Analytical solution for free strain consolidation of stone column-reinforced soft ground considering spatial variation of total stress and drain resistance

Abstract

This paper provides an analytical solution for consolidation problem of a stone column-improved soft soil layer subjected to an instantly applied loading under free strain condition. The radial and vertical consolidation equations are solved in a coupled fashion for both the stone column and its surrounding soil. A general solution of excess pore water pressure at any point of a unit cell model in terms of a Fourier-Bessel series was achieved using the combination of separation of variables method and orthogonal expansion technique. The obtained solution can capture the drain (well) resistance effect and the space-dependent distribution of total vertical stress induced by the external loading. Indeed, since the permeability and size of the stone column are directly utilised in the governing equations and the analytical solution, the drain resistance is directly captured. The capabilities of the proposed solution are exhibited through a comprehensive worked example, while the accuracy of the solution is verified against a finite element simulation and field measurements of a case history with good agreements. To examine the effect of various factors on consolidation behaviour of the composite ground, a parametric study involving column spacing, modulus and permeability of soft soil along with distribution pattern of total stress and thickness of soil layer is also conducted. A decrease in the column spacing or an increase in the modulus or permeability of soft soil led to the acceleration of the consolidation process of the soil region, while the variation of the total stress with depth and the thickness of soil deposit primarily affected the consolidation rate of stone column. Under the free strain condition, the average differential settlement between the stone column and encircling soil was indeed considerable during the consolidation process.