Semi-analytical solutions to the consolidation of unsaturated composite ground enforced by stone columns under equal strain condition considering smear effect

Composite ground is widely employed in geotechnical engineering as a ground reinforcement method, which can be applied to either saturated or unsaturated natural ground. There is limited existing research on consolidation behaviour of the unsaturated composite ground with stone columns, particularly when smear effect is considered. The smear zone is inevitable due to the disturbance to the ground when constructing stone columns, and the flow rate of either air or water through the smear zone significantly reduces, leading to a slow dissipation of the excess pore pressures. This paper proposes semi-analytical solutions in the equal strain conditions for consolidation problem of unsaturated composite ground with stone columns considering the smear effect. Based on the flow rule of air and water phases in the axisymmetric case and the basic relationship of unsaturated composite ground, we first derived the governing equations of excess pore-air and pore-water pressures. Then, the semi-analytical solutions are obtained with the joint use of expansion of Fourier series, Laplace transform and inverse Laplace transform. For a degenerated case, we compare the proposed solutions with the existing ones in literature for the verification purpose. Furthermore, we perform a series of parametric studies by using the proposed solutions and find that the consolidation rate is underestimated when ignoring the smear effect of the unsaturated composite ground.