Based on the wave propagation theory in saturated porous media and saturated frozen porous media

this study investigates transmission and reflection of P 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 P 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 P wave is significantly lower than that in the saturated frozen soil medium. Therefore

a critical angle arises when the P 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 P wave. Variations in temperature and cementation parameters of the saturated frozen soil medium significantly affect the transmission and reflection amplitude ratios of wave.