# Predictive Modeling and Experimental Analysis of Cyclic Shear Behavior in Sand-Fly Ash Mixtures
## 6 Conclusions  
In this study, the cyclic behaviors of clean sand and sand-fly ash mixtures were investigated through a detailed experimental program. Trakya sand and fly ash, a byproduct of burning pulverized coal, were used in the experiments. The shear strength characteristics of the specimens were obtained using strain-controlled constant normal load cyclic direct  
Figure 14: Predicted and measured stress–strain responses for specimens during fifth cycle; (**a**) Clean sand and mixtures of (**b**) 2.5 (%) FA, (**c**) 5 (%) FA, (**d**) 10 (%) FA, (**e**) 15 (%) FA and (**f**) 20 (%) FA.  
shear tests, which were conducted on clean sand and sand-fly ash mixtures with 2.5%, 5%, 10%, 15%, and 20% fly ash content. The results revealed distinct behaviors between clean sand and the sand-fly ash mixtures.  
At lower fly ash contents, the inclusion of fly ash results in a reduction in shear strength and higher volumetric strain under cyclic loading. Additionally, the hysteresis loops progressively narrow as the fly ash content increases, indicating a decrease in resistance to cyclic deformation. Beyond 15% fly ash, the mixture transitions to a more fine-dominated behavior, with higher fly ash content influencing both shear strength and compressibility. While the addition of fly ash initially reduces shear strength at lower contents, the shear strength increases at higher fly ash levels, reaching a maximum at 20% fly ash content. The reduction in shear strength at lower fly ash contents is explained by the disruption of the sand grain skeleton and insufficient fine-grain bonding. As the fly ash content increases, the mixture's structure evolves, leading to better cohesion and load distribution at higher contents. The maximum shear strength observed at 20% fly ash results from an optimal balance between sand-grain interlocking and fine-grain cohesion, where both mechanisms synergize effectively to resist cyclic deformation.  
In addition to the experimental analysis, this research highlights the value of data-driven approaches for predicting the cyclic behavior of geotechnical materials and soil composites. The Nonlinear Autoregressive Model with External Input (NARX) used in this study demonstrated exceptional predictive accuracy, with an R\({}^{2}\) value of 0.99. By leveraging data from the fifth loading cycle, the model successfully predicted the final shear response across various fly ash contents, showcasing its robustness and adaptability in simulating complex cyclic behaviors.  
The insights derived from this study underscore the potential of incorporating fly ash into sand mixtures for soil stabilization in geotechnical engineering. By optimizing the fly ash content, engineers can tailor the cyclic performance characteristics to meet specific project requirements. The study also emphasizes the importance of carefully balancing fly ash content in soil stabilization projects, as excessive amounts can negatively impact soil structure and mechanical properties. Furthermore, the integration of advanced machine learning techniques, such as the NARX model, offers a powerful tool for predicting the behavior of soil mixtures, supporting more effective, data-driven decision-making in geotechnical applications. This research not only advances the understanding of cyclic shear behavior in fly ash-sand mixtures but also provides a framework for using data-driven methodologies to address complex geotechnical challenges.  
Conceptualization, O.Y. and A.F.C.; Investigation, O.Y. and A.F.C.; Analysis, O.Y.; Writing, O.Y. and A.F.C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflicts of interest.