## 4 Concluding Remarks  
This paper presents the findings from a series of monotonic triaxial, and resonant column tests conducted on sandy specimens with varying characteristics. The primary objective of the study is to determine the dynamic and static stiffness of sandy soils and their interrelationship. Based on the results of this study, the following conclusions can be drawn:  
* This study examines sands classified as fine sand \"SC\" (S1 and S3) and well graded \"SW\" (S2, S4 and S5) according to the Unified Soil Classification System (USCS). These soils were tested with varying fine content (FC = 0-45%) and different levels of relative density (D\({}_{\rm R}\) = 45% and DR = 70-90%). Therefore, the results obtained are valid for sandy soil with similar properties to the tested specimens.
* The measured E\({}_{\rm dyn}\)/E\({}_{\rm stat}\) values are generally underestimated by the Alpan approach. When Poisson's ratio is assumed to be small, the Alpan curve is approximated more closely. The results reveal that Poisson's ratio significantly affects E\({}_{\rm dyn}\) and hence the E\({}_{\rm dyn}\)/E\({}_{\rm stat}\) ratio.
* The ratio between dynamic and static modulus as proposed by Alpan, the static elastic modulus (E\({}_{\rm stat}\)) is not explicitly defined. The coefficient R\({}_{\rm sec}\) = E\({}_{\rm stat}\)/E\({}_{\rm 50}\) was introduced that E\({}_{\rm stat}\) is a multiple of E\({}_{\rm 50}\). Test results revealed the best agreement between dynamic and static stiffness ratio (E\({}_{\rm dyn}\)/E\({}_{\rm stat}\)) and static modulus of elasticity (E\({}_{\rm stat}\)) for R\({}_{\rm sec}\) = 2 (when v is assumed 0.2). Statistical error analyses support this finding.
* According to the experimental results, it is safe to say that [PERSON]'s empirical approach is still valid when the values of Poisson's ratio and E\({}_{\rm stat}\) in the small deformation region are used. Ref. [3] diagram was found to be practical and appropriate when both static and dynamic tests were not performed on a soil.
* Since there are limited studies on E\({}_{\rm dyn}\)/E\({}_{\rm stat}\) ratio in the literature, it is thought that the findings in this paper will contribute to engineers and researchers. However, this work would also assist engineers in selecting appropriate stiffness parameters for calibrating constitutive models.
* It is observed that E\({}_{\rm dyn}\)/E\({}_{\rm stat}\) increases as the fine content increases. This and the updating of the mathematical expression originally proposed by [3] through new index properties (such as C\({}_{\rm u}\) and D\({}_{\rm 50}\)), confining stress and relative density are the subject of ongoing research.  
Conceptualization, S.O.; Methodology, G.K., S.S. and S.O.; Investigation, G.K.; Data curation, G.K. and S.S.; Writing--original draft, G.K.; Writing--review & editing, S.S. and S.O. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case Definition** & **MAE** & **MSE** & **RMSE** & **R\({}^{2}\)** & **Slope** & **Intercept** \\ \hline R\({}_{\rm sec}\) = 3, \(\
u\) = 0.2 & 3.3274 & 12.316 & 3.5095 & 0.63 & 0.70 & \(-\)1.37 \\ R\({}_{\rm sec}\) = 3, \(\
u\) = 0.3 & 3.0612 & 10.702 & 3.2714 & 0.59 & 0.76 & \(-\)1.49 \\ R\({}_{\rm sec}\) =  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
**Acknowledgments:** This work is supported by the Scientific and Technological Research Council of Turkiye (TUBITAK) with a 1001 Project No. 12 IM760.  
**Conflicts of Interest:** The authors declare no conflict of interest.