非达西渗流效应对深埋圆形隧洞弹塑性解的影响
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摘要
基于Izbash非Darcy渗流模型,求解深埋圆形隧洞围岩的非线性渗流场解析解;将渗透水压力视为体积力作用于应力场,推导隧洞围岩弹性解析解和基于Mohr-Coulomb屈服准则的塑性解析解。结合算例,对Izbash非线性渗流模型与Darcy模型中隧洞围岩水力坡度与应力分布曲线、隧洞内外水压差与塑性区半径的关系曲线、围岩特征曲线进行对比与验证。研究表明:隧洞内外水头高差相同条件下,与Darcy渗流模型相比,Izbash非线性渗流模型中水力坡度曲线较平缓,但两模型水力梯度曲线会相交;隧洞围岩径向和切向压力均偏大,围岩塑性区半径偏小;位于高水压地区的深埋隧洞,应考虑非线性渗流对隧洞弹塑性解的影响。
Based on Izbash's non-Darcy seepage model,the analytical solution for nonlinear seepage field of deep-buried circular openings was derived.Taking into account of seepage force,which was regarded as the volume force acting on the stress field,the elastic solution of circular openings was derived.Furthermore,the plastic solution of circular openings was concluded by using Mohr-Coulomb failure criterion.Numerical examples were used to compare and verify the distribution curve of hydraulic gradient and stress of the tunnel surrounding rock,the relation curve between hydraulic head pressure and radius of plastic zone inside and outside the tunnel,and the characteristic curve of the surrounding rock under Izbash's seepage model and Darcy's seepage model.The results show that under the same hydraulic head pressure difference and compared with Darcy's seepage model,the curve of hydraulic gradient under Izbash's seepage model is flat,but the two curves of the two models will intersect each other.Both the axial and radial stress of the surrounding rock is larger and the radius of plastic zone is smaller.The influence of non-Darcy seepage effect on elastoplastic solutions of a deep-buried circular opening located in high hydraulic pressure area should be considered.
Based on Izbash's non-Darcy seepage model,the analytical solution for nonlinear seepage field of deep-buried circular openings was derived.Taking into account of seepage force,which was regarded as the volume force acting on the stress field,the elastic solution of circular openings was derived.Furthermore,the plastic solution of circular openings was concluded by using Mohr-Coulomb failure criterion.Numerical examples were used to compare and verify the distribution curve of hydraulic gradient and stress of the tunnel surrounding rock,the relation curve between hydraulic head pressure and radius of plastic zone inside and outside the tunnel,and the characteristic curve of the surrounding rock under Izbash's seepage model and Darcy's seepage model.The results show that under the same hydraulic head pressure difference and compared with Darcy's seepage model,the curve of hydraulic gradient under Izbash's seepage model is flat,but the two curves of the two models will intersect each other.Both the axial and radial stress of the surrounding rock is larger and the radius of plastic zone is smaller.The influence of non-Darcy seepage effect on elastoplastic solutions of a deep-buried circular opening located in high hydraulic pressure area should be considered.
引文
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[14]PRADA A,CIVAN F.Modification of Darcy’s Law for the Threshold Pressure Gradient[J].Journal of Petroleum Science and Engineering,1999,22(4):237-240.
[15]HANSBO S.Aspects of Vertical Drain Design:Darcian or Non-Darcian Flow[J].Geotechnique,1997,47(5):983-992.
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[18]李菲菲,谢康和,邓岳保.考虑指数流的真空预压竖井地基固结解析解[J].中南大学学报(自然科学版),2015,46(3):1075-1081.LI Feifei,XIE Kanghe,DENG Yuebao,Analytical Solution for Consolidation by Vertical Drains with Exponential Flow under Vacuum Preloading[J].Journal of Central South University(Science and Technology),2015,46(3):1075-1081.
[19]赵阳升.矿山岩石流体力学[M].北京:煤炭工业出版社,1994.
[20]李健.多孔介质中非达西流动的实验研究[D].北京:中国农业大学,2007.
[21]翟云芳.渗流力学[M].2版.北京:石油工业出版社,2003.
[22]陈明祥.弹塑性力学[M].2版.北京:科学出版社,2007.
[2]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 Flow Field[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(8):1291-1295.
[3]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.Elastic-plastic Analytical Solution of Deep Buried Circle Tunnel Considering Stress Redistribution[J].Engineering Mechanics,2009,26(2):16-20.
[4]LEE S W,JUNG J W,NAM S W,et al.The Influence of Seepage Forces on Ground Reaction Curve of Circular Opening[J].Tunneling and Underground Space Technology,2006,22(1):28-38.
[5]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 Soil Mechanics,2010,31(5):1627-1632.
[6]黄阜,杨小礼.渗流效应对基于广义非线性屈服准则洞室弹塑性解的影响[J].中南大学学报(自然科学版),2009,40(6):1737-1743.HUANG Fu,YANG Xiaoli.Influence of Seepage Effect on Solutions for Elastic and Plastic around an Opening Based on Generalized Nonlinear Yield Criterion[J].Journal of Central South University(Science and Technology),2009,40(6):1737-1743.
[7]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 of Rock Mechanics and Engineering,2004,23(5):741-744.
[8]张常光,张庆贺,赵均海.考虑应变软化、剪胀和渗流的水工隧洞解析解[J].岩土工程学报,2009,31(12):1941-1946.ZHANG Changguang,ZHANG Qinghe,ZHAO Junhai.Analytical Solutions of Hydraulic Tunnels Considering Strain Softening,Shear Dilation and Seepage[J].Chinese Journal of Geotechnical Engineering,2009,31(12):1941-1946.
[9]卞康,肖明,刘会波.考虑脆性损伤和渗流的圆形水工隧洞解析解[J].岩土力学,2012,33(1):209-215.BIAN Kang,XIAO Ming,LIU Huibo.Analytical Solutions of Circular Hydraulic Tunnel Considering Brittle Damage and Seepage[J].Rock and Soil Mechanics,2012,33(1):209-215.
[10]邹金锋,李帅帅,张勇,等.考虑轴向力和渗透力时软化围岩隧洞解析[J].力学学报,2014,46(5):747-755.ZOU Jinfeng,LI Shuaishuai,ZHANG Yong,et al.Solution and Analysis of Circular Tunnel for the Strain-softening Rock Masses Considering the Axial In situ Stress and Seepage Force[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(5):747-755.
[11]许渊,李亮,邹金锋,等.考虑轴向力和渗透力时圆形隧洞广义Hoek-Brown解[J].岩土力学,2015,36(10):2837-2847.XU Yuan,LI Liang,ZOU Jinfeng,et al.Generalized Hoek-Brown Solution of Circular Tunnel Considering Effects of Axial Stress and Seepage Force[J].Rock and Soil Mechanics,2015,36(10):2837-2847.
[12]吕晓聪,许金余.海底圆形隧洞在渗流场影响下的弹塑性解[J].工程力学,2009,26(2):216-221.LUXiaocong,XU Jinyu.Elastic-plastic Solution for Subsea Circular Tunnel under the Influence of Seepage Field[J].Engineering Mechanics,2009,26(2):216-221.
[13]刘建军,刘先贵,胡雅衽.低渗透岩石非线性渗流规律研究[J].岩石力学与工程学报,2003,22(4):556-561.LIU Jianjun,LIU Xiangui,HU Yaren.Study on Nonlinear Seepage of Rock of Low Permeability[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(4):556-561.
[14]PRADA A,CIVAN F.Modification of Darcy’s Law for the Threshold Pressure Gradient[J].Journal of Petroleum Science and Engineering,1999,22(4):237-240.
[15]HANSBO S.Aspects of Vertical Drain Design:Darcian or Non-Darcian Flow[J].Geotechnique,1997,47(5):983-992.
[16]LI T,MEI T T,SUN X H,et al,A Study on a Water-inrush Incident at Laohutai Coalmine[J].International Journal of Rock Mechanics and Mining Sciences,2013,59(4):151-159.
[17]HANSBO S.Deviation for Darcy’s Law Observed in Onedimensional Consolidation[J].Geotechnique,2003,53(6):601-605.
[18]李菲菲,谢康和,邓岳保.考虑指数流的真空预压竖井地基固结解析解[J].中南大学学报(自然科学版),2015,46(3):1075-1081.LI Feifei,XIE Kanghe,DENG Yuebao,Analytical Solution for Consolidation by Vertical Drains with Exponential Flow under Vacuum Preloading[J].Journal of Central South University(Science and Technology),2015,46(3):1075-1081.
[19]赵阳升.矿山岩石流体力学[M].北京:煤炭工业出版社,1994.
[20]李健.多孔介质中非达西流动的实验研究[D].北京:中国农业大学,2007.
[21]翟云芳.渗流力学[M].2版.北京:石油工业出版社,2003.
[22]陈明祥.弹塑性力学[M].2版.北京:科学出版社,2007.