An analytical solution for the settlement of stone columns beneath rigid footings

This paper presents a new approximate solution to study the settlement of rigid footings resting on a soft soil improved with groups of stone columns. The solution development is fully analytical, but finite element analyses are used to verify the validity of some assumptions, such as a simplified geometric model, load distribution with depth and boundary conditions. Groups of stone columns are converted to equivalent single columns with the same cross-sectional area. So, the problem becomes axially symmetric. Soft soil is assumed as linear elastic, but plastic strains are considered in the column using the Mohr-Coulomb yield criterion and a non-associated flow rule, with a constant dilatancy angle. Soil profile is divided into independent horizontal slices, and equilibrium of stresses and compatibility of deformations are imposed in the vertical and horizontal directions. The solution is presented in a closed form and may be easily implemented in a spreadsheet. Comparisons of the proposed solution with numerical analyses show a good agreement for the whole range of common values, which confirms the validity of the solution and its hypotheses. The solution also compares well with a small-scale laboratory test available in the literature.