Diffraction of plane P waves by a circular unlined tunnel in an unsaturated poroelastic half-space

Purpose In the study of circular unlined tunnel, scholars commonly simplify the foundation to be single-phase or saturated soil. However, such conditions are relatively rare; unsaturated soil remains the predominant state in many areas, particularly in arid and semi-arid zones. Consequently, investigating wave scattering by tunnels in unsaturated soils has significant practical. Methods Based on the unsaturated porous elastic media theory, the study investigates the plan P-waves scattering of an unlined tunnel within an unsaturated half-space. The analysis employs the Fourier-Bessel series expansion for wave functions for this purpose. Through numerical examples, this study analyzes how physical and mechanical parameters like wave frequency, angle, saturation and burial depth affect the surface displacement amplitude in an unlined tunnel within an unsaturated soil half-space under P-wave incidence. Results The results indicate that the saturation has a significant effect on the change of surface displacement amplitude, and the maximum surface displacement amplitude under unsaturated unlined tunnel is greater than the maximum surface displacement amplitude caused by soil saturation. Under different incident frequencies, the amplitude of surface displacement inside and on the left side of the unlined tunnel changes very sharply and the amplitude is high. The amplitude of surface displacement on the right side of the unlined tunnel is relatively flat and the amplitude is low. This change is more significant when the frequency increases. When the frequency is high, the displacement amplitude of the circular unlined tunnel decreases with the increase of the buried depth. When the incident wave frequency is low, the displacement amplitude of the circular unlined tunnel exhibits a marked change with burial depth increment. Conclusions This conclusion promotes the application of fluctuation theory in geotechnical engineering seismic resistance, seismic exploration, and other engineering practices and has significant practical value and guiding significance for actual engineering.