3D Digital Analysis of Cracking Behaviors of Rocks through 3D Reconstruction Model under Triaxial Compression
Publication: Journal of Engineering Mechanics
Volume 146, Issue 8
Abstract
The cracking behaviors of rocks significantly affect their mechanical properties. In this paper, a digital analysis approach with X-ray Computed Tomography (CT) imagery is developed to investigate the cracking and mechanical behaviors of rocks. The damage ratio, integrity, and porosity of rocks subjected to triaxial compression are firstly defined based on X-ray CT image and the pixel coordinate system. Then, the evolution process of two-dimensional (2D) and three-dimensional (3D) cracks are studied via 2D CT images and reconstructed 3D fracture models, respectively. Finally, the stress–strain relationship of rocks is simulated by converting the reconstructed models to the finite-element (FE) models. The results show that the rock damage ratio, integrity, and porosity are good factors to describe the cracking behaviors, in which the evolution process of cracks is divided into five stages including: (1) the compaction of initial fissures; (2) the initiation and propagation of microcracks; (3) microcracks coalescence, i.e., the formation and stable propagation of macrocracks; (4) the unstable propagation of macrocracks; and (5) the complete failure of rock samples. The numerical stress–strain curves are in good agreement with the experiment data.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all datasets and codes for this paper can be obtained by contacting the corresponding author Xiao-Ping Zhou upon reasonable request.
Acknowledgments
This work was supported by National Natural Science Foundation of China (Grant Nos. 51839009 and 51679017).
References
Al-Kharusi, A. S., and M. J. Blunt. 2007. “Network extraction from sandstone and carbonate pore space images.” J. Pet. Sci. Eng. 56 (4): 219–231. https://doi.org/10.1016/j.petrol.2006.09.003.
Attene, M., and B. Falcidieno. 2006. “ReMESH: An interactive environment to edit and repair triangle meshes.” In Proc., IEEE Int. Conf. on Shape Modeling and Applications, 41. New York: IEEE. https://doi.org/10.1109/SMI.2006.29.
Brewick, P. T., V. G. DeGiorgi, A. B. Geltmacher, and S. M. Qidwai. 2019. “Modeling the influence of microstructure on the stress distributions of corrosion pits.” Corros. Sci. 158 (Sep): 108111. https://doi.org/10.1016/j.corsci.2019.108111.
Dyskin, A. V., E. Sahouryeh, R. J. Jewell, H. Joer, and K. B. Ustinov. 2003. “Influence of shape and locations of initial 3-D cracks on their growth in uniaxial compression.” Eng. Fract. Mech. 70 (15): 2115–2136. https://doi.org/10.1016/S0013-7944(02)00240-0.
Ebrahimi, A. N., S. Jamshidi, S. Iglauer, and R. B. Boozarjomehry. 2013. “Genetic algorithm-based pore network extraction from micro-computed tomography images.” Chem. Eng. Sci. 92 (14): 157–166. https://doi.org/10.1016/j.ces.2013.01.045.
Elaqra, H., N. Godin, G. Peix, M. R’ Milli, and G. Fantozzi. 2007. “Damage evolution analysis in mortar, during compressive loading using acoustic emission and X-ray tomography: Effects of the sand/cement ratio.” Cem. Concr. Res. 37 (5): 703–713. https://doi.org/10.1016/j.cemconres.2007.02.008.
Fang, J. Y., F. N. Dang, Y. T. Xiao, W. H. Ding, and J. X. Fang. 2015. “Quantitative study on the CT test process of siltstone under triaxial compression.” Chin. J. Rock Mech. Eng. 34 (10): 1976–1984. https://doi.org/10.13722/j.cnki.jrme.2015.0974.
Fu, C. 2016. “Dynamic behavior of a simply supported bridge with a switching crack subjected to seismic excitations and moving trains.” Eng. Struct. 110 (Mar): 59–69. https://doi.org/10.1016/j.engstruct.2015.11.055.
Hackston, A., and E. Rutter. 2016. “The mohr–coulomb criterion for intact rock strength and friction—A re-evaluation and consideration of failure under polyaxial stresses.” Solid Earth 7 (2): 493–508. https://doi.org/10.5194/se-7-493-2016.
Hatheway, A. W. 2009. “The complete ISRM suggested methods for rock characterization, testing and monitoring; 1974–2006” Environ. Eng. Geosci. 15 (1): 47–48. https://doi.org/10.2113/gseegeosci.15.1.47.
He, Z., G. Li, S. Tian, H. Wang, Z. Shen, and J. Li. 2016. “Sem analysis on rock failure mechanism by supercritical Co2, jet impingement.” J. Pet. Sci. Eng. 146 (Oct): 111–120. https://doi.org/10.1016/j.petrol.2016.04.023.
Huang, X. C., and X. P. Zhou. 2020. “Probabilistic assessment for slope using the generalized Chebyshev inequalities.” Int. J. Geomech. 20 (4): 06020003. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001638.
Jiang, Z., M. I. J. Van Dijke, S. Geiger, J. Ma, G. D. Couples, and X. Li. 2017. “Pore network extraction for fractured porous media.” Adv. Water Resour. 107 (Sep): 280–289. https://doi.org/10.1016/j.advwatres.2017.06.025.
Lai, J., G. Wang, Z. Wang, J. Chen, X. Pang, S. Wang, Z. Zhou, Z. He, Z. Qin, and X. Fan. 2018. “A review on pore structure characterization in tight sandstones.” Earth Sci. Rev. 177 (Feb): 436–457. https://doi.org/10.1016/j.earscirev.2017.12.003.
Li, G., X. Zhao, K. Du, F. Ru, and Y. Zhang. 2017a. “Recognition and evaluation of bridge cracks with modified active contour model and greedy search-based support vector machine.” Autom. Constr. 78 (Jun): 51–61. https://doi.org/10.1016/j.autcon.2017.01.019.
Li, J., H. Jiang, C. Wang, Y. Zhao, Y. Gao, Y. Pei, C. Wang, and H. Dong. 2017b. “Pore-scale 518 investigation of microscopic remaining oil variation characteristics in water-wet sandstone using ct scanning.” J. Nat. Gas Sci. Eng. 48 (Dec): 36–45. https://doi.org/10.1016/j.jngse.2017.04.003.
Li, Y., A. Kalantari-Dahaghi, A. Zolfaghari, P. Dong, S. Negahban, and D. Zhou. 2018. “Fractal-based real gas flow model in shales: An interplay of nano-pore and nano-fracture networks.” Int. J. Heat Mass Transfer 127 (Dec): 1188–1202. https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.077.
Li, Z., D. Liu, Y. Cai, P. G. Ranjith, and Y. Yao. 2017c. “Multi-scale quantitative characterization of 3-D pore-fracture networks in bituminous and anthracite coals using FIB-SEM tomography and X-ray -CT.” Fuel 209 (Dec): 43–53. https://doi.org/10.1016/j.fuel.2017.07.088.
Liu, S., S. Sang, G. Wang, J. Ma, X. Wang, W. Wang, Y. Du, and T. Wang. 2017. “Fib-sem and X-ray CT characterization of interconnected pores in high-rank coal formed from regional metamorphism.” J. Pet. Sci. Eng. 148 (Jan): 21–31. https://doi.org/10.1016/j.petrol.2016.10.006.
Masaki, K., Y. Sano, and K. Kajiwara. 2017. “Os05f096 investigation of fatigue crack propagation behavior by CT with synchrotron radiation.” Biophys. Chem. 104 (1): 14.
Mathews, J. P., Q. P. Campbell, H. Xu, and P. Halleck. 2017. “A review of the application of X-ray computed tomography to the study of coal.” Fuel 209 (Dec): 10–24. https://doi.org/10.1016/j.fuel.2017.07.079.
Nasseri, M. H. B., F. Rezanezhad, and R. P. Young. 2011. “Analysis of fracture damage zone in anisotropic granitic rock using 3D X-ray CT scanning techniques.” Int. J. Fract. 168 (1): 1. https://doi.org/10.1007/s10704-010-9551-0.
Nie, B., X. Liu, L. Yang, J. Meng, and X. Li. 2015. “Pore structure characterization of different rank coals using gas adsorption and scanning electron microscopy.” Fuel 158 (Oct): 908–917. https://doi.org/10.1016/j.fuel.2015.06.050.
Øren, P. E., and S. Bakke. 2003. “Reconstruction of berea sandstone and pore-scale modelling of wettability effects.” J. Pet. Sci. Eng. 39 (3–4): 177–199. https://doi.org/10.1016/S0920-4105(03)00062-7.
Otsu, N. 1979. “A threshold selection method from gray-level histogram.” IEEE Trans. Syst. Man Cybern. 9 (1): 62–66. https://doi.org/10.1109/TSMC.1979.4310076.
Rau, J. Y., K. W. Hsiao, J. P. Jhan, S. H. Wang, W. C. Fang, and J. L. Wang. 2017. “Bridge crack detection using multi-rotary uav and object-base image analysis.” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. 42: 311–318. https://doi.org/10.5194/isprs-archives-XLII-2-W6-311-2017.
Shao, X., X. Pang, F. Jiang, L. Li, Y. Huayan, and D. Zheng. 2017. “Reservoir characterization of tight sandstones using NMR and IPMI experiments: Implication for tight sand gas reservoir quality.” Energy Fuel 31 (10): 10420–10431. https://doi.org/10.1021/acs.energyfuels.7b01184.
Sharqawy, M. H. 2016. “Construction of pore network models for berea and Fontainebleau sandstones using non-linear programing and optimization techniques.” Adv. Water Resour. 98 (Dec): 198–210. https://doi.org/10.1016/j.advwatres.2016.10.023.
Shi, P., X. Fan, J. Ni, Z. Khan, and L. Min. 2017. “A novel underwater dam crack detection and classification approach based on sonar images.” PLoS One 12 (6): e0179627. https://doi.org/10.1371/journal.pone.0179627.
Shiozawa, D., Y. Nakai, T. Murakami, and H. Nosho. 2014. “Observation of 3d shape and propagation mode transition of fatigue cracks in TI–6AL–4V under cyclic torsion using ct imaging with ultra-bright synchrotron radiation.” Int. J. Fatigue 58 (Jan): 158–165. https://doi.org/10.1016/j.ijfatigue.2013.02.018.
Su, K., X. Zhou, X. Tang, X. Xu, and Q. Liu. 2017. “Mechanism of cracking in dams using a hybrid fe-meshfree method.” Int. J. Geomech. 17 (9): 04017071. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000950.
Tao, K., and W. Zheng. 2018. “Real-time damage assessment of hydrous sandstone based on synergism of AE-CT techniques.” Eng. Fail. Anal. 91 (Sep): 465–480. https://doi.org/10.1016/j.engfailanal.2018.04.046.
Valença, J., I. Puente, E. Júlio, H. González-Jorge, and P. Arias-Sánchez. 2017. “Assessment of cracks on concrete bridges using image processing supported by laser scanning survey.” Constr. Build. Mater. 146 (Aug): 668–678. https://doi.org/10.1016/j.conbuildmat.2017.04.096.
Wang, L. B., J. D. Frost, G. Z. Voyiadjis, and T. P. Harman. 2003. “Quantification of damage parameters using X-ray tomography images.” Mech. Mater. 35 (8): 777–790. https://doi.org/10.1016/S0167-6636(02)00206-5.
Westover, L. 1990. “Footprint evaluation for volume rendering.” In Vol. 24 of Proc., 17th Annual Conf. on Computer Graphics and Interactive Techniques, 367–376.
Yang, S. Q., P. G. Ranjith, and Y. L. Gui. 2015. “Experimental study of mechanical behavior and X-ray micro CT observations of sandstone under conventional triaxial compression.” Geotech. Test. J. 38 (2): 20140209. https://doi.org/10.1520/GTJ20140209.
Zhao, Y., Y. Sun, S. Liu, K. Wang, and Y. Jiang. 2016. “Pore structure characterization of coal by NMR cryoporometry.” Fuel 190 (Feb): 359–369. https://doi.org/10.1016/j.fuel.2016.10.121.
Zhao, Z., and X. P. Zhou. 2019. “Digital energy grade-based approach for crack path prediction based on 2D X-ray CT images of geomaterials.” Fatigue Fract. Eng. Mater. Struct. 42 (6): 1292–1307. https://doi.org/10.1111/ffe.12979.
Zhao, Z., X. P. Zhou, and Q. H. Qian. 2020. “Fracture characterization and permeability prediction by pore scale variables extracted from X-ray CT images of porous geomaterials.” In Science China technological sciences, 1–13. Beijing: Science China Press.
Zhou, H. W., J. C. Zhong, W. G. Ren, X. Y. Wang, and H. Y. Yi. 2018a. “Characterization of pore-fracture networks and their evolution at various measurement scales in coal samples using X-ray μCT and a fractal method.” Int. J. Coal Geol. 189 (Mar): 35–49. https://doi.org/10.1016/j.coal.2018.02.007.
Zhou, X. P., X. C. Huang, P. F. Liu, and T. F. Li. 2018b. “A probabilistic method to analyze collapse failure of shallow rectangular tunnels.” Tunnelling Underground Space Technol. 82 (Dec): 9–19. https://doi.org/10.1016/j.tust.2018.07.029.
Zhou, X. P., and N. Xiao. 2019. “Analysis of fracture properties of three-dimensional reconstructed rock model using hierarchical-fractal annealing algorithm.” Eng. Geol. 256 (Jun): 39–56. https://doi.org/10.1016/j.enggeo.2019.04.017.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 146 • Issue 8 • August 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Oct 11, 2019
Accepted: Mar 26, 2020
Published online: Jun 11, 2020
Published in print: Aug 1, 2020
Discussion open until: Nov 11, 2020
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.