Semi-Analytical Solution for the Vertical Vibration of a Single Pile Embedded in a Frozen Poroelastic Half-Space

The theory of vertical pile vibration is the essential basis for pile integrity determination and dynamic analysis. The pile vibration characteristics are inevitably affected when the surrounding soil is frozen due to the low environmental temperature. Therefore, the investigation of pile vibration considering the surrounding soil as a saturated frozen porous medium is of great importance. In this paper, an analytical model for vertical pile vibration was established by employing the theory of composite saturated porous media, that is, by simplifying the upper frozen soil layer as a homogeneous isotropic saturated frozen porous medium and the foundation soil beneath the pile as an elastic half-space subjected to the motion of a rigid disk. By employing the integral transform and variable separation method, analytical solutions for the proposed model were derived under the three-dimensional axisymmetric condition. The analytical model and its solutions were verified by comparing them with the existing solutions for an end-bearing pile embedded in a homogeneously frozen soil layer as well as for a saturated half-space. A parametric study was conducted by utilizing the proposed solutions, and the results indicated that the pile bottom stiffness, the freezing temperature, the shear modulus of the unfrozen soil, etc., had a significant influence on the dynamic responses of the vertical pile vibration in both the frequency and the time domains.