Integrated Viscoelastoplastic and Finite Element Analysis of Tunnel–Track Interaction in Weak Rock: Influence of Geometry and Dynamic Loading

Abstract

Underground railway systems provide a vital solution to urban spatial constraints, yet their construction in weak rock formations poses severe geotechnical challenges. Issues such as ground settlement and tunnel deformation under dynamic train loads can compromise structural integrity and operational safety. This study addresses these complexities by integrating a novel two-dimensional Finite Element model with a complementary viscoelastoplastic analytical framework. This dual approach effectively correlates global dynamic responses with localised continuum effects. A detailed parametric study reveals that axle loads exert a more pronounced effect on the track structure than the tunnel lining, increasing track displacement by 23.9% compared to only 12.3% for the lining. At high operational speeds, the numerical analysis identifies a stability plateau attributed to radiation damping, while the analytical model predicts a conservative upper-bound response. The analysis further demonstrates that increasing the Young’s modulus of the surrounding rock beyond 1000 MPa reduces vertical displacement to negligible levels. Geometrically, while circular cross-sections offer superior radial confinement, they exhibit an 18.5% increase in localised invert settlement compared to horseshoe profiles due to a punching shear mechanism. By establishing a mechanical hierarchy, this study provides engineers with a strategy to use analytical methods for safety baselines and numerical modelling for realistic serviceability limits.