Analytical Method for Longitudinal Response of Shield Tunnels Under Arbitrary Loading Based on the Kerr Foundation Model

ABSTRACT The operational safety of existing shield tunnels is increasingly threatened by construction activities in the proximity domain. Accurate prediction of their longitudinal response is thus of great importance. Previous research usually adopted the Winkler or Vlasov foundation models coupled with Euler‐Bernoulli beams to establish analytical solutions. However, the solutions were tailored solely to and available for a specific disturbance scenario, which required an extension when encountering diverse ones. In addition, they are insufficient to capture the behavior of the soil continuum. To address these issues, this paper presents a comprehensive model by integrating the more advanced three‐parameter Kerr foundation model with Timoshenko beam theory. By introducing the state‐space method, a unified solution procedure is developed for predicting the tunnel response. The method's validity and versatility are demonstrated through comparisons with field measurements and existing solutions under three distinct scenarios: new tunnel undercrossing, adjacent pit excavation, and surface surcharge. Finally, a sensitivity analysis for the excavation case examines the influences of soil elastic modulus, pit‐tunnel angle, and burial depth. The proposed framework offers a unified and efficient approach applicable to various disturbances, providing an efficient tool for the prediction of shield tunnel deformation.