# Predictive Modeling and Experimental Analysis of Cyclic Shear Behavior in Sand-Fly Ash Mixtures
###### Abstract  
This study presents a comprehensive investigation into the cyclic shear behavior of sand-fly ash mixtures through experimental and data-driven modeling approaches. Cyclic direct shear tests were conducted on mixtures containing fly ash at 0%, 2.5%, 5%, 10%, 15%, and 20% by weight to examine the influence of fly ash content on the shear behavior under cyclic loading conditions. The tests were carried out under a constant stress of 100 kPa to simulate field-relevant stress conditions. Results revealed that the fly ash content initially reduces shear strength at lower additive contents, but shear strength increases and reaches a maximum at 20% fly ash content. The findings highlight the trade-offs in mechanical behavior associated with varying fly ash proportions. To enhance the understanding of cyclic shear behavior, a Nonlinear Autoregressive Model with External Input (NARX) model was employed. Using data from the loading cycles as input, the NARX model was trained to predict the final shear response under cyclic conditions. The model demonstrated exceptional predictive performance, achieving a coefficient of determination (R\({}^{2}\)) of 0.99, showcasing its robustness in forecasting the cyclic shear performance based on the composition of the mixtures. The insights derived from this research underscore the potential of incorporating fly ash in sand mixtures for soil stabilization in geotechnical engineering. Furthermore, the integration of advanced machine learning techniques such as NARX models offers a powerful tool for predicting the behavior of soil mixtures, facilitating more effective and data-driven decision-making in geotechnical applications. Evidently, this study not only advances the understanding of cyclic shear behavior in fly ash-sand mixtures but also provides a framework for employing data-driven methodologies to address complex geotechnical challenges. c pacs: 29 November 2024  
Revised: 24 December 2024  
Accepted: 29 December 2024  
Published: 2 January 2025  
**Citation:** [PERSON]; [PERSON] Predictive Modeling and Experimental Analysis of Cyclic Shear Behavior in Sand-Fly Ash Mixtures. _Appl. Sci._**8025**, 153, 339, 340,  
(37.13%), structural fills and embankments (18.06%), and blended cement (10.40%). These uses emphasize its significance in sustainable infrastructure [1]. Studies have explored the use of various waste materials in geotechnical applications, aiming to leverage the advantageous properties of each material over traditional soils [2; 3; 4; 5; 6; 7]. In geotechnics, the use of this extremely fine powder was suggested as an effective alternative to increase strength and stiffness through chemical reactions in soil stabilization, as it contains pozzolans such as lime (CaO), silica (SiO\({}_{2}\)), and alumina (Al\({}_{2}\)O\({}_{3}\)) [8; 9]. The lime (CaO) present in fly ash undergoes a chemical reaction, leading to the formation of cementitious and pozzolanic gels comprising calcium silicate hydrate (CSH) and calcium aluminate hydrate (CAH) gel, effectively bind the soil particles, resulting in increased strength and stiffness of the soil [10]. There are numerous studies that explain that the fly ash was used to stabilize soils for mechanical, hydraulic, physical, or chemical purposes [11; 12; 13; 14]. For instance, [PERSON] [15] explored the improvements in the engineering characteristics of compacted soils. It was recognized for its effectiveness in the stabilization of organic soils, as evidenced by the work of [PERSON] et al., [PERSON] et al., and [PERSON] [16; 17; 18]. Studies by [PERSON] et al. and [PERSON] et al. [19; 20] have demonstrated the potential of fly ash in enhancing the mechanical properties of cohesive soils. Similarly, the mechanical properties of sand were also positively influenced by the incorporation of fly ash, as highlighted by [PERSON] et al. [21]. Fly ash application in road pavement and embankment is as a substitute for cement and/or sand [22].