Simplified analytical solution for time dependent deformation of soft soil improved with pervious column considering load transfer between column and soil

Abstract

This paper presents a simplified analytical solution to analyse the coupled excess pore water pressure dissipation and deformation response of a composite stone column – soft soil foundation. The mathematical formulation is derived considering the combined radial – vertical flows of excess pore water pressure in stone column and soft soil areas (orthotropic permeability for each area), and adopting the settlement pattern for the composite ground suggested by an existing study in the literature. The homogeneous consolidation formulations are solved first to develop Green’s function for final excess pore water pressure solutions, employing the method of separation of variables and eigenfunction expansion technique. Then, the final solutions for excess pore water pressure corresponding to the nonhomogeneous consolidation formulations are derived in terms of Green’s formula, which can be expanded readily into a double series solution. The obtained analytical solutions can be used to examine the variation of excess pore water pressure against time at any point in the composite foundation. Thus, the consolidation settlements of stone column and soft soil areas and the differential settlement between them can be captured. The average differential settlement between the soil and column areas is used to compute the shear strains and shear stresses in the composite ground during the consolidation process. The proposed analytical solution is validated via a worked example in conjunction with a verification exercise against finite element simulation. The analytical predictions are presented in terms of the total vertical stress variations and excess pore water pressure dissipations against depth and time, the settlements and average degrees of consolidation for stone column and surrounding soft soil, and the shear stress distribution in the soil region. The capability of proposed analytical solution is also verified against field measurements of a full-scale test of soil - column composite ground (pervious column). The verifications show that the obtained analytical solution can predict the coupled excess pore water pressure dissipation – deformation response of soft soils improved by pervious columns such as stone columns and soil- deep cement mixing columns reasonably well.