**3.1 Model setup**

Based on the DEM data of 2013 and 2014, several structured meshes covering the study domain from JiJi Weir to Minchu Bridge were generated, which embed the combinations of the planned weir structures and lateral channel excavations.

As shown in **Figure 5**, zones representing erodible bedrocks, alluvium, structures (non-erodible), have been identified and embedded in simulation domain based on the satellite image of 2014. The erodible bedrock zone resulted from the channel incisions and head-cut development, where both the bedrock erosion and sediment transport simulations are to be conducted. The alluvial zone is covered with pebbles

**Figure 5.** *Erodible bedrock zone.*

*Erosion Control at Downstream of Reservoir Using In-stream Weirs DOI: http://dx.doi.org/10.5772/intechopen.108169*

**Figure 6.** *Bedrock erodibility index.*

and gravels, and no bedrock erosion simulation will be applied. The non-erodible zone represents the weir structures and other bank/bed protection measures (i.e., concrete blocks) and is assumed non-erodible during the simulations. Therefore, the distribution of non-erodible zones changes with the simulated erosion control plans.

**Figure 6** shows the measured bedrock erodibility index distribution in 2014. The whole domain was divided into 11 zones with different erodibility index, *kh*, varying from 310 (high rock strength) to 29 (low rock strength) [2]. The aforementioned channel bed properties (**Figures 5** and **6**) are applied to all cases. Adjustments are made accordingly for the installations of weir structures in different erosion control plans.

### **3.2 Model calibration and validation**

The site-specific parameters (*a*, *b*, and *c*) in Equation (8) and the lateral slope parameters *r* and *k* in Equation (11) need to be calibrated before applications. In this

**Figure 7.** *Flood hydrograph of Typhoons Morakot (8/2009) and Matmo (7/2014).*

**Figure 8.** *Comparisons of cross-sectional profiles for P0-1 with Typhoon Matmo.*

study, two cases without any control structures, P0-1 with Typhoon Marmo and P0-2 with Typhoon Morakot, are used to calibrate these parameters and validate the bedrock erosion model, respectively.

*Erosion Control at Downstream of Reservoir Using In-stream Weirs DOI: http://dx.doi.org/10.5772/intechopen.108169*

#### **Figure 9.**

*Comparisons of cross-sectional profiles for P0-2 with Typhoon Morakot.*

In the calibration step, the parameters are adjusted to obtain the best fit of the simulations to the data; while in the validation step, no parameters are changed. **Figure 7** shows the hydrographs of these two typhoons, which are considered as the major hydrological events causing significant bed morphological changes in this channel. Due to its high peak discharge (*Q* = 12,600 *m<sup>3</sup> /s*), Typhoon Morakot was selected for all other erosion control plans.

Through the numerical calibration tests, the parameter set for the stream power method was found to be: *a* = 0.005, *b* = 0.75, and *c* = 0.2. For the lateral erosion effects, the slope exponential parameter *r* = 1 and the slope scale factor *k* = 6 were used. **Figures 8** and **9** compare the profiles at the selected cross sections for P0-1 with Typhoon Matmo and P0-2 with Typhoon Morakot, respectively. In general, good agreements between the measurements and the simulations were observed for both cases at those cross sections, especially for channel incisions. As for the lateral erosion observed at sections JiJi-28, 27, and 26, although more discrepancies exist, the improved stream power method with considering the slope effects (Equation 7) has proved its capability of capturing these lateral erosion phenomena in the complicated bedrock erosion processes.

#### **3.3 Erosion control plans**

Since 2007, WRA has proposed a few erosion control plans attempting to stop the downstream channel of JiJi Weir from incisions and head-cut development. These erosion control plans included multiple in-stream weir structures, lateral channel excavations, and other engineering measures, such as concrete blocks for bank protections, gabions, etc. With the calibrated and validated parameters, CCHE3D bedrock erosion model was used to evaluate all the erosion control plans with different combinations of control structures [2]. According to the numerical simulations, one plan with three weirs at JiJi-22, 25, and 26 and side excavations from JiJi-27 to CS-112 was confirmed as the most effective in the erosion reduction among all proposed erosion control plans. Based on the numerical simulations of these erosion control plans, optimal design was explored.

In the historical channel profiles along thalweg of the downstream channel from 1998 to 2014 as shown in **Figure 1**, the bed slope is 0.0412 near the head-cut reach, 0.0057 in the incision reach, and 0.0028 in the transition reach. The head-cut reach and the incision reach are of bare rock channel, actively eroded; the transition reach is sometimes partially covered with sediments, showing alluvial river morphologic and sediment transport features, and thus considered to be more stable. In this study, it is assumed that the channel will be stabilized if the bed slope can be reduced to 0.0028 approximately by installing erosion control weirs in the channel.

Since the 10 m deep head-cut has reached closer to the JiJi Dam, seriously threatening the safety of the dam structure (**Figure 3**), the protection of the upstream headcut zone (from JiJi-30 to JiJi-22) is considered as the first priority. The high weir structure at JiJi-25 is capable of significantly reducing the bed rock erosion in the reach from JiJi-26 to JiJi-22. As for the reach from JiJi-30 to JiJi-26, a weir structure is planned at CS-115, and the small reservoir behind this weir structure is designed to slow down the flow and thus reduce the erosion.

For downstream of the head-cut zone, the deep incised main channel (from CS-109 to JiJi-26) is relatively narrow, the water surface elevation in this reach will increase during floods to endanger the embankment of the left bank. Channel lateral excavations are proposed in such a way that the thalweg is kept and the widening lateral excavation (150 *m*) is on the right floodplain of the channel from JiJi-27 to CS-108.5. Hydrologic data indicates that the flow discharge in the channel is less than *Q* = 1000 m<sup>3</sup> /s for most time of the year, and the flows in this range are confined in

### *Erosion Control at Downstream of Reservoir Using In-stream Weirs DOI: http://dx.doi.org/10.5772/intechopen.108169*

the main channel. The water depth for this discharge is about 4 m. If no in-stream weir structures are built, the proposed lateral excavations will still allow the water to flow in the deep channel for the most of time of a year, but the water will divert to the widened areas in the flood seasons. The widened channel will reduce the main flow velocity and water surface elevation, which is beneficial to bank protection during floods in addition to promote sediment deposition.

To enhance the erosion reduction effects, two additional low-headed weirs are suggested to be installed at CS-111 and CS-113 in this reach to further control the flow and erosion. To prevent the development of a second head-cut between CS-108 and CS-109 (see **Figure 1**), another low-headed weir structure is proposed as well to be installed at CS-108.5.

The heights of the four weirs at CS-108.5, CS-111, CS-113, and CS-115 are determined in such a way that the small pools formed behind the weirs can approximately protect half of the reach between weirs (slope equal to zero). As illustrated in **Figure 10**, the bed slope of the reach between Weir-A and B is *S0*, the pool behind Weir-A can affect an area about half of the reach (*L/*2). Sediments would fill up the pool behind Weir-A because the surface slope is significantly reduced. Before the deposition filled the channel segment, the bed slope behind Weir-B is larger than *Sd* (= *S*0/2), and it reaches to *Sd* after the segment is filled up, which is the highest slope possible in the design channel. The new established bed slope would be about half of the initial slope *S0*. The protected channel would be stable and filled with sediment. According to this idea, the top elevations of the five weirs are determined as indicated in **Table 1**.

**Figure 11** shows the initial setup for the optimal design. The excavation is denoted in the white polygon area, while six weir strucrures installed at JiJi-25 (CS-116), JiJi-26, CS-115, CS-113, CS-111, and CS-108.5) as non-erodible zones. For the optimal design case simulations, the calibrated parameter sets and the bedrock erodibity index

**Figure 10.** *Sketch of determination of weir height.*


**Table 1.**

*Top elevations of weir structures.*

**Figure 11.** *Model setup for optimal design.*

remain the same. The bed property zone is adjusted if the excavation cuts into the alluvium and exposes the soft rock underneath.

In current sediment transport simulations, both the suspended load and the bedload transport are considered with three representative size diameters: 0.0081, 0.03086, and 0.3006 *m*. Sediment boundary condition is obtained from the measured concentration in a detention pool nearby JiJi Weir during typhoon season, initial conditions and other boundary conditions are the same as the cases of stream power erosion simulations. This simply coupled sediment transport and stream-power-based erosion model was calibrated using the P0-1 conditions and then applied to sedimentation simulations in the optimal design study. The calibrated model could capture the main trend of the channel incision particularly in the reach from the JiJi Dam to CS111 under the P0-1 condition.

The simulation results of the optimal design were compared with those of the cases without any structures. **Figures 12** and **13** show the longitudinal profile of bed changes. In the first 1.2 km reach, where two high weirs at JiJi-25 and JiJi-26 are

**Figure 12.** *Simulated erosion patterns for the case without structures.*

**Figure 13** *Simulated erosion patterns for the case with the optimal design.*

located, much more depositions were observed in the optimal plan, while the erosions are dominant for the case without structures. Further downstream, in general, the erosions are dominant for both cases, except for small regions upstream of the weir structures, where the water surface is increased, and the velocity is slower . The bed change pattern around all the weir structures is similar: there are depositions at upstream but erosions at downstream, which is expected. **Figure 14** shows the bed profile along the thalweg. As can be seen, in the optimal plan, the erosion along the thalweg has been reduced significantly, and the upstream reach with the first two weirs demonstrated obvious deposistion pattern. The two weir structures at JiJi-25 and JiJi-26 do serve the purpose of reducing channel incision and stopping the head-cut development effectively (**Figure 15**).

Despite the simple coupling method, the coupled bedrock erosion and sediment transport model demonstrated the promoting effects of the proposed optimal design on sediment depositions to protect the channel bed from further eroding.

**Figure 14** *Profile of bed changes.*

**Figure 15** *Profile of bed elevation along the thalweg.*
