Deflections of Adjacent Underground Tunnel Induced by Excavation Based on Kerr Foundation Model

Abstract

The soil unloading effect caused by the adjacent excavation will influence both the uplift and the deformation of the adjacent existing tunnel, and even interfere with the normal operation of the tunnel. A simplified calculation method for the longitudinal deformation of the underlying tunnel caused by foundation pit excavation is proposed. The tunnel is simplified into an infinitely long Euler-Bernoulli beam resting on a three-parameter Kerr foundation model. The difference method is combined with the boundary conditions at both ends of the tunnel to obtain the longitudinal deformation difference decomposition of the tunnel. The accuracy of the proposed method is proved by comparing it with the finite element simulation method and some cases study. Compared with the tunnel simplified as the Euler-Bernoulli beam which is placed upon the existing Pasternak foundation model, the Kerr foundation model has more advantages. As the elastic modulus of soil mass and the depth of tunnel axis increase, the longitudinal deflection and the inner force of the tunnel will decrease. The inner force of the tunnel will increase with the increment of the stiffness of the tunnel.

Keywords

• excavation
• existing tunnel
• euler-bernoulli beam
• kerr foundation model
• finite different method