## 3 Results and Discussion
### Modeling Study
#### 3.2.4 Steady-State, Porous Media Capture Model  
The results presented in Figure 6A for the steady-state porous media capture model based on SS concentration indicate wild fluctuations in the coefficient \(X_{C}\) within the ranges of 3.92\(-\)9.29, 3.36\(-\)7.48, and 5.07\(-\)7.65 m\({}^{-1}\) at filtration rates of 20, 30, and 40 m/h, respectively. This result indicates that the steady-state porous media capture model based on SS concentration cannot be used to describe the performance of the media layer. However, the values of \(X_{C}\) in Figure 6A were higher than those reported in previous works. The \(X_{C}\) of  
Figure 5: The \(k\)-C\({}^{*}\) model: (**A,B**) the corrrelation between \(ln(C/C_{0})\) and \(H/u\) during system operation times of (**A**) 10\(-\)20 min and (**B**) 30–300 min; (**C,D**) the correlation between \(ln(L/L_{0})\) and \(H/u\) during system operation times of (**C**) 10\(-\)60 min and (**D**) 90–300 min; (**E**) the correlation between \(ln(\sigma)\) and \(H/u\); (**F**) the time evolution of \(k_{\sigma}\) and \(A_{\sigma}\). geosynthetic filters was in a range of 917-1553 mm\({}^{-1}\)[16], and that of geotextile filters was in a range of 396-1793 mm\({}^{-1}\)[51], indicating a higher SS capture efficiency of the media in this study. By contrast, the results of the model based on varying SS inlet load (Figure 6B) reveals a clear correlation with the coefficient \(X_{L}\). Thus: (i) the \(X_{L}\) value is seen to increase from 3.92 to 6.66 m\({}^{-1}\) under a low filtration velocity (20 m/h); (ii) at the moderate filtration velocity of 30 m/h, the \(X_{L}\) remains steady within the range of 6.06\(-\)6.16 m\({}^{-1}\) during the initial 10\(-\)60 min of operation, subsequently increasing slightly from 6.14 to 6.63 m\({}^{-1}\); and (iii) at the maximum filtration velocity of 40 m/h, the \(X_{L}\) value is seen to decrease from 7.14 to 6.31 m\({}^{-1}\) during the initial 10\(-\)60 min of operation and subsequently remain stable within the range of 6.02\(-\)6.31 m\({}^{-1}\). These results suggest that a low filtration velocity (20 m/h) leads to gradual blockage of the pores in the media layer, and that uniform blockage occurs at 30 m/h. This is probably a result of deep bed filtration behavior due to the removal of a larger fraction of SS in the sedimentation chamber and the introduction of a smaller fraction of SS into the filtration chamber, as described previously [20]. Moreover, the observation of a high \(X_{L}\) value at the beginning of operation at 40 m/h, with a subsequent decrease over the operating time, also suggests that a substantial amount of SS is deposited during the initial period, with a smaller fraction being discharged thereafter. Overall, an increase in the \(X_{L}\) value with increasing filtration velocity is observed during the initial 10\(-\)60 min of operation, thus suggesting an increased amount of blockage with increased inlet SS load [16; 46]. Nevertheless, the present results indicate a convergence of the \(X_{L}\) towards similar values regardless of the filtration velocity as the operation period  
Figure 6: The time and filtration-velocity variations in the filtration coefficients of the media layer based on: (**A**) SS concentration, (**B**) SS load reduction, and (**C**) specific SS deposit. is increased. Thus, the average and standard deviation of the \(X_{L}\) values at operating times of 180\(-\)300 min are 6.31 \(\pm\) 0.27 m\({}^{-1}\) for the flowrate range of 20\(-\)40 m/h. This indicates that similar levels of SS deposition and blockage of the media layer are eventually reached (given sufficient operation time) regardless of filtration velocity. In view of the above results, it was thought that the \(X_{L}\) parameter would be useful for investigating the blockage of the media layer. However, the tendency of the \(X_{L}\) value to vary with both operating time and filtration velocity might not readily allow a clear description of the SS removal.