The Effect of Footing Shape on the Bearing Capacity of Shallow Foundations: A Review

This review paper examines the evolution of shape factors for the bearing capacity of shallow foundations, with a specific focus on rectangular and circular footings. Through a critical examination of methodologies from early empirical approaches to the sophisticated analyses enabled by recent technological advancements, this paper highlights the transformative impact of computational modeling on the field. Specifically, the review utilizes 3D finite element and finite difference analyses to validate and recalibrate shape factors against modern and reliable data. The quantitative findings confirm the reliability of the shape factors developed by Zhu and Michalowski in 2005 through classical finite element analysis in Abaqus. Their \({s}_{\gamma }\) factor, for example, was validated using Flac3D. Particularly notable is the finding that shape factors for circular footings can be effectively expressed by adjusting those for square footings using a simple geometric ratio, \(4/\pi \). This adjustment, based on the perimeter or area ratios of the two shapes, suggests a more efficient approach that challenges the necessity for distinct shape factors for different footing types. Additionally, the review highlights historical gaps such as non-documented factors from early empirical research, limitations due to the scale effects of small-scale tests, and assumptions supporting shape factors derived from limit analysis. It also emphasizes that depending on the aspect ratio of the footing and the friction angle of the soil, the percentage error in bearing capacity calculations using non-acceptable shape factors, including those adopted by various design standards, could be several tens of percentage units. Additionally, the review identifies a gap in current research regarding large-scale experimental validation of these computational models, pointing to future directions in experimental research.