The equivalent modulus of elasticity of layered soil mediums for designing shallow foundations with the Winkler spring hypothesis: A critical review

Abstract

This paper offers a comprehensive review of the available methods calculating the equivalent elastic constants (Eeq, νeq) for the case of transversely loaded horizontally stratified soil mediums. The main finding of the present paper is that, the vast majority of the existing methods return Eeq values that greatly differ from the value effectively representing the original multilayer medium. Thus, the use of the current methods may easily lead to either non-economic or unsafe designs. The methods proposed by Gorbunov-Possadov and Malikova (1973), HariBharghan et al. (2017) and Sadrekarimi and Akbarzad (2009) were found to perform best among all with the maximum relative error for the cases examined herein being in the order of 20% for Gorbunov-Possadov and Malikova's method and 40% for the other two. Egorov and Nichiporovich's (1961) weighted average method (best known as Bowles’ (1996) method), probably the most popular method in academia and in practice, is one of the least reliable methods with the maximum relative error (for the cases examined) being as high as 83% and 63% on the unsafe and safe side respectively. Regarding the modulus of subgrade reaction, the author recommends the use of Vesic's (1961) formula but in combination with the proper equivalent elastic constants. In a Winkler type of analysis, the proper elastic modulus is the one corresponding to Poisson's ratio, ν, equal to zero. Unfortunately, none of the existing methods can reduce the derived Eeq value from an initial ν value to ν = 0. Indeed, the vast majority of the existing methods ignores the Poisson's ratio, whilst the rest of them suggest expressions carrying all the major disadvantages related to the derivation of Eeq. In addition, none of the existing methods cover the very common case of soils with modulus of elasticity linearly varying with depth.