Abstract
The inclusion plays a crucial role in mastering mechanical responses and cracking behaviors of brittle materials. In this work, a series of uniaxial compression tests were performed to investigate the effect of infilling composition (i.e., proportion and grain size) on the mechanical responses of brittle materials. Digital image correlation (DIC) and acoustic emission (AE) techniques were applied, respectively, to measure the surface strain and internal AE signals of brittle materials for further analysis of failure behaviors. The results demonstrate that both infilling proportion and grain size significantly influence the cracking processes and failure modes of brittle materials. The uniaxial compressive strength (UCS) and deformation modulus increase with the increase of the cement proportion or infilling grain size due to the stress redistribution around the inclusions. The debonding behavior between inclusion and matrix becomes significant when the specimens have a higher cement proportion or larger grain sizes. Interestingly, the number of accumulative and peak AE events is negatively correlated to the cement proportion and grain size. Three failure modes (tensile failure, shear failure, and mixed failure) are observed, and the mixed failure mode is the dominant one. Using a bonded-particle model (BPM), the numerical results can verify the experimental observation regarding debonding and cracking behaviors based on the full-field stresses and fragment characteristics analysis, and further reveal the failure mechanism of the specimen with infilling with different infilling compositions. Based on elasticity and complex variable theory, the derived dimensionless stresses around the inclusion interface can well explain the debonding behavior with rigid and soft inclusions, which is in reasonable agreement with numerical results. The current study could provide technical grantees for the safety and reliability of practical engineerings such as slope engineering, back-filling in mining, and tunnelling engineering.
Highlights
-
The cracking processes and failure modes of brittle materials are significantly influenced by both infilling proportion and grain size.
-
The debonding behaviour between inclusion and matrix becomes significant when the specimens have a higher cement proportion or larger grain sizes.
-
The analytical stresses around the inclusion interface can well explain the debonding behaviour of specimens with inclusions of different degree stiffness.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ashby MF, Sammis CG (1990) The damage mechanics of brittle solids in compression. Pure Appl Geophys 133:489–521. https://doi.org/10.1007/BF00878002
Bobet A, Einstein H (1998) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92:221–252. https://doi.org/10.1023/A:1007460316400
Cai M, Kaiser PK, Tasaka Y et al (2004a) Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations. Int J Rock Mech Min Sci 41:833–847. https://doi.org/10.1016/j.ijrmms.2004.02.001
Cai M, Kaiser PK, Uno H et al (2004b) Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the GSI system. Int J Rock Mech Min Sci 41:3–19. https://doi.org/10.1016/S1365-1609(03)00025-X
Cox HL (1952) The elasticity and strength of paper and other fibrous materials. Br J Appl Phys 3:72–79. https://doi.org/10.1088/0508-3443/3/3/302
Duan K (2016) Micromechanical modeling of inherently anisotropic rock and its application in borehole breakout analyses. The University of Hong Kong, Hong Kong
Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond Ser A 241:376–396. https://doi.org/10.1098/rspa.1957.0133
Fan X, Yang Z, Li K (2021) Effects of the lining structure on mechanical and fracturing behaviors of four-arc shaped tunnels in a jointed rock mass under uniaxial compression. Theor Appl Fract Mech 112:102887. https://doi.org/10.1016/j.tafmec.2020.102887
Gao M, Xie J, Gao Y et al (2021) Mechanical behavior of coal under different mining rates: a case study from laboratory experiments to field testing. Int J Min Sci Technol 31:825–841. https://doi.org/10.1016/j.ijmst.2021.06.007
Germanovich LN, Salganik RL, Dyskin AV, Lee KK (1994) Mechanisms of brittle fracture of rock with pre-existing cracks in compression. Pure Appl Geophys 143:117–149. https://doi.org/10.1007/BF00874326
Goodier JN (1933) Concentration of stress around spherical and cylindrical inclusions and flaw. J Appl Mech 55:39–44. https://doi.org/10.1115/1.4012173
Griffith AA (1921) The phenomena of rupture and flow in solids. Philos Trans R Soc Lond Ser A 221:163–198. https://doi.org/10.1098/rsta.1921.0006
Hoek E, Martin CD (2014) Fracture initiation and propagation in intact rock: a review. J Rock Mech Geotech Eng 6:287–300. https://doi.org/10.1016/j.jrmge.2014.06.001
Horii H, Nemat-Nasser S (1985) Compression-induced microcrack growth in brittle solids: Axial splitting and shear failure. J Geophys Res 90:3105. https://doi.org/10.1029/JB090iB04p03105
Jaeger JC, Cook NGW, Zimmerman RW (2007) Fundamentals of rock mechanics.
Janeiro RP, Einstein HH (2010) Experimental study of the cracking behavior of specimens containing inclusions (under uniaxial compression). Int J Fract 164:83–102. https://doi.org/10.1007/s10704-010-9457-x
Jivkov AP (2014) Structure of micro-crack population and damage evolution in quasi-brittle media. Theor Appl Fract Mech 70:1–9. https://doi.org/10.1016/j.tafmec.2014.04.003
Khaund AK, Nicholson PS (1980) Fracture of a brittle composite: influence of elastic mismatch and interfacial bonding. J Mater Sci 15:177–187. https://doi.org/10.1007/BF00552443
Kirsch EG (1898) Die Theorie der Elastizität und die Bedürfnisse der Festigkeitslehre. Z Des Vereins Dtsch Ing 42:797–807
Li JC, Li NN, Li HB, Zhao J (2017) An SHPB test study on wave propagation across rock masses with different contact area ratios of joint. Int J Impact Eng 105:109–116. https://doi.org/10.1016/j.ijimpeng.2016.12.011
Li XF, Zhang QB, Li HB, Zhao J (2018) Grain-based discrete element method (GB-DEM) modelling of multi-scale fracturing in rocks under dynamic loading. Rock Mech Rock Eng 51:3785–3817. https://doi.org/10.1007/s00603-018-1566-2
Li JC, Rong LF, Li HB, Hong SN (2019) An SHPB test study on stress wave energy attenuation in jointed rock masses. Rock Mech Rock Eng 52:403–420. https://doi.org/10.1007/s00603-018-1586-y
Lin Q, Labuz JF (2013) Fracture of sandstone characterized by digital image correlation. Int J Rock Mech Min Sci 60:235–245. https://doi.org/10.1016/j.ijrmms.2012.12.043
Lin Q, Cao P, Cao R et al (2020) Mechanical behavior around double circular openings in a jointed rock mass under uniaxial compression. Arch Civ Mech Eng 20:1–18. https://doi.org/10.1007/s43452-020-00027-z
Lisjak A, Grasselli G (2014) A review of discrete modeling techniques for fracturing processes in discontinuous rock masses. J Rock Mech Geotech Eng J 6:301–314. https://doi.org/10.1016/j.jrmge.2013.12.007
Liu L, Li H, Li X et al (2020a) Underlying mechanisms of crack initiation for granitic rocks containing a single pre-existing flaw: insights from digital image correlation (DIC) analysis. Rock Mech Rock Eng 54:857–873. https://doi.org/10.1007/s00603-020-02286-x
Liu L, Li H, Li X, Wu R (2020b) Full-field strain evolution and characteristic stress levels of rocks containing a single pre-existing flaw under uniaxial compression. Bull Eng Geol Environ 79:3145–3161. https://doi.org/10.1007/s10064-020-01764-4
Luo Y, Gong FQ, Zhu CQ (2022) Experimental investigation on stress-induced failure in D-shaped hard rock tunnel under water-bearing and true triaxial compression conditions. B Eng Geol Environ. https://doi.org/10.1007/s10064-021-02564-0
Maji AK, Shah SP (1989) Application of acoustic emission and laser holography to study microfracture in concrete. In: Lew HS (ed) Nondestructive testing. American Concrete Institute, Washington, pp 83–110
Martin CD, Read RS, Martino JB (1997) Observations of brittle failure around a circular test tunnel. Int J Rock Mech Min Sci 34:1065–1073. https://doi.org/10.1016/s1365-1609(97)90200-8
Mas Ivars D, Pierce ME, Darcel C et al (2011) The synthetic rock mass approach for jointed rock mass modelling. Int J Rock Mech Min Sci 48:219–244. https://doi.org/10.1016/j.ijrmms.2010.11.014
Miao S, Pan PZ, Wu Z et al (2018) Fracture analysis of sandstone with a single filled flaw under uniaxial compression. Eng Fract Mech 204:319–343. https://doi.org/10.1016/j.engfracmech.2018.10.009
Nemat-Nasser S, Horii H (1982) Compression-induced nonplanar crack extension with application to splitting, exfoliation, and rockburst. J Geophys Res 87:6805. https://doi.org/10.1029/JB087iB08p06805
Nguyen TL, Hall SA, Vacher P, Viggiani G (2011) Fracture mechanisms in soft rock: Identification and quantification of evolving displacement discontinuities by extended digital image correlation. Tectonophysics 503:117–128. https://doi.org/10.1016/j.tecto.2010.09.024
Paliwal B, Ramesh KT (2008) An interacting micro-crack damage model for failure of brittle materials under compression. J Mech Phys Solids 56:896–923. https://doi.org/10.1016/j.jmps.2007.06.012
Pan PZ, Miao S, Jiang Q et al (2019) The influence of infilling conditions on flaw surface relative displacement induced cracking behavior in hard rock. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-019-02033-x
Peng J, Rong G, Cai M, Zhou CB (2015) A model for characterizing crack closure effect of rocks. Eng Geol 189:48–57. https://doi.org/10.1016/j.enggeo.2015.02.004
Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41:1329–1364. https://doi.org/10.1016/j.ijrmms.2004.09.011
Rahimzadeh Kivi I, Ameri M, Molladavoodi H (2018) Shale brittleness evaluation based on energy balance analysis of stress-strain curves. J Pet Sci Eng 167:1–19. https://doi.org/10.1016/j.petrol.2018.03.061
Sih GC (1974) Strain-energy-density factor applied to mixed mode crack problems. Int J Fract 10:305–321. https://doi.org/10.1007/BF00035493
Tasdemir MA, Maji AK, Shah SP (1990) Crack propagation in concrete under compression. J Eng Mech 116:1058–1076. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:5(1058)
Walsh JB (1965) The effect of cracks on the compressibility of rock. J Geophys Res 70:381. https://doi.org/10.1029/JZ070i002p00381
Wang F, Cao P, Wang Y et al (2020) Combined effects of cyclic load and temperature fluctuation on the mechanical behavior of porous sandstones. Eng Geol 266:105466. https://doi.org/10.1016/j.enggeo.2019.105466
Wang S, Li J, Li X, He L (2022) Dynamic photoelastic experimental study on the influence of joint surface geometrical property on wave propagation and stress disturbance. Int J Rock Mech Min Sci 149:104985. https://doi.org/10.1016/j.ijrmms.2021.104985
Wong LNY, Einstein HH (2009) Crack coalescence in molded gypsum and carrara marble: part 1. Macroscopic observations and interpretation. Rock Mech Rock Eng 42:475–511. https://doi.org/10.1007/s00603-008-0002-4
Wong LNY, Zou C, Cheng Y (2014) Fracturing and failure behavior of carrara marble in quasistatic and dynamic Brazilian disc tests. Rock Mech Rock Eng 47:1117–1133. https://doi.org/10.1007/s00603-013-0465-9
Wu H, Kulatilake PHSW, Zhao G et al (2019) A comprehensive study of fracture evolution of brittle rock containing an inverted U-shaped cavity under uniaxial compression. Comput Geotech 116:103219. https://doi.org/10.1016/j.compgeo.2019.103219
Xie R, Qu T, Qian G (2007) Structural geology. China University of Mining and Technology Press, Xuzhou
Xie H, Zhu J, Zhou T et al (2020) Conceptualization and preliminary study of engineering disturbed rock dynamics. Geomech Geophys Geo-Energy Geo-Resour. https://doi.org/10.1007/s40948-020-00157-x
Yang SQ, Jiang YZ, Xu WY, Chen XQ (2008) Experimental investigation on strength and failure behavior of pre-cracked marble under conventional triaxial compression. Int J Solids Struct 45:4796–4819. https://doi.org/10.1016/j.ijsolstr.2008.04.023
Yu F, Sun D, Wang J, Hu M (2019) Influence of aggregate size on compressive strength of pervious concrete. Constr Build Mater 209:463–475. https://doi.org/10.1016/j.conbuildmat.2019.03.140
Zaitsev YB, Wittmann FH (1981) Simulation of crack propagation and failure of concrete. Matériaux Constr 14:357–365. https://doi.org/10.1007/BF02478729
Zhang H, Huang G, Song H, Kang Y (2012) Experimental investigation of deformation and failure mechanisms in rock under indentation by digital image correlation. Eng Fract Mech 96:667–675. https://doi.org/10.1016/j.engfracmech.2012.09.012
Zhao Z, Zhou D (2016) Mechanical properties and failure modes of rock samples with grout-infilled flaws: a particle mechanics modeling. J Nat Gas Sci Eng 34:702–715. https://doi.org/10.1016/j.jngse.2016.07.022
Zhao Y, Zhang L, Wang W et al (2016) Cracking and stress-strain behavior of rock-like material containing two flaws under uniaxial compression. Rock Mech Rock Eng 49:2665–2687. https://doi.org/10.1007/s00603-016-0932-1
Zhou C, Xu C, Karakus M, Shen J (2018) A systematic approach to the calibration of micro-parameters for the flat-jointed bonded particle model. Geomech Eng 16:471–482. https://doi.org/10.12989/gae.2018.16.5.471
Zhou C, Xu C, Karakus M, Shen J (2019) A particle mechanics approach for the dynamic strength model of the jointed rock mass considering the joint orientation. Int J Numer Anal Methods Geomech 43:2797–2815. https://doi.org/10.1002/nag.3002
Zhou C, Xie H, Zhu J, Zhou T (2022) Failure criterion considering high temperature treatment for rocks from a micromechanical perspective. Theor Appl Fract Mech 118:103226. https://doi.org/10.1016/j.tafmec.2021.103226
Zhu Q, Li D, Han Z et al (2019) Mechanical properties and fracture evolution of sandstone specimens containing different inclusions under uniaxial compression. Int J Rock Mech Min Sci 115:33–47. https://doi.org/10.1016/j.ijrmms.2019.01.010
Zou C, Wong LNY (2014) Experimental studies on cracking processes and failure in marble under dynamic loading. Eng Geol 173:19–31. https://doi.org/10.1016/j.enggeo.2014.02.003
Zou C, Wong LNY, Loo JJ, Gan BS (2016) Different mechanical and cracking behaviors of single-flawed brittle gypsum specimens under dynamic and quasi-static loadings. Eng Geol 201:71–84. https://doi.org/10.1016/j.enggeo.2015.12.014
Acknowledgements
The work was financially supported by the Program for Guangdong Introducing Innovative and Entrepreneurial Teams (No. 2019ZT08G315), Guangdong Basic and Applied Basic Research Foundation (No. 2020A1515110468, No. 2020A1515111193), National Natural Science Foundation of China (No. 52004162, No. 51827901), and China Postdoctoral Science Foundation (No. 2020M682882, No. 2020TQ0203).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
We have no conflict of interests to declare.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhou, C., Xie, H., Zhu, J. et al. Mechanical and Fracture Behaviors of Brittle Material with a Circular Inclusion: Insight from Infilling Composition. Rock Mech Rock Eng 55, 3331–3352 (2022). https://doi.org/10.1007/s00603-022-02799-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-022-02799-7