Modified Equivalent-Area Method for Calculating Factors of Safety against Deep-Seated Failure of Embankments over Deep-Mixed Foundations

The limit equilibrium method (LEM) and the finite-element method (FEM) commonly have been used in design to calculate the factors of safety (FS) against deep-seated failure of deep-mixed (DM) column-supported embankments over soft clays. Previous studies showed that the LEM with the conventional equivalent-area method (EAM) for column foundations yields higher FS than the three-dimensional (3D) FEM with individual columns. This study investigated the FS against deep-seated failure of embankments over deep-mixed columns using the 3D individual column method and the LEM with the conventional EAM. The roles of DM columns and soft clays in the stability of DM column-supported embankments were assessed by performing a weighted analysis and examining the stress states of the DM columns and the soft clay at failure. The results showed that the conventional EAM had a higher possibility of overestimating the FS against deep-seated failure of embankments over deep-mixed foundations than did the 3D FEM with individual columns. The conventional EAM overestimated the contributions of DM columns to the slope instability because some DM columns had not fully mobilized their shear strengths when the embankment failed in the 3D FEM, especially for soil and DM columns with a large strength difference and for DM columns with a large area replacement ratio. Load transfer almost disappeared at failure in the 3D model. Accordingly, a modified equivalent-area method was proposed and verified by comparing its results with those in the literature.