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The theories of vertical and horizontal subgrade reaction are based on the simplifying assumptions that the subgrade obeys Hooke's law, and that the subgrade reaction on the base of a rigid centrally loaded plate resting on the horizontal surface of the subgrade has the same value at every point of the base. Although these assumptions are not rigorously correct, the theories of subgrade reaction can be used for obtaining approximate solutions of many practical problems, such as the computation of the stresses in continuous footings acted upon by concentrated loads, or in piles that are intended to transfer horizontal load on to the subgrade. However, in order to get reasonably accurate results, the coefficients of subgrade reaction must be assigned values compatible with the deformation characteristics of the subgrade and the dimensions of the loaded area.
The Paper contains a discussion of the factors which determine the value of the coefficients of both vertical and horizontal subgrade reaction of cohesionless sand and stiff clay, and numerical values are proposed for the constants which appear in the equations defining these coefficients. It contains also brief reviews of the practical application of the theories of subgrade reaction.

Géotechnique, Volume 5, Issue 4, 01 December 1955, pages 297–326
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