In a one-dimensional consolidation equation

the permeability coefficient is the function of matric suction in an unsaturated soil. The consolidation equation in one dimension is strongly nonlinear due to the presence of the permeability coefficient. As an analytic solution to nonlinear problems

a homolopy analysis method (HAM) is efficient in the selection of series basis functions and auxiliary linear operators

and easily make the solution convergence. In order to analytically solve the equation

the HAM was introduced in the present study. During the solution

the pore air pressure was assumed as the atmospheric pressure. The equations with two unknown variables were then reduced to dimensionless pore water pressure as only one basic unknown variable subjected to constant pore air pressure. Firstly

a governing equation in a dimensionless form was derived from the basic one-dimensional consolidation theory after the integration with the Richard empirical formula. The method was then used for a mapping technique to transfer the original nonlinear differential equations to a number of linear differential equations. These differential equations are not dependent on any small parameters

which is convenient to control the convergence region. After this transferring

a series solution to the equations was then obtained by the HAM after selection of auxiliary linear operator parameters. Finally

comparisons were carried out between the analytical solutions and the finite difference method in case of compacted kaolin. It can be found that the series solutions indicate that the pore water pressure increases firstly

and then decreases with the depth after the consolidation of the compacted kaolin. The results indicate that the analytical solution in the present study is reasonable.