Abstract：Based on the curved Euler beam theory，this paper presents an analytical solution for the double lining structure of shield tunnels. Partial-interaction composite curved beam theory is employed to simulate the double lining，and mechanical springs are used to reflect the radial joints effect. The solutions for the internal forces and deformations can be derived by the state space method for arbitrary loadings and variable joint distributions. The solutions revalidated by a comparison with the results of the existing analytical method and numerical model. Using the present solutions，the influence of different joint distributions on internal forces and deformations of the lining are discussed，and the variation trends of internal forces and deformations varying with interlayer shear stiffness between inner and outer linings are also examined under different joint stiffness conditions. The results show that：(1) Increasing the interlaminar shear stiffness can enhance the overall stiffness of the double lining，while the axial force increases，and the bending moment decreases. (2) The bending stiffness of the joint has a significant influence on the bending moment and deformation，but has less influence on the axial force；(3) When the tension and compression stiffness of the joint is too small，the double lining with larger interlayer shear stiffness will be more likely to exhibit a deformation mode different from the‘elliptical’mode because of the greater tendency of the inward contraction. The results obtained from this study may provide useful guidance for design of the double lining structure of shield tunnels.
UCHIDA K，WASA Y，KANAI M. Design of the shield tunnel for the trans-Tokyo bay highway[J]. Tunnelling and Underground Space Technology，1992，7(3)：251–261.
[4]
洪开荣，杜闯东，王坤. 广深港高速铁路狮子洋水下盾构隧道修建技术[J]. 中国工程科学，2009，11(7)：53–58.(HONG Kairong，DU Chuangdong，WANG Kun. Construction technology of underwater shield tunnel in Guangzhou-Shenzhen-Hong Kong express rail link[J]. Engineering Sciences，2009，11(7)，53–58.(in Chinese))
[6]
朱合华，陶履彬. 盾构隧道衬砌结构受力分析的梁–弹簧系统模型[J]. 岩土力学，1998，19(2)，19(2)：26–32.(ZHU Hehua，TAO Lubin. Study on two Beam-Spring models for the numerical analysis of segments in shield tunnel[J]. Rock and Soil Mechanics，1998，19(2)：26–32.(in Chinese))
[9]
YAN Q X，YAO C F，YANG W B，et al. An Improved numerical model of shield tunnel with double lining and its applications[J]. Advances in Materials Science and Engineering，2015，15：1–15.
[12]
LEE K M，GE X W. The equivalence of a jointed shield-driven tunnel lining to a continuous ring structure[J]. Canadian Geotechnical Journal，2001，38(3)：461–483.
[14]
黄伟明，王金昌，杨仲轩，等. 基于弹性地基曲梁理论的盾构隧道管片分析方法[J]. 浙江大学：工学版，2020，54(4)：787–795.(HUANG Weiming，WANG Jinchang，XU Riqing，et al. Structural analysis of shield tunnel lining using the theory of curved beam resting on elastic foundation[J]. Journal of Zhejiang University：Engineering Science，2020，54(4)：787–795.(in Chinese))
[1]
姚超凡，晏启祥，何川，等. 一种改进的盾构隧道双层衬砌分析模型及其应用研究[J]. 岩石力学与工程学报，2014，33(1)：80–89.(YAO Chaofan，YAN Qixiang，HE Chuan，et al. An improved analysis model for shield tunnel with double-layer lining and its applications[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(1)：80–89.(in Chinese))
[7]
LEE K M，HOU X Y，GE X W，et al. An analytical solution for a jointed shield-driven tunnel lining[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2001，25(4)：365–390.
[11]
ZHAO C Y，ALIMARDANI L A，BARCIAGA T，et al. Prediction of tunnel lining forces and deformations using analytical and numerical solutions[J]. Tunnelling and Underground Space Technology，2017，64：164–176.
[3]
钮新强. 南水北调中线工程穿黄隧洞关键技术研究[J]. 南水北调与水利科技，2009，7(6)：42–46.(NIU Xinqiang. Research on key technology in Yellow River crossing tunnel construction of South to North Water Diversion middle route project[J]. South-to-North Water Transfers and Water Science and Technology，2009，7(6)：42–46.(in Chinese))
[5]
Working Group No.2，Ita.. Guidelines for the design of shield tunnel lining[J]. Tunnelling and Underground Space Technology，2000，15(3)：303–331.
[8]
张厚美，过迟，吕国梁. 盾构压力隧洞双层衬砌的力学模型研究[J]. 水利学报，2001，32(4)：28–34.(ZHANG Houmei，GUO Chi，LU Guoliang. Mechanical model for shield pressure tunnel with secondary linings[J]. Journal of Hydraulic Engineering，2001，32(4)：28–34.(in Chinese))
[10]
EI NAGGAR H，HINCHBERGER S D. An analytical solution for jointed tunnel linings in elastic soil or rock[J]. Canadian Geotechnical Journal，2008，45(11)：1 572–1 593.
[13]
LIM C W，WANG C M，KITIPOMCHAI S. Timoshenko curved beam bending solutions in terms of Euler-Bernoulli solutions[J]. Archive of Applied Mechanics，1997，67(3)：179–190.
[15]
中华人民共和国国家标准编写组. GB50157—2003 地铁设计规范[S]. 北京：中国计划出版社，2003.(The National Standards Compilation Group of People/s Republic of China. GB50157—2003 Code for design of metro[S]. Beijing：China Planning Press，2003.(in Chinese))
2020, Vol. 39 
