平行三孔小净距隧道相互影响分析及围岩稳定性研究
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摘要
为了满足日益增长的交通需求,平行三孔或三孔以上小净距隧道的建设逐渐受到人们的重视。然而,由于这类隧道特殊的结构型式,使得隧道施工时相互影响较大,这也给设计和施工过程中带来了许多新的问题,因此,对此类隧道进行相关研究就显得十分必要。
本文以韩府山一、二、三号隧道——三孔大断面小净距隧道为工程背景,分别通过理论分析和数值模拟方法,对平行三孔小净距隧道施工相互影响及围岩稳定性进行相关研究。论文主要完成以下几方面的工作：
(1)介绍了求解平面弹性力学问题中相关的复变函数理论,同时对求解双连通问题中使用到的Schwarz交替法基本原理做了简单的介绍。
(2)介绍Schwarz交替法在无限平面含两个洞室问题中的应用,同时对Schwarz交替法在半无限平面内含三个洞室问题中的可行性进行相关论证。
(3)根据“结合洞”思想和复变函数理论及Schwarz交替法原理,首次给出半无限平面含三个圆形洞室问题弹性解析解详细过程及具体公式。
(4)编制Matlab程序实现问题解析解的求解,并验证程序计算结果可靠性。
(5)使用所编制的Matlab计算程序,分别对地表变形及中间岩柱应力的相互影响间距进行研究和讨论,并对如：洞室埋深、地层损失率、弹性模量及泊松比等因素对其的影响进行讨论。
(6)使用有限差分软件FLAC3D对围岩强度折减安全系数进行求解,分析不同隧道净距及埋深情况下围岩安全系数的变化规律,从而针对埋深及净距对围岩稳定性的影响进行相关研究及讨论。
(7)对不同隧道净距及埋深情况下围岩极限破坏状态相关特性进行研究,根据研究结果分析围岩破坏面形状、围岩变形及洞周破坏区域,并讨论净距和埋深对它们的影响。
In order to fulfill the daily increasing transportation demand, the tunnel with more than three cavities which are closely build is more and more popular. However, because of the special structural style, the excavation of different cavities will have interactions on each other, which breeds new problems for the design and construction. Therefore, it is necessary to study on this type of tunnel.
Based on the No.1-3 tunnel of Hanfu Mount, which is the tri-tunnel with the characteristics of large-span and small-distance. The article will study on the interaction of cavities and the stability of surrounding rock during the construction of the parallel tri-tunnel. The thesis has mainly completed the following achievements:
(1) Introduce the relevant theorems of complex variable in solving the mechanical problem in elasticity plane, and the basic principle of Schwarz alternating method in solving the problem of double connected region.
(2) Introduce the application of Schwarz alternating method to the bi-tunnel problem in infinite half plane. Meanwhile, discuss the feasibility of expanding the application to the tri-tunnel problem.
(3) According to the idea of "unite cavity" and the theorems of complex variable and Schwarz alternating method, the elastic analytical solution and function for the problem of triple circular tunnels in infinite half plane will be given in the paper.
(4) Write a program by Matlab to realize the calculation of the analytical solution, and verify the reliability of the result.
(5) Study and discuss the critical interaction distance of the surface deformation and the stress in the shared rock of two cavities, and whose affect factors, such as covering depth, ground loss ratio, elastic modulus and Poisson's ratio.
(6) Use the infinite difference software FLAC3D to obtain the strength reduction coefficient of the surrounding rock, and analyze the changing pattern of which under different inter-distance and covering depth. Thus talk about hoe the stability of surrounding rock affected by the covering depth and inter-distance.
(7) Research on the trait of the limit damage state of the surrounding rock under different inter-distance and covering depth. The result could be used to analyze the shape of the damage face, the deformation and damage region around tunnel, including the affect caused by inter-distance and covering depth.
本文以韩府山一、二、三号隧道——三孔大断面小净距隧道为工程背景,分别通过理论分析和数值模拟方法,对平行三孔小净距隧道施工相互影响及围岩稳定性进行相关研究。论文主要完成以下几方面的工作：
(1)介绍了求解平面弹性力学问题中相关的复变函数理论,同时对求解双连通问题中使用到的Schwarz交替法基本原理做了简单的介绍。
(2)介绍Schwarz交替法在无限平面含两个洞室问题中的应用,同时对Schwarz交替法在半无限平面内含三个洞室问题中的可行性进行相关论证。
(3)根据“结合洞”思想和复变函数理论及Schwarz交替法原理,首次给出半无限平面含三个圆形洞室问题弹性解析解详细过程及具体公式。
(4)编制Matlab程序实现问题解析解的求解,并验证程序计算结果可靠性。
(5)使用所编制的Matlab计算程序,分别对地表变形及中间岩柱应力的相互影响间距进行研究和讨论,并对如：洞室埋深、地层损失率、弹性模量及泊松比等因素对其的影响进行讨论。
(6)使用有限差分软件FLAC3D对围岩强度折减安全系数进行求解,分析不同隧道净距及埋深情况下围岩安全系数的变化规律,从而针对埋深及净距对围岩稳定性的影响进行相关研究及讨论。
(7)对不同隧道净距及埋深情况下围岩极限破坏状态相关特性进行研究,根据研究结果分析围岩破坏面形状、围岩变形及洞周破坏区域,并讨论净距和埋深对它们的影响。
In order to fulfill the daily increasing transportation demand, the tunnel with more than three cavities which are closely build is more and more popular. However, because of the special structural style, the excavation of different cavities will have interactions on each other, which breeds new problems for the design and construction. Therefore, it is necessary to study on this type of tunnel.
Based on the No.1-3 tunnel of Hanfu Mount, which is the tri-tunnel with the characteristics of large-span and small-distance. The article will study on the interaction of cavities and the stability of surrounding rock during the construction of the parallel tri-tunnel. The thesis has mainly completed the following achievements:
(1) Introduce the relevant theorems of complex variable in solving the mechanical problem in elasticity plane, and the basic principle of Schwarz alternating method in solving the problem of double connected region.
(2) Introduce the application of Schwarz alternating method to the bi-tunnel problem in infinite half plane. Meanwhile, discuss the feasibility of expanding the application to the tri-tunnel problem.
(3) According to the idea of "unite cavity" and the theorems of complex variable and Schwarz alternating method, the elastic analytical solution and function for the problem of triple circular tunnels in infinite half plane will be given in the paper.
(4) Write a program by Matlab to realize the calculation of the analytical solution, and verify the reliability of the result.
(5) Study and discuss the critical interaction distance of the surface deformation and the stress in the shared rock of two cavities, and whose affect factors, such as covering depth, ground loss ratio, elastic modulus and Poisson's ratio.
(6) Use the infinite difference software FLAC3D to obtain the strength reduction coefficient of the surrounding rock, and analyze the changing pattern of which under different inter-distance and covering depth. Thus talk about hoe the stability of surrounding rock affected by the covering depth and inter-distance.
(7) Research on the trait of the limit damage state of the surrounding rock under different inter-distance and covering depth. The result could be used to analyze the shape of the damage face, the deformation and damage region around tunnel, including the affect caused by inter-distance and covering depth.
引文
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[2]仇文革.地下工程近接施工力学原理与对策研究：博士学位论文.四川成都：西南交通大学,2003
[3]曾小清.多孔隧道施工的研究进展.地下空间,1999,19(5)：373～378
[4]Yamaguchi I, Yamazaki I, Kiritani Y. Study of ground-tunnel interaction four shield tunnels driven in close proximity, in relation to design and construction of shield tunnels. Tunnelling and Underground Space Technology.1998,16(3): 289～304
[5]中华人民共和国行业标准编写组.JTG D70-2004公路隧道设计规范.北京：人民交通出版社,2004
[6]中华人民共和国行业标准编写组.TB 10003-2005铁路隧道设计规范.北京：中国铁道出版社,2005
[7]Howland RCJ. Stresses in a plate containing an infinite row of holes. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1934,148 (864):471～491
[8]Howland RCJ, Knight RC. Stress functions for a plate containing groups of circular holes. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences,1939,238 (793):357～392
[9]Green AC. General Biharmonic Analysis for a Plate Containing Circular Holes. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences,1940,176 (964):121～139
[10]Ling CB. On the Stresses in a Plate Containing Two Circular Holes. Journal of Applied Physics,1948,19:77～82
[11]潘家铮.相邻水工隧洞的原理分析.地下工程,1979,(1)：2～12
[12]刘新宇,侯学渊.平行圆形隧洞的应力分析.同济大学学报,1985,(3)：15～26
[13]蒋树屏,刘伟(译).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
[14]Ukadgaonker VG. Stress Analysis of a Plate Containing Two Circular Holes Having Tangential Stresses. Journal of AIAA,1982:125～128
[15]Zimmerman RW. Second-order approximation for the compression of an elastic plate containing a pair of circular holes, ZAMM Z. angew. Math. Mech.68 (1988) 11:458-468
[16]Ukadgaonker VG, Naik AP. Interaction Effect of Two Arbitrarily Oriented Cracks-Part I. International Journal of Fracture,1991,51:219～230
[17]张路青,吕爱钟.双孔圆形洞室围岩应力分析的交替法研究.岩石力学与工程学报,1998,17(5)：534～543
[18]张路青,杨志法,吕爱钟.任意布置方式下两任意形状孔洞平面弹性问题的解析方法研究.中国科学D,2000,30(5)：509-518.
[19]Kooi CB, Verruijt A. Interaction of circular holes in an infinite elastic medium. Tunneling and Underground Space Technology,2001,16:59～62
[20]晏莉.并行隧道施工相互影响分析及应用研究：博士学位论文.湖南长沙：中南大学,2008
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