Transmission and reflection of P wave on the interface between elastic medium and saturated porous medium under nonlocal elastic theory

Accurate prediction of wave propagation properties in different media is essential for structural design and material performance evaluation in engineering. Classical elasticity theory has limitations in describing wave propagation, particularly when dealing with high-frequency waves and porous media. To address these shortcomings, this study investigated the transmission and reflection of P-waves on the dividing surface of elastic and saturated porous media based on the nonlocal elasticity theory. Based on the nonlocal medium theory and Helmholtz vector decomposition principle, a mathematical model of elastic wave transmission and reflection at the interlayer interface was established, and the correctness of the model was verified by numerical examples. The effects of incident frequency, incident angle, single nonlocal parameter, and interlayer nonlocal parameter on the amplitude ratio of wave transmission and reflection at the interface are analyzed under the nonlocal elastic theory. The results show that the difference between the amplitude ratios under the two theories gradually increases with the increase of the incident wave frequency, becoming particularly pronounced at higher frequencies. The amplitude ratio of the reflected P1 wave presents the least sensitivity to variations in incident angle under both theories, whereas the other wave types demonstrate comparable angular dependencies, with the maximum observed amplitude ratio difference reaching 33%. It is worth noting that the transmission and reflection patterns of waves at the interfaces are regulated by nonlocal parameters, and changes in the nonlocal parameters of the elastic medium have an extremely weak effect on the amplitude ratio of the transmitted waves. The findings of this study are of significance for the in-depth understanding of wave propagation behavior at the interfaces of different media, and provide new theoretical support and analytical tools for engineering applications such as composite material design, wave propagation prediction, and environmental vibration analysis.