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
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摘要
山岭深埋隧洞具有丰富的地下水,有压隧洞在施工和运营的不同工况条件下,隧洞围岩第一主应力会发生变化。为了研究有压隧洞施工和运营阶段的地下水的渗流影响,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圆形隧洞第一主应力分别为径向应力和切向应力时考虑渗流影响的弹塑性解。结果表明:D-P准则模型计算结果与M-C准则计算结果基本吻合,且计算结果较M-C准则偏于安全,验证了该模型的正确性;考虑渗流作用时弹性区径向应力和切向应力随着径向距离的增加不再关于地应力对称,且随着渗透压力的增大,其偏离地应力程度越大;同种条件下,低内水压阶段随着渗透压力的增大塑性区半径增大,高内水压阶段随着渗透压力的增大塑性区半径减小。
Groundwater is normally rich in the deep-buried mountain tunnels,and the major principal stress of surrounding rocks will change under the different conditions of construction and operation stages of the tunnels.In order to study the effect of groundwater seepage,based on D-P yield criterion and considering seepage effect,the elastoplastic solution for the deep-buried and pressured circular tunnel was derived under the condition of plane strain for cases of the major principal stress to be the radial stress and tangential stress.The study shows that the results of D-P criterion model are mainly consistent with those of M-C criterion and more conservative;the radial stress and tangential stress are no longer symmetrical with ground stress with an increase of radial distance in the elastic zone considering the effect of seepage,moreover the larger of the seepage pressure the greater of the deviations;under the same condition,the radius of plastic zone increases with an increase of seepage pressure in the stage of low internal water pressure while the radius of plastic zone decreases with an increase of seepage pressure in the stage of high internal water pressure.
Groundwater is normally rich in the deep-buried mountain tunnels,and the major principal stress of surrounding rocks will change under the different conditions of construction and operation stages of the tunnels.In order to study the effect of groundwater seepage,based on D-P yield criterion and considering seepage effect,the elastoplastic solution for the deep-buried and pressured circular tunnel was derived under the condition of plane strain for cases of the major principal stress to be the radial stress and tangential stress.The study shows that the results of D-P criterion model are mainly consistent with those of M-C criterion and more conservative;the radial stress and tangential stress are no longer symmetrical with ground stress with an increase of radial distance in the elastic zone considering the effect of seepage,moreover the larger of the seepage pressure the greater of the deviations;under the same condition,the radius of plastic zone increases with an increase of seepage pressure in the stage of low internal water pressure while the radius of plastic zone decreases with an increase of seepage pressure in the stage of high internal water pressure.
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 Aevhitecture&Building Press, 2004.
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[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. Elasto-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-MisesConstitutive Relation and D-P Yield Criterion[J]. Rock and Soil Mechanics, 2009, 30(6):1555-1562.
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[8]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. Elastoplastic Unified Analysis of Pressure Tunnel[J]. Engineering Mechanics, 1998,15(4):57-61.
[9]李宗利,任青文,王亚红.考虑渗流场影响深埋圆形隧洞的弹塑性解[J].岩石力学与工程学报, 2004, 23(8):1291-1295.LI Zongli, REN Qingwen, WANG Yahong. Elasto-plastic Analytical Solution of Deep-buried Circle Tunnel Considering Fluid FlowField[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(8):1291-1295.
[10]刘成学,杨林德,李鹏.考虑应力重分布的深埋圆形透水隧洞弹塑性解[J].工程力学, 2009, 26(2):16-20.LIU Chengxue, YANG Linde, LI Peng. Elasto-plastic Analytical Solution of Deep-buried Circle Tunnel Cconsidering Stress Redis?tribution[J]. Engineering Mechanics, 2009, 26(2):16-20.
[11] LEE S W, JUNG J W, NAM S W, et al. The Influence of Seepage Forces on Ground Reaction Curve of Circular Opening[J]. Tunnel?ling and Underground Space Technology, 2007, 22(1):28-38.
[12]荣传新,程桦.地下水渗流对巷道围岩稳定性影响的理论解[J].岩石力学与工程学报, 2004, 23(5):741-744.RONG Chuanxin, CHENG Hua. Stability Analysis of Rocks around Tunnel with Ground Water Permeation[J]. Chinese Journal ofRock Mechanics and Engineering, 2004, 23(5):741-744.
[13]黄阜,杨小礼.考虑渗透力和原始Hoek-Brown屈服准则时圆形洞室解析解[J].岩土力学, 2010, 31(5):1627-1632.HUANG Fu, YANG Xiaoli. Analytical Solution of Circular Openings Subjected to Seepage in Hoek-Brown Media[J]. Rock and SoilMechanics, 2010, 31(5):1627-1632.
[14]黄阜,杨小礼,黄戡,等.考虑孔隙水压力效应和非线性破坏准则的浅埋地下洞室支护力上限分析[J].岩土工程学报,2011, 33(12):1903-1909.HUANG Fu, YANG Xiaoli, HUANG Kan, et al. Upper Bound Solutions of Supporting Pressure of Shallow Cavities Subjected toPore Water Pressure Based on Nonlinear Failure Criterion[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(12):1903-1909.
[15]张学言.岩土塑性力学[M].北京:人民交通出版社, 1993.ZHANG Xueyan. Geotechnical Plastic Mechanics[M]. Beijing:China Communications Press, 1993.
[16]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 Elasticity and Plasticity[M]. Beijing:Tsinghua University Press, 2011.
[17]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, 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. Elasto-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-MisesConstitutive 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 ConstitutiveRelation and Hoek-Brown Failure Criterion[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(4):765-777.
[7]张常光,张庆贺,赵均海.考虑应变软化及剪胀的井壁稳定统一解[J].煤炭学报, 2009,(5):634-639.ZHANG Changguang, ZHANG Qinghe, ZHAO Junhai. Unified Solutions of Well-bore Stability Considering Strain Softening andShear Dilation[J]. Journal of China Coal Society, 2009,(5):634-639.
[8]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. Elastoplastic Unified Analysis of Pressure Tunnel[J]. Engineering Mechanics, 1998,15(4):57-61.
[9]李宗利,任青文,王亚红.考虑渗流场影响深埋圆形隧洞的弹塑性解[J].岩石力学与工程学报, 2004, 23(8):1291-1295.LI Zongli, REN Qingwen, WANG Yahong. Elasto-plastic Analytical Solution of Deep-buried Circle Tunnel Considering Fluid FlowField[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(8):1291-1295.
[10]刘成学,杨林德,李鹏.考虑应力重分布的深埋圆形透水隧洞弹塑性解[J].工程力学, 2009, 26(2):16-20.LIU Chengxue, YANG Linde, LI Peng. Elasto-plastic Analytical Solution of Deep-buried Circle Tunnel Cconsidering Stress Redis?tribution[J]. Engineering Mechanics, 2009, 26(2):16-20.
[11] LEE S W, JUNG J W, NAM S W, et al. The Influence of Seepage Forces on Ground Reaction Curve of Circular Opening[J]. Tunnel?ling and Underground Space Technology, 2007, 22(1):28-38.
[12]荣传新,程桦.地下水渗流对巷道围岩稳定性影响的理论解[J].岩石力学与工程学报, 2004, 23(5):741-744.RONG Chuanxin, CHENG Hua. Stability Analysis of Rocks around Tunnel with Ground Water Permeation[J]. Chinese Journal ofRock Mechanics and Engineering, 2004, 23(5):741-744.
[13]黄阜,杨小礼.考虑渗透力和原始Hoek-Brown屈服准则时圆形洞室解析解[J].岩土力学, 2010, 31(5):1627-1632.HUANG Fu, YANG Xiaoli. Analytical Solution of Circular Openings Subjected to Seepage in Hoek-Brown Media[J]. Rock and SoilMechanics, 2010, 31(5):1627-1632.
[14]黄阜,杨小礼,黄戡,等.考虑孔隙水压力效应和非线性破坏准则的浅埋地下洞室支护力上限分析[J].岩土工程学报,2011, 33(12):1903-1909.HUANG Fu, YANG Xiaoli, HUANG Kan, et al. Upper Bound Solutions of Supporting Pressure of Shallow Cavities Subjected toPore Water Pressure Based on Nonlinear Failure Criterion[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(12):1903-1909.
[15]张学言.岩土塑性力学[M].北京:人民交通出版社, 1993.ZHANG Xueyan. Geotechnical Plastic Mechanics[M]. Beijing:China Communications Press, 1993.
[16]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 Elasticity and Plasticity[M]. Beijing:Tsinghua University Press, 2011.
[17]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.
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