Seismic ground motion study of layered site of saturated frozen soil under P-wave incidence

Abstract

A two-dimensional model of layered saturated frozen soil over bedrock is developed based on porous media theory, focusing on the seismic response to P-wave incidence. The governing equations for saturated frozen soil are formulated and decoupled using the Helmholtz vector decomposition theorem, yielding a general solution for the potential function. Through the application of the transfer matrix method and interface boundary conditions, an analytical solution for surface displacement in saturated frozen soil is derived. This solution is validated against existing literature. The study comprehensively examines the effects of incident frequency, angle, the surface layer's porosity, medium temperature, cementation parameter, contact parameter, soil stiffness, and surface layer thickness on the seismic response. The key findings are as follows: A layered foundation model demonstrates the seismic effects of stratification on ground motion. Compared to uniform foundations, layered models better represent real-world conditions and reveal the amplification and frequency-dependent characteristics of soil stratification under the idealized analytical framework of this study. For constant incident frequency or medium temperature, the peak horizontal displacement amplification factor is higher in an upper-soft and lower-hard foundation compared to an upper-hard and lower-soft foundation. Horizontal and vertical displacement amplification coefficients exhibit periodic fluctuations with variations in soil thickness. High-frequency seismic waves induce pronounced fluctuations in the horizontal displacement amplification coefficient. Under the idealized analytical framework, the vertical displacement amplification coefficient tends to exceed the horizontal one across all frequencies. These findings provide theoretical insights but require validation through field measurements and numerical simulations to assess their applicability to real-world conditions.