Soils are commonly existing in unsaturated condition on the earth’s surface. Compared with the classic Biot consolidation theory for saturated soils

the consolidation theory of unsaturated soils is still largely unexplored. Based on the Fredlund’s double stress variables consolidation theory of unsaturated soils

this paper derives the governing equations of axisymmetric fully-coupled consolidation of unsaturated soils under varying loadings

by removing the assumption that the total stress remains unchanged during the consolidation. With the aid of Laplace-Hankel transform

the governing equations are converted into ordinary differential equations by eliminate the variables r and t. The extended precise integration method is further applied to solve these equations and obtain solutions of layered unsaturated soils in the transformed domain. The actual solutions are acquired by the inverse Laplace-Hankel transform technique. The feasibility of the presented results is further verified by comparing with those of degenerated saturated soils in the existing literature. At last

three numerical examples are provided to investigate the influence of varying ramp time T0

varying coefficients of the water volume change due to the net normal stress and the stratification on the consolidation characteristics of unsaturated soils.