Empirical Relationships Between the Elastic Settlement of Rigid Rectangular Foundations and the Settlement of the Respective Flexible Foundations

The problem of settlement of shallow foundations is among the most important ones in classical soil mechanics. And while for the settlement of flexible foundations elastic solutions are widely used, for rigid rectangular foundations where the actual contact pressure distribution is still unknown, the problem is approximated either analytically assuming a contact pressure distribution or semi‐empirically combining the theory of elasticity with experimental and/or numerical results. A third and often attractive choice is the use of simple empirical relationships or relevant tabulated values relating the elastic settlement of rigid foundations (ρ_R) with the settlement of the respective flexible foundations (e.g. at the center, ρ_Ce). Reviewing the relathionships of this third approach, the author revealed serious lack of consesous between the various sources; for example, according to the literature, ρ_R ranges between 68 and 125% of ρ_Ce, the time when it is well-known that ρ_R?ρ_Ce. In this paper, comparison of the settlement of 210 rigid foundation cases derived from 3D elastic finite element analysis, with the settlement of the respective flexible foundations derived from the theory of elasticity, led to simple empirical relationships between ρ_R and ρ_Ce as well as between ρ_R and ρ_Av (ρ_Av?=?average settlement of the flexible foundation) with coefficient of determination (R²) almost unity. The analysis showed that these relationships are largely independent of the aspect ratio of foundations and the thickness and Poisson’s ratio (ν) of the compressible medium, although separate relationships are given for ν?=?0.5, slightly increasing R². Finally, a correction factor for foundation rigidity is given exploting the known linear relationship that exists between the relative stiffness factor of foundations and settlement.