- freely available
Water 2017, 9(5), 324; https://doi.org/10.3390/w9050324
2. Field Data Collection and Formula Derivation
2.1. Site Description
2.2. Field Data
2.3. Proposed Bend Scour Computation Equation
3. Method for Embankment Toe Scour Simulation
3.1. 2D Finite-Volume Hydraulic Model
- The cell interface is the dry edge, when and , in which and are the left and right water depths at the center of the cell interface, respectively. There is no flux estimation.
- The cell interface is the wet edge, when and . The upstream flux-splitting finite-volume scheme coupled with the hydrostatic reconstruction method  is adopted to estimate the well-balanced numerical fluxes.
- The cell interface is the partially wet edge with flux, when , , and , where zb is the bed elevation. The momentum flux is set at 0 and the mass flux (hu)LR at cell interface LR is estimated as:
- The cell interface is the partially wet edge without flux, when , , and . According to the bed elevation condition, there is no flux across the cell interface. Thus, no flux estimation is required.
3.2. General Scour Computation Equation
3.3. Method for Simulating Bend Scour Depth Evolution
- Inputting flow hydrographs (simulation time step is 1 h), setting model parameters (i.e., numerical time step and Manning roughness coefficients), and then simulating the 2D flow field in the bend reach through the proposed 2D finite-volume hydraulic model (Section 3.1). At the end of each simulation time step, the water depth and velocity in each computational cell are outputted.
- After 2D flow simulation, one obtains the approach flow conditions (i.e., entire hydrographs) at the specific computational cell, including water depth, velocities, water surface width, and the centerline radius of the bend.
- For each simulation time step (1 h), one substitutes the approach flow conditions into the general scour computation equation (i.e., Equation (15)) to achieve the estimated general scour depth. After the entire general scour simulation, the evolution of the estimated general scour depth is thus obtained.
- For each simulation time step (1 h), one re-evaluates the water depth by adding the water depth and the estimated general scour depth to obtain the revised water depth: .
- For each simulation time step (1 h), one re-evaluates velocity through unit flow discharge divided by revised water depth and obtains the revised velocity as .
- For each simulation time step (1 h), one substitutes the revised flow conditions (i.e., ) into Equations (1)–(3) and (6) to obtain the bend scour depth. After entire bend scour simulation, the evolution of the estimated bend scour depth is thus obtained.
4. Flow Field and Embankment Toe Scour Simulations
4.1. Verifications of 2D Finite-Volume Model
4.2. Verifications of Proposed Method for Bend Scour Depth
4.3. Practical Embankment Safety Curve
Conflicts of Interest
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|River||Site||Flood Event||Qp (m3/s)||qp (m2/s)||s0||d50 (mm)||R0 (m)||dbs (m)||Remark|
|Cho-Shui River||Cho-Shui Embankment||1. Typhoon Nanmadol (August 2011)||164||1.48||0.0063||3.43||605||0.67||Lin and Lin |
|Fanziliao Embankment||2. Typhoon Talim (June 2012)||346||1.86||0.0071||23.5||418||0.22|
|3. Typhoon Saola (August 2012)||475||2.97||0.0057||7.5||418||0.8|
|Linan Embankment||4. Typhoon Nanmadol (August 2011)||186||1.31||0.0066||85||558||0.36|
|5. Typhoon Saola (August 2012)||2279||13.21||0.0066||34.5||558||2.36|
|Shanhan Embankment||6. Typhoon Talim (June 2012)||562||4.44||0.0153||19.5||471||1.9|
|Aiguoqiao Embankment||7. Typhoon Talim (June 2012)||1182||11.87||0.0112||48||169||0.47|
|8. Typhoon Saola (August 2012)||1837||14.94||0.0148||25.5||169||2.45|
|Shuideliaw Embankment||9. Typhoon Trami (August 2013)||4186||25.37||0.00527||108||800||1.71||Lu |
|10. Typhoon Usagi (September 2013)||5309||18.31||0.00527||108||800||3.30|
|Da-Chia River||Fengzhou Embankment||11. Typhoon Soulik (July 2013)||6692||22.01||0.00755||168||500||5.23|
|12. Typhoon Trami (August 2013)||2393||10.64||0.00755||168||500||0.55|
|Eηp (%)||ETp (%)||R2|
|Typhoon Trami (August 2013)||0.1335||8.69||0.874|
|Typhoon Usagi (September 2013)||0.4600||8.33||0.889|
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