On the modulus of subgrade reaction for shallow foundations on homogenous or stratified mediums

Abstract

As known, the modulus of subgrade reaction of soil, ks, is an essential parameter in designing flexible, shallow foundations based on the Winkler spring hypothesis, where, the foundation soil is modeled as a series of independent (elastic) springs having constant ks. In this paper the various methods for calculating the ks value are discussed, indicating that the more suitable one is Vesic’s ks=0.65[EB4/(EbIb)]1/12E/[B(1–v2)], where, E and ν are the elastic constants of soil and Eb, Ib and B are the modulus of elasticity of the foundation material, the moment of inertial of the cross-section of the foundation and the foundation width respectively. In addition, it is recommended that, the proper soil modulus value is the one corresponding to ν=0 for consistency with the deformation pattern of Winkler’s springs (compression with no lateral deformation). In this respect, the author offers an effective method for calculating the equivalent elastic constants (Eeq, νeq) for horizontally stratified soil mediums supporting shallow foundations. The same method can also be applied to reducing any homogenous (E, ν) soil medium to an equivalent one having νeq=0 and modulus Eeq.