In the soft foundation treatment projects

the phenomenon that the spacing of vertical drains reduces when the consolidation efficiency of the foundation decreases often appears. Given this

the distribution function of horizontal permeability coefficient of soil in overlapping smear zones is established

and then the analytical solutions are obtained for the excess pore pressure and average degree of consolidation of vertical drains foundation with overlapping smear zones. Based on the analysis of the variation of the average degree of consolidation of the foundation with the spacing of the vertical drains for different cases

the reasons are explored when the spacing of the vertical drains reduces and the consolidation efficiency of the foundation decreases. Finally

we discussed the influence of the smear effect and well resistance effect on the minimum critical spacing of vertical drains. The results show that the overlapping of smear zones of adjacent vertical drains is the underlying reason for the minimum critical spacing of vertical drains in the foundation. The greater the smear effect is

the greater the minimum critical spacing of vertical drains is. The specific performance is that the minimum critical spacing of vertical drains increases with the increase of the disturbance degree of the foundation or the radius of the smear zones. The larger the well resistance is

the smaller the minimum critical spacing of vertical drains is. When the permeability coefficient of the vertical drain decreases

the length of the vertical drain increases or the radius of the vertical drain decreases

and the minimum critical spacing of vertical drains decreases accordingly.