An analytical solution for deforming twin-parallel tunnels in an elastic half plane

• Published in: International journal for numerical and analytical methods in geomechanics 2015-04, Vol.39 (5), p.524-538
• Main Authors: Fu, Jinyang, Yang, Junsheng, Yan, Li, Abbas, Syed Muntazir
• Format: Article
• Language: English
• Subjects: analytical solution; Complex variables; Deformation; Elastic deformation; Gain; ground movement; Grounds; Half planes; interaction; Mathematical analysis; Mathematical models; Tunnels (transportation); twin tunnels
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.2322

Summary The interaction between twin‐parallel tunnels affects the tunnelling‐induced ground deformation, which may endanger the nearby structures. In this paper, an analytical solution is presented for problems in determining displacements and stresses around deforming twin‐parallel tunnels in an elastic half plane, on the basis of complex variable theory. As an example, a uniform radial displacement was assumed as the boundary condition for each of the two tunnels. Special attention was paid to the effects of tunnel depth and spacing between the two tunnels on the surface movement to gain deep insight into the effect of the interaction between twin‐parallel tunnels using the proposed analytical approach. It is revealed that the influence of twin tunnel interaction on surface movements diminishes with both the increase of the tunnel depth and the spacing between the two tunnels. The presented analytical solution manifests that, similar to most of the existing numerical results, the principle of superposition can be applied to determine ground deformation of twin‐parallel tunnels with a certain large depth and spacing; otherwise, the interaction effect between the two tunnels should be taken into account for predicting reliable ground movement. Copyright © 2014 John Wiley & Sons, Ltd.