不同围压时含孔洞模型裂缝扩展的连续—非连续数值模拟
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摘要
为了有效地模拟连续介质向非连续介质的转化,发展了一种拉格朗日元方法、变形体离散元方法及虚拟裂纹模型耦合且考虑四边形单元沿对角线开裂的连续—非连续方法。利用该方法,模拟了不同围压时含孔洞模型的变形—开裂过程,统计了拉裂缝及剪裂缝区段数目,监测了一些单元的最大主应力。研究结果表明:当围压较小时,初始拉裂缝首先出现在孔洞的顶、底部,然后向模型的上、下端扩展,在初始拉裂缝的左、右两侧的拉应力集中区中产生远场拉裂缝,随后在孔洞的左、右两侧出现剪裂缝,最后,剪裂缝贯穿模型;当围压较大时,远场拉裂缝数量较少,未充分发展,远场拉裂缝与剪裂缝的发展阶段的界限不分明。含孔洞模型的最大承载力的下降是由于孔洞左、右两侧的剪裂缝向外扩展造成的。随着围压的增加,开始出现初始拉裂缝的时步数目增大,初始拉裂缝两侧的远场拉裂缝数目变少、出现变晚。
To effectively simulate the transition process from continuum medium to discontinuum medium, a continuum-discontinuum method was developed, which is a combination of the Lagrangian element method, the deformational discrete element method and the fictitious crack method. In this method, the cracking along the diagonal line of the quadrilateral element is taken into consideration. Deformation-cracking processes of the models with a hole under different confining pressures were simulated through this method. The number of tensile and shear crack segments was calculated, and the maximum principal stresses for some elements were monitored. The following results are found. At the low confining pressure, the initial tensile cracks first appear at the roof and floor of the hole, and then they extend towards the top and bottom of the model respectively. At both sides of the initial tensile cracks, remote tensile cracks appear in tensile stress concentration zones, and then shear cracks appear at both sides of the hole; finally, shear cracks go through the model. At high confining pressure, few remote tensile cracks are found, and the dividing line between the stage of remote tensile crack propagation and the stage of shear crack propagation is not clear. The decrease of the maximum carrying capacity is due to shear crack propagation at the both sides of the hole. With an increase of the confining pressure, the number of timesteps of the initial tensile cracks increases, while that of the remote tensile cracks at both sides of the initial tensile cracks decreases and it takes more time for them to appear.
To effectively simulate the transition process from continuum medium to discontinuum medium, a continuum-discontinuum method was developed, which is a combination of the Lagrangian element method, the deformational discrete element method and the fictitious crack method. In this method, the cracking along the diagonal line of the quadrilateral element is taken into consideration. Deformation-cracking processes of the models with a hole under different confining pressures were simulated through this method. The number of tensile and shear crack segments was calculated, and the maximum principal stresses for some elements were monitored. The following results are found. At the low confining pressure, the initial tensile cracks first appear at the roof and floor of the hole, and then they extend towards the top and bottom of the model respectively. At both sides of the initial tensile cracks, remote tensile cracks appear in tensile stress concentration zones, and then shear cracks appear at both sides of the hole; finally, shear cracks go through the model. At high confining pressure, few remote tensile cracks are found, and the dividing line between the stage of remote tensile crack propagation and the stage of shear crack propagation is not clear. The decrease of the maximum carrying capacity is due to shear crack propagation at the both sides of the hole. With an increase of the confining pressure, the number of timesteps of the initial tensile cracks increases, while that of the remote tensile cracks at both sides of the initial tensile cracks decreases and it takes more time for them to appear.
引文
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[9] 王学滨, 白雪元, 祝铭泽. 基于连续—非连续方法的地质体材料变形—拉裂过程模拟——以岩样紧凑拉伸试验为例[J]. 地质力学学报, 2018, 24(3): 332～340.WANG Xuebin, BAI Xueyuan, ZHU Mingze. Modeling of deformation-cracking processes of geomaterials based on a continuum-discontinuum method: a case study of compact tension test[J]. Journal of Geomechanics, 2018, 24(3): 332～340. (in Chinese with English abstract)
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[11] 郭翔, 王学滨, 白雪元, 等. 加载方式及抗拉强度对巴西圆盘试验影响的连续—非连续方法数值模拟[J]. 岩土力学, 2017, 38(1): 214～220.GUO Xiang, WANG Xuebin, BAI Xueyuan, et al. Numerical simulation of effects of loading types and tensile strengths on Brazilian disk test by use of a continuum-discontinuum method[J]. Rock and Soil Mechanics, 2017, 38(1): 214～220. (in Chinese with English abstract)
[12] 侯艳丽, 张楚汉. 用三维离散元实现混凝土I型断裂模拟[J]. 工程力学, 2007, 24(1): 37～43.HOU Yanli, ZHANG Chuhan. Mode I-fracture simulation of concrete based on 3D distinct element method[J]. Engineering Mechanics, 2007, 24(1): 37～43. (in Chinese with English abstract)
[13] 张楚汉, 金峰, 侯艳丽, 等. 岩石和混凝土离散—接触—断裂分析[M]. 北京: 清华大学出版社. 2008.ZHANG Chuhan, JIN Feng, HOU Yanli. et al. Discrete-contact-fracture analysis of rock and concrete[M]. Beijing: Tsinghua University Press, 2008. (in Chinese)
[14] 郑宏, 葛修润, 李焯芬. 脆塑性岩体的分析原理及其应用[J]. 岩石力学与工程学报, 1997, 16(1): 8～21.ZHENG Hong, GE Xiurun, Lee C F. Analysis principle for rock mass with brittle-plasticity and its applications[J]. Chinese Journal of Rock Mechanics and Engineering, 1997, 16(1): 8～21. (in Chinese with English abstract)
[15] Munjiza A. The combined finite-discrete element method[M]. England: John Wiley & Sons Ltd.
[2] 宋义敏, 潘一山, 章梦涛, 等. 洞室围岩三种破坏形式的试验研究[J]. 岩石力学与工程学报, 2010, 29(S1): 2741～2745.SONG Yimin, PAN Yishan, ZHANG Mengtao, et al. Experimental investigation on fracture of three types of underground caverns[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(S1): 2741～2745. (in Chinese with English abstract)
[3] 郭晓菲, 马念杰, 赵希栋, 等. 圆形巷道围岩塑性区的一般形态及其判定准则[J]. 煤炭学报, 2016, 41(8): 1871～1877.GUO Xiaofei, MA Nianjie, ZHAO Xidong, et al. General shapes and criterion for surrounding rock mass plastic zone of round roadway[J]. Journal of China Coal Society, 2016, 41(8): 1871～1877. (in Chinese with English abstract)
[4] 张纯旺, 宋选民, 王伟, 等. 双向不等压圆形巷道围岩塑性区理论分析及数值模拟[J]. 煤矿安全, 2017, 48(11): 217～221.ZHANG Chunwang, SONG Xuanmin, WANG Wei, et al. Theoretical analysis and numerical simulation on plastic zone in circular tunnel under bidirectional non-uniform stress field[J]. Safety in Coal Mines, 2017, 48(11): 217～221. (in Chinese with English abstract)
[5] 黎崇金, 李夕兵, 李地元. 含孔洞大理岩破坏特性的颗粒流分析[J]. 工程科学学报, 2017, 39(12): 1791～1801.LI Chongjin, LI Xibing, LI Diyuan. Particle flow analysis of fracture characteristics of marble with a single hole[J]. Chinese Journal of Engineering, 2017, 39(12): 1791～1801. (in Chinese with English abstract)
[6] 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.
[7] Mahabadi O, Kaifosh P, Marschall P, et al. Three-dimensional FDEM numerical simulation of failure processes observed in Opalinus Clay laboratory samples[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2014, 6(6): 591～606.
[8] 王学滨. 拉格朗日元方法、变形体离散元方法及虚拟裂纹模型耦合的连续—非连续介质力学分析方法研究[R]. 北京: 中国矿业大学(北京), 2015.WANG Xuebin. A method for continuum-discontinuum medium based on the coupled Lagrangian element method, deformational discrete element method and fictitious crack model[R]. Beijing: China University of Mining and Technology (Beijing), 2015. (in Chinese with English abstract)
[9] 王学滨, 白雪元, 祝铭泽. 基于连续—非连续方法的地质体材料变形—拉裂过程模拟——以岩样紧凑拉伸试验为例[J]. 地质力学学报, 2018, 24(3): 332～340.WANG Xuebin, BAI Xueyuan, ZHU Mingze. Modeling of deformation-cracking processes of geomaterials based on a continuum-discontinuum method: a case study of compact tension test[J]. Journal of Geomechanics, 2018, 24(3): 332～340. (in Chinese with English abstract)
[10] 王学滨, 陈忠元, 郭瑞, 等. 预设V形缺口的单向拉伸岩样变形—开裂过程模拟——基于连续—非连续方法[J]. 防灾减灾工程学报, 2018, 38(2): 209～215.WANG Xuebin, CHEN Zhongyuan, GUO Rui, et al. Modeling of deformation-cracking processes of rock specimens with V-shaped notches in uniaxial tension—based on a continuum-discontinuum method[J]. Journal of Disaster Prevention and Mitigation Engineering, 2018, 38(2): 209～215. (in Chinese with English abstract)
[11] 郭翔, 王学滨, 白雪元, 等. 加载方式及抗拉强度对巴西圆盘试验影响的连续—非连续方法数值模拟[J]. 岩土力学, 2017, 38(1): 214～220.GUO Xiang, WANG Xuebin, BAI Xueyuan, et al. Numerical simulation of effects of loading types and tensile strengths on Brazilian disk test by use of a continuum-discontinuum method[J]. Rock and Soil Mechanics, 2017, 38(1): 214～220. (in Chinese with English abstract)
[12] 侯艳丽, 张楚汉. 用三维离散元实现混凝土I型断裂模拟[J]. 工程力学, 2007, 24(1): 37～43.HOU Yanli, ZHANG Chuhan. Mode I-fracture simulation of concrete based on 3D distinct element method[J]. Engineering Mechanics, 2007, 24(1): 37～43. (in Chinese with English abstract)
[13] 张楚汉, 金峰, 侯艳丽, 等. 岩石和混凝土离散—接触—断裂分析[M]. 北京: 清华大学出版社. 2008.ZHANG Chuhan, JIN Feng, HOU Yanli. et al. Discrete-contact-fracture analysis of rock and concrete[M]. Beijing: Tsinghua University Press, 2008. (in Chinese)
[14] 郑宏, 葛修润, 李焯芬. 脆塑性岩体的分析原理及其应用[J]. 岩石力学与工程学报, 1997, 16(1): 8～21.ZHENG Hong, GE Xiurun, Lee C F. Analysis principle for rock mass with brittle-plasticity and its applications[J]. Chinese Journal of Rock Mechanics and Engineering, 1997, 16(1): 8～21. (in Chinese with English abstract)
[15] Munjiza A. The combined finite-discrete element method[M]. England: John Wiley & Sons Ltd.