Integral equation method for the pile groups and layer poroelastic half space to harmonic axial loads

The traffic load-train-railway track-soil foundation system is often modeled by considering the railway track as anelastic foundation beam supported by discrete concrete sleepers. Despite extensive research on environmental vibrations induced by traffic loading, previous studies have overlooked the impact of pore water pressure. To address this, we utilized Biot's theory and employed the Fourier transform to derive solutions in the time domain for a half-space scenario. Building upon this foundation, we employed the Transmission and Reflection Matrices (TRM) method to tackle the issue of environmental vibrations in layered, water-saturated poro-elastic half-spaces subject to traffic loading. Our analysis delved deeply into the effects of various soil layer parameters on ground vibration responses. These parameters included train speed, infiltration coefficient, porosity, fluid viscosity, shear wave velocity, and the characteristics of layered saturated soils. By examining these factors, we gained a more nuanced understanding of their influence on ground vibrations, thereby contributing to more accurate and comprehensive assessments of traffic-induced environmental vibrations.