Seismic responses of P wave incident stratified unsaturated soil site under thermal effects

Drawing upon the fundamental principles of mixture continuum and thermodynamics, a planar P wave incident model for layered unsaturated soil is formulated. Employing the Helmholtz vector decomposition principle, the wave field within the layered unsaturated soil is analyzed using the transfer matrix method, accounting for the influence of thermal effects. A conversion matrix for the wave amplitude coefficients in layered unsaturated soil layers is derived in the bedrock-layered unsaturated soil system. An analytical solution is obtained for the seismic response in layered unsaturated soil under the action of thermal effect. Numerical calculations are employed to analyze the effect of thermal physical parameters, including temperature and solid relative heat, on ground motion within layered unsaturated soil. A substantial disparity exists in the magnification factors for surface displacement obtained under the modeling of the two theories with thermal effect and thermo-free effects, and the displacement amplifying coefficient of the layered unsaturated foundation under thermal effect is different from that of the homogeneous unsaturated soil foundation. The influence of solid relative heat on the displacement amplifying coefficient is primarily determined by the thermal stability of the soil, while the impact of the thermal expansion coefficient on this factor is intricately linked to the magnitude of solid relative heat within the soil. As the saturation grows, the horizontal and vertical displacement amplifying coefficient rises continuously. The orders of arrangement of soft and hard soil layers, temperature, and frequency have noteworthy effects on the displacement amplifying coefficient.