寒区非圆形隧道冻胀力的解析解

李岩松; 陈寿根

doi:10.6052/0459-1879-19-226

寒区非圆形隧道冻胀力的解析解

doi: 10.6052/0459-1879-19-226

李岩松^*2), ,,
陈寿根^†

^* 中国五冶集团有限公司, 成都 610063
^? 西南交通大学交通隧道工程教育部重点实验室, 成都 610031

基金项目: 1) 中央高校基本科研业务费专项资金项目(SWJTU11ZT33);教育部创新团队发展计划(IRT0955)

详细信息

通讯作者:
李岩松

中图分类号: TU91
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- 被引次数: 0
出版历程
- 收稿日期: 2019-08-20
- 刊出日期: 2020-02-10

ANALYTICAL SOLUTION OF FROST HEAVING FORCE IN NON-CIRCULAR COLD REGION TUNNELS

Li Yansong^{*2)
, ,},
Chen Shougen^†

^* China MCC5 Group Corp. Ltd, Chengdu 610063, China
^? MOE Key Laboratory of Transportation Tunnel Engineering, Southwest Jiaotong University, Chengdu 610031, China

摘要

摘要: 利用复变函数相应理论引入一种求解考虑衬砌结构的季节性冻土地区非圆形隧道冻胀力和冻胀变形的方法. 方法克服了隧道断面形状为非圆形状并且同时考虑非圆形隧道支护、冻胀圈、未冻围岩时, 经典的复变函数理论不能直接应用求解非圆形隧道应力和位移的问题. 方法通过将经典复变函数理论与连续性条件结合, 导出了非圆形隧道衬砌-冻胀圈-未冻围岩系统在正交曲线坐标系$\zeta $平面内的解析式, 然后通过保角变换求得直角坐标系$Z$平面上考虑衬砌支护的寒区非圆形隧道冻胀力和冻胀变形. 将推导的解析式应用于鹧鸪山隧道洞口段研究中, 得到鹧鸪山隧道洞口段冻胀应力和冻胀位移解析解, 并将解析解与数值解进行对比,验证解析解的正确性. 由结果可知: 围岩冻胀力对衬砌影响明显, 在拱顶、拱脚、拱底处因冻胀造成的环向附加应力显著增大; 在拱脚及两侧拱肩处会受到较大的法向附加应力; 由于衬砌几何形状的原因, 造成了衬砌冻胀变形的不均匀, 进而造成冻胀力分布不均.应用复变函数理论将冻胀圈考虑为马蹄形、直墙拱形等非圆形状较以往将冻胀圈考虑为单一圆环的冻胀力研究更符合实际, 较以往研究更能反映实际工况. 研究结果为季节性冻土地区非圆形隧道冻胀力的弹塑性分析奠定了基础.
- 季节性冻土隧道 /
- 非圆形衬砌 /
- 复变函数 /
- 冻胀力 /
- 解析解
Abstract: A complex variable method is presented of stress and displacement problems for non-circular cold region tunnels. The complex variable method considers the non-circle tunnel support, the frost heaving circle and the unfrozen surrounding rock at the same time, making the problem from the single connected domain to multi connected domain problem, and can not directly apply the classical complex function theory to solve the problem of the stress and displacement of the non-circular tunnel. The analytical formula in Zeta plane orthogonal curvilinear coordinate system of non-circular tunnel lining to frozen surrounding rock to unfrozen surrounding rock system is derived by using classical complex variable method and continuity condition with power series and conformal transformation. Then, the frost heaving force and frost heaving deformation of the non-circular cold region tunnel are obtained by conformal transformation. This complex variable method is applied to Zhegushan tunnel research, and the analytical solution of Zhegushan tunnel openning frost heave stress and frost heave displacement is obtained. Comparing the analytical solution with the numerical solution to verify the correctness of the analytical solution. It can be seen from the results that frost heaving force has an obvious influence on the lining, and the additional circumferential stresses caused by frost heaving at the vault, arch foot and arch bottom are significantly increased. The additional normal stresses caused by frost heaving at the vault and both sides of arch shoulder are significantly increased. Because of the geometric configurations of lining, the frost heaving deformation is uneven, which leads to uneven distribution of frost heaving forces. Compared with previous studies, which consider the frost heaving ring as a single ring, the complex variable method is more practical. And the research results were expected to provide a referenced basis for elasto-plastic analysis of cold-region tunnel.
- cold-region tunnel /
- non-circular lining /
- complex variables /
- frost force /
- analytic solution

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参考文献(1)

[1]	Lai YM, Liu SY, Wu ZW , et al. Approximate analytical solution for temperature fields in cold regions circular tunnels. Cold Reg. Sci. Technol, 2002,34:43-49
[2]	Zhang XF, Lai YM, Yu WB , et al. Non-linear analysis for the freezing--thawing situation of the rock surrounding the tunnel in cold regions under the conditions of different construction seasons, initial temperatures and insulations. Tunnelling Underground Space Technol, 2002,17:315-325
[3]	Zhang SJ, Lai YM, Zhang XF , et al. Study on the damage propagation of surrounding rock from a cold-region tunnel under freeze--thaw cycle condition. Tunnelling Underground Space Technol, 2004,19:295-302
[4]	Lai YM, Wu H, Wu ZW , et al. Analytical viscoelastic solution for frost force in cold-region tunnels. Cold Reg. Sci. Technol., 2000,31:227-234
[5]	Gao GY, Chen QS, Zhang QS , et al. Analytical elasto-plastic solution for stress and plastic zone of surrounding rock in cold region tunnels. Cold Reg. Sci. Technol., 2012,72:50-57
[6]	Feng Q, Zhang BS, Qiang JG , et al. Analytical elasto-plastic solution for stress and deformation of surrounding rock in cold region tunnels. Cold Reg. Sci. Technol., 2014,108:59-68
[7]	夏才初, 黄继辉, 卞跃威等. 融化作用下多年冻土隧道围岩的弹塑性解及其与支护的相互作用分析. 岩土力学, 2013,34(7):1987-1994
[7]	( Xia Caichu, Huang Jihui, Bian Yuewei , et al. Elastoplastic analysis of surrounding rock of permafrost tunnel with thawing effect and its interaction with support. Rock and Soil Mechanics, 2013,34(7):1987-1994 (in Chinese))
[8]	张常光, 徐飞, 张庆贺等. 岩石隧道塑性位移新解. 岩石力学与工程学报, 2011,30(增2):3551-3556
[8]	( Zhang Changguang, Xu Fei, Zhang Qinghe , et al. New plastic solution for displacement of rock tunnles. Chinese Journal of Rock Mechanics and Engineering, 2011,30(supp.2):3551-3556 (in Chinese))
[9]	谭贤君 . 高海拔寒区隧道冻胀机理及其保温技术研究. [博士论文]. 武汉: 中国科学院武汉岩土力学研究所, 2010
[9]	( Tan Xianjun . Study on the meehanism of frost heave of tunnel in cold region with high altitude and related insulation technology. [PhD Thesis]. Wuhan: Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, 2010 (in Chinese))
[10]	杨罡 . 兰新高铁祁连山隧道围岩温度场及冻胀力研究. [硕士论文]. 西安: 西安科技大学, 2017
[10]	( Yang Gang . Study on surrounding rock temperature field and frost heave force of Qilian mountain tunnel of Lanxin railway. [Master Thesis]. Xi'An: Xi'an University of Science and Technology, 2017 (in Chinese))
[11]	黄继辉, 夏才初, 韩常领等. 寒区公路隧道冻胀力荷载的分布形式和简化计算方法. 现代隧道技术, 2016,53(5):63-70
[11]	( Huang Jihui, Xia Caichu, Han Changling , et al. The distribution form and simplified calculation method of frost heaving force load in highway tunnels in cold regions. Modern Tunneling Technology, 2016,53(5):63-70 (in Chinese))
[12]	黄继辉, 夏才初, 韩常领等. 考虑围岩不均匀冻胀的寒区隧道冻胀力解析解. 岩石力学与工程学报, 2015,34(增2):3766-3774
[12]	( Huang Jihui, Xia Caichu, Han Changling , et al. Analytical solution of frost heave force acting on cold-region tunnel liner considering anisotropy frost heave of surrounding rock. Chinese Journal of Rock Mechanics and Engineering, 2015,34(supp.2):3766-3774 (in Chinese))
[13]	苏林军 . 寒区隧道冻害预测与对策研究. [硕士论文]. 成都: 西南交通大学, 2007
[13]	( Su Linjun . Study on forcasting of frost damage and antifreezing strategies of tunnel in cold area. [Master Thesis]. Chengdu: Southwest Jiaotong University, 2007 (in Chinese))
[14]	吴剑 . 随道冻害机理及冻胀力计算方法的研究. [硕士论文]. 成都: 西南交通大学, 2004
[14]	( Wu Jian . Study on principle of tunnel freeze injure and calculation method of frost force. [Master Thesis]. Chengdu: Southwest Jiaotong University, 2004 (in Chinese))
[15]	Zheng H, Shunji KN, Niu FJ , et al. Three-dimensional frost heave evaluation based on practical Takashi's equation. Cold Regious Science & Technology, 2015,118:30-37
[16]	Tan XJ, Chen WZ, Wu GJ , et al. Numerical simulations of heat transfer with ice-water phase change occurring in porous media and application to a cold-region tunnel. Tunnelling Underground Space Technol., 2013,38:170-179
[17]	李岩松, 陈寿根 . 基于复变函数理论的非圆形隧道解析解. 西南交通大学学报, 2019, DOI: 10.3969/j.issn.0258-2724.20180243
[17]	( Li Yansong, Chen Shougen . Stress and deformation study of lining and surrounding rock in a non-circular tunnel based on the complex variable method Seepage. Journal of Southwest Jiaotong University, 2019, DOI: 10.3969/j.issn.0258-2724.20180243 (in Chinese))
[18]	李岩松, 陈寿根 . 考虑注浆加固作用下非圆形隧道应力和变形解析解. 中国公路学报, 2018,31(10):255-265
[18]	( Li Yansong, Chen Shougen . Analytic solution on stress and deformation of non-circular tunnel considering grouting circle. China Journal of Highway and Transport, 2018,31(10):255-265 (in Chinese))
[19]	吕爱钟, 张路青 . 地下隧洞力学分析的复变函数方法. 北京: 科学出版社, 2007
[19]	( Lü Aizhong, Zhang Luqing. Complex Function Method for Mechanical Analysis of Underground Tunnel. Beijing: Science Press, 2007 (in Chinese))
[20]	Kargar AR, Rahmannejad R, Hajabasi MA . A semi-analytical elastic solution for stress field of lined non-circular tunnels at great depth using complex variable method. International Journal of Solids and Structures, 2014,51:1475-1482
[21]	Lu AZ, Zhang N, Kuang L . Analytic solutions of stress and displacement for a non-circular tunnel at great depth including support delay. International Journal of Rock Mechanics & Mining Sciences, 2014,70:69-81
[22]	Lu AZ, Zhang N, Qin Y . Analytical solutions for the stress of a lined non-circular tunnel under full-slip contact conditions. International Journal of Rock Mechanics & Mining Sciences, 2015,79:183-192
[23]	陈子荫 . 围岩力学分析中的解析方法. 北京: 煤炭工业出版社, 1994
[23]	( Chen Ziyin. Analytical Method in Mechanical Analysis of Surrounding Rock. Beijing: China Coal Industry Publishing House, 1994 (in Chinese))
[24]	张治国, 杨轩, 宫剑飞等. 复变函数法分析盾构隧道开挖引起的土体位移和衬砌变形. 岩土工程学报, 2017,39(9):1626-1635
[24]	( Zhang Zhiguo, Yang Xuan, Gong Jianfei , et al. A complex variable analysis of soil displacement and liner deformation induced by shield excavation. Chinese Journal of Geotechnical Engineering, 2017,39(9):1626-1635 (in Chinese))
[25]	Li YS, Chen SG . A complex variable solution for lining stress and deformation in a non-circular deep tunnel II practical application and verification. Mathematical and Computational Applications, 2018,23, 43, doi: 10.3390/mca23030043
[26]	覃爱民, 骆汉宾 . 基于Mohr-Coulomb准则寒区隧道围岩应力弹塑性解析. 地下空间与工程学报, 2018,14(2):395-402
[26]	( Tan Aimin, Luo Hanbin . Elastoplastic analysis of stress in tunnel surrounding rock in cold region based on mohr-coulomb criterion. Chinese Journal of Underground Space and Engineering, 2018,14(2):395-402 (in Chinese))
[27]	Kargar AR, Rahmannejad R, Hajabasi MA . A semi-analytical elastic solution for stress field of lined non-circular tunnels at great depth using complex variable method. International Journal of Solids and Structures, 2014,51:1475-1482
[28]	赵玉报 . 高原高寒隧道围岩冻胀行为及施工对策研究. [博士论文]. 成都: 西南交通大学, 2011
[28]	( Zhao Yubao . Study on the frost heaving behavior and construction countermeasure for plateau tunnel in cold region after earthquake. [PhD Thesis]. Chengdu: Southwest Jiaotong University, 2011 (in Chinese))
[29]	黄诗冰, 刘泉声, 刘艳章等. 低温热力耦合下岩体椭圆孔(裂)隙中冻胀力与冻胀开裂特征研究. 岩土工程学报, 2018,40(3):459-467
[29]	( Huang Shibing, Liu Quansheng, Liu Yanzhang , et al. Frost heaving pressure and characteristics of frost cracking in elliptical cavity (crack) of rock mass under coupled thermal-mechanical condition at low temperature. Chinese Journal of Geotechnical Engineering, 2018,40(3):459-467 (in Chinese))
[30]	夏明 . 寒区隧道温度场数值分析研究. [硕士论文]. 淮南: 安徽理工大学, 2018
[30]	( Xia Ming . Numerical analysis of tunnel temperature field in cold area. [Master Thesis]. Huainan: Anhui University of Science & Technology, 2018 (in Chinese))
[31]	夏才初, 刘宇鹏, 吴福宝等. 基于西原模型的圆形隧道黏弹-黏塑性解析解. 岩土力学, 2019,40(5):1638-1648
[31]	( Xia Caichu, Liu Yupeng, Wu Fubao , et al. Viscoelasto-viscoplastic solutions for circular tunnel based on Nishihara model. Rock and Soil Mechanics, 2019,40(5):1638-1648 (in Chinese))
[32]	郭健 . 基于变形稳定的隧道结构可靠度分析. [博士论文]. 兰州: 兰州交通大学, 2018
[32]	( Guo Jian . Reliability analysis of tunnel structure based on deformation stability. [PhD Thesis]. Lanzhou: Lanzhou Jiaotong University, 2018 (in Chinese))
[33]	崔芳, 王利, 王云飞 . 非轴对称荷载下圆形隧道弹性围岩应力解析解. 地下空间与工程学报, 2017,13(3):637-642
[33]	( Cui Fang, Wang Li, Wang Yunfei . Analytical solution of stress in elastic surrounding rock of circular tunnel under non-axisymmetric load. Chinese Journal of Underground Space and Engineering, 2017,13(3):637-642 (in Chinese))