Issue 75

M. Ramos et alii, Fracture and structural integrity, 75 (2026) 399-434 ; DOI: 10.3221/IGF-ESIS.75.29

MP 0.697 34 <0.001 Not Normally Distributed DM-01 0.821 23 <0.001 Not Normally Distributed DM-02 0.926 25 0.072 Normally Distributed DM-03 0.902 21 0.038 Not Normally Distributed 0.860 37 <0.001 Not Normally Distributed DM-01 0.823 23 <0.001 Not Normally Distributed DM-02 0.785 25 <0.001 Not Normally Distributed DM-03 0.877 21 0.013 Not Normally Distributed 0.697 37 <0.001 Not Normally Distributed DM-01 0.824 23 <0.001 Not Normally Distributed DM-02 0.925 25 0.068 Normally Distributed DM-03 0.911 21 0.058 Normally Distributed 0.860 37 <0.001 Not Normally Distributed DM-01 0.840 23 0.002 Not Normally Distributed DM-02 0.785 25 <0.001 Not Normally Distributed DM-03 0.877 21 0.013 Not Normally Distributed MP MP MP

Length

Width

28 days

Length

Width

35 days

Length 0.698 37 <.0.001 Not Normally Distributed DM-01 0.825 23 0.001 Not Normally Distributed DM-02 0.922 25 0.057 Normally Distributed DM-03 0.911 21 0.058 Normally Distributed Table 13: Normal distribution test (Shapiro-Wilk) at different ages of concrete. MP

Applying the Shapiro-Wilk statistical test, it was identified that the crack width and length variables in the different sample designs (MP, DM-01, DM-02, and DM-03) and at different concrete ages (7, 14, 21, 28, and 35 days) mostly showed a p-value < 0.05, indicating that they did not follow a normal distribution. However, the crack length did follow a normal distribution in DM-01 (p-value = 0.076), DM-02 (p-value = 0.348), and DM-03 (p-value = 0.417) at 7 days; in DM-02 (p-value = 0.072) at 21 days; and in DM-02 (p-value = 0.068) and DM-03 (p-value = 0.058) at 28 days. In DM 02 (p = 0.057) and DM-03 (p = 0.058) at 35 days, a significant decrease was observed. Since parametric tests, such as ANOVA, require this assumption to be met, and most of the data did not satisfy it, nonparametric tests were used. To compare the four sample designs at each concrete age, the Kruskal-Wallis test was applied, and in cases where significant differences were found, the Mann-Whitney U test was used for pairwise comparisons. This approach ensures appropriate and reliable statistical analysis for interpreting the effect of polypropylene synthetic fiber on concrete cracking. Kruskal-Wallis Statistical Test Since the normality test indicated that not all the data followed a normal distribution, analysis of variance (ANOVA) was not appropriate for this research. Instead, the Kruskal-Wallis test was chosen, as it is more flexible and suitable when the assumption of normality is not met in at least one of the analyzed groups.

Kruskal-Wallis Kruskal-Wallis H gl Sig.

Date

Samples

Width Length Width Length Width Length Width Length Width Length

6.121 1.384 9.537 1.945 8.872 3.313 14.172 3.800 13.590 3.066

3 0.102 3 0.709 3 0.023 3 0.584 3 0.031 3 0.346 3 0.003 3 0.284 3 0.004 3 0.382

7 days MP, DM-01, DM-02 Y DM-03

14 days MP, DM-01, DM-02 Y DM-03

21 days MP, DM-01, DM-02 Y DM-03

28 days MP, DM-01, DM-02 Y DM-03

35 days MP, DM-01, DM-02 Y DM-03

Table 14: Kruskal-Wallis statistical test at different ages of concrete.

The Kruskal-Wallis test results showed that at 7 days there were no significant differences in crack width or length among the different sample designs. However, over time, differences in crack width began to appear, becoming significant at 14 days (p = 0.023), 21 days (p = 0.031), 28 days (p = 0.003), and 35 days (p = 0.004). This suggests that

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