2.5D ITM-FEM approach for the prediction of ground-borne vibrations from two parallel underground railway tunnels

In this contribution an efficient 2.5D coupled Integral Transform Method (ITM) – Finite Element Method (FEM) for the modelling of two parallel tunnels of arbitrary cross section embedded in a homogeneous halfspace is presented. Therein, the analytical ITM solutions of the dynamic wave equation allow to account for the infinite extension of the soil by satisfying the radiation condition. Fundamental solutions for the halfspace and the fullspace with cylindrical excavation are superposed to determine the dynamic stiffness matrix for a halfspace including two cylindrical cavities. The FEM enables to model complex, spatially limited structures and a part of the surrounding soil within a cylindrical outer boundary, on which both methods are coupled enforcing the compatibility conditions. The system is assumed length invariant and thus allows to formulate the total dynamic stiffness matrix of the overall model in the wavenumber frequency domain by a 2.5D approach. The proposed method is verified by comparison with analytical solutions for the homogeneous halfspace. Subsequently, the vibration response of the twin tunnel system on the ground surface due to a harmonic stationary load within the tunnel is investigated and compared to the results for a single tunnel. The effects of the diffraction and reflection of the elastic waves due to the insertion of the second tunnel are illustrated and the importance of including the interaction between the two tunnels for the prediction of the system response is highlighted.     «

In this contribution an efficient 2.5D coupled Integral Transform Method (ITM) – Finite Element Method (FEM) for the modelling of two parallel tunnels of arbitrary cross section embedded in a homogeneous halfspace is presented. Therein, the analytical ITM solutions of the dynamic wave equation allow to account for the infinite extension of the soil by satisfying the radiation condition. Fundamental solutions for the halfspace and the fullspace with cylindrical excavation are superposed to determ...     »