Analytical Solution for Consolidation of Soft Soil with Partially Penetrated Stiffened Deep-Mixed Columns under an Embankment

Abstract Stiffened deep-mixed columns (SDM columns) have increasingly been used to reinforce soft soils. When an embankment is constructed on a thick saturated soft clay, partially penetrated SDM columns are usually adopted. However, limited studies have been carried out to investigate the consolidation characteristics of thick soft soil with partially penetrated SDM columns. This paper conducted a theoretical analysis of the consolidation problem in soft soil with partially penetrated SDM columns under an embankment load. Two types of SDM columns were considered. The length of the outer deep-mixed (DM) column is equal to the length of the core pile or longer than the core pile length. After the load share effect of the core pile was considered under one-dimensional (1D) consolidation, the complex two-dimensional (2D) consolidation problem was transformed into a simplified layered consolidation problem, where equivalent consolidation coefficients were utilized. The effectiveness of the developed solution was confirmed by comparing it with the outcomes from a three-dimensional (3D) finite-element analysis. A systematic investigation was conducted to analyze the consolidation properties of this composite ground, which led to practical recommendations for its application. To validate the proposed solution further, it was implemented in a centrifugal model test that involved an embankment that was supported by partially penetrated SDM columns. The predictions made by the solution aligned well with the actual measurements, which indicated a high level of agreement.