A Study on the Longitudinal Deformation of the Underlying Oblique Crossing Tunnel Induced by Foundation Excavation

Current research on analytical solutions for tunnel longitudinal deformation due to foundation pit excavation predominantly focuses on scenarios where the pit is perpendicular to the tunnel axis, with limited exploration of oblique intersection cases. This study employed the layer-wise summation method, grounded in the Mindlin solution, to determine the additional stress in the tunnel resulting from foundation pit excavation. The focus was on situations where the tunnel axis crosses the foundation pit axis at an oblique angle and where the tunnel is beneath the side wall of the foundation pit. A model was introduced to address the synchronized deformation of shield tunnel segment rings due to rotation and dislocation. A variational control equation, derived from the principle of minimum potential energy, evaluates longitudinal displacement, the ring-to-ring rotation angle, and tunnel dislocation. Two batches of engineering examples were assessed for the purposes of calculation and validation. The study reveals that the longitudinal deformation of tunnels intersecting at an oblique angle adheres to a Gaussian distribution and is asymmetrical relative to the center of the foundation pit excavation. In cases where the foundation pit and tunnel intersect obliquely, particularly when the tunnel is not directly below the pit, discrepancies between calculated and measured values can reach up to 5%. By contrast, not accounting for the oblique intersection can result in discrepancies of up to 300%. Therefore, the proposed method of calculation delivers a more accurate portrayal of the actual deformation behavior of tunnels in engineering practice.