During pile installation, construction disturbances alter soil mechanical properties near the pile, significantly affecting the dynamic response of the pile. This paper develops a three-dimensional (3D) analytical model to investigate the vertical dynamic response (VDR) of a pile in radially inhomogeneous saturated soil. Firstly, by employing the separation variable method and incorporating the continuity and boundary conditions of the soilpile system, the exact solution of the whole system in the frequency domain was derived. Subsequently, the timedomain velocity response under semi-sinusoidal vertical excitation is obtained using Fourier inverse transform and the convolution theorem. The accuracy and superiority of the proposed solution were validated through comparison with previous analytical solutions. Finally, the developed solution is then used to examine the impact of parameters of saturated soil and pile on the VDR of a pile. The results demonstrate that the proposed saturated model better captures the VDR of a pile in radially inhomogeneous saturated soil compared to the single-phase model. The VDR of a pile is significantly influenced by the pore water, porosity, disturbed degree and range of the saturated soil, as well as the elastic modulus of the pile.

This work presents an analytical method for determining vertical dynamic impedance and displacement response factor of a rigid cylindrical foundation embedded in unsaturated poroelastic soils. The foundation is assumed to be perfectly boned to its surrounding soil and its overlying half-space of unsaturated poroelastic soil, subjected to harmonic vertical loadings. The soil surrounding the circumference of the cylinder is modeled as a number of infinitely thin horizontal soil layers. Based on the Biot-type soil constitutive model, the equations governing the interaction of unsaturated soils with the cylindrical foundation are derived. Solutions are obtained by solving ordinary differential equations transformed from partial differential governing equations using the Hankel transform. The proposed solutions are verified against existing solutions of benchmark elastodynamic problems for embedded cylindrical foundations in dry and saturated soils. Using the derived solutions, several influencing parameters defining the stiffness and mass of the foundation system are examined to investigate the dynamics of the foundation interacting with it adjacent soils. It is concluded that the dynamic displacement response factor is sensitive to soil saturation. It is believed that the proposed solution should be beneficial to dynamic design with cylindrical foundations embedded in unsaturated soils.

Subgrades constructed from loess-a loose and porous material-demonstrate significant compressibility and collapsibility. To study these properties of loess subgrades, this article proposes a vertical vibration compaction method (VVCM) that provides a reliable simulation of field compaction and investigates the factors influencing the deformation characteristics of loess subgrade by VVCM-prepared specimens. The results show that the correlation between the compression modulus of loess samples prepared by VVCM and that of core samples obtained from the construction site is more than 85 %. In addition, the deformation resistance of the VVCM sample is better than that of the traditional quasistatic compaction method (QSCM) sample. Under the same compaction factor and water content, the compressive modulus of VVCM sample is at least 10 % higher and its collapsibility coefficient is 10 % lower than that of QSCM sample. With the increase in compaction factor, the compression modulus increases and the collapsibility coefficient decreases, indicating improved resistance to compressive deformation and reduced susceptibility to collapse in loess. With the increase in water content, the compression modulus and collapsibility coefficient decrease, reflecting greater compressibility and increased collapse resistance in loess.