Analytical determination of the dynamic response of layered saturated frozen foundation to moving loads under plane strain conditions

Based on the theory of solid porous media with pores, a calculation model of two-dimensional layered saturated frozen soil foundation is established. The study focuses on the dynamic response of layered saturated frozen soil medium placed on an impermeable rigid bedrock when subjected to a uniform surface moving strip load in motion. Firstly, the governing equation of saturated frozen soil is established. Then, the Helmholtz vector decomposition theorem, coordinate transformation, and Fourier integral transformation are used to decouple the governing equation of saturated frozen soil, and the general solution of the potential function is obtained, and the general solution of the stress and displacement of each layer of saturated frozen soil is derived. Using the transfer and reflection matrix (TRM) method, the semi-analytical solution of layered saturated frozen soil medium in the frequency domain is derived. Finally, the dynamic response of each phase of the saturated frozen soil in the time domain is obtained by the fast Fourier transform. After verifying the accuracy of the solution by comparing the model degradation with the existing literature, the effects of soil shear modulus, load moving speed, temperature, porosity, contact parameter, and frequency on the dynamic response of homogeneous foundation, soft interlayer foundation, and hard interlayer foundation are analyzed in detail. The results show that the stratification of the foundation is of great significance for accurately evaluating the dynamic response of saturated frozen soil.