This paper presents semianalytical solutions to the consolidation of drainage well foundations in unsaturated soils with radial semipermeable drainage boundary subjected to time-dependent loading, and radial boundary condition is employed to illustrate the smear effect. First, the governing equations of excess pore-air and pore-water pressures are transformed into equivalent partial differential equations. Afterwards, the final semianalytical solutions of the equations based on the free strain assumption are obtained by introducing the Bessel functions and Laplace transform techniques. The inverse Laplace transform is performed to derive the solutions in the time domain by means of Crump's method. Furthermore, the solutions are verified to be reliable by the regressive solutions and the numerical solutions by finite difference method (FDM). Finally, instantaneous loading, ramp loading, exponential loading, and sinusoidal loading are adopted to illustrate the changing regularity of excess pore-air and pore-water pressures against the ratios of air-water permeability, radial semipermeability coefficient parameters, and loading parameters.

In real practice, the construction of drainage wells is always accompanied by smear effect, whereas it is scarcely discussed in the field of unsaturated soils. In this case, on the basis of the widely-accepted consolidation theory for unsaturated stratum by Fredlund, this paper studies the equal strain consolidation characteristics of unsaturated foundation with drain wells affected by smear effect under time-varying loading (exponential loading as a case). Firstly, with the consideration of corresponding boundary conditions, the governing equations under the equal strain hypothesis are obtained. Afterwards, decoupling process, constant variation method and Fourier series expansion theory are utilized to get the analytical solutions, which are then verified to be credible by means of the finite difference method. Finally, the consolidation patterns of the drainage well foundation modeling in unsaturated soils are studied against hydraulic coefficients, modeling sizes and loading parameter. It reveals that the smear effect can significantly restrain the consolidation process of the foundation by drain wells, while different parameters will lead to various results.