Study on the Dynamic Response Characteristics of Plane P-Waves in Free-Field Sites of Unsaturated Soils

Based on the wave theory of unsaturated porous medium, this paper establishes a free-field model of unsaturated soil with a thickness of H overlying a horizontal, uniform, semi-infinite bedrock layer under P-wave incidence. Drawing upon the Helmholtz principle, the wave field within an unsaturated soil site is examined, and the analytical solutions for the dispersion characteristics of bulk waves and the attenuation coefficient are derived. Through numerical simulations, the dispersion phenomenon induced by plane P-wave incidence is analyzed, and the effects of frequency, angle of incidence, saturation level, porosity, and soil layer thickness on the amplitude attenuation coefficient in an unsaturated soil free-field under P-wave excitation are discussed. The findings show that within a specific frequency range, P₁-wave and S-wave in an unsaturated soil free-field exhibit no dispersion characteristics, whereas P₂-wave and P₃-wave demonstrate distinct dispersion behavior. The amplitude attenuation coefficient generally rises with increasing frequency and initially increases before decreasing as the incident angle grows. Simultaneously, the change of amplitude attenuation coefficient with saturation, porosity and soil thickness shows different trends in different incident angle ranges. However, at most incident angles, the amplitude attenuation coefficient is greater than 1, indicating that seismic waves usually produce vibration amplification effect, and vibration attenuation effect occurs only when the incident angle is close to vertical.