破裂全过程模拟的改进非连续变形分析方法
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摘要
研究工程岩体中裂纹的萌生、扩展和贯通机制以及后续沿着软弱结构面的滑动机制对于揭示岩体变形和破坏规律具有十分重要的意义。非连续变形分析(DDA)方法对于模拟由宏观结构面切割而成的离散块体系统的滑动变形具有与生俱来的优势,但在模拟岩体由连续到非连续的破坏演化过程方面存在不足。通过引入虚拟节理技术将连续区域离散为子块体,并设定虚拟节理强度为岩石本身强度的方式,在一定程度上加强了DDA对于岩体连续特性的模拟。但这种方式仅考虑虚拟节理达到抗拉强度之前的黏结作用,而忽略了岩石应力-应变全过程曲线中应变软化阶段的强度。因此,通过在子块体间插入一种能够描述岩石应变软化阶段的应变软化黏结单元的方式对上述不足进行了改进,进一步加强了DDA对于岩体连续特性的模拟,并保留了DDA在非连续变形模拟方面的优势。最后,将其应用于求解几个典型的破裂问题。结果表明,模拟的破裂路径与参考解较为一致,证实了改进DDA方法的有效性和正确性。
It is of great important significance to study the mechanism of initiation, propagation and coalescence in engineering rock mass and the subsequent sliding mechanism along the weak structural plane for revealing the law of deformation and failure of rock mass. Discontinuous deformation analysis(DDA) method owns an inherent advantage in simulating the sliding deformation of discrete block system, which is formed by the intersections of various macroscopic structural planes. But it is slightly inadequate in the simulation of the evolution process from continuum to discontinuum. DDA has strengthened its ability in the simulation of continuous characteristics of rock mass to a certain extent by introducing virtual joint technology to discretize the continuous area into sub blocks and then setting strength of virtual joint as that of the rock itself. However, this treatment only considers the bonding effect of virtual joints before reaching the tensile strength and ignores the strength of the strain softening stage in the complete stress-strain curve of rock. Therefore, the above deficiencies have been improved by inserting a so-called strain softening cohesive element between the sub blocks which can describe the strain softening stage in the stress-strain curve of rock. This further strengthens the ability of DDA in the simulation of continuous attributes of materials and also retains its inherent advantages in the simulation of discontinuous deformation. Finally, it is applied to solve several typical crack problems. The results show that the simulated fracture paths are in good accordance with the reference solutions, proving the validity and correctness of the improved DDA method.
It is of great important significance to study the mechanism of initiation, propagation and coalescence in engineering rock mass and the subsequent sliding mechanism along the weak structural plane for revealing the law of deformation and failure of rock mass. Discontinuous deformation analysis(DDA) method owns an inherent advantage in simulating the sliding deformation of discrete block system, which is formed by the intersections of various macroscopic structural planes. But it is slightly inadequate in the simulation of the evolution process from continuum to discontinuum. DDA has strengthened its ability in the simulation of continuous characteristics of rock mass to a certain extent by introducing virtual joint technology to discretize the continuous area into sub blocks and then setting strength of virtual joint as that of the rock itself. However, this treatment only considers the bonding effect of virtual joints before reaching the tensile strength and ignores the strength of the strain softening stage in the complete stress-strain curve of rock. Therefore, the above deficiencies have been improved by inserting a so-called strain softening cohesive element between the sub blocks which can describe the strain softening stage in the stress-strain curve of rock. This further strengthens the ability of DDA in the simulation of continuous attributes of materials and also retains its inherent advantages in the simulation of discontinuous deformation. Finally, it is applied to solve several typical crack problems. The results show that the simulated fracture paths are in good accordance with the reference solutions, proving the validity and correctness of the improved DDA method.
引文
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[9]MUNJIZA A,OWEN D R J,BICANIC N.A combined finite‐discrete element method in transient dynamics of fracturing solids[J].Engineering Computations,2013,12(2):145-174.
[10]严成增,郑宏,孙冠华,等.模拟水压致裂的二维FDEM-flow方法[J].岩石力学与工程学报,2015,34(1):67-75.YAN Cheng-zeng,ZHENG Hong,SUN Guan-hua,et al.A 2D FDEM-flow method for simulating hydraulic fracture[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(1):67-75.
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[14]徐栋栋,郑宏,杨永涛,等.多裂纹扩展的数值流形法[J].力学学报,2015,47(3):471-481.XU Dong-dong,ZHENG Hong,YANG Yong-tao,et al.Multiple crack propagation based on the numerical manifold method[J].Chinese Journal of Theoretical and Applied Mechanics,2015,47(3):471-481.
[15]徐栋栋,杨永涛,郑宏,等.基于环路更新的物理覆盖和接触环路生成算法[J].岩土工程学报,2015,37(10):1865-1875.XU Dong-dong,YANG Yong-tao,ZHENG Hong,et al.Algorithm for generation of physical cover and contact loops based on loop updating[J].Chinese Journal of Geotechnical Engineering,2015,37(10):1865-1875.
[16]王水林,葛修润,章光.受压状态下裂纹扩展的数值分析[J].岩石力学与工程学报,1999,18(6):671-675.WANG Shui-lin,GE Xiu-run,ZHANG Guang.Numerical analysis of crack propagation under compression[J].Chinese Journal of Rock Mechanics and Engineering,1999,18(6):671-675.
[17]ZHENG H,XU D.New strategies for some issues of numerical manifold method in simulation of crack propagation[J].International Journal for Numerical Methods in Engineering,2014,97(13):986-1010.
[18]SHI G H.Discontinuous deformation analysis-a new numerical model for the statics and dynamics of block systems[D].Berkeley:University of California,1988.
[19]马永政,蔡可键,郑宏.混合多位移模式的非连续变形分析法研究[J].岩土力学,2016,37(3):867-874.MA Yong-zheng,CAI Ke-jian,ZHENG Hong.An analysis of discontinuous deformation with mixed multiple deformation modes[J].Rock and Soil Mechanics,2016,37(3):867-874.
[20]甯尤军,杨军,陈鹏万.节理岩体爆破的DDA方法模拟[J].岩土力学,2010,31(7):2259-2263.NING You-jun,YANG Jun,CHEN Peng-wan.Numerical simulation of rock blasting in jointed rock mass by DDAmethod[J].Rock and Soil Mechanics,2010,31(7):2259-2263.
[21]焦玉勇,张秀丽,刘泉声,等.用非连续变形分析方法模拟岩石裂纹扩展[J].岩石力学与工程学报,2007,26(4):682-691.JIAO Yu-yong,ZHANG Xiu-li,LIU Quan-sheng,et al.Simulation of rock crack propagation using discontinuous deformation analysis method[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(4):682-691.
[22]JIAO Y Y,ZHANG X L,ZHAO J.Two-dimensional DDA contact constitutive model for simulating rock fragmentation[J].Journal of Engineering Mechanics,2012,138(2):199-209.
[23]SHI G H.Manifold method of material analysis[C]//Transactions of the 9th Army Conference on Applied Mathematics and Computing.Report No.92-1.U.S.Army Research Office,Minneapolis:[s.n.],1991:57-76.
[24]姜清辉,周创兵,漆祖芳.基于Newmark积分方案的DDA方法[J].岩石力学与工程学报,2009,28(增刊1):2778-2783.JIANG Qing-hui,ZHOU Chuang-bing,QI Zu-fang.Discontinuous deformation analysis method based on Newmark integration algorithm[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(Suppl.1):2778-2783.
[25]EVANS R H,MARATHE M S.Microcracking and stress-strain curves for concrete in tension[J].Materials&Structures,1968(1):61-64.
[26]MUNJIZA A,ANDREWS K R F,WHITE J K.Combined single and smeared crack model in combined finitediscrete element analysis[J].International Journal for Numerical Methods in Engineering,1999,44(1):41-57.
[27]NING Y J,AN X M,MA G W.Footwall slope stability analysis with the numerical manifold method[J].International Journal of Rock Mechanics&Mining Sciences,2011,48(6):964-975.
[28]AL-SHAYEA NASER A.Crack propagation trajectories for rocks under mixed mode I-II fracture[J].Engineering Geology,2005,81(1):84-97.
[29]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&Mining Sciences,2014,67:20-28.
[30]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 Yong-tao.Multiple dynamic crack propagation based on the numerical manifold method[D].Beijing:University of Chinese Academy of Sciences,2015.
[31]MAHABADI O K.Investigating the influence of micro-scale heterogeneity and microstructure on the failure and mechanical behaviour of geomaterials[D].Toronto:University of Toronto,2012.
[32]付晓东,盛谦,张勇慧.基于Open MP的非连续变形分析并行计算方法[J].岩土力学,2014,35(8):2401-2407.FU Xiao-dong,SHENG Qian,ZHANG Yong-hui.Parallel computing method for discontinuous deformation analysis using Open MP[J].Rock and Soil Mechanics,2014,35(8):2401-2407.
[2]TANG C A,YANG W T,FU Y F,et al.A new approach to numerical method of modelling geological processes and rock engineering problems--continuum to discontinuum and linearity to nonlinearity[J].Engineering Geology,1998,49(49):207-214.
[3]TANG C A,KAISER P K.Numerical simulation of cumulative damage and seismic energy release during brittle rock failure--part I:fundamentals[J].International Journal of Rock Mechanics&Mining Sciences,1998,35(2):113-121.
[4]张振南,陈永泉.一种模拟节理岩体破坏的新方法:单元劈裂法[J].岩土工程学报,2009,31(12):1858-1865.ZHANG Zhen-nan,CHEN Yong-quan.Novel numerical approach to jointed rock mass simulation:element partition method[J].Chinese Journal of Geotechnical Engineering,2009,31(12):1858-1865.
[5]BELYTSCHKO T,BLACK T.Elastic crack growth in finite elements with minimal remeshing[J].International Journal for Numerical Methods in Engineering,1999,45(5):601-620.
[6]师访,高峰,李玺茹,等.模拟岩石压剪状态下主次裂纹萌生开裂的扩展有限元法[J].岩土力学,2014,35(6):1809-1817.SHI Fang,GAO Feng,LI Xi-ru,et al.Modeling initiation and propagation of main and secondary cracks of rock under combined compression and shear loading using extended finite element method[J].Rock and Soil Mechanics,2014,35(6):1809-1817.
[7]庄晓莹,黄润秋,朱合华.基于水平集坐标的二维压剪节理动态扩展过程无网格法模拟研究[J].岩石力学与工程学报,2012,31(11):2187-2196.ZHUANG Xiao-ying,HUANG Run-qiu,ZHU He-hua.Simulation for 2D compression-shear joint dynamic propagation process using meshless methods based on level sets coordinates[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(11):2187-2196.
[8]王杰,李世海,张青波.基于单元破裂的岩石裂纹扩展模拟方法[J].力学学报,2015,47(1):105-118.WANG Jie,LI Shi-hai,ZHANG Qing-bo.Simulation of crack propagation of rock based on splitting elements[J].Chinese Journal of Theoretical and Applied Mechanics,2015,47(1):105-118.
[9]MUNJIZA A,OWEN D R J,BICANIC N.A combined finite‐discrete element method in transient dynamics of fracturing solids[J].Engineering Computations,2013,12(2):145-174.
[10]严成增,郑宏,孙冠华,等.模拟水压致裂的二维FDEM-flow方法[J].岩石力学与工程学报,2015,34(1):67-75.YAN Cheng-zeng,ZHENG Hong,SUN Guan-hua,et al.A 2D FDEM-flow method for simulating hydraulic fracture[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(1):67-75.
[11]严成增,郑宏,孙冠华,等.基于FDEM-flow研究地应力对水力压裂的影响[J].岩土力学,2016,37(1):237-246.YAN Cheng-zeng,ZHENG Hong,SUN Guan-hua,et al.Effect of in-situ stress on hydraulic fracturing based on FDEM-flow[J].Rock and Soil Mechanics,2016,37(1):237-246.
[12]严成增,郑宏,孙冠华,等.基于Open MP的二维有限元-离散元并行分析方法[J].岩土力学,2014,35(9):2717-2724.YAN Cheng-zeng,ZHENG Hong,SUN Guan-hua,et al.Parallel analysis of two-dimensional finite-discrete element method based on OpenMP[J].Rock and Soil Mechanics,2014,35(9):2717-2724.
[13]严成增,孙冠华,郑宏,等.爆炸气体驱动下岩体破裂的有限元-离散元模拟[J].岩土力学,2015,36(8):2419-2425.YANG Cheng-zeng,SUN Guan-hua,ZHENG Hong,et al.Simulation of explosive gas-driven rock fracture by FEM/DEM[J].Rock and Soil Mechanics,2015,36(8):2419-2425.
[14]徐栋栋,郑宏,杨永涛,等.多裂纹扩展的数值流形法[J].力学学报,2015,47(3):471-481.XU Dong-dong,ZHENG Hong,YANG Yong-tao,et al.Multiple crack propagation based on the numerical manifold method[J].Chinese Journal of Theoretical and Applied Mechanics,2015,47(3):471-481.
[15]徐栋栋,杨永涛,郑宏,等.基于环路更新的物理覆盖和接触环路生成算法[J].岩土工程学报,2015,37(10):1865-1875.XU Dong-dong,YANG Yong-tao,ZHENG Hong,et al.Algorithm for generation of physical cover and contact loops based on loop updating[J].Chinese Journal of Geotechnical Engineering,2015,37(10):1865-1875.
[16]王水林,葛修润,章光.受压状态下裂纹扩展的数值分析[J].岩石力学与工程学报,1999,18(6):671-675.WANG Shui-lin,GE Xiu-run,ZHANG Guang.Numerical analysis of crack propagation under compression[J].Chinese Journal of Rock Mechanics and Engineering,1999,18(6):671-675.
[17]ZHENG H,XU D.New strategies for some issues of numerical manifold method in simulation of crack propagation[J].International Journal for Numerical Methods in Engineering,2014,97(13):986-1010.
[18]SHI G H.Discontinuous deformation analysis-a new numerical model for the statics and dynamics of block systems[D].Berkeley:University of California,1988.
[19]马永政,蔡可键,郑宏.混合多位移模式的非连续变形分析法研究[J].岩土力学,2016,37(3):867-874.MA Yong-zheng,CAI Ke-jian,ZHENG Hong.An analysis of discontinuous deformation with mixed multiple deformation modes[J].Rock and Soil Mechanics,2016,37(3):867-874.
[20]甯尤军,杨军,陈鹏万.节理岩体爆破的DDA方法模拟[J].岩土力学,2010,31(7):2259-2263.NING You-jun,YANG Jun,CHEN Peng-wan.Numerical simulation of rock blasting in jointed rock mass by DDAmethod[J].Rock and Soil Mechanics,2010,31(7):2259-2263.
[21]焦玉勇,张秀丽,刘泉声,等.用非连续变形分析方法模拟岩石裂纹扩展[J].岩石力学与工程学报,2007,26(4):682-691.JIAO Yu-yong,ZHANG Xiu-li,LIU Quan-sheng,et al.Simulation of rock crack propagation using discontinuous deformation analysis method[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(4):682-691.
[22]JIAO Y Y,ZHANG X L,ZHAO J.Two-dimensional DDA contact constitutive model for simulating rock fragmentation[J].Journal of Engineering Mechanics,2012,138(2):199-209.
[23]SHI G H.Manifold method of material analysis[C]//Transactions of the 9th Army Conference on Applied Mathematics and Computing.Report No.92-1.U.S.Army Research Office,Minneapolis:[s.n.],1991:57-76.
[24]姜清辉,周创兵,漆祖芳.基于Newmark积分方案的DDA方法[J].岩石力学与工程学报,2009,28(增刊1):2778-2783.JIANG Qing-hui,ZHOU Chuang-bing,QI Zu-fang.Discontinuous deformation analysis method based on Newmark integration algorithm[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(Suppl.1):2778-2783.
[25]EVANS R H,MARATHE M S.Microcracking and stress-strain curves for concrete in tension[J].Materials&Structures,1968(1):61-64.
[26]MUNJIZA A,ANDREWS K R F,WHITE J K.Combined single and smeared crack model in combined finitediscrete element analysis[J].International Journal for Numerical Methods in Engineering,1999,44(1):41-57.
[27]NING Y J,AN X M,MA G W.Footwall slope stability analysis with the numerical manifold method[J].International Journal of Rock Mechanics&Mining Sciences,2011,48(6):964-975.
[28]AL-SHAYEA NASER A.Crack propagation trajectories for rocks under mixed mode I-II fracture[J].Engineering Geology,2005,81(1):84-97.
[29]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&Mining Sciences,2014,67:20-28.
[30]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 Yong-tao.Multiple dynamic crack propagation based on the numerical manifold method[D].Beijing:University of Chinese Academy of Sciences,2015.
[31]MAHABADI O K.Investigating the influence of micro-scale heterogeneity and microstructure on the failure and mechanical behaviour of geomaterials[D].Toronto:University of Toronto,2012.
[32]付晓东,盛谦,张勇慧.基于Open MP的非连续变形分析并行计算方法[J].岩土力学,2014,35(8):2401-2407.FU Xiao-dong,SHENG Qian,ZHANG Yong-hui.Parallel computing method for discontinuous deformation analysis using Open MP[J].Rock and Soil Mechanics,2014,35(8):2401-2407.
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