Analysis of Rayleigh-type surface wave propagation in a self-reinforced layer embedded overlying a sandy semi-infinite half-space

This work explores a complex system consisting of two separate layers: an upper layer consisting of a self-reinforced medium and a bottom layer made up of a half-space, especially a dry sandy medium. The surroundings that Rayleigh waves travel through are these two layers. Analytical solutions for the self-reinforced layer and the dry sandy half-space have been methodically derived using the variables separation method approach. After that, dispersion relation of the system has been found within a predetermined range. The computational capacity of MATHEMATICA software has allowed for the quantitative illustration of some important Rayleigh wave features. The characteristics give a thorough knowledge of wave behaviour in such layered material and include phase velocity, group velocity, and wave attenuation. The results draw special attention to the important ramifications for a range of real-world applications, especially in the areas of military infrastructure and coastal marine constructions. The design and stability of foundations subjected to wave-induced forces in marine structures depend heavily on an understanding of Rayleigh wave behaviour. The knowledge gained can be applied to military settings to improve the resilience and lifespan of structures by designing them to withstand the impact of vibrations and waves. Thorough investigation and findings of this study deepen our understanding of wave mechanics in layered media and provide important insights for engineering applications where complicated geological features and wave interactions are crucial. Emphasizing the wider significance and application of the research findings, this study not only increases theoretical knowledge but also offers helpful guidance for the design and analysis of structures in difficult situations. The study ends with conclusions and an outlook on possible future research directions.