Abstract: Based on the wave propagation theory in saturated porous media and saturated frozen porous media, this study investigates transmission and reflection of P₁ waves at the interface between saturated soil and saturated frozen soil. Using the Helmholtz vector decomposition principle and considering the boundary conditions at the interface between saturated soil and saturated frozen soil, analytical solutions for the transmission and reflection amplitude ratios of P₁ waves from the saturated soil layer to the interface with saturated frozen soil layer is obtained. Through numerical calculations, the influences of incident frequency, incident angle, permeability of the saturated soil medium, cementation parameters, temperature, and contact parameters of the saturated frozen soil medium on the transmission and reflection amplitude ratios at the soil interface were analyzed. The research findings indicate that the propagation velocity of the incident P₁ wave is significantly lower than that in the saturated frozen soil medium. Therefore, a critical angle arises when the P₁ wave propagates from the saturated soil medium to the saturated frozen soil medium, and the amplitude ratio undergoes a sudden change when the incident angle equals the critical angle. The permeability of saturated soil has a minor impact on the transmission and reflection amplitude ratios of wave but has a prominent effect on the reflected P₂ wave. Variations in temperature and cementation parameters of the saturated frozen soil medium significantly affect the transmission and reflection amplitude ratios of wave.

Key words: saturated soil, saturated frozen soil, wave propagation, reflection amplitude ratio, transmission amplitude ratio