Analytical model for mechanical response of existing tunnel considering randomness of soil parameters under foundation pit excavation

With the continuous in-depth development of urban underground space, there has been a growing number of projects where newly-built foundation pits are adjacent to existing tunnels. The soil stress redistribution caused by excavation will lead to uneven deformation of the existing tunnels, posing a threat to the structural safety of the tunnels. To address this issue, this paper establishes a tunnel mechanical analytical model that considers the spatial variability of soil parameters. Combining the Pasternak foundation theory with the Mindlin solution, a two-stage solution strategy is designed to achieve accurate calculation of soil free-field displacement and tunnel additional deformation response. Furthermore, the random field theory is introduced to quantify the uncertainty of soil mechanical parameters. By means of Latin hypercube sampling and Cholesky decomposition to construct an autocorrelation matrix, a method for generating log-normal random fields is established. Taking a foundation pit project in Shanghai as an example, a systematic analysis is conducted on the mechanical response characteristics of the tunnel under foundation pit excavation disturbance. The results show that the maximum horizontal displacement of the tunnel has a linear increasing relationship with the length of the foundation pit and a monotonic decreasing relationship with the soil elastic modulus, while soil discontinuous surfaces significantly intensify the variability of its deformation. This paper combines the random field theory with the two-stage method to quantify the spatial variability of soil elastic modulus. The predicted tunnel deformation is in high agreement with the measured data, which can effectively capture the uneven deformation evolution of adjacent existing tunnels under foundation pit excavation disturbance and provide reliable theoretical support for the safety assessment of complex stratum structures.