Numerical simulations of crack propagation in rock based on the RKPM-PD coupling method
CUI Hao1,2, YAN Zihai1, HU Jianhua1, ZHENG Hong2
1. Power China Huadong Engineering Co., Ltd., Hangzhou 311122, Zhejiang, China; 2. Faculty of Architecture, Civil and Transportation Engineering, Beijing University of Technology, Beijing 100124, China
Abstract: The peridynamic method had great advantages in solving the problem of crack propagation in rock material due to its nonlocal characteristics. However, the method also faced problems such as zero-energy mode and boundary effects. In order to solve the above problems, the paper first proved that the non-ordinary state-based peridynamic(NOSB-PD)method was equivalent to the Galerkin weak form with nodal integral scheme. The equation of solving the deformation gradient F in NOSB-PD method was extended to a more general form, namely the peridynamic differential operator(PDDO)approximation. Since the PDDO had the same displacement approximation with the reconstruction kernel particle method(RKPM), this paper compared the difference between the two methods in the approximations of displacement derivatives in detail. The RKPM-PD coupling method with higher accuracy was proposed in the paper. Several numerical examples proved the accuracy of the new method in predicting the dynamic crack propagation in rock.
崔昊, 闫自海, 胡建华, 郑宏. 基于RKPM-PD方法的岩石裂纹扩展数值模拟[J]. 隧道与地下工程灾害防治, 2021, 3(3): 59-75.
CUI Hao, YAN Zihai, HU Jianhua, ZHENG Hong. Numerical simulations of crack propagation in rock based on the RKPM-PD coupling method. Hazard Control in Tunnelling and Underground Engineering, 2021, 3(3): 59-75.
周宗青,李利平,石少帅,等.隧道突涌水机制与渗透破坏灾变过程模拟研究[J].岩土力学,2020,41(11): 3621-3631. ZHOU Zongqing, LI Liping, SHI Shaoshuai, et al. Study on tunnel water inrush mechanism and simulation of seepage failure process[J]. Rock and Soil Mechanics, 2020, 41(11):3621-3631.
[2]
佘诗刚,林鹏. 中国岩石工程若干进展与挑战[J]. 岩石力学与工程学报, 2014,33(3): 433-457. SHE Shigang, LIN Peng. Some developments and challenging issues in rock engineering field in China[J]. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(3): 433-457.
[3]
SILLING S A. Reformulation of elasticity theory for discontinuities and long-range forces[J]. Journal of the Mechanics and Physics of Solids, 2000, 48(1):175-209.
[4]
SILLING S A,EPTON M, WECKNER O, et al. Peridynamic states and constitutive modeling[J]. Journal of Elasticity, 2007, 88(2): 151-184.
[5]
HA Y D, LEE J, HONG J W. Fracturing patterns of rock-like materials in compression captured with peridynamics[J]. Engineering Fracture Mechanics, 2015, 144:176-193.
[6]
LEE J, HA Y D, HONG J W.Crack coalescence morphology in rock-like material under compression[J]. International Journal of Fracture, 2017, 203(1): 211-236.
[7]
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 and Mining Sciences, 2015, 80:241-254.
[8]
WANG Y T, ZHOU X P, XU X.Numerical simulation of propagation and coalescence of flaws in rock materials under compressive loads using the extended non-ordinary state-based peridynamics[J]. Engineering Fracture Mechanics, 2016, 163:248-273.
[9]
谷新保.近场动力学理论及其在岩石类材料变形破坏过程的数值模拟[D]. 重庆: 重庆大学, 2015. GU Xinbao. Peridynamic theory and its numerical simulation in the deformation and damage process of the rock-like materials[D]. Chongqing: Chongqing University, 2015.
BESSA M A, FOSTER J T, BELYTSCHKO T, et al. A meshfree unification: reproducing kernel peridynamics[J]. Computational Mechanics, 2014, 53(6):1251-1264.
[12]
杨永涛.多裂纹动态扩展的数值流形法[D]. 北京: 中国科学院大学, 2015. YANG Yongtao. Multiple dynamic crack propagation based on the numerical manifold method[D]. Beijing: University of Chinese Academy of Sciences, 2015.
[13]
BELYTSCHKO T, GUO Y, LIU W K,et al. A unified stability analysis of meshless particle methods[J]. International Journal for Numerical Methods in Engineering, 2000, 48(9):1359-1400.
[14]
SUN G H, LIN S, ZHENG H, et al. The virtual element method strength reduction technique for the stability analysis of stony soil slopes[J]. Computers and Geotechnics, 2020, 119: 103349.
[15]
MADENCI E, BARUT A, FUTCH M. Peridynamic differential operator and its applications[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 304: 408-451.
[16]
LIU G R, GU Y T. An introduction to meshfree methods and their programming[M]. Berlin, Germany: Springer, 2005:97-106.
[17]
张雄, 刘岩. 无网格法[M]. 北京: 清华大学出版社, 2004.
[18]
CUI H, LI C G, ZHENG H. Ahigher-order stress point method for non-ordinary state-based peridynamics[J]. Engineering Analysis with Boundary Elements, 2020, 117:104-118.
[19]
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.
[20]
RABCZUK T, REN H L. A peridynamics formulation for quasi-static fracture and contact in rock[J]. Engineering Geology, 2017, 225:42-48.
[21]
HAERI H, SHAHRIAR K, MARJI 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 and Mining Sciences, 2014, 67:20-28.
[22]
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.
[23]
YANG S K, MA G W, REN X H, et al. Cover refinement of numerical manifold method for crack propagation simulation[J]. Engineering Analysis with Boundary Elements, 2014, 43:37-49.
[24]
NING Y J, YANG J, AN X M, et al. Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation within the discontinuous deformation analysis framework[J]. Computers and Geotechnics, 2011, 38(1):40-49.
[25]
CARPINTERI A, VALENTE S, FERRARA G, et al. Experimental and numerical fracture modelling of a gravity dam[J]. Fracture Mechanics of Concrete Structures, 1994: 351-360.
[26]
BARPI F, VALENTE S. Numerical simulation of prenotched gravity dam models[J]. Journal of Engineering Mechanics, 2000, 126(6):611-619.
[27]
ZHENG H, YANG Y T, SHI G H. Reformulation of dynamic crack propagation using the numerical manifold method[J].Engineering Analysis with Boundary Elements, 2019, 105: 279-295.
[28]
SHI M G, ZHONG H, OOI E T, et al. Modelling of crack propagation of gravity dams by scaled boundary polygons and cohesive crack model[J]. International Journal of Fracture, 2013, 183(1): 29-48.
[29]
吴宪锴.岩石三维裂纹扩展机制的物理与数值试验研究[D]. 大连: 大连理工大学, 2016. WU Xiankai. Experimental and numerical study on propagation mechanism of three-dimension crack of rock specimens[D]. Dalian: Dalian University of Technology, 2016.
[30]
徐栋栋.多裂纹扩展的数值流形法[D]. 北京: 中国科学院大学, 2014. XU Dongdong. Multiple crack propagation based on the numerical manifold method[D]. Beijing: University of Chinese Academy of Sciences, 2014.
2021, Vol. 3 
