Scale effects on the ultimate bearing capacity of rectangular footings placed on slopes

Abstract

Evaluating the bearing capacity of footing near slopes is typically performed under two-dimensional conditions. However, rectangular footings, particularly with footing aspect ratios approaching unity do not adhere to the assumption of plane-strain conditions. In this study, the scale effects of rectangular footings near slopes are investigated by using upper- and lower-bound finite element limit analysis. The results indicate that when the longitudinal directions of a footing and slope are parallel, ignoring scale effects may result in overly conservative design for bearing capacity. However, when the longitudinal directions of a footing and slope are orthogonal, rectangular footings may have more significant scale effects than square footings and it may not be conservative to simplify three-dimensional conditions to plane-strain solutions. In addition, footing shape has a significant influence on the observed failure mechanism, demonstrating a transition in failure mechanism with changing aspect ratio. Generally, the presence of a larger internal friction angle amplifies observed bearing capacity scale effects. However, contrasting behavior may occur when the longitudinal direction of footings is perpendicular to the longitudinal direction of slope face. Finally, bearing capacity scale effects become most significant when the footing is embedded with rough sidewalls near tall and steep slopes.