meth. Geomech.,29(9), 941–970.
Perzyna, P. (1966). “Fundamental problems in viscoplasticity.” Adv. Appl. Mech.,9, 243–377.
Shalabi, F. I. (2005). “FE analysis of time-dependent behavior of tunneling in squeezing ground using two different creep models.” Tunnelling Underground Space Technol.,20(3), 271–279.
Shao, J. F., Zhu, Q. Z., and Su, K. (2003). “Modeling of creep in rock materials in terms of material degradation.” Comput. Geotech.,30(7), 549–555.
Sterpi, D., and Gioda, G. (2009). “Visco-plastic behaviour around advancing tunnels in squeezing rock.” Rock Mech. Rock Eng.,42(2), 319–339.
Tomanovic, Z. (2006). “Rheological model of soft rock based on test on marl.” Mech. Time-Depend. Mater.,10(2), 135–154.
Tsai, L. S., Hsieh, Y. M., and Weng, M. C. (2008). “Time-dependent deformation behaviors of weak sandstones.” Int. J. Rock Mech. Min. Sci.,45(2), 144–154.
Weng, M. C., Tsai, L. S., Hsieh, Y. M., and Jeng, F. S. (2010). “An associated elastic–viscoplastic constitutive model for sandstone involving shear-induced volumetric deformation.” Int. J. Rock Mech. Min. Sci.,47(8), 1263–1272.
Xia, C. H., Wang, X. D., Xu, C. B., and Zhang, C. S. (2008). “Method to identify rheological models by unified rheological model theory and case study.” Chin. J. Rock Mech. Eng.,27, 1594–1600 (in Chinese).
Yang, S.-Q., and Jing, H.-W. (2013). “Evaluation on strength and deformation behavior of red sandstone under simple and complex loading paths.” Eng. Geol.,164, 1–17.
Yang, S.-Q., Peng, X., Ranjith, P. G., Chen, G.-F., and Jing, H.-W. (2015). “Evaluation of creep mechanical behavior of deep-buried marble under triaxial cyclic loading.” Arabian J. Geosci.,8(9), 6567–6582.
Yang, W., Zhang, Q., Li, S., and Wang, S. (2014). “Time-dependent behavior of diabase and a nonlinear creep model.” Rock Mech. Rock Eng.,47(4), 1211–1224.
Zhang, H., Wang, Z., Zheng, Y., Duan, P., and Ding, S. (2012a). “Study on tri-axial creep experiment and constitutive relation of different rock salt.” Saf. Sci.,50(4), 801–805.
Zhang, Z. L., Xu, W. Y., Wang, W., and Wang, B. (2012b). “Triaxial creep tests of rock from the compressive zone of dam foundation in Xiangjiaba Hydropower Station.” Int. J. Rock Mech. Min. Sci.,50(Feb), 133–139.
Zhao, Y. L., Cao, P., Wen, Y. D., Wang, Y., and Chai, H. (2008). “Elastovisco-plastic rheological experiment and nonlinear rheological model of rocks.” Chin. J. Rock Mech. Eng.,27, 477–487 (in Chinese).
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 18 • Issue 1 • January 2018
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Oct 20, 2016
Accepted: Jul 18, 2017
Published online: Nov 2, 2017
Published in print: Jan 1, 2018
Discussion open until: Apr 2, 2018
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.