Analytical study of fractional viscoelastic transversely isotropic media along shallow-buried square tunnels

This paper presents an analytical method for calculating the mechanical characteristics of fractional viscoelastic transversely isotropic surrounding rock along a shallow-buried square tunnel. By employing the Schwarz alternating method, in conjunction with the complex function theory and Flamant’s elastic half-space solution, the analytical solution for a shallow-buried square tunnel in a transversely isotropic half-space is iteratively derived. The solution is then extended from the elastic space to the viscoelastic one using the Laplace transform. Finally, the inverse Laplace transform is applied to obtain the viscoelastic solution in the time domain. The presented analytical solution is validated by comparing the results with those from ABAQUS simulations. Subsequently, case studies are conducted to analyze the influence of various parameters on tunnel deformation and stress.