Green’s function analytical solution for free strain consolidation of soft soil improved by stone columns subjected to time-dependent loading

Abstract

This paper proposes an analytical solution in terms of Green’s function formulations for axisymmetric consolidation of a stone column improved soft soil deposit subjected to time-dependent loading under free strain condition. The mathematical derivations incorporate the pore water flows in radial and vertical directions in stone column and soft soil synchronously. The capabilities of the proposed analytical solution are evaluated via worked examples investigating the influences of three common time-dependent external surcharges (namely step, ramp and sinusoidal loadings) on consolidation response of the composite ground. The examples show that a faster increase of load from an initial surcharge to an expected loading might generate more significant excess pore water pressure to be dissipated during the early stages of consolidation, but the dissipation rate in soft soil would speed up significantly afterwards. The column and soil settlements along with the differential settlement between them also proceed faster corresponding to the acceleration of loading – unloading processes. Finally, the proposed analytical solution is employed to evaluate the excess pore water pressure dissipation rate at an investigation point in soft clay of a case history foundation. The calculation results exhibit a reasonable agreement with field measurement data when various constant values of stress concentration ratio are substituted into the solution to reflect the increase of stress concentration ratio with consolidation time in real practice.