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| Three-dimensional numerical simulation of rock failure process based on the modified rigid-body-spring method |
| HE Chen1,YAO Chi1,JIANG Qinghui2,ZHOU Chuangbing1 |
| (1. School of Infrastructure Engineering,Nanchang University,Nanchang,Jiangxi 330031,China;
2. School of Civil Engineering,Wuhan University,Wuhan,Hubei 430072,China) |
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Abstract Based on the rigid-body-spring method,a new three-dimensional discrete numerical model is proposed to simulate the progressive failure process of brittle rocks. The model describes the interaction between rigid blocks by means of spring-set groups distributed on the interface of blocks. Thus,the progressive crack propagation is naturally considered. To obtain a basic mesh with high homogeneous and isotropic crack direction,a new random Voronoi mesh technology with a growth “nucleus” place strategy is proposed based on the “point saturation” strategy. Then,the basic functions of three-dimensional modified rigid-body-spring method are proposed. Considering mesoscopic shear and tensile failure modes,a failure criterion based on Mohr-Coulomb criterion with maximum tensile strength is established,and the calibration strategy of mesoscopic parameters of the new model is provided. Finally,the proposed model is validated by comparing with the results of laboratory triaxial tests. Effects of the pattern of the spring-sets configuration and the block size on the simulation results are also discussed. The results show that the proposed model can correctly describe non-linear stress-strain responses,evolution of micro-cracks,and macroscopic failure mode of the rocks under different confining pressures.
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| [1] LISJAK A,GRASSELLI G. A review of discrete modeling techniques for fracturing processes in discontinuous rock masses[J]. Journal of Rock Mechanics and Geotechnical Engineering,2014,6(4):301–314.
[2] ZHANG Y,WONG L N Y. A review of numerical techniques approaching microstructures of crystalline rocks[J]. Computers and Geosciences,2018,115:167–187.
[3] DONZé F V,RICHEFEU V,MAGNIER S A. Advances in discrete element method applied to soil[J]. Rock and Concrete Mechanics,2009,8(1):44.
[4] CUNDALL P A,STRACK O D L. A discrete numerical model for granular assemblies[J]. Geotechnique,1979,29(1):47–65.
[5] WANG Z,YANG S,LI L,et. al. A 3D Voronoi clump based model for simulating failure behavior of brittle rock[J]. Engineering Fracture Mechanics,2021,248:107720.
[6] KOZICKI J,DONZé F V. YADE‐OPEN DEM:An open‐source software using a discrete element method to simulate granular material[J]. Engineering Computations,2009,26(7):786–805.
[7] LIU C,LIU H,ZHANG H. MatDEM-fast matrix computing of the discrete element method[J]. Earthquake Research Advances,2021:100010.
[8] LAMBERT C,COLL C. Discrete modeling of rock joints with a smooth-joint contact model[J]. Journal of Rock Mechanics and Geotechnical Engineering,2014,6(1):1–12.
[9] ZHOU J,LAN H,ZHANG L,et al. Novel grain-based model for simulation of brittle failure of Alxa porphyritic granite[J]. Engineering Geology,2019,251:100–114.
[10] CHEN W,KONIETZKY H. Simulation of Heterogeneity,creep,damage and lifetime for loaded brittle rocks[J]. Tectonophysics,2014,633:164–175.
[11] SHI G. Discontinuous deformation analysis:a new numerical model for the statics and dynamics of deformable block structures[J]. Engineering Computations,1992,9(2):157–168.
[12] MUNJIZA A A. The combined finite-discrete element method[M]. [S. l.]:John Wiley and Sons,2004:29–31.
[13] LISJAK A,GARITTE B,GRASSELLI G,et al. The excavation of a circular tunnel in a bedded argillaceous rock(Opalinus Clay):short-term rock mass response and FDEM numerical analysis[J]. Tunnelling and Underground Space Technology,2015,45:227–248.
[14] YAN C,JIAO Y Y,ZHENG H. A fully coupled three-dimensional hydro-mechanical finite discrete element approach with real porous seepage for simulating 3D hydraulic fracturing[J]. Computers and Geotechnics,2018,96:73–89.
[15] YAN C,WANG X,HUANG D,et al. A new 3D continuous-discontinuous heat conduction model and coupled thermomechanical model for simulating the thermal cracking of brittle materials[J]. International Journal of Solids and Structures,2021,229:111123.
[16] YAN C,ZHENG Y,KE W,et al. A FDEM 3D moisture migration-fracture model for simulation of soil shrinkage and desiccation cracking[J]. Computers and Geotechnics,2021,140:104425.
[17] YAN C,XIE X,REN Y,et al. A FDEM-based 2D coupled thermal-hydro-mechanical model for multiphysical simulation of rock fracturing[J]. International Journal of Rock Mechanics and Mining Sciences,2022,149:104964.
[18] 郭汝坤,冯 春,李战军,等. 岩体强度对牙轮单齿作用下破碎坑的体积及形态影响研究[J]. 岩土力学,2016,37(10):2 971–2 978. (GUO Rukun,FENG Chun,LI Zhanjun,et al. Influence of rock mass strength on volume and shape of fragmental pit generated by a single tooth of roller bit[J]. Rock and Soil Mechanics,2016,37(10):2 971–2 978.(in Chinses))
[19] 姚 池,姜清辉,邵建富,等. 一种模拟岩石破裂的细观数值计算模型[J]. 岩石力学与工程学报,2013,32(增2):3 146–3 153.(YAO Chi,JIANG Qinghui,SHAO Jianfu,et al. A mesoscopic numerical model for simulation of rock fracturing[J]. Chinese Journal of Rock Mechanics and Engineering,2013,32(Supp.2):3 146–3 153.(in Chinese))
[20] KAWAI T. New element models in discrete structural analysis[J]. Journal of the Society of Naval Architects of Japan,1977,1977(141):174–180.
[21] BOLANDER J E,SAITO S. Fracture analyses using spring networks with random geometry[J]. Engineering Fracture Mechanics,1998,61(5):569–591.
[22] ASAHINA D,ITO K,HOUSEWORTH J E,et al. Simulating the Poisson effect in lattice models of elastic continua[J]. Computers and Geotechnics,2015,70:60–67.
[23] RASMUSSEN L L,DE FARIAS M M,DE ASSIS A P. Extended rigid body spring network method for the simulation of brittle rocks[J]. Computers and Geotechnics,2018,99:31–41.
[24] YAMAMOTO Y,NAKAMURA H,KURODA I,et al. Crack propagation analysis of reinforced concrete wall under cyclic loading using RBSM[J]. European Journal of Environmental and Civil Engineering,2014,18(7):780–792.
[25] NAGAI K,SATO Y,UEDA T. Mesoscopic simulation of failure of mortar and concrete by 3D RBSM[J]. Journal of Advanced Concrete Technology,2005,3(3):18.
[26] YAO C,JIANG Q H,SHAO J F. Numerical simulation of damage and failure in brittle rocks using a modified rigid block spring method[J]. Computers and Geotechnics,2015,64:48–60.
[27] QIAN L,ZHANG X,QIAN,et. al. Rigid finite element and its applications in engineering[J]. Acta Mechanica Sinica,1995,11(1):46–52.
[28] 卓家寿,赵 宁. 不连续介质静、动力分析的刚体–弹簧元法[J]. 河海大学学报,1993,21(5):34–43.(ZHUO Jiashou,ZHAO Ning. Piecewise rigid body-interface spring method for problems of discontinuous medium[J]. Journal of Hohai University,1993,21(5):34–43.(in Chinese))
[29] 章 青,卓家寿. 三峡船闸高边坡稳定分析的界面元法与评判准则[J]. 岩石力学与工程学报,2000,19(3):285–288.(ZHANG Qing,ZHUO Jiashou. Interface element method and criterion for stability analysis of high slopes in three gorges shiplock[J]. Chinese Journal of Rock Mechanics and Engineering,2000,19(3):285–288.(in Chinese))
[30] 姚 池,李 瑶,姜清辉,等. 应力作用下软硬互层岩石破裂过程的细观模拟[J]. 岩石力学与工程学报,2015,34(8):1 542–1 551. (YAO Chi,LI Yao,JIANG Qinghui,et al. Mesoscopic model of failure process of interlayered rock under compression[J]. Chinese Journal of Rock Mechanics and Engineering,2015,34(8):1 542–1 551.(in Chinese))
[31] 赵 宁,卓家寿. 动力分析的刚体-界面元与有限元耦合法[J]. 河海大学学报,1994,22(6):8–15.(ZHAO Ning,ZHUO Jiashou. Coupling method of rigid-body interface stress element(RISE) with finite element(FE) in dynamic analysis[J]. Journal of Hohai University,1994,22(6):8–15.(in Chinese))
[32] 钱令希,张 雄. 结构分析中的刚体有限元法[J]. 计算结构力学及其应用,1991,8(1):1–14.(QIAN Lingxi,ZHANG Xiong. Rigid body finite element method in structural analysis[J]. Computational Structural Mechanics and Applications,1991,8(1):1–14.(in Chinese))
[33] 姚 池,何 忱,蒋水华,等. 脆性各向异性岩石破坏过程数值模拟[J]. 工程力学,2019,36(2):96–103.(YAO Chi,HE Chen,JIANG Shuihua,et al. Numerical simulation of damage and failure process in anisotropic brittle rocks[J]. Engineering Mechanics,2019,36(2):96–103.(in Chinese))
[34] 姚 池,赵 明,杨建华,等. 基于改进刚体弹簧方法的二维水压致裂模型[J]. 岩石力学与工程学报,2017,36(9):2 169–2 176. (YAO Chi,ZHAO Ming,YANG Jianhua,et al. A Coupled RBSM-DFN model for simulating hydraulic fracturing[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(09):2 169–2 176.(in Chinese))
[35] YAO C,JIANG Q H,SHAO J F. A numerical analysis of permeability evolution in rocks with multiple fractures[J]. Transport in Porous Media,2015,108(2):289–311.
[36] XU T,FU T-F,HEAP M J,et al. Mesoscopic damage and fracturing of heterogeneous brittle rocks based on three-dimensional polycrystalline discrete element method[J]. Rock Mechanics and Rock Engineering,2020,53(12):5 389–5 409.
[37] SCHOLTèS L. A DEM model for soft and hard rocks role of grain interlocking on strength[J]. Journal of the Mechanics and Physics of Solids,2013,61(2):352–369.
[38] HAMMER P C,MARLOWE O J,STROUD A H. Numerical integration over simplexes and cones[J]. Mathematical Tables and Other Aids to Computation,1956,10(55):130–137.
[39] 赵 超. 基于刚体弹簧法的钢筋混凝土结构破坏过程模拟方法[博士学位论文][D]. 北京:中国矿业大学(北京),2018.(ZHAO Chao. Simulating method for failure process of RC structures based on RBSM[Ph. D. Thesis][D]. Beijing:China University of Mining and Technology(Beijing),2018.(in Chinese))
[40] HUANG G,XU Y,YI X,et al. Highly efficient iterative methods for solving linear equations of three-dimensional sphere discontinuous deformation analysis[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2020,44(9):1 301–1 314.
[41] ASAHINA D,AOYAGI K,KIM K,et al. Elastically-homogeneous lattice models of damage in geomaterials[J]. Computers and Geotechnics,2017,81:195–206.
[42] BOLANDER J E,ELIá? J,CUSATIS G,et al. Discrete mechanical models of concrete fracture[J]. Engineering Fracture Mechanics,2021,257:108030.
[43] 胡训健,卞 康,刘 建,等. 细观结构的非均质性对花岗岩蠕变特性影响的离散元模拟研究[J]. 岩石力学与工程学报,2019,38(10):2 069–2 083.(HU Xunjian,BIAN Kang,LIU Jian,et al. Discrete element simulation study on the influence of microstructure heterogeneity on the creep characteristics of granite[J]. Chinese Journal of Rock Mechanics and Engineering,2019,38(10):2 069–2 083.(in Chinese))
[44] 孙美玲,江 山. 有限元方法的Gauss积分和Hammer积分方案[J]. 南通职业大学学报,2009,23(3):67–70.(SUN Meiling,JIANG Shan. The gauss integral scheme and hammer integral scheme in the finite element method[J]. Journal of Nantong Vocational College,2009,23(3):67–70.(in Chinese))
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