基于D-P准则有压圆形衬砌隧洞弹塑性解
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摘要
随着大型水利工程的建设,出现了大量的深埋水工压力隧洞。由于深埋有压隧洞在施工和运营不同工况条件下,隧道衬砌和围岩主应力会发生变化。文章基于D-P屈服准则,在平面应变条件下推导了深埋有压衬砌圆形隧洞第一主应力分别为径向应力和切向应力时隧洞的弹塑性解。研究结果表明:该理论模型计算值与M-C准则计算值基本吻合,验证了该模型的正确性,且较M-C准则计算结果偏于安全;在不同地应力水平与内水压力工况下,衬砌与围岩的塑性区半径发生变化;随着内水压力的增大,塑性区分布可分为5个阶段,且在高水压阶段水压力增大对衬砌屈服半径的发展较为迅速。
With the construction of large-scale water conservancy projects in China, many deep-buried hydraulic pressure tunnels have been built. The principal stress of tunnel lining and surrounding rock will be changed under different conditions of construction and operation for the deep buried pressure tunnel. Based on D-P yield criterion,the elastoplastic solution of the deep-buried circular pressure tunnel was derived when the first principal stress is the radial stress or tangential stress under the condition of plane strain. The research shows that the calculated values by this model were consistent with the calculated values by M-C criterion, which verifies the correctness of this model and it is more conservative compared with the calculated results by M-C criterion; radiuses of plastic zones of lining and surrounding rock will change in different stresses levels and internal water pressures; plastic zone distribution can be divided into five stages and the yield radius of lining develops faster with an increase of internal water pressure during high water pressure stage.
With the construction of large-scale water conservancy projects in China, many deep-buried hydraulic pressure tunnels have been built. The principal stress of tunnel lining and surrounding rock will be changed under different conditions of construction and operation for the deep buried pressure tunnel. Based on D-P yield criterion,the elastoplastic solution of the deep-buried circular pressure tunnel was derived when the first principal stress is the radial stress or tangential stress under the condition of plane strain. The research shows that the calculated values by this model were consistent with the calculated values by M-C criterion, which verifies the correctness of this model and it is more conservative compared with the calculated results by M-C criterion; radiuses of plastic zones of lining and surrounding rock will change in different stresses levels and internal water pressures; plastic zone distribution can be divided into five stages and the yield radius of lining develops faster with an increase of internal water pressure during high water pressure stage.
引文
[1]张永兴,贺永年.岩石力学[M].北京:中国建筑工业出版社,2004.ZHANG Yongxing,HE Yongnian.Rock Mechanics[M].Beijing:China Architecture&Building Press,2004.
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[10]李政林,吴瑞祥,李龙剑,王晓艳.基于损伤理论的隧道围岩松动圈确定方法[J].地下空间与工程学报,2011(6):1060-1064.LI Zhenglin,WU Ruixiang,LI Longjian,WANG Xiaoyan.Method for Defining the Loose Zone of Tunnel Surrounding Rock Based on Damage Theory[J].Chinese Journal of Underground Space and Engineering,2011(6):1060-1064.
[11]王明斌,李术才.含衬砌圆形压力隧洞弹塑性新解[J].岩石力学与工程学报,2007,26(增2):3770-3775.WANG Mingbin,LI Shucai.New Elastoplastic Solutions to Circular Pressured Tunnel with Lining[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(S2):3770-3775.
[12]王睢,钟祖良,刘新荣.基于D-P屈服准则考虑渗流影响的深埋有压圆形隧洞弹塑性解[J].现代隧道技术,2019,56(1):39-46.WANG Sui,ZHONG Zuliang,LIU Xinrong.D-P Yield Criterion Based Elastoplastic Solution for a Deep-buried and Pressured Circular Tunnel Considering Seepage Effect[J].Modern Tunnelling Technology,2019,56(1):39-46.
[13]张学言.岩土塑性力学[M].北京:人民交通出版社,1993.ZHANG Xueyan.Plastic Mechanics of Rock and Soil[M].Beijing:China Communications Press,1993.
[14]杨桂通.弹塑性力学引论[M].北京:清华大学出版社,2011.YANG Guitong.Introduction to Elastoplastic Mechanics[M].Beijing:Tsinghua University Press,2011.
[15]徐芝纶.弹性力学[M].北京:高等教育出版社,1998.XU Zhilun.Elasticity[M].Beijing:Higher Education Press,1998.
[2]H KASTNER.Statik des tunel und Stollenbauess[M].Berlin:Springer-Verlag,1962.
[3]任青文,张宏朝.关于芬纳公式的修正[J].河海大学学报,2001,29(6):109-111.REN Qingwen,ZHANG Hongchao.A Modification of Fanner Formula[J].Journal of Hohai University(Natural Sciences),2001,29(6):109-111.
[4]任青文,邱颖.具有衬砌圆形隧洞的弹塑性解[J].工程力学,2005,22(2):212-217.REN Qingwen,QIU Ying.Elastic-plastic Solution of Circular Tunnel with Liner[J].Engineering Mechanics,2005,22(2):212-217.
[5]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.
[6]侯公羽,牛晓松.基于Levy-Mises本构关系及Hoek-Brown屈服准则的轴对称圆巷理想弹塑性解[J].岩石力学与工程学报,2010,29(4):765-777.HOU Gongyu,NIU Xiaosong.Perfect Elastoplastic Solution of Axisymmetric Cylindrical Cavity Based on Levy-Mises Constitutive Relation and Hoek-Brown Failure Criterion[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(4):765-777.
[7]侯公羽,李晶晶,杨悦,等.基于幂强化本构模型的轴对称圆巷弹塑性解[J].岩土力学,2014,35(1):134-142.HOU Gongyu,LI Jingjing,YANG Yue,et al.Elastoplastic Solution of Axisymmetric Circular Tunnel Based on Power-hardening Model[J].Rock and Soil Mechanics,2014,35(1):134-142.
[8]徐栓强,俞茂宏,胡小荣.基于双剪统一强度理论的地下圆形洞室稳定性的研究[J].煤炭学报,2003,28(5):522-526.XU Shuanqiang,YU Maohong,HU Xiaorong.The Stability Analysis of Circular Tunnel Based the Twin Shear Unified Strength Theory[J].Journal of China Coal Society,2003,28(5):522-526.
[9]宋俐,张永强,俞茂宏.压力隧洞弹塑性分析的统一解[J].工程力学,1998,15(4):57-61.SONG Li,ZHANG Yongqiang,YU Maohong.Unified Solution of Elastoplastic Analysis of Pressure Tunnel[J].Engineering Mechanics,1998,15(4):57-61.
[10]李政林,吴瑞祥,李龙剑,王晓艳.基于损伤理论的隧道围岩松动圈确定方法[J].地下空间与工程学报,2011(6):1060-1064.LI Zhenglin,WU Ruixiang,LI Longjian,WANG Xiaoyan.Method for Defining the Loose Zone of Tunnel Surrounding Rock Based on Damage Theory[J].Chinese Journal of Underground Space and Engineering,2011(6):1060-1064.
[11]王明斌,李术才.含衬砌圆形压力隧洞弹塑性新解[J].岩石力学与工程学报,2007,26(增2):3770-3775.WANG Mingbin,LI Shucai.New Elastoplastic Solutions to Circular Pressured Tunnel with Lining[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(S2):3770-3775.
[12]王睢,钟祖良,刘新荣.基于D-P屈服准则考虑渗流影响的深埋有压圆形隧洞弹塑性解[J].现代隧道技术,2019,56(1):39-46.WANG Sui,ZHONG Zuliang,LIU Xinrong.D-P Yield Criterion Based Elastoplastic Solution for a Deep-buried and Pressured Circular Tunnel Considering Seepage Effect[J].Modern Tunnelling Technology,2019,56(1):39-46.
[13]张学言.岩土塑性力学[M].北京:人民交通出版社,1993.ZHANG Xueyan.Plastic Mechanics of Rock and Soil[M].Beijing:China Communications Press,1993.
[14]杨桂通.弹塑性力学引论[M].北京:清华大学出版社,2011.YANG Guitong.Introduction to Elastoplastic Mechanics[M].Beijing:Tsinghua University Press,2011.
[15]徐芝纶.弹性力学[M].北京:高等教育出版社,1998.XU Zhilun.Elasticity[M].Beijing:Higher Education Press,1998.