Application of numerical manifold method in crack propagation
-
摘要: 针对传统的断裂准则难以模拟混合型多裂纹扩展问题,在已有数值流形法程序基础上,对已有的裂纹扩展准则进行改进使数值流形法能够适应于多种类型裂纹扩展模拟。研究中以莫尔–库仑准则和最大周向应力准则为基础,将二者结合确定裂纹扩展方向。采用C语言开发相应计算程序计算了半圆盘拉伸试验和四点双边剪切试验,数值模拟和试验结果的裂纹扩展路径一致,并且裂纹能够穿过流形单元内部。随后模拟了重力坝开裂问题,发现重力坝开裂主要是拉伸破坏,并且裂纹扩展路径与有限元结果近似。最后通过模拟边坡滑移问题,计算结果与DEM和其他方法对比具有高度一致性。结果不仅验证了提出的强度准则在模拟各类型的裂纹扩展问题是有效的,同时为NMM模拟工程实际问题打下基础。Abstract: In order to solve the problem that the traditional fracture criterion is difficult to simulate the mixed multi-crack propagation, based on the existing numerical manifold method program, the existing crack propagation criterion is improved so that the numerical manifold method can be adapted to the simulation of various types of crack propagation. Based on the Mohr-Coulomb criterion and the maximum circumferential stress criterion, the crack propagation direction is determined by combining the two criteria. The corresponding program developed by C language is used to calculate the half disk tensile tests and four-point bilateral shear tests. The crack propagation paths of the numerical simulation and test results are consistent, and the crack can pass through the interior of manifold element. Subsequently, the cracking problem of gravity dams is simulated, and it is found that the cracking of gravity dams is mainly tensile failure, and the crack propagation path is similar to the finite element results. Finally, by simulating the slope slip problem, the calculated results are highly consistent with those by DEM and other methods. The results of this study verify the effectiveness of the proposed strength criterion in simulating various types of crack propagation problems and lay a foundation for NMM to simulate practical engineering problems.
-
Keywords:
- numerical manifold method /
- crack propagation /
- stretching /
- shear /
- slope
-
-
![]()
图 5 半圆盘弯曲拉伸试验结果和NMM模拟对比
Figure 5. Comparison of bending tensile test results of half disc and NMM simulation
-
[1] ZHANG G X, SUGIURA Y, KOZO S. Failure simulation of foundation by manifold method and comparison with experiment[J]. Journal of Applied Mechanics, 1998(1): 427-436. http://www.onacademic.com/detail/journal_1000040291858710_fed7.html
[2] 陈远强, 杨永涛, 郑宏, 等. 饱和–非饱和渗流的数值流形法研究与应用[J]. 岩土工程学报, 2019, 41(2): 149-158. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201902014.htm CHEN Yuan-qiang, YANG Yong-tao, ZHENG Hong, et al. Saturated-unsaturated seepage by numerical manifold method[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(2): 149-158. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201902014.htm
[3] MA G, AN X, HE L E I. The numerical manifold method: a review[J]. International Journal of Computational Methods, 2010, 7(1): 1-32. doi: 10.1142/S0219876210002040
[4] 徐栋栋, 郑宏, 杨永涛. 线性无关高阶数值流形法[J]. 岩土工程学报, 2014, 36(3): 482-488. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201403015.htm XU Dong-dong, ZHENG Hong, YANG Yong-tao. Linearly independent higher-order numerical manifold method[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(3): 482-488. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201403015.htm
[5] 李伟, 郑宏. 基于数值流形法的渗流问题边界处理新方法[J]. 岩土工程学报, 2017, 39(10): 1867-1873. doi: 10.11779/CJGE201710015 LI Wei, ZHENG Hong. New boundary treatment for seepage flow problem based on numerical manifold method[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(10): 1867-1873. (in Chinese) doi: 10.11779/CJGE201710015
[6] NING Y J, AN X M, MA G W. Footwall slope stability analysis with the numerical manifold method[J]. International Journal of Rock Mechanics and Mining Sciences, 2011, 48(6): 964-975. doi: 10.1016/j.ijrmms.2011.06.011
[7] WU Z, WONG L N Y. Frictional crack initiation and propagation analysis using the numerical manifold method[J]. Computers and Geotechnics, 2012, 39: 38-53. doi: 10.1016/j.compgeo.2011.08.011
[8] TI K S, HUAT B B, NOORZAEI J, et al. A review of basic soil constitutive models for geotechnical application[J]. Electronic Journal of Geotechnical Engineering, 2009, 14: 1-18.
[9] HACKSTON A, RUTTER E. The Mohr–Coulomb criterion for intact rock strength and friction – a re-evaluation and consideration of failure under polyaxial stresses[J]. Solid Earth, 2016, 7(2): 493-508. doi: 10.5194/se-7-493-2016
[10] AN X, NING Y, MA G, et al. Modeling progressive failures in rock slopes with non-persistent joints using the numerical manifold method[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, 38(7): 679-701. doi: 10.1002/nag.2226
[11] XU Y, DAI F, XU N W, et al. Numerical investigation of dynamic rock fracture toughness determination using a semi-circular bend specimen in split hopkinson pressure bar testing[J]. Rock Mechanics and Rock Engineering, 2015, 49(3): 731-745.
[12] AYATOLLAHI M R, ALIHA M R M, HASSANI M M. Mixed mode brittle fracture in PMMA—An experimental study using SCB specimens[J]. Materials Science and Engineering: A, 2006, 417(1/2): 348-356.
[13] XIE Y, CAO P, JIN J, et al. Mixed mode fracture analysis of semi-circular bend (SCB) specimen: A numerical study based on extended finite element method[J]. Computers and Geotechnics, 2017, 82: 157-172. doi: 10.1016/j.compgeo.2016.10.012
[14] BERGARA A, DORADO J I, MART N-MEIZOSO A, et al. Fatigue crack propagation in complex stress fields: experiments and numerical simulations using the extended finite element method (Xfem)[J]. International Journal of Fatigue, 2017, 103: 112-121. doi: 10.1016/j.ijfatigue.2017.05.026
[15] LANG C, MAKHIJA D, DOOSTAN A, et al. A simple and efficient preconditioning scheme for heaviside enriched XFEM[J]. Computational Mechanics, 2014, 54(5): 1357-1374. doi: 10.1007/s00466-014-1063-8
[16] BOCCA P, CARPINTERI A, VALENTE S. Size effects in the mixed mode crack propagation: softening and snap-back analysis[J]. Engineering Fracture Mechanics, 1990, 35(1): 159-170.
[17] GEERS M G D, BORST R D, PEERLINGS R H J. Damage and crack modeling in single-edge and double-edge notched concrete beams[J]. Engineering Fracture Mechanics, 2000, 65(2/3): 247-261.
[18] ZHU W C, TANG C A. Numerical simulation on shear fracture process of concrete using mesoscopic mechanical model[J]. Construction & Building Materials, 2002, 16(8): 453-463.
[19] OLIVER J, HUESPE A E, SAMANIEGO E, et al. Continuum approach to the numerical simulation of material failure in concrete[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 2004, 28: 609-632.
[20] DIAS I F, OLIVER J, LEMOS J V, et al. Modeling tensile crack propagation in concrete gravity dams via crack-path-field and strain injection techniques[J]. Engineering Fracture Mechanics, 2016, 154: 288-310. doi: 10.1016/j.engfracmech.2015.12.028
[21] ROTH S-N, L GER P, SOULA MANI A. A combined XFEM-damage mechanics approach for concrete crack propagation[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 923-955.
[22] CAMONES L A M, VARGAS E D A, DE FIGUEIREDO R P, et al. Application of the discrete element method for modeling of rock crack propagation and coalescence in the step-path failure mechanism[J]. Engineering Geology, 2013, 153: 80-94.
[23] LI T, PENG Y, ZHU Z, et al. Discrete element method simulations of the inter-particle contact parameters for the mono-sized iron ore particles[J]. Materials, 2017, 10(5): 520.
[24] WONG L N Y, WU Z. Application of the numerical manifold method to model progressive failure in rock slopes[J]. Engineering Fracture Mechanics, 2014, 119: 1-20.
-
期刊类型引用(6)
1. 张德沧，毛佳，戴妙林，邵琳玉，赵兰浩. 圆化离散单元法的改进及其在岩体断裂过程中的应用. 岩土工程学报. 2024(09): 1974-1983 . 
本站查看
2. 何荣兴，张智源，张星宇，章雅雯. 诱导下岩体裂隙扩展规律研究存在问题及对策. 中国矿业. 2024(10): 168-176 . 百度学术
3. 刘洋，吴志军，储昭飞，翁磊，徐翔宇，周原，高波，毛春光. 基于FDEM的围压条件下机械冲击破岩机理研究. 中南大学学报(自然科学版). 2023(03): 866-879 . 百度学术
4. 杨奎斌，朱彦鹏. 考虑后缘裂缝影响的均质土坡滑动面形式及搜索研究. 应用基础与工程科学学报. 2022(05): 1216-1227 . 百度学术
5. 张亚军，莫思阳，张友良. 基于修正牛顿-拉普森迭代的数值流形法. 计算机仿真. 2022(09): 394-397+440 . 百度学术
6. 韩笑. 基于高阶块体元-有限元建模的混凝土细观数值分析. 粉煤灰综合利用. 2021(03): 56-63 . 百度学术
其他类型引用(7)
下载:
计量
- 文章访问数: 306
- HTML全文浏览量: 25
- PDF下载量: 92
- 被引次数: 13
