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

Stiffness parameters are very important and effective in the constitutive models used in finite element analysis. It is not easy and 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. The initial or maximum modulus of elasticity (E₀), secant modulus of elasticity (E₅₀) and derived reloading modulus (Eur) are considered as static stiffness parameters assuming Estat = Rsec × E₅₀. The dynamic modulus of elasticity (Edyn) was calculated using the small deformation shear modulus (G₀) obtained from resonant column experiments and assuming Poisson's ratio (ν= 0.2, 0.3, 0.4). The Edyn/Estat ratio was compared with Alpan's empirical approach and also evaluated with the data of other researchers who have studied the same topic. Comparing the results with the Alpan approach, it was observed that the best agreement for the dynamic and static stiffness ratio in the sand specimens in this study was obtained with v=0.2 and Rsec =2-3.