Part I: A Generalized Formulation of Continuum Models for Elastic Foundations

A generalized model is presented for a subgrade idealized as an elastic layer overlying a rigid base. In contrast to previous works no stresses, strains or displacements are neglected a priori. A second-order partial differential equation is obtained similar to Kerr's mechanical model. It is demonstrated that several variants of the model can be obtained by specifying two relations: a function for the horizontal-to-vertical stress ratio and another for the variation of the vertical shear stresses with depth. Two such variants are presented. Also, lower-order models are obtained by making just the necessary assumptions. Accordingly, models of the order of two-parameter mechanical models are obtained when the horizontal deformations alone are neglected; Winkler-type models result only when the vertical shear stresses are omitted. Two variants of each of these lower-order models are provided. The proposed models have applications in the analysis of beams and plates on elastic foundations. Such an application together with a calibration work is demonstrated on beams in the companion paper (Part II).