Modulus of Subgrade Reaction: New Perspective

Abstract

A review of the current state-of-the-art concerning the use of the modulus of subgrade reaction (Winkler) model indicates that there is considerable disagreement concerning the correct method for interpreting and evaluating the modulus of subgrade reaction, k. Extension of previous work, which used the simplified continuum approach to solve a problem in the theory of elasticity, shows that the Winkler subgrade model actually defines an elastic body of finite thickness in which all stress and strain components are assumed to be zero except for the vertical normal stress and strain. Furthermore, the modulus of subgrade reaction, k, is defined explicitly to be a function of the Young's modulus and thickness of the elastic body. Solutions for a Young's modulus that is constant with depth, as well as one that varies linearly and with the square root of depth, are presented. Although the simplified continuum approach offers an analytically rigorous and consistent method for evaluating the modulus of subgrade reaction, the more important result is that the very crude stress and strain assumptions implicit in the Winkler model are identified for the first time.