Analytical solution of shallow arbitrarily shaped tunnels in fractional viscoelastic transversely isotropic strata

An analytical method is proposed to obtain the stress and displacement around shallow arbitrarily shaped tunnels excavated in viscoelastic transversely isotropic strata. Firstly, combined with the fractional calculus theory, the fractional viscoelastic half-plane solution is obtained by displacement modification. Then, based on the solution of the half-plane, the Schwartz alternating method and the conformal mapping technique are introduced to obtain the solution of the fractional viscoelastic arbitrarily shaped shallow tunnels. According to the proposed theory, a MATLAB program is developed, and the accuracy of the theory is proved by degraded comparison with results of the existing literature and finite element software ABAQUS. Finally, numerical examples are designed to discuss the influence of tunnel shapes, transverse isotropy and viscoelastic parameters on the boundary stress and displacement around shallow arbitrarily shaped tunnels.