Standardized sign conventions and notation for generally loaded foundations

TLDR

Recent research on the load‑displacement response of rigid shallow foundations under general loading has focused mainly on two‑dimensional cases, yet conflicting sign conventions and notations have been used. This note proposes adopting a specific right‑handed coordinate system with a clockwise positive convention and a comprehensive notation for load and displacement components and their normalized dimensionless counterparts. The proposed system applies consistently to all such problems, providing a unified framework for describing loads, displacements, and their dimensionless forms. Six additional specific recommendations are made to further standardize sign conventions and notation.

Abstract

There has recently been increasing research on the classical geotechnical problem of the load-displacement response of rigid shallow foundations under general loading conditions. Most of the published experimental data and mathematical models relate to the problem's two-dimensional version, where a footing of given breadth supports given vertical and horizontal loads and given in-plane moment. Unfortunately, different authors have used different, often conflicting, sign conventions and notations. This note proposes adopting a specific right-handed coordinate system, with the clockwise positive convention, which can be applied consistently to all such problems, and a comprehensive notation for load and displacement components and their normalised dimensionless counterparts. Six other specific recommendations are made.