Electroosmosis and surcharge preloading represent two effective soil consolidation methodologies. Their combined application has been proven to be effective in shortening the consolidation period and mitigating the degradation of electroosmotic consolidation performance due to crack generation. In this study, an axisymmetric free-strain consolidation analytical model incorporating a continuous drainage top boundary was established. A semi-analytical solution was then derived utilizing Laplace-Hankel transform and boundary condition homogenization. The validity of the proposed solution was confirmed by comparing it with three cases documented in the existing literature. Additionally, a comparison with indoor model box test results demonstrated the rationality of setting the top boundary as a continuous drainage boundary. Parameter analysis revealed several key insights: firstly, under the free strain assumption, the spatiotemporal distribution of excess pore water pressure aptly captured the coupled effects of the radial electric field. Secondly, the combination of electro-osmosis and preloading technology significantly improved consolidation efficiency, with this effect becoming more pronounced as the applied voltage increased. Lastly, the general solution based on the continuous drainage boundary proved to be suitable for addressing the consolidation of soft soils enhanced by vertical drainage, applicable to real foundation consolidation problems with top boundaries exhibiting different permeabilities.

This paper presents a consolidation model for stone column-reinforced soft ground subjected to time-dependent loading under free strain condition. Smear effects and three types of loadings, namely, constant loading, ramp loading, and sinusoidal loading, are considered in the developed consolidation model, which is solved by a numerical method based on a partial differential equation solver. The applicability of the proposed consolidation model and the reliability of the numerical method are demonstrated and verified by well-predicting the consolidation behaviors of two practical engineering cases and one laboratory experiment. The verified model and the numerical method are then employed to investigate the effects of smear zone and time-dependent loading on consolidation characteristics of stone column-improved soft ground. The results indicate that the excess pore water pressure undergoes a sharp change at the interface between the smear zone and the undisturbed zone due to smear effects. The smaller the range of the smear zone, the faster the settlement of the composite foundation develops. The faster the loading rate, the faster the dissipation of excess pore water pressure and the faster the settlement develops. In addition, for the foundation subjected to sinusoidal loading, the higher loading frequency results in a larger amplitude corresponding to the excess pore water pressure and a smaller amplitude corresponding to the settlement of the soil.

Existing solutions for axisymmetric consolidation of viscoelastic soil are derived based on equal strain assumptions, which cannot account for soil deformation along the radial direction. This study develops a general solution for axisymmetric consolidation of viscoelastic soil under free strain conditions. The fractional -derivative Merchant model is introduced into the governing equations to account for the viscoelastic behaviour of soil around the vertical drains. The general solutions consisting of eigenfunctions and eigenvalues are proposed. Subsequently, the Laplace transform is utilized to convert the time variable tin partial differential equations into the Laplace complex argument p. Based on the boundary condition and continuity condition, the solution in the frequency domain is derived. By using Abate's fixed Euler Algorithm, the solutions in the time domain are obtained. The proposed solution is verified with finite element simulation and experimental data in the literature. Then, a series of parametric studies are conducted to investigate the influences of soil permeability, elastic modulus, viscosity coefficient, and fractional order on the axisymmetric consolidation of viscoelastic soils under free strain conditions.