## 3 Results and Discussion
### The Influence of Independent Variables on the Hydraulic Conductivity  
To examine the effect of the independent variables on the response, three-dimensional (3D) surface and contour plots were produced. To this effect, two variables were varying at a time, while the third variable was kept constant at the central (0) level.  
The Effect of Independent Variables on the Hydraulic Conductivity  
Figure 9 depicts the surface and contour plots of the interactive effect of olivine content and carbonation time on the hydraulic conductivity at constant carbonation pressure (150 kPa). As seen from the figure, the hydraulic conductivity has a decreasing trend at constant carbonation pressure as the olivine content and carbonation time increases within the experimental range. Besides, the olivine content effectiveness on the hydraulic conductivity is more significant at higher carbonation durations, in contrast to the specimen's carbonated at shorter carbonation durations. Since olivine carbonation and the hydration activity of olivine, leading to the formation of hydrated magnesium carbonates, depends on the CO\({}_{2}\) exposure time, hence carbonation duration should be considered a vital parameter of carbonated-olivine-treated soil. Therefore, the interaction of olivine content and carbonation time is vital in decreasing the hydraulic conductivity of olivine-admixed soils.  
Figure 10 depicts the effect of carbonation time and carbonation pressure on the hydraulic conductivity of the carbonated admixed-clay at constant olivine content (20%). As observed from the figure, the interactive effect of carbonation time and carbonation pressure is less considerable to decrease the hydraulic conductivity of the carbonated treated-clay relative to the interactive effect of olivine content and carbonation duration (as seen in Figure 9). This could be due to the constant olivine content (20%), which is not the optimum olivine content to facilitate adequate carbonation and the subsequent hydration leading to the formation of the hydrated magnesium carbonates, which contribute to hydraulic conductivity reduction. Nonetheless, increasing carbonation time and carbonation pressure at constant olivine content intensifies the positive impact of each other on decreasing the hydraulic conductivity of the carbonated treated specimen.  
Figure 8: Perturbation chart.  
Figure 9: Response surface and contour plots demonstrating the interactive effects of carbonation, time and carbonation pressure on the hydraulic conductivity while keeping olivine content at central level.  
The effect of olivine content and carbonation pressure on the hydraulic conductivity at constant carbonation time (14.8 h) is demonstrated in Figure 11 by surface and contour plots. As seen from the figure, the hydraulic conductivity decreases when olivine content increases from 10% to 30% and carbonation pressure increase from 100 to 200 kPa. The  
Figure 10: Response surface and contour plots demonstrating the interactive effects of carbonation time and carbonation pressure on the hydraulic conductivity while keeping olivine content at central level.  
formation of hydrated magnesium carbonates is responsible for the decline in the hydraulic conductivity upon adding olivine under varying carbonation pressure at constant carbonation time. These findings demonstrate that olivine content, carbonation time, and carbonation pressure play a critical role in the reduction of the hydraulic conductivity of carbonated-olivine admixed soils since olivine carbonation, and the hydration activity of olivine leading to the formation of hydrated magnesium carbonates depends on the olivine content, CO\({}_{2}\) exposure time, and carbonation pressure.  
Figure 11: Response surface and contour plots demonstrating the interactive effects of olivine content and carbonation pressure on the hydraulic conductivity while keeping carbonation time at central level.