Numerical Investigation of Damage Evolution and Localized Fracturing of Brittle Rock in Compression
Publication: Journal of Performance of Constructed Facilities
Volume 31, Issue 5
Abstract
In the present paper, a numerical model for deformation and fracturing of brittle rocks is used to study the damage evolution and localized fracturing of brittle rocks based on statistical mesoscopic damage mechanics. In the model, material heterogeneity and the mesoscopic renormalization concept are introduced to consider the interaction among microcracks in rock. The temporal and spatial evolution of acoustic emissions in the stressed rock are also described. Correspondingly, numerical tests on rock specimens with different heterogeneities, porosities, and scales are performed to investigate the damage evolution and localized fracturing of brittle rocks. The localized damage and fracturing of brittle rocks induced by microstructural damage is investigated. The study shows that heterogeneity, porosities, and scales of rock specimen have significant impact on damage evolution and localized fracturing mode. In addition, the study reveals that the postpeak response of stress-strain curve is due to the deformation of the structural elements, and localization means that the descending branch of the stress-strain curve of the rock specimen is size dependent, and the stress-strain curve can therefore not be regarded as a pure material property.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The joint support provided by NSFC (Grant Nos. 51474051, 41672301, and 51404067) and the National Basic Research Program of China (2013CB227900 and 2014CB047100), Fundamental Research Funds for the Central Universities (N150102002 and L1501004), and Partenariats Hubert Curien (PHC) grant—Programme Cai Yuanpei (Grant No. 36605ZB) is highly 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), B11201.
Bai, Y. L., Bai, J., Li, H. L., Ke, F. J., and Xia, M. F. (2000). “Damage evolution, localization and failure of solids subjected to impact loading.” Int. J. Impact Eng., 24(6–7), 685–701.
Barton, N. (2016). “Non-linear shear strength for rock, rock joints, rockfill and interfaces.” Innovative Infrastruct. Solutions, 1(1), 1–19.
Bažant, Z. P. (1984). “Size effect in blunt fracture: Concrete, rock, metal.” J. Eng. Mech., 518–535.
Bažant, Z. P. (1989). “Identification of strain-softening constitutive relation from uniaxial tests by series coupling model for localization.” Cem. Concr. Res., 19(6), 973–977.
Bažant, Z. P., and Ozbolt, J. (1992). “Compression failure of quasibrittle material: Nonlocal microplane model.” J. Eng. Mech., 540–556.
Bažant, Z. P., and Pijaudier-Cabot, G. (1988). “Nonlocal continuum damage, localization instability and convergence.” J. Appl. Mech., 55(2), 287–293.
Blair, S., and Cook, N. (1998a). “Analysis of compressive fracture in rock using statistical techniques. Part I: A non-linear rule-based model.” Int. J. Rock Mech. Min. Sci., 35(7), 837–848.
Blair, S., and Cook, N. (1998b). “Analysis of compressive fracture in rock using statistical techniques. Part II: Effect of microscale heterogeneity on macroscopic deformation.” Int. J. Rock Mech. Min. Sci., 35(7), 849–861.
Brady, B. H. G., and Brown, E. T. (2004). Rock mechanics for underground mining, Kluwer Academic Publishers, London.
Carmona, J. R., and Ruiz, G. (2014). “Bond and size effects on the shear capacity of RC beams without stirrups.” Eng. Struct., 66(0), 45–56.
Carpinteri, A., Lacidogna, G., and Niccolini, G. (2007). “Acoustic emission monitoring of medieval towers considered as sensitive earthquake receptors.” Nat. Hazards Earth Syst. Sci., 7(2), 251–261.
Cox, S., and Meredith, P. (1993). “Microcrack formation and material softening in rock measured by monitoring acoustic emissions.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 30(1), 11–24.
Cusatis, G., Pelessone, D., and Mencarelli, A. (2011). “Lattice discrete particle model (LDPM) for failure behavior of concrete. I: Theory.” Cem. Concr. Compos., 33(9), 881–890.
Darlington, W. J., Ranjith, P. G., and Choi, S. K. (2011). “The effect of specimen size on strength and other properties in laboratory testing of rock and rock-like cementitious brittle materials.” Rock Mech Rock Eng., 44(5), 513–529.
Dequiedt, J. L. (2013). “Localization in heterogeneous materials: A variational approach and its application to polycrystalline solids.” Int. J. Plast., 48(0), 92–110.
Fanella, D., and Krajcinovic, D. (1988). “A micromechanical model for concrete in compression.” Eng. Fract. Mech., 29(1), 49–66.
Gibowicz, S. J., and Lasocki, S. (2001). “Seismicity induced by mining: Ten years later.” Adv. Geophys., 44, 39–181.
Golshani, A., Okui, Y., Oda, M., and Takemura, T. (2006). “A micromechanical model for brittle failure of rock and its relation to crack growth observed in triaxial compression tests of granite.” Mech. Mater., 38(4), 287–303.
Hao, S., Wang, H., Xia, M., Ke, F., and Bai, Y. (2007). “Relationship between strain localization and catastrophic rupture.” Theor. Appl. Fract. Mech., 48(1), 41–49.
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(9), 1–15.
Hicher, P., Wahyudi, H., and Tessier, D. (1994). “Microstructural analysis of strain localisation in clay.” Comput. Geotech., 16(3), 205–222.
Ingraham, M., Issen, K., and Holcomb, D. (2013). “Use of acoustic emissions to investigate localization in high-porosity sandstone subjected to true triaxial stresses.” Acta Geotech., 8(6), 645–663.
Jin, C. F., He, Q. C., and Shao, J. F. (2013). “An energy-based analysis for aggregate size effect on mechanical strength of cement-based materials.” Eng. Fract. Mech., 102(0), 207–217.
Klai, M., and Bouassida, M. (2016). “Study of the behavior of Tunis soft clay.” Innovative Infrastructure Solutions, 1(1), 31.
Krajcinovic, D., and Vujosevic, M. (1998). “Strain localization—Short to long correlation length transition.” Int. J. Solids Struct., 35(31–32), 4147–4166.
Kueppers, U., Scheu, B., Spieler, O., and Dingwell, D. B. (2005). “Field-based density measurements as tool to identify preeruption dome structure: Set-up and first results from Unzen volcano, Japan.” J. Volcano. Geotherm. Res., 141(1), 65–75.
Labuz, J. F., and Biolzi, L. (1991). “Class I vs class II stability: A demonstration of size effect.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 28(2), 199–205.
Lan, H., Martin, C. D., and Hu, B. (2010). “Effect of heterogeneity of brittle rock on micromechanical extensile behavior during compression loading.” J. Geophys. Res.: Solid Earth, 115(B1), 1–14.
Lemaitre, J., and Chaboche, J. L. (2001). Mécanique des matériaux solides, Dunod, Paris.
Lemaitre, J., and Desmorat, R. (2005). Engineering damage mechanics, Springer, Berlin.
Li, T., Cai, M. F., and Cai, M. (2007). “A review of mining-induced seismicity in China.” Int. J. Rock Mech. Min. Sci., 44(8), 1149–1171.
Liu, H. Y., Roquete, M., Kou, S. Q., and Lindqvist, P. A. (2004). “Characterization of rock heterogeneity and numerical verification.” Eng. Geol., 72(1–2), 89–119.
Liu, X., Scarpas, A., and Blaauwendraad, J. (2005). “Numerical modelling of nonlinear response of soil. Part 2: Strain localization investigation on sand.” Int. J. Solids Struct., 42(7), 1883–1907.
Lockner, D., Byerlee, J., Kuksenko, V., Ponomarev, A., and Sidorin, A. (1991). “Quasi-static fault growth and shear fracture energy in granite.” Nature, 350(6313), 39–42.
Markeset, G., and Hillerborg, A. (1995). “Softening of concrete in compression—Localization and size effects.” Cem. Concr. Res., 25(4), 702–708.
Matic, P., and Geltmacher, A. B. (2001). “A cellular automaton-based technique for modeling mesoscale damage evolution.” Comput. Mater. Sci., 20(1), 120–141.
Mattei, N. J., Mehrabadi, M. M., and Zhu, H. (2007). “A micromechanical constitutive model for the behavior of concrete.” Mech. Mater., 39(4), 357–379.
Negi, P., Chakraborty, T., and Bhalla, S. (2017). “Damage monitoring of dry and saturated rocks using piezo transducers.” J. Test. Eval., 45(1), 169–181.
Noorian-Bidgoli, M., and Jing, L. (2015). “Stochastic analysis of strength and deformability of fractured rocks using multi-fracture system realizations.” Int. J. Rock Mech. Min. Sci., 78(0), 108–117.
Oka, F., Adachi, T., and Yashima, A. (1995). “A strain localization analysis using a viscoplastic softening model for clay.” Int. J. Plast., 11(5), 523–545.
Oka, F., Higo, Y., and Kimoto, S. (2002). “Effect of dilatancy on the strain localization of water-saturated elasto-viscoplastic soil.” Int. J. Solids Struct., 39(13), 3625–3647.
Schlangen, E., and Garboczi, E. (1997). “Fracture simulations of concrete using lattice models: Computational aspects.” Eng. Fract. Mech., 57(2), 319–332.
Sellers, E., and Napier, J. (1997). “A comparative investigation of micro-flaw models for the simulation of brittle fracture in rock.” Comput. Mech., 20(1), 164–169.
Shea, T., Houghton, B. F., Gurioli, L., Cashman, K. V., Hammer, J. E., and Hobden, B. J. (2010). “Textural studies of vesicles in volcanic rocks: An integrated methodology.” J. Volcanol. Geotherm. Res., 190(3), 271–289.
Song, J.-J., Lee, C.-I., and Seto, M. (2001). “Stability analysis of rock blocks around a tunnel using a statistical joint modeling technique.” Tunnelling Underground Space Technol., 16(4), 341–351.
Tang, C., et al. (2008a). “Fracture spacing in layered materials: A new explanation based on two-dimensional failure process modeling.” Am. J. Sci., 308(1), 49–72.
Tang, C. A. (1997). “Numerical simulation of progressive rock failure and associated seismicity.” Int. J. Rock Mech. Min. Sci., 34(2), 249–261.
Tang, C. A., et al. (2008b). “Fracture spacing in layered materials: A new explanation based on two-dimensional failure process modeling.” Am. J. Sci., 308(1), 49–72.
Wang, E., and Shrive, N. (1995). “Brittle fracture in compression: Mechanisms, models and criteria.” Eng. Fract. Mech., 52(6), 1107–1126.
Wasantha, P., Ranjith, P., and Viete, D. R. (2014). “Specimen slenderness and the influence of joint orientation on the uniaxial compressive strength of singly jointed rock.” J. Mater. Civ. Eng., .
Wawersik, W., and Fairhurst, C. (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(3), 293–297.
Wright, H. M., Cashman, K. V., Gottesfeld, E. H., and Roberts, J. J. (2009). “Pore structure of volcanic clasts: Measurements of permeability and electrical conductivity.” Earth Planet. Sci. Lett., 280(1), 93–104.
Wu, X. Y., Baud, P., and Wong, T.-F. (2000). “Micromechanics of compressive failure and spatial evolution of anisotropic damage in darley dale sandstone.” Int. J. Rock Mech. Min. Sci., 37(1), 143–160.
Xenos, D., Grégoire, D., Morel, S., and Grassl, P. (2015). “Calibration of nonlocal models for tensile fracture in quasi-brittle heterogeneous materials.” J. Mech. Phys. Solids, 82, 48–60.
Xu, T., Ranjith, P., Wasantha, P., Zhao, J., Tang, C., and Zhu, W. (2013). “Influence of the geometry of partially-spanning joints on mechanical properties of rock in uniaxial compression.” Eng. Geol., 167, 134–147.
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.
Xu, X. H., Ma, S. P., Xia, M. F., Ke, F. J., and Bai, Y. L. (2004). “Damage evaluation and damage localization of rock.” Theor. Appl. Fract. Mech., 42(2), 131–138.
Yan, F., Feng, X.-T., Pan, P.-Z., and Li, S.-J. (2014). “Discontinuous cellular automaton method for crack growth analysis without remeshing.” Appl. Mathem. Modell., 38(1), 291–307.
Yang, S. Q., Xu, T., He, L., Jing, H. W., Wen, S., and Yu, Q. L. (2015). “Numerical study on failure behavior of brittle rock specimen containing pre-existing combined flaws under different confining pressure.” Arch. Civ. Mech. Eng., 15(4), 1085–1097.
Zang, A., Wagner, C. F., and Dresen, G. (1996). “Acoustic emission, microstructure, and damage model of dry and wet sandstone stressed to failure.” J. Geophys. Res.: Solid Earth (1978–2012), 101(B8), 17507–17521.
Zhang, J., and Yang, J. (2013). “Advances in micromechanical constitutive theories and modeling in asphalt mixture: A review.” Procedia—Social Behav. Sci., 96(0), 1304–1314.
Zhang, L., Ren, Z., and Lu, Q. (2017). “Simulation of mesofracture process of asphalt mixture using digital image processing and extended finite-element method.” J. Test. Eval., 45(1), 281–293.
Zhao, G.-F., Khalili, N., Fang, J., and Zhao, J. (2012). “A coupled distinct lattice spring model for rock failure under dynamic loads.” Comput. Geotech., 42, 1–20.
Information & Authors
Information
Published In
Journal of Performance of Constructed Facilities
Volume 31 • Issue 5 • October 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Mar 21, 2016
Accepted: Feb 6, 2017
Published online: Apr 26, 2017
Discussion open until: Sep 26, 2017
Published in print: Oct 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.