Explicit analytical solutions for surrounding rock stress of a shallow buried tunnel considering seepage effect

Abstract

Because of difficulty in mathematic solution, analysis of surrounding rock stress of shallow buried tunnel considering seepage force has always been a difficult problem. Seepage body force is introduced into governing equations and boundary conditions of an elastic plane. Then traditional complex variable method is expanded for the analysis of plane strain problems in relation to an elastic plane considering seepage effect. Subsequently, explicit analytical solutions of seepage field and stress field of a shallow underwater tunnel excavated in an elastic rock mass with uniform distribution of pressure and total water head on tunnel boundary as well as stress free on ground surface are derived. The analytical solutions are validated by numerical simulations and can be used to analyse stress variations of surrounding rock mass under seepage effect. Based on an example, influence of buried depth and water head difference between ground surface and tunnel boundary on the circumferential effective stress around the tunnel are discussed. It is found that directions of major and minor principal stress will exchange with each other with increase of total water head difference between ground surface and tunnel boundary, and stress distribution around tunnel tend to be uniform with increase of buried depth.