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.

In this study, electro-osmotic consolidation considering smear effect and free strain under cyclic loading was investigated. The analytical solution of radial consolidation of electroosmosis-vacuum-surcharge combined preloading is derived by using the Bessel function and eigenfunction methods. Subsequently, the effectiveness of the proposed method is validated through comparison with existing numerical solutions. Based on the derived solutions, the influence of the smear effect, applied voltage, vacuum pressure, and cyclic loading on soil consolidation characteristics was analyzed. The results showed that the smearing effect slows the rate of consolidation, but the final average consolidation and negative excess pore water pressure are enhanced. Compared with only cyclic loading, the combined effect of electroosmosis, vacuum, and surcharge preloading enables the soil to achieve higher strength and consolidation. When the effect of electroosmosis alone on reinforcing low-permeability soils is not significant, the combination of electroosmosis with vacuum preloading helps enhance the soil reinforcement effect.

The combining of electroosmotic, vacuum, and surcharge preloading is an emerging technique for soft foundation treatment. Considering smear effects and free strain, an analytical solution for the radial consolidation of combined electroosmotic, vacuum, and surcharge preloading was derived based on the characteristic function method and Bessel function. The correctness of the proposed solution was verified by comparing with existing solutions and numerical results. On this basis, the influence of smear effects, vacuum pressure, surcharge load, and applied voltage on the consolidation characteristics of soil was further analyzed. The results showed that when the electroosmosis permeability coefficient of the undisturbed zone was greater than that of the smear zone, the excess pore-water pressure at the interface between the smear zone and the undisturbed zone increased in the early stage of consolidation owing to the electroosmotic effect. Vacuum pressure had a great influence on soil consolidation in the smear zone, while applied voltage had a great influence on the consolidation of soil in the undisturbed zone.