Analytical solution for consolidation by vertical drains considering actual shape of influence zone

In view of the shortcomings that the influence zone of vertical drain is always assumed to be a circle in the existing analytical consolidation theories for vertical drains; the consolidation by vertical drains installed in a regular triangle pattern with a regular hexagon shape of influence zone was studied. By establishing new consolidation equation and introducing new boundary conditions, the general analytical solutions accounting for variation of soil horizontal permeability coefficient were derived. Then, according to three types of variation patterns of the horizontal permeability, the corresponding solutions were obtained. Furthermore, the influences of three main dimensionless parameters on the consolidation behavior were analyzed, and the obtained solutions were compared with the existing ones. The results show that the greater the size of influence zone or disturbed smear zone is, the slower the consolidation is; the less the ratio of the maximum to the minimum horizontal permeability coefficient of soil is, the faster the consolidation is; under the same conditions, the consolidation of pattern two considering a linearly changed permeability coefficient within the disturbed zone is the fastest and the solutions of pattern one considering a constant permeability coefficient within the disturbed zone are very close to the existing analytical ones, which indicated that the assumption that the influence zone of vertical drain is a circle adopted in the existing theories is reasonable.