Fractal Study on Mesodamage Evolution of Three-Dimensional Irregular Fissured Sandstone
Publication: International Journal of Geomechanics
Volume 23, Issue 11
Abstract
In the present study, a numerical model was established to investigate the influence of the prefabricated cracks of different dimensions on the mechanical properties and damage evolution of irregular sandstone. To this end, prefabricated cracks of different dimensions were considered in the analysis, and the real mesoscopic structure inside the sandstone was characterized using microcomputed tomography (micro-CT) scanning and digital image processing technology. Combined with the rock failure process analysis system, the effects of the prefabricated cracks of different dimensions on its macroscopic mechanical behavior and damage evolution were studied. The irregular sandstone fissure field was extracted, the three-dimensional (3D) fissure field was visualized, and the corresponding damage degree was calculated on the MATLAB platform using the modified crack volume damage method. Based on the box dimension theory and the digital image storage principle, a 3D irregular rock fracture box dimension algorithm was developed. Moreover, the fractal dimension of irregular rock failure was calculated at the mesoscale, and the corresponding relationship between the fractal dimension of the crack region and the crack volume damage degree (Du) was established. The obtained results showed that the overall energy accumulation and internal failure of the specimen with nonpenetrating cracks have the characteristics of spatial–temporal inconsistency before reaching the elastic limit point, and the failure degree decreases along the fracture surface toward the intact surface. When the total volume of cracks was 1,800 mm3, the influence of crack parameters on the compressive strength of irregular sandstone was depth > length > opening width. It was found that the damage degree of irregular sandstone has a good consistency with the fractal dimension. This study helps to understand the failure mechanism of irregular rock particles and provides a new idea to investigate the damage evolution of irregular rock particles.
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Data Availability Statement
Some or all data, models, or codes generated or used during the study are available from the corresponding author by request, including all experimental data involved in this study and box dimension algorithm codes based on the 3D fissure field of irregular sandstone.
Acknowledgments
This study was supported by the program of the China Scholarship Council (No. 202006670005), the National Natural Science Foundation of China (Project Nos. 51964007, 52264004, 52104080, and 41962008), the High-level Innovative Talents Training Project in Guizhou Province (Project No. 2016-4011), and the Scientific and Technological Innovation Talents Team in Guizhou Province [Project No. (2019)5619].
References
Bahaaddini, M., G. Sharrock, and B. K. Hebblewhite. 2013. “Numerical investigation of the effect of joint geometrical parameters on the mechanical properties of a non-persistent jointed rock mass under uniaxial compression.” Comput. Geotech. 49: 206–225. https://doi.org/10.1016/j.compgeo.2012.10.012.
Bobet, A., and H. H. Einstein. 1998. “Fracture coalescence in rock-type materials under uniaxial and biaxial compression.” Int. J. Rock Mech. Min. Sci. 35 (7): 863–888. https://doi.org/10.1016/S0148-9062(98)00005-9.
Carlsson, B., E. Nordlund, Y. Andersson, and U. Lindfors. 1999. “The failure process and the acoustic emission of brittle rock under compression.” In Proc., 9th Int. Society for Rock Mechanics Congress, 569–572. Rotterdam, Netherlands: A.A. Balkema.
Chen, D. H., T. C. Li, X. A. Lu, and Y. Li, 2016. “Three-dimensional extension mode of red sandstone with different opening surface crack.” [In Chinese.] J. Shandong Univ. Sci. Technol. 35 (5): 63–69. https://doi.org/10.16452/j.cnki.sdkjzk.2016.05.016.
Chen, M., J. Mao, F. P. Bierlein, T. Norman, and P. J. Uttley. 2011. “Structural features and metallogenesis of the Carlin-type Jinfeng (Lannigou) gold deposit, Guizhou Province, China.” Ore Geol. Rev. 43 (1): 217–234. https://doi.org/10.1016/j.oregeorev.2011.06.009.
Chiu, C.-C., M.-C. Weng, and T.-H. Huang. 2016. “Modeling rock joint behavior using a rough-joint model.” Int. J. Rock Mech. Min. Sci. 89: 14–25. https://doi.org/10.1016/j.ijrmms.2016.08.001.
Gonzalez. 2000. Digital image processing (MATLAB edition). Beijing: Electronic Industry Press.
Guo, Y. S., C. Lin, W. Zhu, and S. Li. 2008. “Experimental research on propagation and coalescence process of three-dimensional flaw-sets.” [In Chinese.] Chin. J. Rock Mech. Eng. 27 (Supp. 1): 3191–3195.
Hao, Z., Y. Zuo, H. Liu, Z. Zhu, J. Lin, W. Sun, C. Pan, and L. Zheng. 2022. “Mesoscopic damage evolution characteristics of jointed sandstone under different loading conditions.” Geomech. Geophys. Geo-Energy Geo-Resour. 8 (3): 92. https://doi.org/10.1007/s40948-022-00390-6.
Herrmann, W. 1969. “Constitutive equation for the dynamic compaction of ductile porous materials.” J. Appl. Phys. 40 (6): 2490–2499. https://doi.org/10.1063/1.1658021.
Huang, M., and T. Xiao. 2020. “Study on mechanical and deformation characteristics of precast single fracture rock under uniaxial compression.” [In Chinese.] J. Yangtze Univ. 17 (1): 115–120. https://doi.org/10.16772/j.cnki.1673-1409.2020.01.020.
Ishihara, S., and J. Kano. 2019. “ADEM simulation for analysis of particle breakage of irregular shaped particles.” ISIJ Int. 59 (5): 820–827. https://doi.org/10.2355/isijinternational.ISIJINT-2018-688.
Justusson, B. I. 1981. “Median filtering: Statistical properties.” In Vol. 43 of Two-dimensional Digital Signal Prcessing II, 161–196. Heidelberg, Germany: Springer.
Li, Z., L. Li, B. Huang, L. Zhang, M. Li, J. Zuo, A. Li, and Q. Yu. 2017. “Numerical investigation on the propagation behavior of hydraulic fracture in shale reservoir based on the DIP technique.” J. Pet. Sci. Eng. 154: 302–314. https://doi.org/10.1016/j.petrol.2017.04.034.
Liu, H., L. Zheng, Y. Zuo, Z. Wu, W. Sun, L. Zheng, C. Pan, J. Lin, Z. Zhu, and Z. Hao. 2021a. “Study on mesoscopic damage evolution characteristics of single joint sandstone based on micro-CT image and fractal theory.” Shock Vib. 2021: 6547028. https://doi.org/10.1155/2021/6547028.
Liu, H., Y. Zuo, Z. Wu, W. Sun, L. Zheng, Y. Lou, J. Lin, and R. Wan. 2021b. “Fractal analysis of mesoscale failure evolution and microstructure characterization for sandstone using DIP, SEM-EDS, and micro-CT.” Int. J. Geomech. 21 (9): 04021153. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002110.
Mao, L. T., X. Y. Lian, and L. N. Hao. 2014. “The fractal calculation of 3D cracks based on digital volumetric images and its application.” [In Chinese.] J. Chin. Univ. Min. Technol. 43 (6): 1134–1139. https://doi.org/10.13247/j.cnki.jcumt.000249.
Petrou, M., and P. Bosdogianni. 1999. Image processing: The fundamentals. Hoboken, NJ: John Wiley & Sons Ltd.
Rossi, F., A. Di Carlo, and P. Lugli. 1998. “Microscopic theory of quantum-transport phenomena in mesoscopic systems: A Monte Carlo approach.” Phys. Rev. Lett. 80 (15): 3348–3351. https://doi.org/10.1103/PhysRevLett.80.3348.
Rubinstein, R. Y., and D. P. Kroese. 2011. Simulation and the Monte Carlo method. Hoboken, NJ: Wiley.
Rueden, C., and K. Eliceiri. 2019. “Imagej for the next generation of scientific image data.” Microsc. Microanal. 25 (S2): 142–143. https://doi.org/10.1017/S1431927619001442.
Schneider, C. A., W. S. Rasband, and K. W. Eliceiri. 2012. “NIH image to ImageJ: 25 years of image analysis.” Nat. Methods 9 (7): 671–675. https://doi.org/10.1038/nmeth.2089.
Shang, L. M., T. C. Li, W. Chen, Y. Li, and F. Gao. 2015. “Research on size effect of three-dimensional internal crack in rocks.” [In Chinese.] J. Wuhan Univ. Technol. 37 (8): 72–77. https://doi.org/10.3963/j.issn.1671-4431.2015.08.014.
Su, W. C., W. D. Dong, X. C. Zhang, and N. P. Shen. 2018. “Carlin-type gold deposits in the Dian-Qian-Gui ‘golden triangle’ of southwest China.” Econ. Geol. 20: 157–185. https://doi.org/10.5382/rev.20.05.
Sun, X. Z., Y. Li, N. Jinag, and B. Shen. 2016. “Experimental study of 3D crack propagation characteristics in rock-like materials.” [In Chinese.] Rock Soil Mech. 37 (4): 965–972. https://doi.org/10.1155/2021/6552847.
Tang, C. A. 1997. “Numerical simulation of progressive rock failure and associated seismicity.” Int. J. Rock Mech. Min. Sci. 34 (2): 249–261. https://doi.org/10.1016/S0148-9062(96)00039-3.
Tang, C. A., J. A. Hudson, and X. H. Xu. 1993. Rock failure instability and related aspects of earthquake mechanisms. Beijing: China Coal Industry Publishing House.
Tang, C. A., H. Y. Liu, W. C. Zhu, T. H. Yang, W. H. Li, L. Song, and P. Lin. 2004. “Numerical approach to particle breakage under different loading conditions.” Powder Technol. 143–144: 130–143. https://doi.org/10.1016/j.powtec.2004.04.026.
Tang, C. A., L. G. Tham, S. H. Wang, H. Liu, and W. H. Li. 2007. “A numerical study of the influence of heterogeneity on the strength characterization of rock under uniaxial tension.” Mech. Mater. 39 (4): 326–339. https://doi.org/10.1016/j.mechmat.2006.05.006.
Wang, G., J. Shen, S. Liu, C. Jiang, and X. Qin. 2019. “Three-dimensional modeling and analysis of macro-pore structure of coal using combined X-ray CT imaging and fractal theory.” Int. J. Rock Mech. Min. Sci. 123 (2019): 104082. https://doi.org/10.1016/j.ijrmms.2019.104082.
Wang, S. Y., S. W. Sloan, D. C. Sheng, and C. A. Tang. 2016. “3D numerical analysis of crack propagation of heterogeneous notched rock under uniaxial tension.” Tectonophysics 677–678: 45–67. https://doi.org/10.1016/j.tecto.2016.03.042.
Weibull, W. 1951. “A statistical distribution function of wide applicability.” J. Appl. Mech. 18 (3): 293–297. https://doi.org/10.1115/1.4010337.
Wu, N., Z.-z. Liang, Y.-c. Li, H. Li, W.-r. Li, and M.-l. Zhang. 2019. “Stress-dependent anisotropy index of strength and deformability of jointed rock mass: Insights from a numerical study.” Bull. Eng. Geol. Environ. 78 (8): 5905–5917. https://doi.org/10.1007/s10064-019-01483-5.
Xiao, J., X. Zhang, D. Zhang, L. Xue, S. Sun, J. Stránský, and Y. Wang. 2020. “Morphological reconstruction method of irregular shaped ballast particles and application in numerical simulation of ballasted track.” Transp. Geotech. 24: 100374. https://doi.org/10.1016/j.trgeo.2020.100374.
Xie, H. P. 1993. Fractals in rock mechanics. Rotterdam, Netherlands: A.A. Balkema.
Xu, R. 2019. “Influence of flaw inclination angle on cracking behavior of rock-like materials under uniaxial compression.” Adv. Mater. Sci. Eng. 2019: 6942586. https://doi.org/10.1155/2019/6942586.
Yu, Q., H. Liu, T. Yang, and H. Liu. 2018. “3D numerical study on fracture process of concrete with different ITZ properties using X-ray computerized tomography.” Int. J. Solids Struct. 147: 204–222. https://doi.org/10.1016/j.ijsolstr.2018.05.026.
Yu, Q., S. Yang, P. G. Ranjith, W. Zhu, and T. Yang. 2016. “Numerical modeling of jointed rock under compressive loading using X-ray computerized tomography.” Rock Mech. Rock Eng. 49 (3): 877–891. https://doi.org/10.1007/s00603-015-0800-4.
Zeng, J. J., Z. J. Zhang, and W. X. Zhang. 2020. “Fracture test and analysis of horizontal fractured rock specimen influenced by aperture.” [In Chinese.] Chin. J. Geotech. Eng. 42 (3): 523–532. https://doi.org/10.11779/CJGE202003014.
Zhang, T. J., H. L. Guo, and J. Chen. 2021. “Meso-crack damage evolution mechanism of porous soft coal samples during failure process.” [In Chinese.] Coal Sci. Technol. 49 (12): 96–103. https://doi.org/110.13199/j.cnki.cst.2021.12.012.
Zheng, L., L. Zheng, Y. Zuo, H. Liu, B. Chen, Z. Wu, W. Sun, and Y. Wang. 2021. “Study on mesoscale damage evolution characteristics of irregular sandstone particles based on digital images and fractal theory.” Adv. Mater. Sci. Eng. 2021: 6552847. https://doi.org/10.1155/2021/6552847.
Zhu, J. B., T. Zhou, Z. Y. Liao, L. Sun, X. B. Li, and R. Chen. 2018. “Replication of internal defects and investigation of mechanical and fracture behaviour of rock using 3D printing and 3D numerical methods in combination with X-ray computerized tomography.” Int. J. Rock Mech. Min. Sci. 106: 198–212. https://doi.org/10.1016/j.ijrmms.2018.04.022.
Zhu, W. C., and C. A. Tang. 2004. “Micromechanical model for simulating the fracture process of rock.” Rock Mech. Rock Eng. 37 (1): 25–56. https://doi.org/10.1007/s00603-003-0014-z.
Zuo, Y.-J., Q. Zhang, T. Xu, Z.-H. Liu, Y.-Q. Qiu, and W.-C. Zhu. 2015. “Numerical tests on failure process of rock particle under impact loading.” Shock Vib. 2015: 1–12. https://doi.org/10.1155/2015/678573.
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International Journal of Geomechanics
Volume 23 • Issue 11 • November 2023
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© 2023 American Society of Civil Engineers.
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Received: Jul 14, 2022
Accepted: May 21, 2023
Published online: Aug 31, 2023
Published in print: Nov 1, 2023
Discussion open until: Jan 31, 2024
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