Potential link between the Golde ratio and the At-Rest Earth pressure in normally consolidated soils

Abstract

The paper deals with the prediction of the at-rest earth pressure coefficient K0 (≡ K0(NC)) for normally consolidated soils as a function of the mobilised proportion Φ’mob of the shearing resistance angle Φ’ in the one-dimensional virgin compression process. By carrying out a back analysis of a wealth of published experimental (K0(NC), Φ’) pairs, the author previously derived, with no assumptions and in a straightforward manner, an empirical equation for K0(NC) in terms of the mobilised angle Φ’mob of shearing resistance. Further focusing on the numerical value of the mobilising factor of Φ’ in the one-dimensional virgin compression process showed the possible emergence of the Golden Ratio τ = 1.618 as the ratio between the shearing resistance angle Φ’ and its mobilised proportion in the above process, i.e. Φ’/Φ’mob = 1.618 or Φ’mob = 0.618Φ’. The resulting empirical equation has the same basis, in terms of soil behaviour, as the previously obtained K0(NC) equation and a slightly better predictive capability for the full range of the Φ’ values considered; it is also better than several other K0(NC) equations, including Jaky’s approximate equation. The link between K0 and the Poisson’s ratio ν for elastic materials, combined with the connection between Φ’ and Φ’mob, suggests a correlation between ν and Φ’ for normally consolidated soils. However, this correlation is a borderline case for these soils, thus requiring experimental validation.