Simulations of crack propagation in rock-like materials by peridynamics based on SED criterion

MA Peng-fei; LI Shu-chen; YUAN Chao; ZHOU Hui-ying; WANG Man-ling; WANG Xiu-wei

doi:10.11779/CJGE202106014

Volume 43 Issue 6

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Chinese Journal of Geotechnical Engineering > 2021 > 43(6): 1109-1117. > DOI: 10.11779/CJGE202106014

MA Peng-fei, LI Shu-chen, YUAN Chao, ZHOU Hui-ying, WANG Man-ling, WANG Xiu-wei. Simulations of crack propagation in rock-like materials by peridynamics based on SED criterion[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(6): 1109-1117. DOI: 10.11779/CJGE202106014

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Simulations of crack propagation in rock-like materials by peridynamics based on SED criterion

1.
Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China
2.
School of Civil Engineering, Shandong University, Jinan 250061, China

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Received Date: October 27, 2020
Available Online: December 02, 2022

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Abstract

Abstract

Based on the peridynamic theory, the strain energy density (SED) criterion is introduced to reflect the failure characteristics of rock-like materials. At the same time, the critical failure condition obeying the Weibull distribution is used to describe the heterogeneity of rock, which makes up for the deficiency that the peridynamic method cannot reflect the strain-softening characteristics and heterogeneity of rock when simulating the crack propagation of rock materials. The peridynamic method based on the SED criterion is used to simulate the crack propagation process of rock with single crack with different dip angles under uniaxial compression. The propagation mechanisms of airfoil cracks, secondary coplanar shear cracks and anti-airfoil cracks are analyzed. The proposed method is used to simulate the crack propagation process of rock with double parallel cracks under uniaxial compression. The results show that the failure process of rock with double parallel cracks can be divided into three stages: the first penetration of airfoil cracks, the second penetration of shear cracks to form a closed failure ring, and the formation of macro-cracks leading to failure. Finally, the simulated results are compared with those of the previous laboratory tests and numerical simulations to verify the effectiveness of this method. Through comparison, it is found that the proposed theory can better simulate the process of crack propagation of rock materials and has a good application prospect.
- rock mechanics,
- peridynamics,
- crack propagation,
- SED criterion

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References (25)

References

[1]	WONG R H C, CHAU K T, TANG C A, et al. Analysis of crack coalescence in rock-like materials containing three flaws—Part I: experimental approach[J]. International Journal of Rock Mechanics & Mining Sciences, 2001, 38(7): 909-924.
[2]	HAERI H, SHAHRIAR K, MARJT M F, et al. Experimental and numerical study of crack propagation and coalescence in pre-cracked rock-like disks[J]. International Journal of Rock Mechanics & Mining Sciences, 2014, 67: 20-28.
[3]	CAO P, LIU T, PU C, et al. Crack propagation and coalescence of brittle rock-like specimens with pre-existing cracks in compression[J]. Engineering Geology, 2015, 187: 113-121. doi: 10.1016/j.enggeo.2014.12.010
[4]	赵延林, 万文, 王卫军, 等. 类岩石材料有序多裂纹体单轴压缩破断试验与翼形断裂数值模拟[J]. 岩土工程学报, 2013, 35(11): 2097-2109. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201311024.htm ZHAO Yan-ling, WAN Wen, WANG Wei-jun, et al. Fracture experiments on ordered multi-crack body in rock-like materials under uniaxial compression and numerical simulation of wing cracks[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(11): 2097-2109. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201311024.htm
[5]	MOES N, DOLBOW J, BELYTSCHKO T. A finite element method for crack growth without remeshing[J]. International Journal for Numerical Methods in Engineering, 2015, 46(1): 131-150.
[6]	BELYTSCHKO T, BLACK T. Elastic crack growth in finite elements with minimal remeshing[J]. International Journal for Numerical Methods in Engineering, 2015, 45(5): 601-620.
[7]	JONATHAN B, LIONEL G, JÉRÉMIE R, et al. A joined finite element based method to simulate 3D crack network initiation and propagation in mechanical and thermal fatigue[J]. International Journal of Fatigue, 2012, 44: 279-291. doi: 10.1016/j.ijfatigue.2012.04.005
[8]	WAGNER G J, MOES N, LIU W K, et al. The extended finite element method for rigid particles in Stokes flow[J]. International Journal for Numerical Methods in Engineering, 2001, 51(3): 293-313. doi: 10.1002/nme.169
[9]	YUAN C, MOSCARIELLO M, CUOMO S, et al. Numerical simulation of wetting-induced collapse in partially saturated granular soils[J]. Granular Matter, 2019, 21(3): 64. doi: 10.1007/s10035-019-0921-7
[10]	DMITRIEV A I, PSAKHIE S G. Molecular-dynamics study of the initial stage of nanoscale deformation localization in the surface layers of a loaded solid[J]. Technical Physics Letters, 2004, 30(7): 578-579. doi: 10.1134/1.1783407
[11]	SILLING S A. Reformulation of elasticity theory for discontinuities and long-range forces[J]. Journal of Mechanics Physics of Solids, 2000, 48(1): 175-209. doi: 10.1016/S0022-5096(99)00029-0
[12]	SILLING S A, BOBARU F. Peridynamic modeling of membranes and fibers[J]. International Journal of Non-Linear Mechanics, 2005, 40(2): 395-409.
[13]	黄丹, 章青, 乔丕忠, 等. 近场动力学方法及其应用[J]. 力学进展, 2010(4): 94-105. https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201004007.htm HUANG Dan, ZHANG Qing, QIAO Pi-zhong, et al. A review on peridynamics method and its applications[J]. Advances in Mechanics, 2010(4): 94-105. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201004007.htm
[14]	HUANG D, LU G, WANG C, et al. An extended peridynamic approach for deformation and fracture analysis[J]. Engineering Fracture Mechanics, 2015, 141: 196-211. doi: 10.1016/j.engfracmech.2015.04.036
[15]	ZHOU X P, GU X B, WANG Y T. Numerical simulations of propagation, bifurcation and coalescence of cracks in rocks[J]. International Journal of Rock Mechanics & Mining Sciences, 2015, 80: 241-254.
[16]	谷新保, 周小平. 裂纹扩展和连接过程的近场动力学数值模拟[J]. 岩土力学, 2017, 38(2): 610-616. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201702039.htm GU Xing-bao, ZHOU Xiao-ping. Numerical simulation of propagation and coalescence of cracks using peridynamic theory[J]. Rock and Soil Mechanics, 2017, 38(2): 610-616. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201702039.htm
[17]	王超, 熊伟鹏, 叶礼裕, 等. 冰桨接触过程中的遮蔽效应分析[J]. 华中科技大学学报(自然科学版), 2018, 46(6): 105-110, 132. https://www.cnki.com.cn/Article/CJFDTOTAL-HZLG201806019.htm WANG Chao, XIONG Wei-peng, YE Li-yu, et al. Analysis of shadowing effect during propeller-ice contact process[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2018, 46(6): 105-110, 132. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HZLG201806019.htm
[18]	ZHANG H, QIAO P. A state-based peridynamic model for quantitative elastic and fracture analysis of orthotropic materials[J]. Engineering Fracture Mechanics, 2018, 211: 217-235. doi: 10.1007/s10704-018-0285-8
[19]	CHENG Z, JIN D, YUAN C, et al. Dynamic fracture analysis of functionally gradient materials with two cracks by peridynamic modeling[J]. Computer Modeling in Engineering and Sciences, 2019, 121(2): 445-464. doi: 10.32604/cmes.2019.06374
[20]	朱其志, 倪涛, 赵伦洋, 等. 岩石类材料裂纹扩展贯通的近场动力学方法模拟[J]. 岩石力学与工程学报, 2016, 35(增刊2): 3507-3515. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2016S2008.htm ZHU Qi-zhi, NI Tao, ZHAO Lun-yang, et al. Simulations of crack propagation in rock-like materials using peridynamic method[J]. Chinese Journal of Rock Mechanics & Engineering, 2016, 35(S2): 3507-3515. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2016S2008.htm
[21]	SILLING S A, ASKARI E. A meshfree method based on the peridynamic model of solid mechanics[J]. Computers & Structures, 2005, 83(17): 1526-1535.
[22]	CARPINTERI , ALBERTO . Mechanical Damage and Crack Growth in Concrete: Plastic Collapse to Brittle Fracture[M]. Kluwer Academic, 1986.
[23]	SIH G C. Some basic problems in fracture mechanics and new concepts[J]. Engineering Fracture Mechanics, 1973, 5(2): 365-377.
[24]	YANG L, JIANG Y, BO L I, et al. Application of the expanded distinct element method for the study of crack growth in rock-like materials under uniaxial compression[J]. Frontiers of Structural and Civil Engineering, 2012, 6(2): 121-131.
[25]	LI Y P, WANG Y H, CHEN L Z. Experimental research on pre-cracked marble under compression[J]. International Journal of Solids and Structures, 2005, 42(9): 2505-2516.