# Predictive Modeling and Experimental Analysis of Cyclic Shear Behavior in Sand-Fly Ash Mixtures
## 2 Materials and Methods  
The materials, sand and fly ash, were obtained from Trakya and Soma in Turkey, respectively. The grain size distribution and SEM pictures of Trakya sand (TS) provide insights into its characteristics and potential suitability for geotechnical applications. The grain size distribution curve shows that TS has a broad range of particle sizes, with significant values including a D\({}_{10}\) of 0.28 mm, a D\({}_{30}\) of 0.31 mm, a D\({}_{50}\) of 0.36 mm, and a D\({}_{60}\) of 0.40 mm (Figure 1). The coefficient of uniformity (C\({}_{\text{u}}\)) is 1.44, which is relatively high and indicates a well-graded sand, meaning it has a wide range of particle sizes. This wide gradation typically enhances the compatibility and stability of the sand, making it more suitable for engineering purposes. However, the coefficient of curvature (C\({}_{\text{c}}\)) is 0.86, which is slightly lower than the typical range for well-graded soils, possibly suggesting minor irregularities in the distribution, though overall the sand remains well graded due to the high C\({}_{\text{u}}\). The SEM image of the sand grains reveals some details about the shape and texture of the particles (Figure 2). The sand grains appear sub-rounded to angular, indicating a moderate degree of transport or weathering. This angularity contributes to higher inter-particle friction, which is beneficial for the shear strength of sand in foundational and structural applications. The particles also show color variations, suggesting mineral diversity within the sand. This mineralogical variation may influence the chemical reactivity and long-term behavior of the sand under load or exposure to different environmental conditions. Together, the well-graded particle size distribution and the angularity of the particles make TS a potentially suitable material for applications requiring stability and strength.  
The chemical composition of fly ash, as reported by [PERSON] [35], reveals that it primarily consists of silicon dioxide (SiO\({}_{2}\)) at 50.50%, followed by aluminum oxide (Al\({}_{2}\)O\({}_{3}\)) at 23.70%, and a smaller percentage of iron oxide (Fe\({}_{2}\)O\({}_{3}\)) at 5.80%. The presence of calcium oxide (CaO) at 9.30% indicates that the fly ash could be classified as a Class C type, which is beneficial for self-hardening applications due to the cementitious behavior of CaO. Minor constituents include magnesium oxide (MgO) at 2.60%, sulfur trioxide (SO\({}_{3}\)) at 1.40%, and sodium oxide (Na\({}_{2}\)O) at 0.34%, with each potentially affecting the chemical stability and reactivity of the fly ash in various environments. The low loss on ignition (LOI) value of 0.19% suggests a high degree of combustion, meaning there is minimal unburned carbon, which enhances its suitability for use in the construction industry without affecting air entrainment or stability (Table 1). The physical analysis of fly ash grains given in Table 2 indicates that particle size distribution is relatively varied, with 23.3% of particles retained on a 45 mm sieve, suggesting a significant portion of coarse particles. Finer particles retained on the 90 mm (9.93%) and 200 mm (2.74%) sieves imply that fly ash also contains a fraction of fine particles, which contribute to filling the voids, thereby improving density and reducing permeability. The variation in particle size distribution is important as it influences both the pozzolanic activity and the rheological properties of cement mixtures.  
Figure 1: Grain size distribution of Takya sand (TS).  
Figure 2: SEM pictures of Takya sand grains.