Winkler's single-parameter subgrade model from the perspective of an improved approach of continuum-based subgrade modeling

Abstract

Based on an isotropic elastic continuum of thickness H overlying a rigid stratum, a generalized formulation for the classical single-parameter Winkler's subgrade model is presented. In this formulation, all the normal components of the stress tensor are taken into consideration, whereas the shear stresses are intentionally dropped with the purpose of providing a useful perspective, with which Winkler's model and its associated coefficient of subgrade reaction can be viewed. The formulation takes into account the variation of the elasticity modulus with depth. It only demands specifying a relationship between the vertical and horizontal normal stresses. Accordingly, two such different assumptions are made to obtain two new Winkler-type subgrade models with the corresponding closed-form relations for the subgrade modulus. The models give consistently larger stiffness for the Winkler springs as compared to previously proposed similar continuum-based models that ignore the lateral stresses. It has also been pointed out that it is only if the shear stress components of the subgrade are taken into consideration that a multi-parameter model evolves regardless of whether the lateral normal stresses are included. Finally, the effective stiffness per unit area of the multiple beds of springs of such a higher order model is exactly the same as the subgrade modulus of the corresponding single-parameter Winkler model presented in this work.

Keywords: Heterogeneous subgrade, Reissner's simplified continuum, Shear interaction, Simplified continuum, Winkler model, Winkler-type models.