Solutions for consolidation considering column consolidation and parabolic distribution of soil permeability

In the traditional consolidation theories for composite foundation,there is an inconsistency between the equal strain assumption and the assumption of flow continuity at the column-soil interface.To remedy this inconsistency,the radial flow within the column instead of the equal flow assumption at the column-soil interface is considered to account for the consolidation and deformation of the column.In addition,the parabolic distribution of the horizontal permeability of soil in the disturbed zone due to the influence of the column construction is considered too.The governing equations for this type of consolidation problem are derived and the solutions to the governing equations are obtained.Then the solution of the average degree of consolidation is obtained and discussed.It can be seen that whenever the radius ratio(radius ratio of the influence zone to the column) approaches 1 or ∞,the present solution for composite foundation all can be reduced to the solution of Terzaghi’s one-dimensional consolidation for natual foundation.Finally,a comparison between the present solution and some previous solutions is made.The results show that the rate of consolidation calculated by the present solution is rapider than that by the solutions which assume the horizontal permeability of soil in the disturbed zone is linearly changed or kept constant as a reduced value.The difference between the average degree calculated by the present solution and that by the previous solutions increases with the reduction in the radius ratio.