Equal volumetric strain solutions for radial and vertical consolidation with vertical drains under surcharge preloading

The available analytical solutions for ground consolidation with vertical drains are mostly established based on the traditional equal vertical strain assumption. Moreover, in the aspect of considering the effects of seepage and compression of the soil within the smeared zone, the vertical hydraulic conductivity and the coefficient of volume compressibility of the smeared soil are not really embodied, and then their impacts on the ground consolidation are not clear. Therefore, the equal volumetric strain assumption is adopted to solve the axisymmetric problem of radial and vertical ground consolidation with vertical drains. The effects of well resistance and smear are considered, together with a linearly time-varied surcharge preloading and an arbitrarily distributed mean stress increase in the ground. Solutions are derived from a complete set of partial differential equations of radial and vertical consolidation. Explicit expressions for the excess pore water pressure and degree of consolidation are presented. The influences of the lateral deformation, i.e., Poisson’s ratio effect, the vertical hydraulic conductivity and the three-dimensional coefficient of volume compressibility of the smeared soil, on the overall mean values of degree of ground consolidation are analyzed. It shows that the Poisson’s ratio effect is significant. The solutions derived based on the traditional equal vertical strain assumption overestimate the consolidation rate of the ground. The solutions derived without consideration of the volume compressibility of the smeared soil also overestimate the consolidation rate, but to a limited extent. Nevertheless, the influence of the vertical hydraulic conductivity of the smeared soil on the ground consolidation is negligible.