Stress and Displacement Fields of Elliptical Tunnels in Fractional Order Viscoelastic Transversely Isotropic Medium

ABSTRACT This paper presents the fractional viscoelastic solutions of transversely isotropic surrounding rock for deeply buried elliptical tunnels by using the Fourier series fitting, complex function method, and conformal transformation technique. The elastic–viscoelastic correspondence principle and the Laplace transformation technique are introduced to derive the solutions, and the accuracy of the theory in this paper is verified by comparing with that in existing literature. Numerical examples are designed to analyze the accuracy of the series fitting terms, the influence of the transversely isotropic parameters, the shape of the tunnel, and the lateral pressure coefficient on the mechanical response of the surrounding rock of the deeply‐buried tunnel, providing useful suggestions for the practice of tunnel engineering.