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A simple way of computer implementation of an effective two-parameter subgrade model for the routine analysis of flexible foundations on an elastic subgrade is presented. It is based on a rigorous analytical subgrade model recently proposed by one of the authors that takes full account of the soil–structure interaction. The details of both finite element (FE) and analytical implementation of the model to beams are presented. Fully established closed-form relationships are provided for the subgrade parameters. The essence in the method is that the soil shear resistance within the loaded region is transferred to the foundation element as an additional rigidity in form of a geometric stiffness, thereby leaving the Winkler spring bed to take care of the vertical compression as accustomed. Additional edge springs are introduced to account for the edge forces due to the shear continuity extending beyond the edges. By so doing, the attractiveness of the long-enduring Winkler’s model is maintained, whereas the missing shear interaction is taken care of through the introduction of the geometric stiffness and the edge springs. The FE discretisation is thus limited to the foundation unit alone as initially intended. Subject classification codes: soil–foundation interaction

Analytical formulation and finite-element implementation technique of a rigorous two-parameter foundation model to beams on elastic foundations