Peridynamic Simulation of Heterogeneous Rock Based on Digital Image Processing and Low-Field Nuclear Magnetic Resonance Imaging
Publication: International Journal of Geomechanics
Volume 22, Issue 6
Abstract
Rock heterogeneity is one of the most important factors when numerically simulating the rock failure process and crack propagation. This paper presents an approach for capturing rock heterogeneity that combines peridynamic theory, digital image processing (DIP), and low-field nuclear magnetic resonance (NMR) imaging. By processing the magnetic resonance images (MRIs) of the rock material, the microstructure distribution is obtained, and the attenuation coefficient is defined and calculated by the number and value of pixels of the rock MRI. Based on bond-based peridynamic theory, the density, bond constant, and critical stretch associated with the material point and bond are revised by the attenuation coefficient and have the same distribution with real rock microstructure. Then, this new approach is used to simulate the crack bifurcation of red sandstone under tension and the failure process of mudstone in an unconfined compression test. The influence of the element’s pixel number on the calculation result is discussed. Numerical results show that the crack propagation and the failure process based on the new approach are both distributed nonsymmetrically. In addition, the acoustic emission rule in the peridynamic simulation, which is defined by the number of broken bonds in each loading step, is consistent with the experimental results. The comparison of the numerical and experimental results reveals that the present approach can be used as a supplementary method for analyzing rock damage and failure.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work is financially supported by the National Natural Science Foundation of China (51874352 and 51774323), the Fundamental Research Funds for the Central Universities of Central South University (2018zzts213), and the Natural Science Foundation of Hunan Province (2020JJ4704 and 2020JJ4712). The authors thank Zhen Jian for providing the MRI of red sandstone. The first author Yanan Zhang gratefully acknowledges the financial support from the China Scholarship Council (No. 201906370132).
References
Basu, A., D. A. Mishra, and K. Roychowdhury. 2013. “Rock failure modes under uniaxial compression, Brazilian, and point load tests.” Bull. Eng. Geol. Environ. 72 (3–4): 457–475. https://doi.org/10.1007/s10064-013-0505-4.
Chen, S., Z. Q. Yue, and L. G. Tham. 2004. “Digital image-based numerical modeling method for prediction of inhomogeneous rock failure.” Int. J. Rock Mech. Min. Sci. 41 (6): 939–957. https://doi.org/10.1016/j.ijrmms.2004.03.002.
Chen, S., Z. Q. Yue, and L. G. Tham. 2007. “Digital image based approach for three-dimensional mechanical analysis of heterogeneous rocks.” Rock Mech. Rock Eng. 40 (2): 145–168. https://doi.org/10.1007/s00603-006-0105-8.
Cheng, Z., W. Sui, Z. Ning, Y. Gao, Y. Hou, C. Chang, and J. Li. 2018. “Microstructure characteristics and its effects on mechanical properties of digital core.” Chin. J. Rock Mech. Eng. 37 (2): 449–460.
Cheng, Z., Z. Sui, H. Yin, and H. Feng. 2019. “Numerical simulation of dynamic fracture in functionally graded materials using peridynamic modeling with composite weighted bonds.” Eng. Anal. Boundary Elem. 105: 31–46. https://doi.org/10.1016/j.enganabound.2019.04.005.
Dyson, A. P., Z. Tang, and A. Tolooiyan. 2018. “Use of stochastic XFEM in the investigation of heterogeneity effects on the tensile strength of intermediate geotechnical materials.” Finite Elem. Anal. Des. 145: 1–9. https://doi.org/10.1016/j.finel.2018.03.003.
Gao, F., D. Stead, and D. Elmo. 2016. “Numerical simulation of microstructure of brittle rock using a grain-breakable distinct element grain-based model.” Comput. Geotech. 78: 203–217. https://doi.org/10.1016/j.compgeo.2016.05.019.
Gui, Y. L., Z. Y. Zhao, J. Ji, X. M. Wang, K. P. Zhou, and S. Q. Ma. 2016. “The grain effect of intact rock modelling using discrete element method with Voronoi grains.” Géotechnique Lett. 6 (2): 136–143. https://doi.org/10.1680/jgele.16.00005.
He, Q., L. Zhu, Y. Li, D. Li, and B. Zhang. 2021. “Simulating hydraulic fracture re-orientation in heterogeneous rocks with an improved discrete element method.” Rock Mech. Rock Eng. 54 (6): 2859–2879. https://doi.org/10.1007/s00603-021-02422-1.
Jiang, Z., S. Yu, H. Deng, J. Deng, and K. Zhou. 2019. “Investigation on microstructure and damage of sandstone under cyclic dynamic impact.” IEEE Access 7: 133145–133158. https://doi.org/10.1109/ACCESS.2019.2929234.
Kou, M.-M., X.-R. Liu, Z.-Q. Wang, and M. Nowruzpour. 2021a. “Mechanical properties, failure behaviors and permeability evolutions of fissured rock-like materials under coupled hydro-mechanical unloading.” Eng. Fract. Mech. 254: 107929. https://doi.org/10.1016/j.engfracmech.2021.107929.
Kou, M.-M., X.-R. Liu, Z.-Q. Wang, and S.-D. Tang. 2021b. “Laboratory investigations on failure, energy and permeability evolution of fissured rock-like materials under seepage pressures.” Eng. Fract. Mech. 247: 107694. https://doi.org/10.1016/j.engfracmech.2021.107694.
Li, J., K. Zhou, W. Liu, and H. Deng. 2016. “NMR research on deterioration characteristics of microscopic structure of sandstones in freeze–thaw cycles.” Trans. Nonferrous Met. Soc. China 26 (11): 2997–3003. https://doi.org/10.1016/S1003-6326(16)64430-8.
Li, T., Q. Zhang, X. Xia, and X. Gu. 2018. “A peridynamic model for heterogeneous concrete materials.” Appl. Math. Mech. 39 (8): 913–924.
Li, X. F., H. B. Li, and J. Zhao. 2019. “The role of transgranular capability in grain-based modelling of crystalline rocks.” Comput. Geotech. 110: 161–183. https://doi.org/10.1016/j.compgeo.2019.02.018.
Liu, C., H. Deng, Y. Wang, Y. Lin, and H. Zhao. 2017. “Time-Varying characteristics of granite microstructures after cyclic dynamic disturbance using nuclear magnetic resonance.” Crystals 7 (10): 1–11.
Liu, H., P.-A. Lindqvist, U. Åkesson, S. Kou, and J.-E. Lindqvist. 2012. “Characterisation of rock aggregate breakage properties using realistic texture-based modelling.” Int. J. Numer. Anal. Methods Geomech. 36 (10): 1280–1302. https://doi.org/10.1002/nag.1053.
Madenci, E., and E. Oterkus. 2014. “Peridynamic theory.” In Peridynamic theory and its applications, edited by C. Spencer, 19–43. New York: Springer.
Martínez-Martínez, J., D. Benavente, M. Gomez-Heras, L. Marco-Castaño, and MÁ García-del-Cura. 2013. “Non-linear decay of building stones during freeze–thaw weathering processes.” Constr. Build. Mater. 38: 443–454. https://doi.org/10.1016/j.conbuildmat.2012.07.059.
Nadimi, S., I. Miscovic, and J. McLennan. 2016. “A 3D peridynamic simulation of hydraulic fracture process in a heterogeneous medium.” J. Pet. Sci. Eng. 145: 444–452. https://doi.org/10.1016/j.petrol.2016.05.032.
Ni, T., M. Zaccariotto, Q.-Z. Zhu, and U. Galvanetto. 2021. “Coupling of FEM and ordinary state-based peridynamics for brittle failure analysis in 3D.” Mech. Adv. Mater. Struct. 28 (9): 875–890. https://doi.org/10.1080/15376494.2019.1602237.
Shen, F., L. Tian, Q. Zhang, and D. Huang. 2018. “Study on the inhomogeneous peridynamics model of concrete based on DIP technology.” J. Zhengzhou Univ. 50 (4): 112–116.
Silling, S. A. 2000. “Reformulation of elasticity theory for discontinuities and long-range forces.” J. Mech. Phys. Solids 48 (1): 175–209. https://doi.org/10.1016/S0022-5096(99)00029-0.
Silling, S. A., and E. Askari. 2005. “A meshfree method based on the peridynamic model of solid mechanics.” Comput. Struct. 83 (17–18): 1526–1535. https://doi.org/10.1016/j.compstruc.2004.11.026.
Silling, S. A., M. Epton, O. Weckner, J. Xu, and E. Askari. 2007. “Peridynamic states and constitutive modeling.” J. Elast. 88 (2): 151–184. https://doi.org/10.1007/s10659-007-9125-1.
Tang, C. A., L. G. Tham, P. K. K. Lee, Y. Tsui, and H. Liu. 2000. “Numerical studies of the influence of microstructure on rock failure in uniaxial compression—part II: Constraint, slenderness and size effect.” Int. J. Rock Mech. Min. Sci. 37 (4): 571–583. https://doi.org/10.1016/S1365-1609(99)00122-7.
Wang, H., E. Oterkus, and S. Oterkus. 2018a. “Predicting fracture evolution during lithiation process using peridynamics.” Eng. Fract. Mech. 192: 176–191. https://doi.org/10.1016/j.engfracmech.2018.02.009.
Wang, Y., X. Zhou, and M. Kou. 2018b. “A coupled thermo-mechanical bond-based peridynamics for simulating thermal cracking in rocks.” Int. J. Fract. 211 (1–2): 13–42. https://doi.org/10.1007/s10704-018-0273-z.
Wang, Y., X. Zhou, and Y. Shou. 2017. “The modeling of crack propagation and coalescence in rocks under uniaxial compression using the novel conjugated bond-based peridynamics.” Int. J. Mech. Sci. 128-129: 614–643. https://doi.org/10.1016/j.ijmecsci.2017.05.019.
Wang, Y., X. Zhou, Y. Wang, and Y. Shou. 2018c. “A 3-D conjugated bond-pair-based peridynamic formulation for initiation and propagation of cracks in brittle solids.” Int. J. Solids Struct. 134: 89–115. https://doi.org/10.1016/j.ijsolstr.2017.10.022.
Wang, Y., X. Zhou, and X. Xu. 2016. “Numerical simulation of propagation and coalescence of flaws in rock materials under compressive loads using the extended non-ordinary state-based peridynamics.” Eng. Fract. Mech. 163: 248–273. https://doi.org/10.1016/j.engfracmech.2016.06.013.
Xie, K., D. Jiang, Z. Sun, J. Chen, W. Zhang, and X. Jiang. 2018. “NMR, MRI and AE statistical study of damage due to a low number of wetting–drying cycles in sandstone from the three gorges reservoir area.” Rock Mech. Rock Eng. 51 (11): 3625–3634. https://doi.org/10.1007/s00603-018-1562-6.
Yang, J., W. Chen, D. Yang, and J. Yuan. 2015. “Numerical determination of strength and deformability of fractured rock mass by FEM modeling.” Comput. Geotech. 64: 20–31. https://doi.org/10.1016/j.compgeo.2014.10.011.
Yue, Z. Q., S. Chen, and L. G. Tham. 2003. “Finite element modeling of geomaterials using digital image processing.” Comput. Geotech. 30 (5): 375–397. https://doi.org/10.1016/S0266-352X(03)00015-6.
Zhang, Y., H. Deng, J. Deng, C. Liu, and B. Ke. 2019a. “Peridynamics simulation of crack propagation of ring-shaped specimen like rock under dynamic loading.” Int. J. Rock Mech. Min. Sci. 123: 104093. https://doi.org/10.1016/j.ijrmms.2019.104093.
Zhang, Y., H. Deng, J. Deng, C. Liu, and S. Yu. 2020. “Peridynamic simulation of crack propagation of non-homogeneous brittle rock-like materials.” Theor. Appl. Fract. Mech. 106: 102438. https://doi.org/10.1016/j.tafmec.2019.102438.
Zhang, Y., and E. Madenci. 2021. “A coupled peridynamic and finite element approach in ANSYS framework for fatigue life prediction based on the kinetic theory of fracture.” J. Peridyn. Nonlocal Model. 255: 113006.
Zhang, Y., L. N. Y. Wong, and K. K. Chan. 2019b. “An extended grain-based model accounting for microstructures in rock deformation.” J. Geophys. Res.: Solid Earth 124 (1): 125–148. https://doi.org/10.1029/2018JB016165.
Zhou, X.-P., and Y.-T. Wang. 2021. “State-of-the-art review on the progressive failure characteristics of geomaterials in peridynamic theory.” J. Eng. Mech. 147 (1): 03120001. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001876.
Zhou, X.-P., Y.-T. Wang, and Y.-D. Shou. 2020. “Hydromechanical bond-based peridynamic model for pressurized and fluid-driven fracturing processes in fissured porous rocks.” Int. J. Rock Mech. Min. Sci. 132: 104383. https://doi.org/10.1016/j.ijrmms.2020.104383.
Zhou, X., Y. Wang, Y. Shou, and M. Kou. 2018. “A novel conjugated bond linear elastic model in bond-based peridynamics for fracture problems under dynamic loads.” Eng. Fract. Mech. 188: 151–183. https://doi.org/10.1016/j.engfracmech.2017.07.031.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 22 • Issue 6 • June 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jul 15, 2021
Accepted: Jan 25, 2022
Published online: Apr 7, 2022
Published in print: Jun 1, 2022
Discussion open until: Sep 7, 2022
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.