Dynamic analysis of segmental linings of shield tunnels using a state space method and its application in physical test interpretation. (July 2023)

• Record Type: Journal Article
• Authors: Chen, Z.P.; Wang, J.C.; Xu, R.Q.; Yang, Z.X.; Gong, X.N.
• Is Part Of: Tunnelling and underground space technology. Volume 137(2023)
• Publication Date: 2023-07
• Subjects: Analytical solution -- Dynamic response -- Segmental lining -- State space method -- curved Euler–Bernoulli beam; Tunneling -- Periodicals; Underground construction -- Periodicals; Tunnels -- Periodicals; Underground areas -- Periodicals; 624.193
• DOI: 10.1016/j.tust.2023.105103
• Languages: English
• ISSNs: 0886-7798

Abstract

Highlights: A new analytical method to analyze the dynamic response of segmental linings under arbitrary dynamic loads is proposed. The effects of joints and soil damping on the dynamic response of segmental linings are involved. The orthogonality relationship of the vibration modal shapes of the tunnel lining is derived. Abstract: Based on the state space method and D'Alembert's principle, a new analytical method is established to study the dynamic response of circular segmental linings of shield tunnels. The tunnel lining segments are considered to be curved Euler–Bernoulli beams, the joints connecting the segments are modeled by a series of distributed springs, and the lining–surrounding soil interaction is represented by distributed reaction springs with viscous dampers. With the state space method, the governing equations can be concisely expressed in matrix form, and a separate variable method in conjunction with a frequency scanning strategy is employed to obtain the natural frequencies and corresponding modal shapes of the free vibration of the linings. The orthogonality of the vibration modes of the linings is demonstrated using a symplectic inner product, and the response of the linings under arbitrary dynamic loads is solved using the modal superposition method. Numerical and model experimental examples are presented to verify the efficiency and robustness of the proposed method. We prove that the proposed method can solve the dynamic response of segmental linings by considering the effect of joint and asymmetric loading conditions with high efficiency and accuracy.