Based on the Fredlund's one-dimensional consolidation theory for unsaturated soil

one-dimensional consolidation of unsaturated soil subjected to an exponentially variable vertical load is investigated with a semi-analytical method. Elastic and visco-elastic soils with a finite thickness are considered while the soil top surface is penetrable and the bottom is impenetrable to water and air. Semi-analytical solutions are obtained for two soils with variable water and gas permeability coefficients and variable water permeability coefficient

respectively. A typical example result is given to analyze the changes of the excess pore-air pressure

excess pore-water pressure and sedimentation rate of soil under different conditions. The semi-analytical solutions are compared with those without considering the variation of permeability coefficient. It is shown that the permeability coefficient changes nonlinearly in the process of consolidation; when considering variable water permeability coefficient only

the dissipation of excess pore-air pressure is trivial

while excess pore-water pressure dissipates quickly; in the other situation

excess pore-air pressure and excess pore-water pressure dissipate significantly; and accordingly the sedimentation rate of soil also speeds up; the variation of gas permeability coefficients can substantially influence dissipation of excess pore-air pressure

with little effect on dissipation of excess pore-water pressure. The results are useful in analyzing the one-dimensional consolidation of unsaturated soils .