## 3 Experimental Test Results and Analysis
### Capillary Water Absorption (CWA)  
Figure 11 represents the measured and calculated mass of water absorbed per unit of area over 72 h versus the square root of time (t\(\%\)) at 28 days. As elucidated in the curve, the control mixture exhibits the lowest mass of water-absorbed magnitude, standing at 10.3 kg/m\({}^{2}\). With increasing OWA levels, the water absorption shows fluctuations. In the first 24 h, pastes with 5 and 10% OWA exhibit similar values for S and D. Nonetheless, after this period, a slight difference appears, with the lowest measurements noted in the 10% OWA paste. Beyond this level, the mass of water absorbed increases again to reach 38.8 kg/m\({}^{2}\) for the samples of 20% OWA substitution, displaying the biggest rise of 270% compared to the reference specimen. Including excessive amounts of OWA accelerates water uptake by capillarity, with the best performance observed in 10% OWA pastes. This may be interpreted by the increased porosity observed in the paste, as shown in the density tests (decrease in the density). This explanation is proved by previous works indicating OWA's impact on material porosity [13; 51]. Figure 10: Effect of OWA on TWA after 28 days. Furthermore, the proposed capillary-diffusive model accurately predicts the mass of absorbed water per unit of area, yielding a high degree of correlation between the estimated and the experimental data. In particular, the coefficient of determination (R\({}^{2}\)) is approximately 0.99 for all replacement levels after 28 days of curing. The results of the capillary-diffusive model are presented in Table 4. The evolution of both sorptivity (S) and diffusion (D) on day 28 is illustrated in Figure 12. All samples follow the same trend as for CWA analysis, meaning that S and D behave identically to CWA. Due to the diffusion mechanism, the water continues to flow through the capillary pores after it has been absorbed, hence justifying the strong relationship between those two characteristics (S and D) [54]. To further visualize the link between S and D, a regression equation is calculated, indicating a high coefficient of determination R\({}^{2}\) = 0.91, as inferred in Figure 13.  
Figure 11: Mass of water absorbed per unit of area after 28 days (Experimental and Estimated). Figure 12: Evolution of sorptivity and diffusion at 28 days. As observed from the curve, the reference sample records the lowest sorptivity and diffusion across all mixtures. More precisely, the S and D values recorded for the reference specimen are 0.158 kg/m\({}^{2}\)-s\(\
icefrac{{1}}{{2}}\) and 5.5 \(\times\) 10\({}^{-8}\) m\({}^{2}\)/s after 72 h. As the percentage of OWA rises, these two variables fluctuate, achieving optimal performance for 10% OWA pastes. Beyond this threshold, S and D increase again with the highest magnitudes of 0.305 kg/m\({}^{2}\)-s\(\
icefrac{{1}}{{2}}\) and 1.59 \(\times\) 10\({}^{-8}\) m\({}^{2}\)/s for the sample made with 20% OWA. This is equivalent to growth rates of 92% and 180%, respectively, relative to the control paste. Such increase is primarily due to the porous nature of OWA, which makes the paste become more integrated with pores (increased porosity), thus leading to a greater water uptake [13]. In addition, the rise in \(D\) values suggests that OWA may accelerate the diffusion of water, promoting the ease with which water can pass through the paste. This water absorption behavior is identical to that observed when using banana leaf ash. However, rice husk ash contributes to the reduction in permeability. All in all, OWA can be a major contributor to facilitating the passage of water through capillary action and diffusion, thus leading to the formation of a paste that absorbs water quickly near the surface and promotes water penetration in the deeper layers [49; 50; 51]. In such scenarios, OWA-based paving blocks with high water absorption capabilities can be ideal in permeable pavement systems, limiting surface runoff and refilling groundwater.