Multimode tunnel deformation analysis under oblique normal faulting considering gap formation and horizontal intersection

Tunnels affected by normal faulting at an oblique angle are susceptible to multiple-mode deformation, which include not only the commonly discussed bending, shearing, and flattening modes but also torsional and warping deformation. Existing analytical ground–tunnel interaction models typically fail to consider torsion, flattening and warping and disregard the formation of gaps between the tunnel and the ground. To mitigate this gap, this paper proposes a new quasi-three-dimensional (3D) ground–tunnel interaction model grounded in generalized beam theory, which considers gap formation and an arbitrary 3D intersection angle with normal faults. In the proposed model, the tunnel was idealized as a pipeline resting on a Winkler foundation, with five deformation modes considered: shearing, bending, flattening, torsion, and warping. To capture the effects of varying ground behaviour, three-dimensional heterogeneous ground models were developed to represent active and passive ground resistance, discontinuous contact at the ground–tunnel interface, and spatially variable stiffness within shear zones. The corresponding finite element formulation is established through the application of the minimum potential energy principle. Through three case studies, the validity of the proposed approach was demonstrated, highlighting its advantages over traditional analytical methods. Finally, parametric studies were performed to investigate the influence of the intersection angle and shear zone on tunnel deformation behaviour. The proposed methods contribute to a better understanding of ground–tunnel interactions and complicated cross-sectional deformation under normal faults, which is beneficial for the design and protection of existing tunnels.