Comparative Experimental Study on the Dynamic and Static Stiffness of Sandy Soils Utilizing Alpan’s Empirical Approach

Stiffness parameters are very important and effective in the constitutive models used in finite element analysis. It is not easy or common to obtain these parameters in the laboratory. However, even if the modulus is determined in the small and medium deformation range, there is a need to make transitions in both static and dynamic parameters. In almost all studies, the Alpan approach is used for the relationship between static and dynamic moduli of elasticity. Therefore, a better understanding of this approach is required. In this study, the relationship between static and dynamic stiffness was determined by monotonic triaxial and resonant column tests on five different sand samples with different relative stiffness and grain distributions, and the results were compared with Alpan’s approach. It is not clear which of the initial or maximum modulus of elasticity (E0), unloading-reloading modulus (Eur) or secant modulus of elasticity (E50) are used by Alpan for static modulus of elasticity (Estat). Therefore, the coefficient Rsec = Estat/E50 was introduced and queried to indicate which Estat is a multiple of E50. In connection with this, the dynamic modulus of elasticity (Edyn) was calculated using the small deformation shear modulus (G0) obtained from resonant column experiments and assuming Poisson’s ratios (ν = 0.2, 0.3, 0.4). It was found that Alpan’s empirical approach achieved a significant degree of agreement for the sands in this study and the studies of other researchers. It was observed that the best agreement between dynamic and static stiffness ratio (Edyn/Estat) and static modulus of elasticity (Estat) for sand specimens in this study was obtained with υ = 0.2 and Rsec = 2. According to the experimental results, it is safe to say that Alpan’s empirical approach is still valid when the values of Poisson’s ratio and Estat in the very small deformation region are used. Since there are limited studies on Edyn/Estat ratio in the literature, it is thought that the findings in this paper will assist engineers and researchers. However, this work would also assist engineers in selecting appropriate stiffness parameters for calibrating constitutive models.