# Predictive Modeling and Experimental Analysis of Cyclic Shear Behavior in Sand-Fly Ash Mixtures
## 4 Results and Discussion
Beyond this threshold, additional fly ash disrupts the packing structure of the sand and introduces excess fines, leading to greater volume expansion during shearing. This threshold level is defined as 15% FA content by dry weight, and it is indicated that beyond 15% of fly ash content, an increase in fly ash content started replacing the sand grains [42]. [PERSON] et al. [8] indicated that the addition of fly ash to soil changed the inter-particle void ratio. Also, in soil-fly ash mixtures, the micro fabric is a combination of grains that contribute to giving rise to a considerably large inter-particle void [43]). Soils normally have an air void content ranging between 1% and 5% at maximum dry density, whereas fly ash contains between 5% and 15% [44]. The higher void content could tend to limit the buildup of pore pressures during compaction thus allowing the fly ash to be compacted over a larger range of water content [45]. This change highlights a transition point where the fly ash content begins to dominate the mechanical behavior of the mixture, causing significant variations in the volume response. This understanding is critical for optimizing fly ash content in soil stabilization projects, as excessive fly ash may impact soil compressibility and shear characteristics. Similar results were observed by the studies performed on different additives in sand [31]. At 15% fly ash (FA15), the mixture experiences a more rapid accumulation of volumetric strain, signifying a notable decrease in stiffness and a greater tendency for deformation under cyclic stress (Figure 5e). The FA20 specimen, with the highest fly ash content (20%), implies that at high concentrations, fly ash significantly reduces the sand-fly ash mixture's resistance to cyclic deformation, likely due to diminished particle interlocking and cohesion (Figure 5f). The dilatancy response  
increases with the increase in fly ash proportions. This finding may also be explained by the role of the non-plastic nature of fly ash, which contributes to making the soil structure less compressible and consequently increasing the dilatancy phase of the binary assemblies under consideration. Figure 6 illustrates the horizontal stress versus horizontal strain behavior of sand-fly ash mixtures with varying fly ash contents. At lower strain levels (up to approximately 0.5%), mixtures with higher fly ash content (15% and 20%) exhibit higher horizontal stress, indicating increased initial strength and resistance to deformation due to better particle interlocking and denser packing. However, as strain levels increase, mixtures with lower fly ash content (e.g., 0% and 2.5%) and clean sand demonstrate higher horizontal stress, suggesting superior shear strength and frictional resistance at larger deformations. This transition indicates that while higher fly ash content enhances strength at small strains, its contribution diminishes at higher strains, where the frictional behavior of sand becomes dominant. This initial portion of the hysteresis loop reflects the material's response to the first application of cyclic loading, where the mixtures with higher fly ash content appear to possess greater resistance to deformation at lower strains. Figure 5: The variation in the volumetric strain of the tested specimens of; (**a**) Clean sand and mixtures of (**b**) 2.5 (%) FA, (**c**) 5 (%) FA, (**d**) 10 (%) FA, (**e**) 15 (%) FA and (**f**) 20 (%) FA. Figure 7 illustrates how shear stress varies with strain in different sand-fly ash mixtures under cyclic loading. The cyclic shear creates a characteristic hysteresis loop in each plot, which highlights the changes in shear stress as strain increases and decreases through each cycle. The behavior of the loop during shearing is dependent on the material properties, number of contact points, open fabric structure in the specimens, and stick-slip behavior between the soil grains [37]. In the case of clean sand, the hysteresis loop is wide and almost symmetric, indicating effective energy dissipation and strong resistance to deformation.