Analytical Solution of SH-Wave Scattering by Arbitrary Shape Tunnels in Nonlocal Fractional-Order Viscoelastic Half-Space

In this paper, an analytical solution for the scattering of plane SH waves by arbitrarily shaped tunnels in a nonlocal fractional-order viscoelastic half-space is presented by using complex variable theory. First, the complex dynamical boundary science problem is simplified by introducing a conformal mapping function that maps an arbitrarily shaped tunnel to a unit circle. Then, a fractional-order viscoelastic model is introduced to portray the viscoelastic properties of the soil, and nonlocal effects, such as the particle scale of the soil, are considered in conjunction with nonlocal theory. The wave function expansion method constructs the scattered field displacement potential function that satisfies the zero-stress condition at the ground-surface boundary. Finally, the effects of incident wave property, tunnel shape, and soil behaviors on the dynamic stress concentration factor of the tunnel are analyzed using numerical examples. The results show that the incident-wave frequency, tunnel shape, and soil properties have a significant effect on the distribution of dynamic concentration factors in tunnels, noncircular tunnels have noticeable scattering and interfering effects on plane SH waves, and the distribution of dynamic stress concentration factors on the inner surfaces of the tunnel is more complicated.