Analytical solutions for mechanical response of circular tunnels with double primary linings in squeezing grounds

Multi-layered primary linings have been proved to be highly effective for tunneling in severe squeezing grounds. But there still has not existed well-established design method for it. Basically, there are two main critical problems in this method, including determinations of allowable deformation and distribution of support stiffness. In order to address such problems, an attempt to investigate the mechanical response of a circular tunnel with double primary linings is performed in this paper. Analytical solutions in closed form for stresses and displacements around tunnels are derived. In addition, the effectiveness and reliability of theoretical formulas provided are well validated by using the numerical method. Finally, based on the analytical solutions, a parametric investigation on the effects of allowable deformation and distribution of support stiffness on tunnel performance is conducted. Results show that the rock pressure and displacement are significantly affected by these two design parameters. It can be found that rock pressure decreases as either allowable deformation increases or stiffness of the first primary lining decreases, but rock displacement shows an opposite trend. This paper can provide a useful guidance for the design of multi-layered primary linings.