Longitudinal structural vulnerability analysis of shield tunnels under adjacent excavation disturbances

Abstract

This paper proposes a longitudinal vulnerability-based analysis method to evaluate the impact of foundation pit excavation on shield tunnels, accounting for geological uncertainties. First, the shield tunnel is modeled as an Euler-Bernoulli beam resting on the Pasternak foundation incorporating variability in subgrade parameters along the tunnel’s length. A random analysis method using random field theory is introduced to evaluate the tunnel’s longitudinal responses to excavation. Next, a risk assessment index system is established. The normalized relative depth between the excavation and the shield tunnel is used as a risk index, while the maximum longitudinal deformation, the maximum circumferential opening, and the maximum longitudinal bending moment serve as performance indicators. Based on these, a method for analyzing the longitudinal fragility of shield tunnels under excavation-induced disturbances is proposed. Finally, the technique is applied to a case study involving a foundation pit excavation above a shield tunnel, which is the primary application scenario of this method. Vulnerability curves for different performance indicators are derived, and the effects of tunnel stiffness and subgrade stiffness on the tunnel vulnerability are explored. The results reveal significant differences in vulnerability curves depending on the performance index used. Compared to the maximum circumferential opening and the maximum longitudinal bending moment, selecting the maximum longitudinal deformation as the control index better ensures the tunnel’s usability and safety under excavation disturbances. The longitudinal vulnerability of the shield tunnel nonlinearly decreases with the increase of the tunnel stiffness and subgrade stiffness, and the subgrade stiffness has a more pronounced effect. Parametric analyses suggest that actively reinforcing the substratum is more effective on reducing the risk of tunnel failure due to adjacent excavations than passive reinforcement of the tunnel structure.

1. Introduction

With the rapid expansion of urban rail transit networks in China, excavation projects adjacent to existing shield tunnels have become increasingly common [1, 2]. Excavating the foundation pit leads to stress release in the surrounding soil, which imposes additional loads on nearby tunnels. For shield tunnels, this often results in longitudinal differential deformation, causing misalignment, joint openings, concrete cracking, and potential waterproofing failure and structural damage [3−5]. Accurately assessing the safety risks of shield tunnels in such scenarios is crucial, especially when the tunnel is directly beneath the excavation.

Previous studies have focused on the additional responses of shield tunnels to excavation-induced disturbances. From a mechanical perspective, these responses are essentially the interaction between the soil and tunnel structure under unloading conditions. Research on this issue often uses the elastic foundation beam theory to analyze tunnel responses through different representations of the soil-tunnel interaction [6 −10]. Various foundation models, such as Winkler [6−10], Pasternak [11−14], Vlasov [15, 16], and Kerr [17 −19], are used to describe soil-tunnel interaction. Among these, two-parameter models like Pasternak and Vlasov improve on Winkler’s model by incorporating shear effects while remaining simpler than the more complex Kerr model [15, 16].

The longitudinal structural analysis of shield tunnels is typically performed using the longitudinal equivalent continuous model (LECM) [20] and the longitudinal beam-spring model (LBSM) [21]. The LECM simplifies the tunnel as a homogeneous beam and adjusts the beam stiffness to account for circumferential joint influences. In contrast, the LBSM simulates segmental rings with short beams and models joint behavior with spring elements for bending, shear, and axial deformation. While the LBSM provides a more accurate simulation, the LECM is more straightforward and more widely used for tunnel response analysis [22, 23]. The shield tunnel can be modeled as either an Euler-Bernoulli (E-B) beam (for bending deformation) or a Timoshenko beam (for both bending and shear deformations) within the LECM framework [24, 25]. The E-B model primarily considers longitudinal bending deformation, which is simpler and widely used.