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.