Analytical modeling of dynamic responses and vulnerable zones in curved finite tunnels with deformation joints

Abstract

Curved tunnels are critical weak points in seismic design due to geometric coupling and high dynamic sensitivity. While current seismic assessment methods mainly focus on transverse responses, simplified analytical models for longitudinal behavior, especially those accounting for deformation joints, remain limited. A dual-criterion vulnerable-zone identification method, based on a moment-capacity ratio and joint-opening displacement, is established and applied to quantitatively analyze the influence of tunnel curvature, joint stiffness, traveling-wave velocity, and foundation stiffness on the spatial distribution of vulnerable zones. The results show that the vicinity of deformation joints is an intrinsic weak region, whose extent shrinks with increasing foundation stiffness but never disappears. To address this gap, this study develops a longitudinal analytical model for curved tunnels with deformation joints. The tunnel is idealized as a finite-length, curved Euler-Bernoulli beam resting on a two-parameter Pasternak-type viscoelastic foundation. The governing equations are derived using viscoelastic foundation beam theory, with joint deformations (shear dislocation and flexural rotation) incorporated via a virtual force formulation. Closed-form dynamic solutions are obtained via modal superposition and validated through degeneration analysis and finite element simulations. A parametric study examines the effects of joint stiffness, tunnel curvature radius, traveling-wave velocity, and foundation stiffness, complemented by a quantitative sensitivity analysis that ranks the relative influence of parameter uncertainties on the peak dynamic response. The results reveal the governing mechanical mechanisms of these parameters and theoretically confirm the critical role of joints in inducing discontinuous dynamic responses. This work advances the understanding of soil-structure interaction in curved tunnel systems and provides a practical analytical framework for seismic design and vulnerability assessment of jointed curved tunnels under realistic engineering conditions.

Keywords

analytical modeling / curved tunnel / deformation joint / vulnerable zone / dynamic response / soil-structure interaction / traveling-wave effect / viscoelastic foundation

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