Considering the deficiency of the nonlinear consolidation calculations of vertical drains foundations solved by approximate equivalent method

and based on the assumption of plastic drainage plate elliptical column

the horizontal permeability coefficient and compression of foundation soil are deduced using the soft soil consolidation theory. An analytical solution for the nonlinear consolidation is given by the nonlinear differential equation theory

which considered the drainage plate under the influence of compressive modulus with nonlinear variation of the consolidation process. By comparing with the results in Indraratna (2005)

it is considered that the larger the ideal vertical drains foundations preload load (the larger Nu) is

the greater the error obtained by the approximation method in Indraratna et al. (2005)

and this error can be up to 16% compared with the results in this paper when the Cc/Ck=1.8 and Nu=5. The results reveal that the analytical solution proposed in this paper is aligned with the exact numerical solution

and the theory suggested is more effective in engineering application.