Dynamic response of a fractional layered viscoelastic foundation with an embedded circular tunnel subjected to underground moving loads

This paper presents an analytical solution for the vibration of a fractional layered viscoelastic foundation containing an embedded circular tunnel subjected to underground moving loads. The tunnel structure is simplified as a viscoelastic lining with linear hysteretic damping, while the surrounding ground is modeled as a layered viscoelastic medium described by the fractional Zener model. The wave function expansion method is employed to construct the scattered wave fields in the layered fractional viscoelastic medium and the lining structure. The unknown coefficients in the scattered wave fields are then solved through the displacement and stress continuity conditions at the tunnel-soil interface. On this basis, a systematic parametric study is conducted to investigate the effects of the fractional order, relaxation time factor, and soil profile characteristics on the spatial and temporal distribution of the ground dynamic responses. The results indicate that the fractional viscoelastic model can effectively capture the frequency-dependent attenuation characteristics of ground vibrations. The fractional order and relaxation time factor exhibit a profound modulating effect on the ground vibration responses, and their variations directly govern the dissipation efficiency and propagation range of the vibration energy.