Numerical Simulation of Rock Creep Behavior with a Damage-Based Constitutive Law
Publication: International Journal of Geomechanics
Volume 17, Issue 1
Abstract
Time-dependent creep behavior of rocks is crucial not only for assessing geophysical hazards, such as earthquake rupture and volcanic eruption, but also for analyzing the long-term stability of rock engineering structures, such as underground mines and underground excavations. In the present paper, multiple stress-stepping creep tests on green sandstone under uniaxial stress conditions were performed. Results from stress-stepping creep experiments show that creep strain rates are highly dependent on the level of applied stress. Then, a time-dependent creep model based on damage constitutive law at a mesoscale was proposed to model the time-dependent behavior of heterogeneous brittle rocks. In the proposed model, the rock heterogeneity is considered by assuming the rock parameters following a statistical Weibull distribution, and both the maximum tensile strain criterion and the Mohr-Coulomb criterion are used as two damage thresholds to control the rock damage. The damage-based creep model is implemented by programming on the basis of finite-element software. Then the model was validated by comparing the numerical simulations with the experimental results. The model accurately captures the time-dependent creep behavior observed in the laboratory. It was then used to simulate the time-dependent evolution of damaged zone around an opening under different lateral pressure coefficients. The distribution of damage around the opening is realistically reproduced, and the simulations indicated that the spatial distribution of damage zones, as well as time to failure, is closely related to the lateral pressure coefficient.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work is funded by National Science Foundation of China (Grant Nos. 51525402, 51374049, 51474051 41172265, and 51404067), the Key Project of Chinese Ministry of Education (No. 113019A), the Fundamental Research Funds for the Central Universities of China (Grant nos. N140106002, N140105001, N120301002, and N150102002), and the China Postdoctoral Science Foundation funded project (Grant No. 2013M541238). This support is gratefully acknowledged.
References
Amitrano, D., and Helmstetter, A. (2006). “Brittle creep, damage, and time to failure in rocks.” J. Geophys. Res. B: Solid Earth, 111(B11), 1–17.
Ashby, M. F., and Sammis, C. G. (1990). “The damage mechanics of brittle solids in compression.” Pure Appl. Geophys., 133(3), 489–521.
Atkinson, B. K. (1984). “Subcritical crack growth in geological materials.” J. Geophys. Res. B: Solid Earth, 89(B6), 4077–4114.
Aubertin, M., Gill, D. E., and Ladanyi, B. (1991). “An internal variable model for the creep of rocksalt.” Rock Mech. Rock Eng., 24(2), 81–97.
Baud, P., and Meredith, P. G. (1997). “Damage accumulation during triaxial creep of darley dale sandstone from pore volumometry and acoustic emission.” Int. J. Rock Mech. Min. Sci., 34(3–4), 24e.1–24.e10.
Bell, A. F., Greenhough, J., Heap, M. J., and Main, I. G. (2011). “Challenges for forecasting based on accelerating rates of earthquakes at volcanoes and laboratory analogues.” Geophys. J. Int., 185(2), 718–723.
Bérest, P., Blum, P. A., Charpentier, J. P., Gharbi, H., and Valès, F. (2005). “Very slow creep tests on rock samples.” Int. J. Rock Mech. Min. Sci., 42(4), 569–576.
Brantut, N., Baud, P., Heap, M. J., and Meredith, P. G. (2012). “Micromechanics of brittle creep in rocks.” J. Geophys. Res. B: Solid Earth, 117(B8).
Brantut, N., Heap, M. J., Baud, P., and Meredith, P. G. (2014a). “Rate- and strain-dependent brittle deformation of rocks.” J. Geophys. Res. B: Solid Earth, 119, 1818–1836.
Brantut, N., Heap, M. J., Baud, P., and Meredith, P. G. (2014b). “Mechanisms of time-dependent deformation in porous limestone.” J. Geophys. Res. B: Solid Earth, 119, 5444–5463.
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, 17–43.
Brouard, B., Bérest, P., Greef, V., Beraud, J. F., Lheur, C., and Hertz, E. (2013). “Creep closure rate of a shallow salt cavern at Gellenoncourt, France.” Int. J. Rock Mech. Min. Sci., 62, 42–50.
Charles, R. J. (1958). “Static fatigue of glass. I.” J. Appl. Phys., 29(11), 1549–1553.
Chen, L., et al. (2014). “A damage-mechanism-based creep model considering temperature effect in granite.” Mech. Res. Commun., 56, 76–82.
Chen, Z., and Bai, W. (2006). “Fault creep growth model and its relationship with occurrence of earthquakes.” Geophys. J. Int., 165(1), 272–278.
Costin, L. S. (1985). “Damage mechanics in the post-failure regime.” Mech. Mater., 4(2), 149–160.
Desai, C. S., Basaran, C., and Zhang, W. (1997). “Numerical algorithms and mesh dependence in the disturbed state concept.” Int. J. Numer. Methods Eng., 40(16), 3059–3083.
Desai, C. S., and Toth, J. (1996). “Disturbed state constitutive modeling based on stress-strain and nondestructive behavior.” Int. J. Solids Struct., 33(11), 1619–1650.
Eslami, J., Hoxha, D., and Grgic, D. (2012). “Estimation of the damage of a porous limestone using continuous wave velocity measurements during uniaxial creep tests.” Mech. Mater., 49, 51–65.
Fabre, G., and Pellet, F. (2006). “Creep and time-dependent damage in argillaceous rocks.” Int. J. Rock Mech. Min. Sci., 43(6), 950–960.
Fujii, Y., Kiyama, T., Ishijima, Y., and Kodama, J. (1999). “Circumferential strain behavior during creep tests of brittle rocks.” Int. J. Rock Mech. Min. Sci., 36(3), 323–337.
Golshani, A., Oda, M., Okui, Y., Takemura, T., and Munkhtogoo, E. (2007). “Numerical simulation of the excavation damaged zone around an opening in brittle rock.” Int. J. Rock Mech. Min. Sci., 44(6), 835–845.
Heap, M. J., Baud, P., and Meredith, P. G. (2009a). “Influence of temperature on brittle creep in sandstones.” Geophys. Res. Lett, 36, L19305.
Heap, M. J., Baud, P., Meredith, P. G., Bell, A. F., and Main, I. G. (2009b). “Time-dependent brittle creep in Darley Dale sandstone.” J. Geophys. Res. D: Atmos., 114(B07203), 1–22.
Heap, M. J., Baud, P., Meredith, P. G., Vinciguerra, S., Bell, A. F., and Main, I. G. (2011). “Brittle creep in basalt and its application to time-dependent volcano deformation.” Earth Planet. Sci. Lett., 307(1–2), 71–82.
Heap, M. J., Xu, T., and Chen, C. F. (2014). “The influence of porosity and vesicle size on the brittle strength of volcanic rocks and magma.” Bull. Volcanol., 76, 856–871.
Heap, M. J., Brantut, N., Baud, P., and Meredith, P. G. (2015). “Time-dependent compaction band formation in sandstone.” J. Geophys. Res. B: Solid Earth, 120(7), 4808–4830.
Jeng, F. S., Weng, M. C., Huang, T. H., and Lin, M. L. (2002). “Deformational characteristics of weak sandstone and impact to tunnel deformation.” Tunnelling Underground Space Technol., 17(3), 263–274.
Jeong, H., Kang, S. S., and Obara, Y. (2007). “Influence of surrounding environments and strain rates on the strength of rocks subjected to uniaxial compression.” Int. J. Rock Mech. Min. Sci., 44(3), 321–331.
Kranz, R. L., Harris, W. J., and Carter, N. L. (1982). “Static fatigue of granite at 200°C.” Geophys. Res. Lett., 9(1), 1–4.
Kranz, R. L., and Scholz, C. H. (1977). “Critical dilatant volume of rocks at the onset of tertiary creep.” J. Geophys. Res. B: Solid Earth, 82(30), 4893–4898.
Lajtai, E. Z., and Schmidtke, R. H. (1986). “Delayed failure in rock loaded in uniaxial compression.” Rock Mech. Rock Eng., 19(1), 11–25.
Lockner, D. A. (1993). “Room temperature creep in saturated granite.” J. Geophys. Res. B: Solid Earth, 98(B1), 475–487.
Lu, Y. L., Elsworth, D., and Wang, L. G., (2014). “A dual-scale approach to model time-dependent deformation, creep and fracturing of brittle rocks.” Comput. Geotech, 60, 61–76.
Lyakhovsky, V., and Ben-Zion, Y. (2008). “Scaling relations of earthquakes and aseismic deformation in a damage rheology model.” Geophys. J. Int., 172(2), 651–662.
Ma, L., and Daemen, J. J. K. (2006). “An experimental study on creep of welded tuff.” Int. J. Rock Mech. Min. Sci., 43(2), 282–291.
Main, I. G. (2000). “A damage mechanics model for power-law creep and earthquake aftershock and foreshock sequences.” Geophys. J. Int., 142(1), 151–161.
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., Vogler, U. W., and Drescher, K. (1997). “Time-dependent behaviour of hard rock in deep level gold mines.” J. S. Arf. Inst. Min. Metall., 97, 135–148.
Molladavoodi, H., and Mortazavi, A. (2011). “A damage-based numerical analysis of brittle rocks failure mechanism.” Finite Elem. Anal. Des., 47(9), 991–1003.
Mortazavi, A., and Molladavoodi, H. (2012). “A numerical investigation of brittle rock damage model in deep underground openings.” Eng. Fract. Mech., 90, 101–120.
Nabarro, F. R. N. (2004). “Do we have an acceptable model of power-law creep?” Mater. Sci. Eng., A., 387–389, 659–664.
Nadimi, S., Shahriar, K., Sharifzadeh, M., and Moarefvand, P. (2011). “Triaxial creep tests and back analysis of time-dependent behaviour of Siah Bisheh cavern by 3-dimensional distinct element method.” Tunnelling Underground Space Technol., 26(1), 155–162.
Nara, Y., Takada, M., Mori, D., Owada, H., Yoneda, T., and Kaneko, K. (2010). “Subcritical crack growth and long-term strength in rock and cementitious material.” Int. J. Fract., 164(1), 57–71.
Niemeijer, A. R., Spiers, C. J., and Bos, B. (2002). “Compaction creep of quartz sand at 400–600°C: Experimental evidence for dissolution-controlled pressure solution.” Earth Planet. Sci. Lett., 195(3–4), 261–275.
Okubo, S., Fukui, K., and Hashiba, K. (2010). “Long-term creep of water-saturated tuff under uniaxial compression.” Int. J. Rock Mech. Min. Sci., 47(5), 839–844.
Phienwej, N., Thakur, P. K., and Cording, E. J. (2007). “Time-dependent response of tunnels considering creep effect.” Int. J. Geomech., 296–306.
Salganik, R. L., and Gotlib, V. A. (2000). “Continuum versus discontinuum damage mechanics of creep caused by microcracking.” Int. J. Fract., 101(3), 181–201.
Schoenball, M., Sahara, D. P., and Kohl, T. (2014). “Time-dependent brittle creep as mechanism for time-delayed wellbore failure.” Int. J. Rock Mech. Min. Sci., 70, 400–406.
Sornette, D., Vanneste, C., and Knopoff, L. (1992). “Statistical model of earthquake foreshocks.” Phys Rev A, 45(12), 8351–8357.
Su, C. J., et al. (2013). “Measurement of power-law creep parameters by instrumented indentation methods.” J. Mech. Phys. Solids, 61(2), 517–536.
Sulem, J., Panet, M., and Guenot, A. (1987). “Closure analysis in deep tunnels.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 24(3), 145–154.
Tang, C. A. (1997). “Numerical simulation of progressive rock failure and associated seismicity.” Int. J. Rock Mech. Min. Sci., 34(2), 249–261.
Tsai, L. S., Hsieh, Y. M., Weng, M. C., Huangd, T. H., and Jeng, F. S. (2008). “Time-dependent deformation behaviors of weak sandstones.” Int. J. Rock Mech. Min. Sci., 45(2), 144–154.
Wang, G. J., Zhang, L., Zhang, Y. W., and Ding, G. S. (2014). “Experimental investigations of the creep–damage–rupture behaviour of rock salt.” Int. J. Rock Mech. Min. Sci., 66, 181–187.
Wong, T. F., David, C., and Zhu, W. (1997). “The transition from brittle faulting to cataclastic flow in porous sandstones: mechanical deformation.” J. Geophys. Res. B: Solid Earth, 102(B2), 3009–3025.
Xu, T., Tang, C. A., Zhao, J., Li, L. C., and Heap, M. J. (2012). “Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks.” Geophys. J. Int., 189(3), 1781–1796.
Yahyaa, O. M. L., Aubertina, M., and Julien, M. R. (2000). “A unified representation of the plasticity, creep and relaxation behavior of rock salt.” Int. J. Rock Mech. Min. Sci., 37(5), 787–800.
Yang, C. H., Bai, S. W., and Wu, Y. M. (2000). “Stress level and loading path effect on time dependent properties of rock salt (in Chinese).” Chin. J. Rock Mech. Engng., 19, 270–275.
Yoon, J. (2007). “Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation.” Int. J. Rock Mech. Min. Sci., 44(6), 871–889.
Zhang, H. B., Wang, Z. Y., Zheng, Y. L., Duan, P. J., and Ding, S. L. (2012). “Study on triaxial creep experiment and constitutive relation of different rock salt.” Saf. Sci., 50(4), 801–805.
Zhu, W. C., Liu, J., Tang, C. A., and Zhao, X. D. (2005). “Simulation of progressive fracturing processes around underground excavations under biaxial compression.” Tunnelling Underground Space Technol., 20(3), 231–247.
Zhu, W. C., and Tang, C. A. (2004). “Micromechanical model for simulating the fracture process of rock.” Rock Mech. Rock Eng., 37(1), 25–56.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 17 • Issue 1 • January 2017
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jun 16, 2015
Accepted: Mar 31, 2016
Published online: May 5, 2016
Discussion open until: Oct 5, 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.