双向八车道小净距公路隧道支护反力上限分析与支护参数优化研究
|
摘要
为适应不断增大的交通量,双向八车道小净距隧道己越来越多的出现在人们眼中。八车道的大断面小净距隧道具有大断面和小净距隧道各自的施工、设计难点。断面过大,受净空的要求,势必会造成隧道的扁平率过大,对支护的要求就强于一般隧道；过小的净距会使后行洞开挖对先行洞的稳定性造成较大的影响,同时,中间岩柱成为另一个施工设计中需重点加固的位置。由于对这种形式的隧道研究仍处在起步阶段,目前还没有完善的规范能对此种类型的隧道设计进行指导。
本文根据极限分析上限定理,结合牛头山小净距大断面高速公路隧道实际施工设计情况,采用大型有限差分软件,通过理论和数值计算的手段对大断面的小净距隧道施工力学和支护参数进行了研究。主要内容包括：
1.利用极限分析上限法则,讨论了由库伦材料组成的双平行圆形隧道支护反力最小上限解,并采用数值分析软件Matlab对最小上限解的一些影响参数进行了分析研究。
2.采用有限差分软件对牛头山隧道锚杆支护进行优化研究。主要研究其锚杆的布置形式,在不同围岩等级下,根据规范中对三车道锚杆间距的建议,推广到四车道大断面隧道的锚杆间距取值范围,分别对矩形布置或是梅花形式布置进行计算比较,改变不同的横向与纵向锚杆间距,最后得出较为合理的布置形式和横、纵向间距,为施工和设计提供参考。
3.分析主要的几种支护组合对围岩稳定性的影响,包括开挖、锚杆、喷混和二衬。在不同的支护组合下,得出各种支护对围岩稳定性的影响。对小净距隧道中间岩柱加固的方式进行了研究探讨,采取不同的加固方式进行计算,最后得出适合不同条件的加固方式。
4.对牛头山隧道现场监测数据进行简单的分析,并与计算结果进行比较,为计算结果提供一定的可靠性证明。
The eight lanes bidirectional tunnel has been normally built, so as to accommodate the increase busy traffic nowadays. Thereby brought many difficulties for the construction and design which assembles the one of large-span tunnel and the close-distance tunnel. Firstly, the large-span tunnel has a higher demand for support than the traditional tunnel due to the span-ratio augmented by clearance requirement. Secondly, for small-distance tunnel, the stability of the former tunnel will be significantly impacted by the later excavated tunnel and the shared rock between the neighboring tunnels needs to be particularly consolidated. While the research on this field is still in its infancy, there is no delicate design criterion refer to.
Based on the limit analysis upper bound law and the example of Niutou Mount highway tunnel with large-span and small-distance, the paper will study on the construction mechanics and support parameter of the closely build tunnels with small distance between by the large infinite difference software and theoretical and numerical computation. The study mainly includes:
1. Discuss the minimum upper boundary solution of the support counter-force of the circular bi-tunnel parallel build in linear elastic medium by the limit analysis upper bound law, and study the relevant parameters by Matlab.
2. Research on how to improve the way of distribution of the anchor support. The norm has given guidance on the inter-distance of anchor, under different rock level, in three lanes tunnel. In order to extend the guidance to four lanes tunnel, the paper has done a comparison for the rectangle and quincuncial arrangement of anchors within a set of latitude and longitude distances, then given the optimal result serving as a reference to the practical engineering.
3. Analyze the stability of the surrounding rock by several support style combined by excavation, anchor, shotcrete and lining. Study on different way of consolidating the rock in middle of the closely built tunnels, and find out the best way of consolidation for different conditions.
4. Simply analyze the monitor data obtained from the Niutou Mount tunnel project, and compare it with the computation result, which can used as a verification for the calculation method in the paper.
本文根据极限分析上限定理,结合牛头山小净距大断面高速公路隧道实际施工设计情况,采用大型有限差分软件,通过理论和数值计算的手段对大断面的小净距隧道施工力学和支护参数进行了研究。主要内容包括：
1.利用极限分析上限法则,讨论了由库伦材料组成的双平行圆形隧道支护反力最小上限解,并采用数值分析软件Matlab对最小上限解的一些影响参数进行了分析研究。
2.采用有限差分软件对牛头山隧道锚杆支护进行优化研究。主要研究其锚杆的布置形式,在不同围岩等级下,根据规范中对三车道锚杆间距的建议,推广到四车道大断面隧道的锚杆间距取值范围,分别对矩形布置或是梅花形式布置进行计算比较,改变不同的横向与纵向锚杆间距,最后得出较为合理的布置形式和横、纵向间距,为施工和设计提供参考。
3.分析主要的几种支护组合对围岩稳定性的影响,包括开挖、锚杆、喷混和二衬。在不同的支护组合下,得出各种支护对围岩稳定性的影响。对小净距隧道中间岩柱加固的方式进行了研究探讨,采取不同的加固方式进行计算,最后得出适合不同条件的加固方式。
4.对牛头山隧道现场监测数据进行简单的分析,并与计算结果进行比较,为计算结果提供一定的可靠性证明。
The eight lanes bidirectional tunnel has been normally built, so as to accommodate the increase busy traffic nowadays. Thereby brought many difficulties for the construction and design which assembles the one of large-span tunnel and the close-distance tunnel. Firstly, the large-span tunnel has a higher demand for support than the traditional tunnel due to the span-ratio augmented by clearance requirement. Secondly, for small-distance tunnel, the stability of the former tunnel will be significantly impacted by the later excavated tunnel and the shared rock between the neighboring tunnels needs to be particularly consolidated. While the research on this field is still in its infancy, there is no delicate design criterion refer to.
Based on the limit analysis upper bound law and the example of Niutou Mount highway tunnel with large-span and small-distance, the paper will study on the construction mechanics and support parameter of the closely build tunnels with small distance between by the large infinite difference software and theoretical and numerical computation. The study mainly includes:
1. Discuss the minimum upper boundary solution of the support counter-force of the circular bi-tunnel parallel build in linear elastic medium by the limit analysis upper bound law, and study the relevant parameters by Matlab.
2. Research on how to improve the way of distribution of the anchor support. The norm has given guidance on the inter-distance of anchor, under different rock level, in three lanes tunnel. In order to extend the guidance to four lanes tunnel, the paper has done a comparison for the rectangle and quincuncial arrangement of anchors within a set of latitude and longitude distances, then given the optimal result serving as a reference to the practical engineering.
3. Analyze the stability of the surrounding rock by several support style combined by excavation, anchor, shotcrete and lining. Study on different way of consolidating the rock in middle of the closely built tunnels, and find out the best way of consolidation for different conditions.
4. Simply analyze the monitor data obtained from the Niutou Mount tunnel project, and compare it with the computation result, which can used as a verification for the calculation method in the paper.
引文
[1]曾中林单拱四车道公路隧道断面设计优化与施工力学研究.长沙：中南大学,2006
[2]关宝树,等.隧道工程施工要点集.北京：人民交通出版社,2001
[3]李云鹏,王芝银,韩常领.不同围岩类别小间距隧道施工过程模拟研究.岩土力学,2006,27(1)：11-16.
[4]李云鹏,王芝银,韩常领.考虑地震影响的小间距隧道围岩流变损伤.长安大学学报(自然科学版),2006,26(2)：51-56.
[5]姚勇,晏启祥,周俐俐.小净距隧道在不同开挖方式下的力学效应分析.西南科技大学学报.,2005,20(2)：53-56.
[6]姚勇,何川,晏启祥.董家山隧道小净距段爆破控制的数值模拟.岩土力学,2004,25(S2)：501-506.
[7]晏启祥,何川,姚勇.小净距隧道施工小导管注浆效果的数值模拟分析.岩土力学,2004,25(S2)：239-242.
[8]晏启祥,何川,姚勇.软岩隧道施工特性及其动态力学行为研究.岩石力学与工程学报,2006,25(3)：572-577.
[9]晏启祥,何川,姚勇.软岩小净距隧道施工力学效应研究.地下空间与工程学报,2005,1(5)：693-697.
[10]靳晓光,刘伟,郑学贵.小净距偏压公路隧道开挖顺序优化.公路交通科技,2005,22(8)：61-64.
[11]刘伟,靳晓光,陈少华.高速公路小净距隧道合理净距的探讨.地下空间,2004,24(3)：380-385.
[12]刘艳青,钟世航,卢汝绥.小净距并行隧道力学状态的试验研究.岩石力学与工程学报,2000,19(9)：590-594.
[13]庄宁,廖少明等.大跨度小净距群洞隧道施工方案优化研究.地下空间与工程学报,2007,3(1)：96-100.
[14]孙元国,李文江,朱永全.客运专线小净距隧道施工效应的数值模拟分析.石家庄铁道学院学报(自然科学版),2007,20(3)：6-14.
[15]舒志乐,刘保县,李月.偏压小净距隧道围岩压力分析.地下空间与工程学报,2007,3(3)：430-433.
[16]曹林,胡居义,黎冬林.小净距公路(双洞)隧道围岩破坏模式研究.2007,18(3)：65-69.
[17]张玉军,朱维申,杨家岭.近距离双隧道开挖与支护稳定性的粘弹塑性有限元计算.岩石力学与工程学报,1999,18(S)：855-559.
[18]陈先国,高波.地铁近距离平行隧道有限元数值模拟.岩石力学与工程学报,2002,21(9)：1330—1334.
[19]近接隧道施工的设计与指南.日本铁道综合技术研究所,1987.
[20]谢卓雄.小净距隧道近接施工围岩稳定性及结构力学行为特征研究.四川成都：西南交通大学,2005.
[21]王景春,殷杰.相邻隧道中心距的研究.石家庄铁道学院学报,1995,8(2)：109-114.
[22]川杉本兴隆,松本嘉司,西周隆.用能量理论对平行双洞隧道进行稳定分析.隧道译丛,1990(2)：30-40.
[23]愕木武著,关宝树译.隧道力学.北京：中国铁道出版社.
[24](日)T.川田,M.大加&M.小林.最小净距的大型双线公路隧道的观测施工.水电技术信息,1996：146-154.
[25]Hiroshi Kuriyama, Tokuji Kong, Takaya OGATA the desigiand construction of pillar reinforcement at horizontal twin tunnels. Proceeding of Tunnel Engineering-JSCE,2000,5(10):125-130.
[26]Solim E,张佳文.小间距双线隧道的二维与三维分析.探矿工程译丛,1995：62-64.
[27]Soliman E, Duddeek H, Aherns H. Two and three dimensional analysis of closely spaced double-tube tunnels. Tunneling and Underground Space Technology, 1993,8(1):13-18.
[28]黄宝龙.复杂环境下小间距隧道施工控制关键技术研究[硕士学位论文].北京：北京交通大学,2006.
[29]Jamshid Ghaboussi, Randall E.Ranken. Interaction between two Parallel tunnels. International Journal for Numerical and Analytical Methods in Geomechanics, 1977,3(1):75-103.
[30]Adachi T, Kimura M, Osada H. Interaction between multi-tunnels under construction//InProc. Of the 11th Southeast Asian Geotechnical Conference, Singapore, National University of Singapore and Nanyang Technological University, Singapore,1993:51-60.
[31]Sang, Hwan Kim. Model testing and analysis of interactions between tunnels in clay [Ph.D.thesis]. UK:University of oxford,1996.
[32]San-Hwan Kim. Interaction behaviors between parallel tunnels in soft ground. Tunneling and Underground Space Technology,2004,19(4):448.
[33]Lee KM, Rowe PK. Finite element modeling of the three-dimensional ground deformation due to tunneling in soft cohesive 5011:Part II-results[J]. Computers and Geotechnics,1990,6(10):87-109.
[34]Duddeek H. Application of numerical and analysis for tunneling international[J]. Journal for Numerical & Analytical Methods in Geotechnics,1991,17(3):1-9.
[35]陆文超.地面荷载下浅埋隧道围岩应力的复变函数解析法.江南大学学报(自然科学版).2002,12,1(4)：409-413.
[36]齐明山,蔡晓鸿,冯翠霞.隧道围岩压力的弹塑性新解.土工基础,2006,20(2)：73-76.
[37]王明年,郭军等.高速铁路大断面深埋黄土隧道围岩压力计算方法.中国铁道科学,2009,30(5)：53-58.
[38]严综雪,房营光,刘庭金.应力路径对特大断面隧道围岩压力的影响.岩石力学与工程学报,2009,28(11)：2228-2234.
[39]谢骏,刘纯贵,于海勇.双平行圆形隧道稳定的塑性极限分析上限解.岩石力学与工程学报,2006,25(9)：1835-1841.
[40]姜功良.浅埋软土隧道稳定性极限分析.土木工程学报,1998,31(5)：65-72.
[41]杨小礼,王作伟.非线性破坏准则下浅埋隧道围岩压力的极限分析.中南大学学报(自然科学版),2010,41(1)：299-302.
[42]Assadi A, Scott W. Sloan. Undrained stability of shallow square tunnel. Journal of Geotechnical Engineering,1991,117(8):1152-1173.
[43]In-Mo Lee, Seok-Woo Nam. The study of seepage forces acting on the tunnel lining and tunnel face in shallow tunnels. Tunneling and Underground Space Technology,2001,16(1):31-40.
[44]Atkinson JH, Potts DM. Stability of shallow tunnel in cohesionless and soil, Geotechnique,1977,27(2):203-215.
[45]Charles E, Augarde, Andrei V. Lyamin, Scott W. Sloan. Stability of an undrained plane strain heading revisited. Computers and Geotechnics,2003,30:419-430.
[46]Abdul-Hamid Soubra, Daniel Dias, etc. Three-dimensional face stability analysis of circular tunnels by a kinematical approach. Geocongress,2008:894-901.
[47]Eisenstein Z, Samarasekera L. Stability of unsupported tunnels in clay, Canada Geotechnical Journal,1992,29:609-613.
[48]肖明清.小间距浅埋隧道围岩压力的探讨.现代隧道技术,2004,41(3)：7-10.
[49]乔春江,朱光仪.超小净距隧道的设计与研究.公路,2006,7：179-184.
[50]郑国平,杨健,高翔.双洞双向8车道公路的方案比选.交通科技,2006,3：35-38.
[51]孙钧.地下结构工程理论与实践.上海：上海科学技术出版社,1995.
[52]孙钧,侯学渊.地下结构(上).北京：科学出版社,1987.
[53]邹志晖,汪志林.锚杆在不同岩体中的工作机理.岩土工程学报,1993,15(5)：71-78.
[54]唐湘民.岩体锚固效应模型试验研究及解析计算[硕士学位论文].武汉：中国科学院武汉岩土力学研究所,1987.
[55]张玉军.锫固岩体流变特性的模型试验及理论研究[博士学位论文].上海：同济大学,1992.
[56]葛修润,刘建武.加锚节理面抗剪性能研究.岩土工程学报,1988,10(1)：8-19.
[57]朱维申,白世伟.预应力锚索加固机理研究.武汉：中国科学院武汉岩土力学研究所,1995.
[58]李术才.加锚断续节理岩体断裂损伤模型及其应用[博士学位论文].武汉：中国科学院武汉岩土力学研究所,1996.
[59]杨延毅,王慎跃.加锚节理岩体的损伤增韧止裂模型研究.岩土工程学报,1995,17(1)：9-17.
[60]Lutz L, Gergeley P. Mechanics of band and slip of deformed bars in concrete[J]. Journal of American Concrete Institute,1967,640(11):711-721.
[61]]Hansor NW. Influence of surface roughness of prestressing strand on band performance. Journal of Prestressed Concrete Institute,1969,14(1):32-45.
[62]Stillborg B. Experimental investigation of steel cables for rock reinforcement in hard rock. Sweden:Lulea University of Technology,1984.
[63]Hyct AL, Bawd en WF, Reichert RD. The Effect of Rock Mass Confinement on the Bond Strength of Fully Grouted Cable Bolts. Int.J.Rock Mech.Min.Sic.& Genomic. Abstr,1992,29(5):503-524.
[64]Jarred DJ, Haberfield CM. Tendon/grout interface performance in grouted anchors. In:Proc.Ground Anchorages and Anchored Structures, London,1997.
[65]Chen WF. Limit analysis and soil plasticity. Elsevier Science,1975:1-48.
[66]Sokolovskii BB. Statics of granular media. Beijing:Geology Press,1956.97-110.
[67]DeJong KA. Analysis of the Behavior of a Class of Genetic Adaptive Systerms. Ann Arbor:Univ Michigan,1975
[68]Spencer E. Circular and logarithmic spiral slip surfaces. J. Soil Mech. And Found. Div ASCE,1969,95(1):227-234.
[69]Terzaghi K. Theoretical soil mechanics. New York:John Wiley and Sons Inc, 1943.
[70]Wu BR, Chiou SY, Lee CJ. Soil movement around parallel tunnels in soft ground. In:Centrifuge'98 Conference. Tokyo:1998,739-744.
[71]Davis EH, Gunn MJ, Mair RJ1. The stability of shallow tunnels and underground openings in cohesive material. Geotechnique,1980,30(4):397-416.
[72]Broms BB, Bennermark H. Stability of clay in vertical openings. J. Soil Mech. Fdns. Div. Am. Soc. Civ. Eng.1967,193(SM1):71-94.
[73]Peck RB. Deep excavations and tunnelling in soft ground. In:Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering. Mexico:1969,225-290.
[74]Schofield AN. Cambridge geotechnical centrifuge operations. Geotechnique, 1980,30(3):227-268.
[75]彭立敏,刘小兵.交通隧道工程.长沙：中南大学出版社,2003.
[76]王文权.大跨软岩地铁隧道施工方法研究：硕士学位论文.成都：西南交通大学,2002.
[77]李老三.单拱四车道公路隧道施工方法数值模拟与抗震响应研究.中南大学硕士学位论文,2007.
[78]李军.大跨度公路隧道动态施工围岩稳定性数值分析.河海大学硕士学位论文,2006.
[79]岳广学.隧道开挖与支护的效果分析：(硕士学位论文),北京交通大学,2008.
[80]彭波.隧道全长粘结式锚杆支护机理及其有限元模拟方法研究.湖南大学硕士学位论文,2006.
[81]李希元等.地下隧道问题的数值计算方法.西安公路交通大学学报,1996,16(2)：56-60.
[2]关宝树,等.隧道工程施工要点集.北京：人民交通出版社,2001
[3]李云鹏,王芝银,韩常领.不同围岩类别小间距隧道施工过程模拟研究.岩土力学,2006,27(1)：11-16.
[4]李云鹏,王芝银,韩常领.考虑地震影响的小间距隧道围岩流变损伤.长安大学学报(自然科学版),2006,26(2)：51-56.
[5]姚勇,晏启祥,周俐俐.小净距隧道在不同开挖方式下的力学效应分析.西南科技大学学报.,2005,20(2)：53-56.
[6]姚勇,何川,晏启祥.董家山隧道小净距段爆破控制的数值模拟.岩土力学,2004,25(S2)：501-506.
[7]晏启祥,何川,姚勇.小净距隧道施工小导管注浆效果的数值模拟分析.岩土力学,2004,25(S2)：239-242.
[8]晏启祥,何川,姚勇.软岩隧道施工特性及其动态力学行为研究.岩石力学与工程学报,2006,25(3)：572-577.
[9]晏启祥,何川,姚勇.软岩小净距隧道施工力学效应研究.地下空间与工程学报,2005,1(5)：693-697.
[10]靳晓光,刘伟,郑学贵.小净距偏压公路隧道开挖顺序优化.公路交通科技,2005,22(8)：61-64.
[11]刘伟,靳晓光,陈少华.高速公路小净距隧道合理净距的探讨.地下空间,2004,24(3)：380-385.
[12]刘艳青,钟世航,卢汝绥.小净距并行隧道力学状态的试验研究.岩石力学与工程学报,2000,19(9)：590-594.
[13]庄宁,廖少明等.大跨度小净距群洞隧道施工方案优化研究.地下空间与工程学报,2007,3(1)：96-100.
[14]孙元国,李文江,朱永全.客运专线小净距隧道施工效应的数值模拟分析.石家庄铁道学院学报(自然科学版),2007,20(3)：6-14.
[15]舒志乐,刘保县,李月.偏压小净距隧道围岩压力分析.地下空间与工程学报,2007,3(3)：430-433.
[16]曹林,胡居义,黎冬林.小净距公路(双洞)隧道围岩破坏模式研究.2007,18(3)：65-69.
[17]张玉军,朱维申,杨家岭.近距离双隧道开挖与支护稳定性的粘弹塑性有限元计算.岩石力学与工程学报,1999,18(S)：855-559.
[18]陈先国,高波.地铁近距离平行隧道有限元数值模拟.岩石力学与工程学报,2002,21(9)：1330—1334.
[19]近接隧道施工的设计与指南.日本铁道综合技术研究所,1987.
[20]谢卓雄.小净距隧道近接施工围岩稳定性及结构力学行为特征研究.四川成都：西南交通大学,2005.
[21]王景春,殷杰.相邻隧道中心距的研究.石家庄铁道学院学报,1995,8(2)：109-114.
[22]川杉本兴隆,松本嘉司,西周隆.用能量理论对平行双洞隧道进行稳定分析.隧道译丛,1990(2)：30-40.
[23]愕木武著,关宝树译.隧道力学.北京：中国铁道出版社.
[24](日)T.川田,M.大加&M.小林.最小净距的大型双线公路隧道的观测施工.水电技术信息,1996：146-154.
[25]Hiroshi Kuriyama, Tokuji Kong, Takaya OGATA the desigiand construction of pillar reinforcement at horizontal twin tunnels. Proceeding of Tunnel Engineering-JSCE,2000,5(10):125-130.
[26]Solim E,张佳文.小间距双线隧道的二维与三维分析.探矿工程译丛,1995：62-64.
[27]Soliman E, Duddeek H, Aherns H. Two and three dimensional analysis of closely spaced double-tube tunnels. Tunneling and Underground Space Technology, 1993,8(1):13-18.
[28]黄宝龙.复杂环境下小间距隧道施工控制关键技术研究[硕士学位论文].北京：北京交通大学,2006.
[29]Jamshid Ghaboussi, Randall E.Ranken. Interaction between two Parallel tunnels. International Journal for Numerical and Analytical Methods in Geomechanics, 1977,3(1):75-103.
[30]Adachi T, Kimura M, Osada H. Interaction between multi-tunnels under construction//InProc. Of the 11th Southeast Asian Geotechnical Conference, Singapore, National University of Singapore and Nanyang Technological University, Singapore,1993:51-60.
[31]Sang, Hwan Kim. Model testing and analysis of interactions between tunnels in clay [Ph.D.thesis]. UK:University of oxford,1996.
[32]San-Hwan Kim. Interaction behaviors between parallel tunnels in soft ground. Tunneling and Underground Space Technology,2004,19(4):448.
[33]Lee KM, Rowe PK. Finite element modeling of the three-dimensional ground deformation due to tunneling in soft cohesive 5011:Part II-results[J]. Computers and Geotechnics,1990,6(10):87-109.
[34]Duddeek H. Application of numerical and analysis for tunneling international[J]. Journal for Numerical & Analytical Methods in Geotechnics,1991,17(3):1-9.
[35]陆文超.地面荷载下浅埋隧道围岩应力的复变函数解析法.江南大学学报(自然科学版).2002,12,1(4)：409-413.
[36]齐明山,蔡晓鸿,冯翠霞.隧道围岩压力的弹塑性新解.土工基础,2006,20(2)：73-76.
[37]王明年,郭军等.高速铁路大断面深埋黄土隧道围岩压力计算方法.中国铁道科学,2009,30(5)：53-58.
[38]严综雪,房营光,刘庭金.应力路径对特大断面隧道围岩压力的影响.岩石力学与工程学报,2009,28(11)：2228-2234.
[39]谢骏,刘纯贵,于海勇.双平行圆形隧道稳定的塑性极限分析上限解.岩石力学与工程学报,2006,25(9)：1835-1841.
[40]姜功良.浅埋软土隧道稳定性极限分析.土木工程学报,1998,31(5)：65-72.
[41]杨小礼,王作伟.非线性破坏准则下浅埋隧道围岩压力的极限分析.中南大学学报(自然科学版),2010,41(1)：299-302.
[42]Assadi A, Scott W. Sloan. Undrained stability of shallow square tunnel. Journal of Geotechnical Engineering,1991,117(8):1152-1173.
[43]In-Mo Lee, Seok-Woo Nam. The study of seepage forces acting on the tunnel lining and tunnel face in shallow tunnels. Tunneling and Underground Space Technology,2001,16(1):31-40.
[44]Atkinson JH, Potts DM. Stability of shallow tunnel in cohesionless and soil, Geotechnique,1977,27(2):203-215.
[45]Charles E, Augarde, Andrei V. Lyamin, Scott W. Sloan. Stability of an undrained plane strain heading revisited. Computers and Geotechnics,2003,30:419-430.
[46]Abdul-Hamid Soubra, Daniel Dias, etc. Three-dimensional face stability analysis of circular tunnels by a kinematical approach. Geocongress,2008:894-901.
[47]Eisenstein Z, Samarasekera L. Stability of unsupported tunnels in clay, Canada Geotechnical Journal,1992,29:609-613.
[48]肖明清.小间距浅埋隧道围岩压力的探讨.现代隧道技术,2004,41(3)：7-10.
[49]乔春江,朱光仪.超小净距隧道的设计与研究.公路,2006,7：179-184.
[50]郑国平,杨健,高翔.双洞双向8车道公路的方案比选.交通科技,2006,3：35-38.
[51]孙钧.地下结构工程理论与实践.上海：上海科学技术出版社,1995.
[52]孙钧,侯学渊.地下结构(上).北京：科学出版社,1987.
[53]邹志晖,汪志林.锚杆在不同岩体中的工作机理.岩土工程学报,1993,15(5)：71-78.
[54]唐湘民.岩体锚固效应模型试验研究及解析计算[硕士学位论文].武汉：中国科学院武汉岩土力学研究所,1987.
[55]张玉军.锫固岩体流变特性的模型试验及理论研究[博士学位论文].上海：同济大学,1992.
[56]葛修润,刘建武.加锚节理面抗剪性能研究.岩土工程学报,1988,10(1)：8-19.
[57]朱维申,白世伟.预应力锚索加固机理研究.武汉：中国科学院武汉岩土力学研究所,1995.
[58]李术才.加锚断续节理岩体断裂损伤模型及其应用[博士学位论文].武汉：中国科学院武汉岩土力学研究所,1996.
[59]杨延毅,王慎跃.加锚节理岩体的损伤增韧止裂模型研究.岩土工程学报,1995,17(1)：9-17.
[60]Lutz L, Gergeley P. Mechanics of band and slip of deformed bars in concrete[J]. Journal of American Concrete Institute,1967,640(11):711-721.
[61]]Hansor NW. Influence of surface roughness of prestressing strand on band performance. Journal of Prestressed Concrete Institute,1969,14(1):32-45.
[62]Stillborg B. Experimental investigation of steel cables for rock reinforcement in hard rock. Sweden:Lulea University of Technology,1984.
[63]Hyct AL, Bawd en WF, Reichert RD. The Effect of Rock Mass Confinement on the Bond Strength of Fully Grouted Cable Bolts. Int.J.Rock Mech.Min.Sic.& Genomic. Abstr,1992,29(5):503-524.
[64]Jarred DJ, Haberfield CM. Tendon/grout interface performance in grouted anchors. In:Proc.Ground Anchorages and Anchored Structures, London,1997.
[65]Chen WF. Limit analysis and soil plasticity. Elsevier Science,1975:1-48.
[66]Sokolovskii BB. Statics of granular media. Beijing:Geology Press,1956.97-110.
[67]DeJong KA. Analysis of the Behavior of a Class of Genetic Adaptive Systerms. Ann Arbor:Univ Michigan,1975
[68]Spencer E. Circular and logarithmic spiral slip surfaces. J. Soil Mech. And Found. Div ASCE,1969,95(1):227-234.
[69]Terzaghi K. Theoretical soil mechanics. New York:John Wiley and Sons Inc, 1943.
[70]Wu BR, Chiou SY, Lee CJ. Soil movement around parallel tunnels in soft ground. In:Centrifuge'98 Conference. Tokyo:1998,739-744.
[71]Davis EH, Gunn MJ, Mair RJ1. The stability of shallow tunnels and underground openings in cohesive material. Geotechnique,1980,30(4):397-416.
[72]Broms BB, Bennermark H. Stability of clay in vertical openings. J. Soil Mech. Fdns. Div. Am. Soc. Civ. Eng.1967,193(SM1):71-94.
[73]Peck RB. Deep excavations and tunnelling in soft ground. In:Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering. Mexico:1969,225-290.
[74]Schofield AN. Cambridge geotechnical centrifuge operations. Geotechnique, 1980,30(3):227-268.
[75]彭立敏,刘小兵.交通隧道工程.长沙：中南大学出版社,2003.
[76]王文权.大跨软岩地铁隧道施工方法研究：硕士学位论文.成都：西南交通大学,2002.
[77]李老三.单拱四车道公路隧道施工方法数值模拟与抗震响应研究.中南大学硕士学位论文,2007.
[78]李军.大跨度公路隧道动态施工围岩稳定性数值分析.河海大学硕士学位论文,2006.
[79]岳广学.隧道开挖与支护的效果分析：(硕士学位论文),北京交通大学,2008.
[80]彭波.隧道全长粘结式锚杆支护机理及其有限元模拟方法研究.湖南大学硕士学位论文,2006.
[81]李希元等.地下隧道问题的数值计算方法.西安公路交通大学学报,1996,16(2)：56-60.