Analysis of Variables Influencing Scour on Large Sand-Bed Rivers Conducted Using Field Data
Abstract
:1. Introduction
2. Methodology
2.1. Influencing Variables
2.2. Data Filtering
2.3. Variable Reduction
3. Results
3.1. MNLR—Multiple Nonlinear Regression
3.2. Comparison with Different Scour Models
3.3. Variable Sensitivity Analysis
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Glossary
Symbol | Unit | Description |
ds | [m] | scour depth |
v | [m/s] | local approach flow velocity (upstream of the pier) |
vc | [m/s] | critical velocity |
y | [m] | approach water depth (upstream of the pier) |
b | [m] | nominal pier width |
l | [m] | pier length |
bef | [m] | effective pier width normal to the flow |
θ | [°] | angle of attack |
B | [m] | the channel width |
S | [1] | stream slope |
τ | [Pa] | local bed shear stress |
τc | [Pa] | critical bed shear stress |
Fr | [1] | Froude number |
Frc | [1] | critical Froude number for incipient motion |
Frd | [1] | densimetric Froude number |
Rep | [1] | particle Reynolds number |
RI | [years] | recurrence interval for measured flow rate |
g | [m/s2] | gravitational acceleration |
d50 | [mm] | sediment median grain size |
d95 | [mm] | the size at which 95% of the sediment particles are smaller |
σg | [1] | geometrical standard deviation of sediment (measure of non-uniformity) |
ρrel | [1] | submerged relative mass density of sediment particles (ρrel = [(ρs − ρ)/ρ] − 1 = 1.65) |
ρs | [kg/m3] | mass density of sediment particles (equal to 2650 kg/m3) |
ρw | [kg/m3] | mass density of water (equal to 1000 kg/m3) |
γs | [N/m3] | specific gravity of sediment (equal to 25,996.5 N/m3) |
γw | [N/m3] | specific gravity of water (equal to 9810 N/m3) |
K1 | [1] | the live-bed vs. clear-water correction factor |
K2 | [1] | the pier shape correction factor |
ν | [m2/s] | kinematic viscosity of fluid (ν = 1.6 × 10−6 m2/s) |
Φ | [°] | angle of repose for sediments |
r | [1] | Pearson correlation coefficient |
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Additional Variable | Equation | |
---|---|---|
Froude number | (1) | |
local shear stress | (2) | |
critical shear stress [34] | (3) | |
critical velocity [35] | (4) | |
critical Froude number | (5) | |
densimetric Froude number | (6) | |
particle Reynolds number | (7) |
Variable | Before Filtering | After Filtering | |||||
---|---|---|---|---|---|---|---|
Range | Average | Standard Deviation | Range | Average | Standard Deviation | ||
Original | ds | 0–10.4 | 1.1 | 1.3 | 0.21–7.8 | 1.5 | 1.3 |
bef | 0.21–28.7 | 2.3 | 2.5 | 0.24–11.6 | 2.0 | 1.9 | |
b | 0.21–19.5 | 1.6 | 1.6 | 0.24–11.6 | 1.3 | 1.4 | |
l | 0.21–39.6 | 6.3 | 5.3 | 0.37–25.3 | 6.3 | 4.7 | |
θ | 0–85.0 | 6.1 | 10.3 | 0–600 | 6.6 | 9.6 | |
d50 | 0.001–228.6 | 14.7 | 25.0 | 0.06–1.82 | 0.59 | 0.41 | |
y | 0–22.5 | 3.9 | 3.2 | 1.5–22.5 | 5.6 | 3.4 | |
v | 0–5.4 | 1.4 | 0.8 | 0.20–3.9 | 1.4 | 0.71 | |
RI | 1–500 | 53.6 | 50.9 | 1–500 | 63.1 | 69.4 | |
σg | 1.2–20.3 | 3.3 | 2.8 | 1.4–20.3 | 3.0 | 1.2 | |
S | 0.00007–0.02 | 0.00086 | 0.00152 | 0.00007–0.0036 | 0.00052 | 0.00044 | |
Additional | B | 5.4–692.5 | 71.5 | 67.1 | 10.5–692.5 | 75.3 | 80.7 |
vc | 0.15–55.7 | 2.4 | 3.2 | 0.76–11.6 | 2.8 | 1.7 | |
τ | 0–180 | 21.3 | 21.8 | 0.015–1.7 | 0.25 | 0.21 | |
τc | 0.025–3.9 | 0.87 | 0.77 | 0.13–0.56 | 0.32 | 0.10 | |
Fr | 0–1.98 | 0.28 | 0.21 | 0.039–0.55 | 0.20 | 0.10 | |
Frc | 0.19–5.77 | 0.40 | 0.34 | 0.19–1.0 | 0.38 | 0.13 | |
Frd | 0–629 | 11.1 | 23.4 | 1.6–88.9 | 16.0 | 9.9 | |
Rep | 0.0025–274,834 | 8222 | 19,074 | 1.2–195.2 | 42.1 | 43.7 | |
Original | Pier type | Single and group | Not affected | ||||
Pier nose shape (drag coefficient) [42] | Cylindrical (1.2), Round (1.33), Square (2.0), Sharp (1.0), Triangular (1.72) |
Influential variables | bef | y | v | vc | τ | τc | Fr | Frc | Frd | Rep |
a | b | c | d | e | f | g | h | i | j | k | |
---|---|---|---|---|---|---|---|---|---|---|---|
dimensional | 3.29 | 0.49 | 1.19 | −0.91 | −0.99 | −0.011 | 0.019 | 0.38 | 0.26 | 0.97 | −0.44 |
non-dimensional | 0.002 | 0.48 | −0.90 | −0.047 | −0.33 | −2.50 | 1.16 | −0.094 |
ID | bef | y | v | vc | τ | τc | Fr | Frc | Frd | Rep | ds | ds,pred | Residuals |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Obs96 | 4.88 | 9.81 | 2.13 | 5.11 | 38.51 | 0.27 | 0.22 | 0.52 | 27.57 | 17.90 | 0.67 | 3.50 | −2.83 |
Obs293 | 11.58 | 4.85 | 2.68 | 2.30 | 95.08 | 0.31 | 0.39 | 0.33 | 29.82 | 28.11 | 2.50 | 5.15 | −2.65 |
Obs252 | 5.54 | 13.47 | 2.35 | 7.44 | 72.45 | 0.26 | 0.20 | 0.65 | 32.61 | 14.39 | 1.80 | 4.08 | −2.28 |
Obs52 | 9.63 | 3.60 | 0.79 | 1.30 | 7.76 | 0.49 | 0.13 | 0.22 | 5.46 | 117.86 | 0.43 | 2.36 | −1.93 |
Obs57 | 2.50 | 9.33 | 1.55 | 4.09 | 17.38 | 0.33 | 0.16 | 0.43 | 16.63 | 31.55 | 0.43 | 2.22 | −1.79 |
Obs340 | 5.97 | 8.35 | 1.22 | 3.28 | 11.47 | 0.37 | 0.13 | 0.36 | 11.37 | 47.57 | 5.15 | 2.95 | 2.20 |
Obs307 | 0.61 | 2.77 | 1.13 | 1.14 | 5.17 | 0.42 | 0.22 | 0.22 | 8.86 | 79.52 | 2.87 | 0.65 | 2.22 |
Obs346 | 6.10 | 22.52 | 2.43 | 9.11 | 66.29 | 0.34 | 0.16 | 0.61 | 24.65 | 36.96 | 7.10 | 4.73 | 2.37 |
Obs324 | 1.07 | 4.54 | 1.77 | 2.17 | 53.46 | 0.31 | 0.26 | 0.33 | 19.65 | 28.11 | 3.66 | 1.27 | 2.38 |
Obs343 | 4.33 | 5.67 | 2.93 | 3.32 | 32.81 | 0.25 | 0.39 | 0.45 | 41.99 | 13.07 | 6.22 | 3.57 | 2.65 |
Obs329 | 1.07 | 4.15 | 1.71 | 2.00 | 48.80 | 0.31 | 0.27 | 0.31 | 18.97 | 28.11 | 4.05 | 1.23 | 2.82 |
Obs316 | 0.61 | 2.19 | 0.67 | 0.97 | 4.52 | 0.42 | 0.14 | 0.21 | 5.27 | 79.52 | 3.29 | 0.47 | 2.82 |
Obs344 | 4.37 | 5.21 | 2.44 | 2.98 | 16.62 | 0.26 | 0.34 | 0.42 | 33.88 | 14.39 | 6.43 | 3.26 | 3.17 |
Obs347 | 4.27 | 9.78 | 2.90 | 5.62 | 9.60 | 0.25 | 0.30 | 0.57 | 41.55 | 13.07 | 7.65 | 3.86 | 3.79 |
Obs348 | 10.09 | 9.00 | 0.65 | 3.60 | 48.40 | 0.36 | 0.07 | 0.38 | 6.24 | 43.61 | 7.80 | 2.90 | 4.90 |
Author | Dataset | Method | Equation | |
---|---|---|---|---|
Annad and Lefkir, 2022 [19] | field (PSDB-2014) | MNLR | (11) | |
Rathod and Manekar, 2022 [28] | field and laboratory (PSDB-2014) | GEP | (12) | |
Hassan and Jalal, 2021 [50] | numerical on a large scale | GEP | (13) | |
Jain and Fischer, 1979 [38] | field and laboratory | conventional MNLR | (14) | |
Azamathulla et al., 2010 [37] | field | MNLR | (15) | |
Our non-dimensional model | field (PSDB-2014) | MNLR | (16) | |
Our dimensional model | field (PSDB-2014) | MNLR | (17) |
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Harasti, A.; Gilja, G.; Adžaga, N.; Žic, M. Analysis of Variables Influencing Scour on Large Sand-Bed Rivers Conducted Using Field Data. Appl. Sci. 2023, 13, 5365. https://doi.org/10.3390/app13095365
Harasti A, Gilja G, Adžaga N, Žic M. Analysis of Variables Influencing Scour on Large Sand-Bed Rivers Conducted Using Field Data. Applied Sciences. 2023; 13(9):5365. https://doi.org/10.3390/app13095365
Chicago/Turabian StyleHarasti, Antonija, Gordon Gilja, Nikola Adžaga, and Mark Žic. 2023. "Analysis of Variables Influencing Scour on Large Sand-Bed Rivers Conducted Using Field Data" Applied Sciences 13, no. 9: 5365. https://doi.org/10.3390/app13095365
APA StyleHarasti, A., Gilja, G., Adžaga, N., & Žic, M. (2023). Analysis of Variables Influencing Scour on Large Sand-Bed Rivers Conducted Using Field Data. Applied Sciences, 13(9), 5365. https://doi.org/10.3390/app13095365