Diffraction of Plane P-Waves by a Single-Layer Lined Tunnel in an Unsaturated Poroelastic Half-Space

Utilizing the unsaturated porous elastic media theory, the study investigates the scattering of plane P-waves by a single-layer lined 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 incident wave frequency, angle, saturation, and burial depth affect the surface displacement amplitude in a single-layer lined tunnel within an unsaturated soil half-space under P-wave incidence. Results indicate that saturation significantly influences the surface displacement amplitude. The maximum surface displacement amplitude in the single-layer lined tunnel at low saturation levels exceeds that observed at high soil saturation. The surface displacement amplitude inside the single-layer lined tunnel and on its left side varies sharply and remains high across different incident frequencies. Conversely, the surface displacement amplitude on the right side of the single-layer lined tunnel exhibits a relatively gentle change and is lower. This variation becomes more pronounced with increasing frequency. At a low wave frequency, the displacement amplitude of the single-layer lined tunnel decreases with the increase of the burial depth. When the incident wave frequency is high, the displacement amplitude of the single-layer lined tunnel exhibits a marked change with burial depth increment.