Tunnelling-induced lateral pile response: a coupled analytical model accounting for tunnel–soil interaction

Tunnelling in close proximity to existing pile foundations induces significant lateral pile responses, compromising structural integrity. Current two-stage analytical methods decouple this problem by first computing free-field soil movements and then imposing them on the pile, inherently neglecting the interactive effect of tunnel lining stiffness — an assumption that becomes invalid at small pile–tunnel separations. This study presents a coupled tunnel–soil–pile interaction (TSSI) analytical model that explicitly incorporates tunnel stiffness. Individual stiffness equations are established for the pile, soil, and tunnel, with force equilibrium and displacement compatibility enforced simultaneously at both the pile–soil and tunnel–soil interfaces. Soil continuity is accounted for via Mindlin's solution, with a regularization technique resolving the inherent singularity. The model is validated against existing analytical solutions, centrifuge test data, and three-dimensional finite-difference simulations under displacement- and force-controlled boundary conditions. Parametric analyses reveal that lateral pile response is governed by three parameters: greenfield ground deformation, structure-to-soil stiffness ratio, and tunnel stiffness. Compared with conventional two-stage methods, the proposed model predicts up to 20–40% larger maximum negative bending moments for closely spaced configurations. A simplified zoning screening criterion — distinguishing crown, near-field, and far-field zones — is established to guide engineers on when the TSSI approach is necessary.