# Predictive Modeling and Experimental Analysis of Cyclic Shear Behavior in Sand-Fly Ash Mixtures
## 4 Results and Discussion  
Figure 4 illustrates the variation in volumetric strain (%) over time (minutes) across five loading cycles in a constant normal load cyclic direct shear test conducted on TS alone. The plot shows a progressive increase in volumetric strain with each cycle, indicating cumulative deformation under cyclic loading. Each cycle follows a consistent pattern, with volumetric strain initially increasing and then partially decreasing, which is characteristic of cyclic shear tests. The trend line points out a positive slope, represented by the equation (y = 0.1837\(\times\) + 2.1213), indicating an overall upward trend in baseline strain over time. The labels (1 st to 5 th cycle) mark distinct loading phases, with a noticeable upward shift in strain baseline after each cycle, suggesting strain accumulation due to repeated shear stresses. This trend provides insights into the deformation behavior of TS under cyclic loading, which is essential for evaluating its suitability in engineering applications that involve repetitive loads. Figure 4: The variation in the volumetric strain at each cycle of loading. Figure 3: Materials and equipment used: (**a**) fly ash, (**b**) Trakya sand, (**c**) cyclic direct shear testing equipment, (**d**) preparing specimens inside the shear box, (**e**) specimens after test. Figure 5 presents the results from constant normal load cyclic direct shear tests conducted on clean sand and sand-fly ash mixtures with varying percentages of fly ash. Each tested specimen demonstrates the variation in volumetric strain over time and the linearly increasing tendency that reflects the rate of strain increase for that mixture. The expansion or contraction of the soil caused by shear loading is a phenomenon which requires the comprehension of the mechanical properties of the interface [39]. The specimen labeled TS, consisting of clean Trakya sand with no fly ash added, exhibited a moderate, steady increase in volumetric strain over time, with minor fluctuations linked to the cyclic loading process. The regression equation reflects a relatively low strain rate, indicating that clean sand resists deformation under cyclic loading (Figure 5a). Adding 2.5% fly ash to the mixture (FA2.5) results in behavior similar to clean sand, with only a slight decrease in the rate of strain accumulation. The regression equation for FA2.5 shows minor reductions in both intercept and slope, suggesting that the low fly ash content has minimal impact on the material's deformation properties (Figure 5b). Depending on factors such as density, shear displacement, stress change and number of cycles, the volumetric behavior emerges as an indicative feature for interfaces [40]. There is an interdependency between the volumetric behavior of ash mixtures with testing conditions such as the confining stress and compacted level [41]. As the fly ash content increases to 5% (FA5), the initial strain level rises slightly, along with a modest increase in the strain rate. This indicates a slight reduction in strength, making the mixture more prone to deformation under cyclic loading, though the change remains moderate (Figure 5c). With the FA10 specimen (10% fly ash), both the initial strain and the deformation rate increase further, showing that the mixture becomes progressively more susceptible to cyclic loading as fly ash content rises (Figure 5d). For both clean sand and a sand-fly ash mixture at 2.5% content, the volumetric behavior appears nearly identical, indicating that a small amount of fly ash does not significantly alter the initial structure of the sand matrix. However, when the fly ash content exceeds 5%, a notable volumetric increase occurs. This behavior can be attributed to the finer grain size of fly ash compared to sand. At around 5% content, fly ash particles fill the available voids within the sand matrix, reaching a level where the pore space becomes saturated with finer particles.