A Novel Approach to Analyzing the Mechanical Response of Pipe Umbrella Support in Shallow Buried Tunnels Considering Construction Characteristics

A novel analytical approach based on the state‐space method (SSM) is proposed to facilitate the rapid and accurate analysis of the mechanical behavior of pipe umbrellas in shallow‐buried tunnels. First, a mechanical analysis model and its governing equations are developed based on the Winkler elastic foundation beam theory, incorporating key construction‐related factors such as the lag effect of primary support, differential stress release in the surrounding rock, and the elasto‐plastic behavior of the stratum. The governing equations are then transformed into a concise matrix form using the SSM and solved based on matrix theory and the continuity conditions between adjacent beam segments. Analytical solutions for deformation and internal forces at any cross‐section of the pipe umbrella are derived under the nonlinear interactions among the pipe umbrella, surrounding rock, and primary support. The accuracy and applicability of the proposed method are verified through comparisons with existing field monitoring data, analytical solutions, and numerical simulation results from other researchers. On this basis, taking the Aketepu Tunnel as a case study, the influences of the surrounding rock stiffness ahead of the tunnel face, excavation footage, steel pipe diameter, and other factors on the deformation and internal forces of the pipe umbrella were investigated, and a recommended design scheme was proposed accordingly. The scheme was subsequently applied in the field, and monitoring results showed that the maximum deformations at two sections were 26.1 and 22.3 mm, respectively, both within the acceptable limits for surrounding rock deformation control.