*3.2. Numerical Model Validation*

For the validation of the numerical model, the simulation domain was selected as the downstream river reach. The reach is approximately 16.5 km long from the Shihmen afterbay weir to the Yuanshan weir, as shown in Figure 3. The water intake is located on the right-hand-side bank of the Yuanshan weir, which delivers withdrawal water to the Bansin water treatment plant and supplies water. Field data collected at the Dasi bridge gauge station during two historical typhoon flood events—Typhoon Changmi and Typhoon Krosa—were used for model validation. By comparing the measured water level and suspended sediment concentration hydrographs, this study determined that the simulated results obtained using the adopted 2D numerical model were highly consistent with the measured data (Figure 4), despite the existence of some discrepancy; for example, a discrepancy was observed in the peak sediment concentration, for which the average relative error was 2.2% for Typhoon Changmi. Accordingly, the adopted 2D numerical model can model velocity and concentration fields in natural rivers with irregular topography.

**Figure 3.** Simulation domain along the downstream river from Shihmen afterbay weir to Yuanshan weir; some of the grid meshes also displayed.

**Figure 4.** Model validation using data of two typhoon flood events at the Dasi bridge gauge station.

After the validation of the numerical model, this study evaluated the most feasible replenishment area for placing the dredged sediment. As presented in Figure 3, the approximately 3.6-km river reach located between the Shihmen afterbay weir (Section 91) and Section 85 may be a suitable area for sediment replenishment due to the cost constraints of dredging pipelines. In part of the simulation domain, the simulated results pertaining to the flow velocity and water depth in the river reach between Section 91 and Section 85 were analyzed, as discussed in the following section.

#### *3.3. Hydraulic Assessment of the Feasible Replenishment Area*

During the selection of suitable replenishment areas, locations near a dam should be considered to reduce the implementation cost of the dredging pipeline system and maintenance work. Moreover, the replenishment areas should be designed for construction on a floodplain. Accordingly, in this study, the candidate replenishment areas were tentatively selected and marked as Zone 1, Zone 2, and Zone 3 (Figure 5).

To resolve the problem associated with the unavailability of suitable sites for the disposal of materials dredged from reservoirs, the replenishment method is typically considered for disposing fine sediment dredged from reservoirs. Hjulstrom (1935) [25] found that the critical scour (or erosion) velocity is proportional to the particle size, and resistance to scour increases for sediment finer than 50 μm; these findings indicate that factors other than particle size and weight influence scour phenomena [26,27]. Sediment dredged from around the dam site exhibited a finer level of cohesiveness than the median particle size (*d*50 = 0.006 mm; Figure 2); therefore, we used *d*25 (0.0023 mm) to represent the replenished sediment particle size, signifying that a critical velocity of approximately 1.5 m/s would be required to initiate the scouring process [28]. Moreover, according to the regulation of water pollution control action [19], the replenishment area should be confined by a filter structure that serves as a permeable barrier to avoid the replenished fine sediment from polluting the water in nearby main channels during low-flow periods. Therefore, sediment that was excavated from the Lofu site and had a median particle size *d*50 of 1.76 mm (classified as coarse sand; Figure 2) was used as the filter material. We used *d*75 (9.5 mm, classified as medium gravel) to represent the replenished sediment particle size; hence, a critical velocity of approximately 1.05 m/s would be required to initiate scouring for the filter structure [28]. On the basis of the preceding analysis, we may adopt a higher critical scour velocity (e.g., 1.5 m/s) with sufficient flow depth to evaluate the incipient motion of both fine sediment and

coarse sediment. Although the concept of critical scour velocity is used herein for illustrative purposes, it indeed provided the preliminary criterion to assess the feasible replenishment area.

**Figure 5.** Candidate sediment replenishment areas.

The validated 2D numerical model was used to model the flow velocity distribution field in the candidate replenishment areas. The simulated results for water depth (Figure 6) revealed that the flow current was confined within the main channel at a discharge of 200 m<sup>3</sup>/s. Accordingly, the 2-, 10-, and 20-year return period floods were determined to have peak discharges of 1700, 3500, and 6100 m<sup>3</sup>/s, respectively [20]. We adopted the flood discharges of 1700 and 6100 m<sup>3</sup>/s in two test cases separately to execute the 2D numerical model for the preliminary selection of the feasible replenishment areas.

**Figure 6.** Downstream river reach for evaluation with a discharge of 200 m<sup>3</sup>/s.

According to the simulated results obtained from the test case that involved the flood discharge of 1700 m<sup>3</sup>/s, the water depth was lower than 1 m in both Zone 2 and Zone 3 (Figure 7a). In Zone 1, the water depth was higher than 1 m in most portions of the replenishment area. In addition, the velocity was lower than 1 m/s in both Zone 2 and Zone 3. However, most portions of Zone 1 had the velocity of more than 1 m/s, whereas the velocity near the main channel was higher than 2 m/s. In the test case that involved the discharge of 6100 m<sup>3</sup>/s, the water depth was still lower than 1 m in most portions of Zone 2 and Zone 3, whereas the depth in Zone 1 increased to more than 3 m in most portions of the replenishment area (Figure 7b). The velocity in most portions of Zone 1 was more than 1.5 m/s. However, the velocities in most portions of Zone 2 and Zone 3 were lower than 1 m/s, except for the portion near the main channel. The simulated flow velocities in Zone 1 in the two test cases (involving flood discharges of 1700 and 6100 m<sup>3</sup>/s separately) satisfied the critical scour velocity criterion (1.5 m/s) for incipient motion of both fine sediment and coarse sediment. Moreover, the simulated water depths ranged from 1.5 to 4 m in Zone 1 of the replenishment area in the two test cases. The height of the filter structure was 2 m, and that of the replenished material was 1.6 m in the replenishment area, which were determined to be subject to flooding. Consequently, Zone 1 was selected as the location for sediment replenishment. The feasible replenishment area—Zone 1—was determined to be on the right-hand-side floodplain (Figure 6). Moreover, for the experimental river reach for the physical model, we considered the reach between the Shihmen afterbay weir (Section 91 as upstream boundary) and Section 90 (downstream boundary) with a narrow cross section.

**Figure 7.** Simulated water depth and flow velocity distributions at flood discharges of (**a**) 1700 and (**b**) 6100 m<sup>3</sup>/s.

#### **4. Physical Model Layout and Scaling**
