In this paper

based on the axisymmetric consolidation theory of unsaturated soil and equal-strain assumption

an analytical solution using the homogenization of boundary conditions and eigenfunction method is proposed to three-dimensional consolidation of unsaturated soil enhanced by vertical drains under instantaneous loading

in which the continuous permeable boundary conditions are properly introduced. Then

the proposed solution is verified by the special cases of double drainage boundary conditions. Finally

the solution is analyzed using examples and the results show that the proposed solution can be used to simulate the arbitrary distribution of permeability of the top and bottom boundary by setting reasonable interface parameters

which makes up for the problem that the permeability of the top and bottom boundary is between pervious and impervious condition or follows an asymmetric distribution. In addition

with a proper ratio of influence radius to drainage well radius and appropriate depth of vertical drain

the influence of vertical flows on the dissipation of excess pore pressures is small when the ratio of radial to vertical permeability coefficient is greater than two. Last but not the least

the above influence of excess pore pressures is more obvious with the enhancement of the permeability of the top and bottom boundary considering the vertical flows.