Vlasov beam based solution for the cross-sectional deformations of rectangular tunnels in fissured ground considering three-dimensional discontinuous ground reactions

Rectangular tunnels under inclined fault dislocation are prone to experience bending, shearing and torsional displacement, which further leads to cross-sectional warping and distortion due to the coordination of the deformation. However, the existing beam models underlying ground-tunnel interactions fail to consider these cross-sectional deformations (CSDs), which inevitably underestimates the structural responses of tunnels. Thus, the paper presents a new Vlasov-beam-based ground-tunnel interaction model for rectangular tunnels in fissured ground. In the new model, the rectangular tunnel is regarded as a Vlasov beam with five CSDs incorporated on Winkler foundation, including bending, shearing, torsion, warping and distortion. Besides, new three-dimensional ground reactions are introduced considering the discontinuous ground-tunnel contact and the active and passive ground-tunnel interactions. A finite element equation for the new model is derived based on the principle of minimum potential energy. Moreover, the proposed method is verified by two case studies, and the superiority of the proposed method over the existing methods is illustrated. Finally, parametric analyses are conducted to explore the effect of critical variables on the deformation behaviors of rectangular tunnels, including cover depths, intersection angles and ground coefficients. Besides, the impacts of cross-section distortion, warping and torsion on tunnels are discussed. The proposed method contributes to a better understanding of structural responses of tunnels under ground fissure, facilitating the new design and countermeasure methods of the disturbed tunnel.