The stiffened deep cement mixing (SDCM) pile, as a new type of rigid–flexible composite pile, significantly enhances the vertical bearing capacity of traditional precast piles, thus holding broad application prospects in the substructure construction of nearshore bridges and marine energy structures. This paper investigates the vertical dynamic response of SDCM piles through theoretical derivation and parameter analysis. Firstly, based on elastic dynamics theory and the three-phase porous media model, vertical vibration control equations for both SDCM piles and fractional-order viscoelastic unsaturated soils are established. Secondly, theoretical derivations yield exact analytical solutions for the surrounding dynamic impedance, top dynamic stiffness, and dynamic damping of the SDCM pile. Finally, through numerical examples and parameter studies, the impact mechanisms of physical parameters in the SDCM pile–unsaturated soil dynamic coupling system on the top dynamic stiffness and dynamic damping of the SDCM pile are analyzed. The research results presented in this paper indicate that reducing the radius of the rigid core pile while increasing the thickness of the exterior pile has a positive effect on enhancing its vibration resistance. Additionally, increasing the length of SDCM piles contributes to improved vibration performance. However, an increase in the elastic modulus of the cement–soil exterior pile is detrimental to the vibration resistance of the rigid composite pile. On the other hand, an increase in the elastic modulus of the concrete core pile only enhances its ability to resist vibration under low-frequency load excitation. Furthermore, enlarging the soil saturation, decreasing the intrinsic permeability, and enlarging the soil relaxation shear modulus have a significant positive impact on improving the vibration resistance of SDCM piles. In contrast, changes in porosity have a negligible effect on the ability to resist vertical vibrations of SDCM piles.
