Technical Papers
Feb 22, 2018

Statistical Micromechanics-Based Modeling for Low-Porosity Rocks under Conventional Triaxial Compression

Publication: International Journal of Geomechanics
Volume 18, Issue 5

Abstract

It is acknowledged that porosity and voids encapsulated in rocks significantly affect the mechanical behavior of specimens from laboratory observations. In this study, a proposed conceptual porosity model was idealized to evaluate the change of voids fraction caused by straining, and the equivalent porosity was introduced to indirectly characterize material properties on a macroscopic scale. A micromechanics-based analytical method was developed to track the progressive failure of specimens induced by the localization strains; in particular, the shear-failure factor was assumed to be a cumulative distribution function of the shear straining. On this basis, a phenomenological constitutive model for low-porosity rocks, generally within 5%, was further developed with only a few model parameters. In addition, predictions of multiaxial stress-strain relation and volumetric strains were examined by comparing the observed results from laboratory data. A parametric study was carried out to address how the variation of porosity impacts mechanical behaviors of rocks in the proposed model.

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Acknowledgments

The research was granted by the National Natural Science Foundation of China (Grants 51608540 and 51478178), and supported by the Fundamental Research Funds for the Central Universities. The authors gratefully thank the anonymous reviewers for their constructive criticism and valuable suggestions.

References

Aubertin, M., and Li, L. (2004). “A porosity-dependent inelastic criterion for engineering materials.” Int. J. Plast., 20(12), 2179–2208.
Bažant, Z. P., and Pang, S. D. (2007). “Activation energy based extreme value statistics and size effect in brittle and quasibrittle fracture.” J. Mech. Phys. Solids, 55(1), 91–131.
Bésuelle, P., Desrues, J., and Raynaud, S. (2000). “Experimental characterisation of the localisation phenomenon inside a Vosges sandstone in a triaxial cell.” Int. J. Rock Mech. Min. Sci., 37(8), 1223–1237.
Borja, R. I. (2002). “Bifurcation of elastoplastic solids to shear band mode at finite strain.” Comput. Methods Appl. Mech. Eng., 191(46), 5287–5314.
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.
Collin, F., Cui, Y. J., Schroeder, C., and Charlier, R. (2002). “Mechanical behaviour of Lixhe chalk partly saturated by oil and water: Experiment and modelling.” Int. J. Numer. Anal. Methods Geomech., 26(9), 897–924.
Crook, T., Willson, S., Yu, J. G., and Owen, R. (2003). “Computational modelling of the localized deformation associated with borehole breakout in quasi-brittle materials.” J. Petrol. Sci. Eng., 38(3–4), 177–186.
Desrues, J. 1998. “Localisation patterns in ductile and brittle geomaterials”. Material instabilities in solid, de Borst, R., and van der Giessen, E., eds., Wiley, New York, pp. 137–158.
Diederichs, M. S., Kaiser, P. K., and Eberhardt, E. (2004). “Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation.” Int. J. Rock Mech. Min. Sci., 41(5), 785–812.
El Bied, A., Sulem, J., and Martineau, F. (2002). “Microstructure of shear zones in Fontainebleau sandstone.” Int. J. Rock Mech. Min. Sci., 39(7), 917–932.
Gramberg, J. (1988). A non-conventional view on rock mechanics and fracture mechanics, Balkema, Rotterdam, Netherlands.
Guo, T. F., Faleskog, J., and Shih, C. F. (2008). “Continuum modeling of a porous solid with pressure-sensitive dilatant matrix.” J. Mech. Phys. Solids, 56(6), 2188–2212.
He, C., Okubo, S., and Nishimatsu, Y. (1990). “A study of the class II behaviour of rock.” Rock Mech. Rock Eng., 23(4), 262–273.
Horii, H., and Nemat-Nasser, S. (1985). “Compression-induced microcrack growth in brittle solids: Axial splitting and shear failure.” J Geophys. Res., 90(B4), 3105–3125.
Hudson, A. J., and Harrison, J. P. (1997). Engineering rock mechanics: An introduction to the principles, Pergamon, Oxford, U.K.
ISRM (International Society of Rock Mechanics). (1979). “Suggested methods for determining water content, porosity, density, absorption and related properties and swelling and slake-durability index properties.” Lisbon, Portugal.
Issen, K. A. (2002). “The influence of constitutive models on localization conditions for porous rock.” Eng. Fract. Mech., 69(17), 1891–1906.
Karner, S. L., Chester, F. M., Kronenberg, A. K., and Chester, J. S. (2003). “Subcritical compaction and yielding of granular quartz sand.” Tectonophysics, 377(3–4), 357–381.
Krajcinovic, D., and Rinaldi, A. (2005). “Statistical damage mechanics—Part I: Theory.” J. Appl. Mech., 72(1), 76–85.
Lade, P. V. (1988). “Effects of voids and volume changes on the behaviour of frictional materials.” Int. J. Numer. Anal. Methods Geomech., 12(4), 351–370.
Lade, P. V., and Kim, M. K. (1995). “Single hardening constitutive model for soil, rock and concrete.” Int. J. Solids Struct., 32(14), 1963–1978.
Lade, P. V., Nelson, R. B., and Ito, Y. M. (1987). “Non-associated flow and stability of granular materials.” J. Eng. Mech., 1302–1318.
Lemaitre, J. (1990). A course on damage mechanics, 2nd Ed., Springer, New York.
Li, C. (1995). “Micromechanics modelling for stress-strain behaviour 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, 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.
Maghous, S., Dormieux, L., and Barthélémy, J. F. (2009). “Micromechanical approach to the strength properties of frictional geomaterials.” Eur. J. Mech. A/Solid, 28(1), 179–188.
Martin, C. D., and Chandler, N. A. (1994). “The progressive fracture of Lac du Bonnet granite.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 31(6), 643–659.
Martínez-Martínez, J., Fusi, N., Galiana-Merino, J. J., Benavente, D., and Crosta, G. B. (2016). “Ultrasonic and X-ray computed tomography characterization of progressive fracture damage in low-porous carbonate rocks.” Eng. Geol., 200, 47–57.
McAuliffe, C., and Waisman, H. (2015). “On the importance of nonlinear elastic effects in shear band modeling.” Int. J. Plast., 71, 10–31.
Menéndez, B., Zhu, W., and Wong, T. F. (1996). “Micromechanics of brittle faulting and cataclastic flow in Berea sandstone.” J. Struct. Geol., 18(1), 1–16.
Priol, G., Collin, F., DeGennaro, V., Delage, P., and Cui, Y. J. (2002). “On the collapse behaviour of oil reservoir chalk.” Géotechnique, 54, 415–420.
Renner, J., and Rummel, F. (1996). “The effect of experimental and microstructural parameters on the transition from brittle failure to cataclastic flow of carbonate.” Tectonophysics, 258(1–4), 151–169.
Rinaldi, A., and Lai, Y. C. (2007). “Statistical damage theory of 2D lattices: Energetics and physical foundations of damage parameter.” Int. J. Plast., 23(10–11), 1796–1825.
Shafiro, B., and Kachanov, M. (1997). “Materials with fluid-filled pores of various shapes: Effective elastic properties and fluid pressure polarization.” Int. J. Solids Struct., 34(27), 3517–3540.
Spiezia, N., Salomoni, V. A., and Majorana, C. E. (2016). “Plasticity and strain localization around a horizontal wellbore drilled through a porous rock formation.” Int. J. Plast., 78, 114–144.
Stefanov, Y. P., Chertov, M. A., Aidagulov, G. R., and Myasnikov, A. V. (2011). “Dynamics of inelastic deformation of porous rocks and formation of localized compaction zones studied by numerical modeling.” J. Mech. Phys. Solids, 59(11), 2323–2340.
Tan, X., Konietzky, H., and Frühwirt, T. (2014). “Laboratory observation and numerical simulation of permeability evolution during progressive failure of brittle rocks.” Int. J. Rock Mech. Min. Sci., 68, 167–176.
Taylor, L. M., Chen, E. P., and Kuszmaul, J. S. (1986). “Microcrack induced damage accumulation in brittle rock under dynamic loading.” Comput. Methods Appl. Mech. Eng., 55(3), 301–320.
Wawersik, W. R., and Fairhurst, C. A. (1970). “A study of brittle rock fracture in laboratory compression experiments.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 7(5), 561–575.
Weibull, W. (1951). “A statistical distribution function of wide applicability.” J. Appl. Mech., 18, 293–297.
Xu, X. H., Ma, S. P., Xia, M. F., Ke, F. J., and Bai, Y. L. (2005). “Synchronous multi-scale observations on rock damage and rupture.” Theor. Appl. Fract. Mech., 44(2), 146–156.
Xue, D. J., et al. (2012). “Deformation analysis of transversely isotropic coal-rock mass with porous and cracks.” Int. J. Min. Sci. Technol., 22(6), 809–815.
Yu, C., Ji, S., and Li, Q. (2016). “Effects of porosity on seismic velocities, elastic moduli and Poisson’s ratios of solid materials and rocks.” J. Rock Mech. Geotech. Eng., 8(1), 35–49.
Yuan, S. C., and Harrison, J. P. (2004). “An empirical dilatancy index for the dilatant deformation of rock.” Int. J. Rock Mech. Min. Sci., 41(4), 679–686.
Yue, Z. Q., Shang, Y. J., Hu, R. L., and Tu, X. B. (2004). “Five test methods for porosity of completely decomposed granite in Hong Kong.” Int. J. Rock Mech. Min. Sci., 41(1), 201–208.
Zeng, T., Shao, J. F., and Xu, W. Y. (2015). “A micromechanical model for the elastic-plastic behavior of porous rocks.” Comput. Geotech., 70, 130–137.
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.
Zhao, H., Shi, C. J., Zhao, M. H., and Li, X. B. (2017). “Statistical damage constitutive model for rocks considering residual strength.” Int. J. Geomech., 04016033.
Zhao, H., Zhang, C., Cao, W. G., and Zhao, M. H. (2016). “Statistical meso-damage model for quasi-brittle rocks to account for damage tolerance principle.” Environ. Earth Sci., 75(10), 862.
Zhou, G. L., Lee, P. K. K., Tham, L. G., and Tsui, Y. (1999). “Strain localization for rocks with shear failure.” Proc., 13th ASCE Engineering Mechanics Division Conf., The Johns Hopkins Univ., Baltimore.
Zhou, G. L., Tham, 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), 391–414.
Zhou, X. P., and Yang, H. Q. (2010). “Micromechanical modeling of dynamic compressive responses of mesoscopic heterogeneous brittle rock.” Theor. Appl. Fract. Mech., 48, 1–20.
Zienkiewicz, O. C. (1982). “Basic formulation of static and dynamic behaviours of soil and other porous media.” Appl. Math. Mech., 3(4), 457–468.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 18Issue 5May 2018

History

Received: Mar 30, 2017
Accepted: Oct 27, 2017
Published online: Feb 22, 2018
Published in print: May 1, 2018
Discussion open until: Jul 22, 2018

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Heng Zhao, Ph.D. [email protected]
Assitant Professor, Institute of Geotechnical Engineering, Hunan Univ., Changsha 410082, People’s Republic of China (corresponding author). E-mail: [email protected]
Ph.D. Candidate, Institute of Geotechnical Engineering, Hunan Univ., Changsha 410082, People’s Republic of China. E-mail: [email protected]
Minghua Zhao [email protected]
Professor, Institute of Geotechnical Engineering, Hunan Univ., Changsha 410082, People’s Republic of China. E-mail: [email protected]
Caijun Shi, M.ASCE [email protected]
Professor, College of Civil Engineering, Hunan Univ., Changsha 410082, People’s Republic of China. E-mail: [email protected]

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