## 4 Discussion of the Results  
### Influence of Physical Properties on Mechanical Strength  
The influence of the physical properties on the mechanical strength was evaluated by calculating the data presented in Table 6. Additionally, Table 7 shows the relationship between the density of the fresh and hardened concrete and the crushed HS replacement percentage. To conduct these analyses, a normality test using the Shapiro-Wilks method was initially performed on each set of data. Then, the correlation test method was selected based on the distribution of the data: Pearson for normally distributed data, and Spearman for non-normally distributed data. A regression analysis was also conducted for each correlation to illustrate the behavior of each relationship graphically and determine the adjustment coefficient. The relationships presented in Table 6 had a correlation coefficient greater than 0.6 or lower than \(-\)0.6 and were deemed significant based on a 5% error significance test [4]. Our findings indicated that the choice of water-to-cement (w/c) ratio significantly influenced the compressive strength of the concrete specimens. Specifically, specimens with a 0.4 w/c ratio consistently exhibited higher strength compared to those with a 0.5 w/c ratio. This observation could be attributed to the well-established principle that a lower w/c ratio results in a denser and more compacted concrete matrix, which generally leads to higher strength. However, the relationship between the w/c ratio and HS content added complexity to this phenomenon. The impact of the HS replacement percentage on the concrete strength was variable. For instance, for the 0.4 w/c ratio specimens, a decreasing trend in strength as the HS replacement percentage increased was observed. This trend could be attributed to the inherent properties of the hazelnut shells, which introduced porosity and discontinuities in the concrete matrix. In contrast, for the 0.5 w/c ratio specimens, an increase in strength was noted with higher HS replacement percentages, indicating a more complex interaction between the w/c ratio and HS content. Notably, the maximum strength was achieved with 2.5% HS replacement for the 0.4 w/c ratio, approaching the standard concrete strength. An important contributing factor to this observation was the improved workability of the mixture, as reflected by the larger slump values. The enhanced workability reduced the challenges encountered during compaction, ultimately leading to improved strength. This correlation between workability and strength, as supported by the strong direct relationship (correlation coefficient, _rs_ = 0.8) highlights the interplay of multiple factors in determining concrete properties. Table 7 reveals a significant inverse correlation between the HS replacement percentage and both the fresh and hardened densities. Specifically, as the HS replacement percentage increased, the bulk and hardened densities of the concrete decreased. This behavior could be attributed to the lower density of crushed HS compared to traditional aggregates, which resulted in the lower overall density of the composite. Hence, the reduced mass of the specimens containing HS was the underlying reason for the observed lower densities, indicating that the HS had a diluting effect on the composite. A critical aspect that merits further investigation is the microstructure of hazelnut shells, which is rough, fibrous, and porous. This inherent porosity was a limiting factor for concrete compressive strength, resulting in an inverse relationship between HS replacement percentage and strength. The porous nature of the hazelnut shells introduced voids within the concrete matrix, reducing its overall density and strength. Additionally, the w/c