A Theoretical Calculation Method to Predict the Structural Response of an Existing Tunnel to a New Overlying Tunnel Considering Axial Force

Abstract

Investigation of the response characteristics of existing tunnels to new tunnels underneath is the basis for a rational evaluation of the serviceability of existing tunnels. Current studies usually regard the existing tunnel as the continuous beam placed on the Winkler or Pasternak foundation and ignore the existence of the longitudinal axial force and the mechanical weakening effect at the joint. Based on the Kerr foundation-Timoshenko beam model, this paper establishes a stress and deformation analysis model of an existing tunnel subjected to the construction disturbance of a new tunnel underneath by considering the influence of the axial internal forces of the tunnel. On this basis, the finite-difference solution of discontinuous beam-Kerr foundation considering joint weakening effect is further derived. Published engineering measured data and previous theoretical methods are reference for comparison and validation, and the influence of the model parameters on the response characteristics of the existing tunnel is further discussed. Finally, a prediction formula for the maximum vertical displacement of the existing tunnel under the construction disturbance of the new tunnel underneath is developed. The results confirm that the calculated results of the theoretical analytical models are in good agreement with the measured data, but the calculated results of the model considering axial force and joint weakening are closer to the measured values. When the relevant parameters in the proposed models are fixed, the proposed model can be simplified to the existing analytical model. With the increase of ground loss rate and elastic modulus of soil, the deformation and internal force of the existing tunnel increases, but the distribution form of deformation and internal force remains unchanged. Increase in the depth of the new tunnel and the axial force of the existing tunnel can effectively minimize the structural response of the existing tunnel. Increasing the intersection angle between the two tunnels can effectively reduce the deformation of the existing tunnel but increase the internal force of the tunnels. The established prediction formula has good engineering applicability, which can provide some support for engineers to quickly predict the structural response of existing tunnels induced by the construction of new tunnels.