Determination of the Spring Constant for the Horizontal Movement of Rigid Rectangular Foundations Resting on Elastic Subsoil

In this paper, a formula for the spring constant Kx for the horizontal movement of rigid rectangular foundations resting on elastic subsoil and spring coefficient βx in this formula was derived, which demonstrates that βx depends on Poisson’s ratio ν. It was also shown that βx, which has already been presented in the literature, was determined for a constant value ν = 0.3. It was shown that the values of βx and Kx, obtained from the formulas derived in this paper and the calculations based on the formulas and nomogram for the βx given in the literature, may differ by 8–11%. For the adopted parameters, among others ν = 0.5, and for the side ratio α = 10, the value of spring constant is in the first case Kx=145.9 MN/m and in the second case Kx = 158.3 MN/m (differ by 8%), while for ν = 0.1, is, respectively, Kx = 517.8 N/m and Kx = 464.3 MN/m (differ by 11%). Numerical FEM 3D analysis verified analytical solutions for the concrete foundation footing and the soil layer beneath it. This paper also provides useful nomograms that can be used to easily read the values Kx and βx. The use of the proposed formulas in this paper, refined formulas for determining Kx and βx in engineering calculations, can improve the accuracy of the analyses related to the influence of soil stiffness in horizontal movement.