Dear friends, about three decades ago I was next to asphalt research and also involved in foundation models for rigid pavements. There are three commonly used foundations models: 1) Winkler foundation (uncoupled springs), 2) Pasternak foundation (coupled springs like a mattress), and 3) Kerr foundation (3 layers: uncoupled springs, an elastic shear layer, uncoupled springs). The pavement with a concrete slab on a Winkler foundation is defined as the well-known Westergaard model (4th-order partial differential equation). Placing a concrete slab on a Pasternak will also lead to a 4th-order differential equation (Pasternak model). A concrete slab on a Kerr foundation leads to a 6th-order differential equation (Kerr model).

When a boundary (edge) exists between two adherent slabs, one needs 4 boundary conditions in the Westergaard and the Pasternak model and 6 boundary conditions when using the Kerr model. Arnold Kerr developed his foundation model because he considered the “sublayer” in the Pasternak model as an elastic shear layer. Therefore the deflections at both sides of the edge must be the same. However, suppose you don’t define it as an elastic shear layer but just as a mathematical response. In that case, there are no reasons why a difference between deflections at an edge is not allowed.

The main reason why I post this item is that 3 of the 4 needed boundary conditions follow from the equilibrium for the forces and moments.

For the remaining 4th boundary condition any equation can be used as long as this equation is not in conflict with the other 3 boundary conditions based on the equilibrium for forces and moments.

I have attached a paper I wrote on this item