基于D-P准则巷道围岩应变软化与破裂膨胀弹塑性分析
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摘要
为了得到考虑围岩应变软化、破裂膨胀和中间主应力情况下的巷道围岩弹塑性解,基于非关联流动法则和DruckerPrager准则,引入中间主应力系数,建立软化和膨胀模型,得到了巷道变形、破裂区和塑性区半径的解析式,并进行了应用分析。研究结果表明:随中间主应力增大,巷道变形、破裂区和塑性区半径先减后增;围岩软化越严重,对巷道变形、破裂区和塑性区半径影响越显著;软化阶段的膨胀行为对塑性区半径不产生影响,但影响巷道破裂区半径和变形;残余阶段的膨胀行为对破裂区和塑性区半径不产生影响,但影响巷道的变形;巷道变形、破裂区和塑性区半径随支护阻力增大而减小,且原岩应力越大,支护对变形影响越显著。
To obtain the elastoplastic solution of roadway surrounding rock considering the strain softening,fracture expansion and intermediate principal stress of surrounding rock,the softening and expansion model was established by introducing into the intermediate principal stress coefficient based on the non-associated flow rule and Drucker-Prager( D-P) criterion. The analytical expressions of roadway deformation,radius of fracture zone and radius of plastic zone were derived,and the calculation case and application analysis were carried out. The results showed that the roadway deformation,radius of fracture zone and radius of plastic zone decreased first and then increased with the increase of intermediate principal stress. The higher the softening degree of surrounding rock,the more significant the influence on the roadway deformation,radius of fracture zone and radius of plastic zone. The expansion behavior in the softening stage would not affect the radius of plastic zone,but affect the roadway deformation and the radius of fracture zone. The expansion behavior in the residual stage would not affect the radius of fracture zone and radius of plastic zone,but affect the roadway deformation. The roadway deformation,radius of fracture zone and radius of plastic zone decreased with the increase of support resistance,and the greater the in situ rock stress,the more significant the influence of support on the deformation.
To obtain the elastoplastic solution of roadway surrounding rock considering the strain softening,fracture expansion and intermediate principal stress of surrounding rock,the softening and expansion model was established by introducing into the intermediate principal stress coefficient based on the non-associated flow rule and Drucker-Prager( D-P) criterion. The analytical expressions of roadway deformation,radius of fracture zone and radius of plastic zone were derived,and the calculation case and application analysis were carried out. The results showed that the roadway deformation,radius of fracture zone and radius of plastic zone decreased first and then increased with the increase of intermediate principal stress. The higher the softening degree of surrounding rock,the more significant the influence on the roadway deformation,radius of fracture zone and radius of plastic zone. The expansion behavior in the softening stage would not affect the radius of plastic zone,but affect the roadway deformation and the radius of fracture zone. The expansion behavior in the residual stage would not affect the radius of fracture zone and radius of plastic zone,but affect the roadway deformation. The roadway deformation,radius of fracture zone and radius of plastic zone decreased with the increase of support resistance,and the greater the in situ rock stress,the more significant the influence of support on the deformation.
引文
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[10]刘万荣,马海峰.考虑中间主应力的地下硐室围岩稳定性分析[J].中国安全科学学报,2014,24(9):116-121.LIU Wanrong,MA Haifeng. Stability analysis of surrounding rock of underground tunnel considering intermediate principal stress[J].China Safety Science Journal,2014,24(9):116-121.
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[12]李文婷,李树忱,冯现大,等.基于莫尔-库仑准则的岩石峰后应变软化力学行为研究[J].岩石力学与工程学报,2011,30(7):1460-1466.LI Wenting,LI Shuchen,FENG Xianda,et al. Study of post-peak strain softening mechanical properties of rock based on Mohr-Coulomb criterion[J]. Chinese Journal of Rock Mechanics and Engineering,2011,30(7):1460-1466.
[13]付国彬.巷道围岩破裂范围与位移的新研究[J].煤炭学报,1995,20(3):304-310.FU Guobin. Recent investigation of extent of fractured zone and displacement of rocks around the roadways[J]. Journal of China Coal Society,1995,20(3):304-310.
[14]苏海健,靖洪文,张春宇,等.软化与膨胀作用下深部巷道围岩黏弹塑性分析[J].采矿与安全工程学报,2012,29(2):185-190.SU Haijian,JING Hongwen,ZHANG Chunyu,et al. Visco-elastoplastic analysis on the deep underground roadway surrounding rocks considering softening and swelling[J]. Journal of Mining&Safety Engineering,2012,29(2):185-190.
[15]罗勇,陶文斌,陶杰.深井高应力软岩巷道锚注机理与应用[J].煤矿安全,2015,46(5):160-163.LUO Yong,TAO Wenbin,TAO Jie. Bolt-grouting mechanism and application of deep mine high stress soft rock roadway[J]. Safety in Coal Mines,2015,46(5):160-163.
[2]蔡美峰.岩石力学与工程[M].北京:科学出版社,2013.
[3]蒋斌松,张强,贺永年,等.深部圆形巷道破裂围岩的弹塑性分析[J].岩石力学与工程学报,2007,26(5):982-986.JIANG Binsong,ZHANG Qiang,HE Yongnian,et al. Elastoplastic analysis of cracked surrounding rocks in deep circular openings[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(5):982-986.
[4]孟龙,高召宁,孟祥瑞.考虑损伤的圆形巷道围岩弹塑性分析[J].中国安全生产科学技术,2013,9(11):11-16.MENG Long,GAO Zhaoning,MENG Xiangrui. Elasto-plastic analysis of circular roadway surrounding rocks under consideration of rock damage[J]. Journal of Safety Science and Technology,2013,9(11):11-16.
[5]彭瑞,孟祥瑞,赵光明.考虑中间主应力对圆形巷道Hoek-Brown准则解的影响[J].中国安全生产科学技术,2014,10(1):11-17.PENG Ru,MENG Xiangrui,ZHAO Guangming. Hoek-Brown criterion solution of circular roadway with considering intermediate principal stress[J]. Journal of Safety Science and Technology,2014,10(1):11-17.
[6]陈立伟,彭建兵,范文,等.基于统一强度理论的非均匀应力场圆形巷道围岩塑性区分析[J].煤炭学报,2007,32(1):20-23.CHEN Liwei,PENG Jianbing,FAN Wen,et al. Analysis of surrounding rock mass plastic zone of round tunnel under non-uniform stress field based on the unified strength theory[J]. Journal of China Coal Society,2007,32(1):20-23.
[7]侯公羽,牛晓松.基于Levy-Mises本构关系及D-P屈服准则的轴对称圆巷理想弹塑性解[J].岩土力学,2009,30(6):1555-1562.HOU Gongyu,NIU Xiaosong. Perfect elastoplastic solution of axisymmetric circular openings in rock mass based on Levy-Mises constitutive relation and D-P yield criterion[J]. Rock and Soil Mechanics,2009,30(6):1555-1562.
[8]胡小荣,俞茂宏.统一强度理论及其在巷道围岩弹塑性分析中的应用[J].中国有色金属学报,2002,12(5):1021-1026.HU Xiaorong,YU Maohong. Unified strength theory and its application in elasto-plastic analysis to tunnel[J]. The Chinese Journal of Nonferrous Metals,2002,12(5):1021-1026.
[9]曾开华,鞠海燕,张常光.深埋圆形隧道弹塑性位移统一解及其比较分析[J].岩土力学,2011,32(5):1315-1319.ZENG Kaihua,JU Haiyan,ZHANG Changguang. Elastoplastic unified solution for displacements around a deep circular tunnel and its comparative analysis[J]. Rock and Soil Mechanics,2011,32(5):1315-1319.
[10]刘万荣,马海峰.考虑中间主应力的地下硐室围岩稳定性分析[J].中国安全科学学报,2014,24(9):116-121.LIU Wanrong,MA Haifeng. Stability analysis of surrounding rock of underground tunnel considering intermediate principal stress[J].China Safety Science Journal,2014,24(9):116-121.
[11]刘志钦,余东明.考虑中间主应力和剪胀特性的深埋圆巷弹塑性应力位移解[J].工程力学,2012,29(8):289-296.LIU Zhiqin,YU Dongming. Elastoplastic stress and displacement analytical solutions to deep-buried circular tunnels considering intermediate principal stress and dilatancy[J]. Engineering Mechanics,2012,29(8):289-296.
[12]李文婷,李树忱,冯现大,等.基于莫尔-库仑准则的岩石峰后应变软化力学行为研究[J].岩石力学与工程学报,2011,30(7):1460-1466.LI Wenting,LI Shuchen,FENG Xianda,et al. Study of post-peak strain softening mechanical properties of rock based on Mohr-Coulomb criterion[J]. Chinese Journal of Rock Mechanics and Engineering,2011,30(7):1460-1466.
[13]付国彬.巷道围岩破裂范围与位移的新研究[J].煤炭学报,1995,20(3):304-310.FU Guobin. Recent investigation of extent of fractured zone and displacement of rocks around the roadways[J]. Journal of China Coal Society,1995,20(3):304-310.
[14]苏海健,靖洪文,张春宇,等.软化与膨胀作用下深部巷道围岩黏弹塑性分析[J].采矿与安全工程学报,2012,29(2):185-190.SU Haijian,JING Hongwen,ZHANG Chunyu,et al. Visco-elastoplastic analysis on the deep underground roadway surrounding rocks considering softening and swelling[J]. Journal of Mining&Safety Engineering,2012,29(2):185-190.
[15]罗勇,陶文斌,陶杰.深井高应力软岩巷道锚注机理与应用[J].煤矿安全,2015,46(5):160-163.LUO Yong,TAO Wenbin,TAO Jie. Bolt-grouting mechanism and application of deep mine high stress soft rock roadway[J]. Safety in Coal Mines,2015,46(5):160-163.