Dynamic Response of a Shallow Circular Tunnel in a Thermoviscoelastic Medium under P-Wave Incidence

This study examines the scattering mechanism and dynamic response of plane P-waves in a thermoviscoelastic half-space containing an underground circular tunnel. Based on the thermoviscoelastic theory, the Helmholtz vector decomposition theorem with the Fourier–Bessel series expansion method is applied, allowing for an analytical solution. The influence of relaxation time, incident angle, medium temperature, solid-phase specific heat capacity, and burial depth on surface displacement amplitude and dynamic stress concentration factor (DSCF) were analyzed. Results indicate that higher incident frequencies make the displacement patterns more complex and reduce the DSCF. Relaxation time and incident angle exhibit strong frequency dependence, affecting the displacement distribution in both horizontal and vertical directions. The DSCF shows spatial heterogeneity along the tunnel periphery. Under high frequencies, elevated temperature decreases, while higher solid-phase specific heat capacity enhances the displacement and DSCF. Increasing burial depth decreases the surface displacement but induces DSCF oscillations. As the buried depth ratio increased from 2 to 10, the maximum reduction in horizontal and vertical displacement reached 22.32% and 23.60%, respectively. Under high-frequency excitation, the corresponding reductions reached 18.61% and 6.53%. These findings provide theoretical support for seismic performance evaluation and structural optimization in thermoviscoelastic environments.