基于裂纹扩展模型的深部硐室围岩致裂规律
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摘要
根据岩体的非均匀性和存在初始裂纹的特征,在二维有限差分程序中建立了非均质体二维模型,并在模型中考虑初始裂纹的影响,利用程序中的自带编译语言,实现了服从不同分布的初始裂纹的长度和角度的赋值。在模型中,利用亚临界裂纹扩展理论描述与时间相关的裂纹亚临界扩展过程,计算过程可体现裂纹扩展的时间效应,从而实现对所模拟结构的寿命预测。模型中裂纹的扩展方式假定为形成翼型裂纹的形式,利用翼型裂纹的简化模型对裂纹的扩展尺寸,应力强度因子等参数进行计算。在每一计算步中,每个单元中的裂纹扩展方向与该时刻单元所受应力情况相关,应力强度因子与该单元所受应力大小及翼型裂纹简化长度相关。利用该模型对高地应力条件下孔洞开挖卸荷导致围岩破坏的过程进行模拟,分析了深部岩体开挖导致的围岩破坏规律,对不同的孔洞形状和初始裂纹的分布情况分别进行了分析,计算结果显示了非连续破裂的形成与初始裂纹角度分布的关系:分区破裂的表现形态与初始裂纹和最大压应力的夹角相关,并且不同初始裂纹角度均值也会导致围岩破裂时间不同。通过建立的多种孔洞形状开挖模型,对不同孔洞形状围岩破裂形态及破坏时间的规律进行总结,发现相同计算步数内方形孔洞周边围岩处破坏单元数量最多,圆形孔洞周边围岩破坏单元数量最少。研究结果证实了裂纹的分布对孔洞周边围岩破坏形态的影响,对裂纹扩展的时间效应的分析可实现对围岩破坏程度和范围的预测,可为深部高地应力条件下诱导致裂非爆连续开采的实施时间和方式提供指导。
A two-dimensional model is established considering the heterogeneity and the existence of initial cracks of rock materials based on a two dimensional finite difference code. Using the inherent compiling language,the different distributions of the initial cracks' lengths and orientations are implemented in each zone of the numerical model. The crack propagation rate is described by the subcritical crack growth theory,thus allowing for the analysis of the time effect of the crack propagation and lifetime prediction of the model. It is assumed in the model that the crack propagates forming wing crack. And a simplified wing crack model is adopted for the calculation of the crack length and stress intensity factors. In each calculation step,the crack propagation direction is influenced by the stress condition the zone is subjected to,and the stress intensity factor of the crack is controlled by the stresses and the length of the simplified wing crack. The model is used to simulate the failure process of surrounding rock under unloading of high geo-stress due to excavations. The fracture pattern in the surrounding rock due to excavations is analyzed,and the influence of different shape of the excavation and initial crack distributions is also discussed. The simulation results present the relation between the formation of non-continuous disintegration and the initial crack orientation distributions.The fracture pattern is affected by the angle between the initial crack and the maximum compressive stress. The fracture time of surrounding rock is also influenced by the mean value of initial crack orientations. The fracture patterns and failure time of surrounding rock with different excavation shapes are studied using the numerical model. According to the model with the different shapes of the excavation,within the same calculation stages,the most failure zones are found around square shaped excavations and the lease failure zones are found around circle excavations. The calculation result verified the influence of the distribution of the initial cracks on the fracture patterns of the surrounding rock of excavations,and the time effect in the crack propagation process can allow for the prediction of the extend and scope of failure of the surrounding rock. The results can provide information and guide the applications of the induced fracturing and non-explosive continuous mining in deep excavation sites under high geo-stresses.
A two-dimensional model is established considering the heterogeneity and the existence of initial cracks of rock materials based on a two dimensional finite difference code. Using the inherent compiling language,the different distributions of the initial cracks' lengths and orientations are implemented in each zone of the numerical model. The crack propagation rate is described by the subcritical crack growth theory,thus allowing for the analysis of the time effect of the crack propagation and lifetime prediction of the model. It is assumed in the model that the crack propagates forming wing crack. And a simplified wing crack model is adopted for the calculation of the crack length and stress intensity factors. In each calculation step,the crack propagation direction is influenced by the stress condition the zone is subjected to,and the stress intensity factor of the crack is controlled by the stresses and the length of the simplified wing crack. The model is used to simulate the failure process of surrounding rock under unloading of high geo-stress due to excavations. The fracture pattern in the surrounding rock due to excavations is analyzed,and the influence of different shape of the excavation and initial crack distributions is also discussed. The simulation results present the relation between the formation of non-continuous disintegration and the initial crack orientation distributions.The fracture pattern is affected by the angle between the initial crack and the maximum compressive stress. The fracture time of surrounding rock is also influenced by the mean value of initial crack orientations. The fracture patterns and failure time of surrounding rock with different excavation shapes are studied using the numerical model. According to the model with the different shapes of the excavation,within the same calculation stages,the most failure zones are found around square shaped excavations and the lease failure zones are found around circle excavations. The calculation result verified the influence of the distribution of the initial cracks on the fracture patterns of the surrounding rock of excavations,and the time effect in the crack propagation process can allow for the prediction of the extend and scope of failure of the surrounding rock. The results can provide information and guide the applications of the induced fracturing and non-explosive continuous mining in deep excavation sites under high geo-stresses.
引文
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[22]ZHOU X P,BI J.Zonal disintegration mechanism of cross-anisotropic rock mass around a deep circular tunnel under dynamic unloading[J].Theoretical and Applied Fracture Mechanics,2012,60(1):15-22.
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[2]谢和平,高峰,鞠杨.深部岩体力学研究与探索[J].岩石力学与工程学报,2015,34(11):2161-2178.XIE Heping,GAO Feng,JU Yang.Research and development of rock mechanics in deep ground engineering[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(11):2161-2178.
[3]何满潮,谢和平,彭苏萍,等.深部开采岩体力学研究[J].岩石力学与工程学报,2005,24(16):2803-2813.HE Manchao,XIE Heping,PENG Suping,et al.Study on rock mechanics in deep mining engineering[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(16):2803-2813.
[4]李夕兵.岩石动力学基础与应用[M].北京:科学出版社,2014.
[5]李夕兵,周健,王少锋,等.深部固体资源开采评述与探索[J].中国有色金属学报,2017,27(6):1236-1262.LI Xibing,ZHOU Jian,WANG Shaofeng.Review and practice of deep mining for solid mineral resources[J].The Chinese Journal of Nonferrous Metals,2017,27(6):1236-1262.
[6]李夕兵.分区破裂化正确认识与准确定位对金属矿山深部开采的意义重大[A].中国科协学会学术部编.新观点新学说学术沙龙文集[C].北京:中国科学技术出版社,2008:32-34.LI Xibing.The significance of correct understanding and accurate location of zone fragmentation to deep mining of metal mines[C].Academic department of China Association for science and technology edit.New ideas,new theories,academic salon collection.Beijing:China Science and Technology Press,2008:32-34.
[7]李夕兵,姚金蕊,杜坤.高地应力硬岩矿山诱导致裂非爆连续开采初探---以开阳磷矿为例[J].岩石力学与工程学报,2013,32(6):1101-1111.LI Xibing,YAO Jinrui,DU Kun.Preliminary study for induced fracture and non-explosive continuous mining in high-geostress hard rock mine-a case study of kaiyang phosphate mine[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(6):1101-1111.
[8]RAUENZAHN R M,TESTER J W.Rock failure mechanisms of flame-jet thermal spallation drilling-theory and experimental testing[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1989,26(5):381-399.
[9]李夕兵,陶明,宫凤强,等.冲击载荷作用下硬岩层裂破坏的理论和试验研究[J].岩石力学与工程学报,2011,30(6):1081-1088.LI Xibing,TAO Ming,GONG Fengqiang,et al.Theoretical and experimental study of hard rock spalling fracture under impact dynamic loading[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(6):1081-1088.
[10]MARTIN C D,MAYBEE W G.The strength of hard-rock pillars[J].International Journal of Rock Mechanics and Mining Sciences,2000,37(8):1239-1246.
[11]LI D Y,LI C C,LI X B.Influence of sample height-to-width ratios on failure mode for rectangular prism samples of hard rock loaded in uniaxial compression[J].Rock Mechanics and Rock Engineering,2011,44(3):253-267.
[12]宫凤强,罗勇,司雪峰,等.深部圆形隧洞板裂屈曲岩爆的模拟试验研究[J].岩石力学与工程学报,2017,36(7):1634-1648.GONG Fengqiang,LUO Yong,SI Xuefeng,et al.Experimental modeling on rockburst in deep hard rock circular tunnels[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(7):1634-1648.
[13]CAI M F.Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries-Insight from numerical modeling[J].International Journal of Rock Mechanics and Mining Sciences,2008,45(5):763-772.
[14]ORTLEPP W.Rock fracture and rockbursts:An illustrative study[M].Lincoln:South African Institute of Mining and Metallurgy,1997.
[15]QIAN Q H,ZHOU X P,YANG H Q,et al.Zonal disintegration of surrounding rock mass around the diversion tunnels in Jinping IIHydropower Station,Southwestern China[J].Theoretical and Applied Fracture Mechanics,2009,51(2):129-138.
[16]QIAN Q H,ZHOU X P.Non-euclidean continuum model of the zonal disintegration of surrounding rocks around a deep circular tunnel in a non-hydrostatic pressure state[J].Journal of Mining Science,2011,47(1):37-46.
[17]QIAN Q H,ZHOU X P,XIA E.Effects of the axial in situ stresses on the zonal disintegration phenomenon in the surrounding rock masses around a deep circular tunnel[J].Journal of Mining Science,2012,48(2):276-285.
[18]唐春安,张永彬.岩体间隔破裂机制及演化规律初探[J].岩石力学与工程学报,2008,27(7):1362-1369.TANG Chun’an,ZHANG Yongbin.Discussion on mechanism and evolution laws of fracture spacing in rock mass[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(7):1362-1369.
[19]王明洋,宋华,郑大亮,等.深部巷道围岩的分区破裂机制及“深部”界定探讨[J].岩石力学与工程学报,2006,25(9):1771-1776.WANG Mingyang,SONG Hua,ZHENG Daliang,et al.On mechanism of zonal disintegration within rock mass around deep tunnel and definition of“deep rock engineering”[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(9):1771-1776.
[20]谢和平,鞠杨,黎立云.基于能量耗散与释放原理的岩石强度与整体破坏准则[J].岩石力学与工程学报,2005,24(17):3003-3010.XIE Heping,JU Yang,LI Liyun.Criteria for strength and structural failure of rocks based on energy dissipation and energy release principles[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(17):3003-3010.
[21]谢和平,鞠杨,黎立云,等.岩体变形破坏过程的能量机制[J].岩石力学与工程学报,2008,27(9):1729-1740.XIE Heping,JU Yang,LI Liyun,et al.Energy mechanism of deformation and failure of rock masses[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(9):1729-1740.
[22]ZHOU X P,BI J.Zonal disintegration mechanism of cross-anisotropic rock mass around a deep circular tunnel under dynamic unloading[J].Theoretical and Applied Fracture Mechanics,2012,60(1):15-22.
[23]ZHOU X P,SONG H F,QIAN Q H.Zonal disintegration of deep crack-weakened rock masses:A non-Euclidean model[J].Theoretical and Applied Fracture Mechanics,2011,55(3):227-236.
[24]ANDERSON T L.Fracture mechanics:Fundamentals and applications Surjya Kumar Maiti[M].Boca Raton:CRC Press,1991.
[25]ATKINSON B K.Fracture mechanics of rock[M].Lausanne:Epfl,2005.
[26]WONG R H C,CHAU K T,TANG C A,et al.Analysis of crack coalescence in rock-like materials containing three flaws-Part I:Experimental approach[J].International Journal of Rock Mechanics and Mining Sciences,2001,38(7):909-924.
[27]Itasca Consulting Group Inc.FLAC2D(Fast Lagrangian Analysis of continum in 2 Dimensions),Version 5.0[R].Minneapolis:Itasca Consulting Group Inc.,2005.
[28]杨卫.宏微观断裂力学[M].北京:国防工业出版社,1995.
[29]黄作宾.断裂力学基础[M].武汉:中国地质大学出版社,1991.
[30]李江腾,曹平,袁海平.岩石亚临界裂纹扩展试验及门槛值研究[J].岩土工程学报,2006,28(3):415-418.LI Jiangteng,CAO Ping,YUAN Haiping.Study on subcritical crack growth and thresholds of rocks[J].Chinese Journal of Geotechnical Engineering,2006,28(3):415-418.
[31]CHARLES R J.Static Fatigue of Glass.II[J].Journal of Applied Physics,1958,29(11):1549-1553.
[32]BAUD P,REUSCHL T,CHARLEZ P.An improved wing crack model for the deformation and failure of rock in compression[J].International Journal of Rock Mechanics and Mining Science and Geomechanics Abstracts,1996,33(5):539-542.
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