In Winkler or subgrade reaction approach the pile is considered as supported by an array of uncoupled springs.
Most of the approaches consider either the theory of subgrade reaction or the theory of elasticity.
Terzaghi  showed that the modulus of subgrade reaction (k) was not an intrinsic physical parameter of the soil, but inversely proportional to foundation width.
Zhou and Wen  indicated that subgrade reaction coefficient k30 can be improved by 3000%, and the deformation can be reduced by 44% by using geocell-reinforced sand cushion.
The most popular model in determining the modulus of subgrade reaction (k) is Winkler model.
Consequently, runway design requirements and pavement evaluation are largely affected by potential deflection, which primarily relates to California bearing ratio (CBR) or modulus of subgrade reaction of soil subgrade of the runway (Ashford, Wright 1992; Horonjeff, McKelvey 1994).
s] is the modulus of subgrade reaction of the runway pavement, and p is the equivalent static contact pressure exerted by landing gear wheels on the runway pavement surface, the following general expression derived by D.
A relationship between deflection and soil pressure known as modulus of subgrade reaction is extensively used in the structural analysis of foundation.
Where q is the contact pressure, Ks is the coefficient of subgrade reaction and d is the displacement.
2]; v--Poisson's ratio of cement concrete slab; h--thickness of concrete slab, m; k--modulus of subgrade reaction, kN/[m.
j] depend on the fatigue law and are related to actual and standard axle load, bending strength of concrete and coefficient [beta], which in turn depends on thickness of a concrete slab h, modulus of subgrade reaction k and other pavement parameters.
s] is the modulus of the subgrade reaction
(spring constant) for the Winkler spring layer as shown in Figure 2.