Scour around Spur Dike in Sand–Gravel Mixture Bed
Abstract
:1. Introduction
2. Experimental Setup and Procedure
3. Results and Discussion
3.1. Maximum Scour Depth and Location
3.2. Influence of Different Parameters on Maximum Scour
3.3. Maximum Scour Depth
3.4. Sensitivity Analysis
4. Conclusions
- The influence of different parameters on maximum equilibrium scour depth was discussed in detail. The dimensionless variation of maximum equilibrium scour depth increases with increase in U/Uca, h/da, Frsm, h/l, and decreases with increase in da/l. The scour processes in sediment mixture are mainly influenced by the property of sediment mixture and maximum scour depth increases with increase in densimetric sediment mixture Froude number. Therefore, scour processes in sediment mixture increases with decrease in non-uniformity of sediment;
- For predicting the maximum equilibrium scour depth at upstream nose of the rectangular spur dike, the non-linear relationship in non-dimensional form was derived. This equation showed good agreements between computed and experimental values of scour depths, as shown in Figure 6a–c and Table 2 and Table 3;
- A sensitivity analysis was completed to compute the most sensible parameter for maximum equilibrium scour depth. Sensitivity analysis indicated that the maximum non-dimensional scour depth heavily depended on densimetric sediment mixture Froude number. Secondary sensible parameters were da/l, h/l, and h/da in Table 2 and Table 3.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
List of Notations
d | Median diameter of sediment mixture |
da | Median diameter of armour or gravel particle |
ds | Median diameter of sand |
d16 | Particle size at 16% finer |
d84 | Particle size at 84% finer |
dsa | Maximum equilibrium scour depth |
dst | Scour depth at time t |
Frd | Densimetric Froude number |
Frsm | Froude number of sediment mixture |
g | Acceleration due to gravitational |
h | Flow depth |
ks | Roughness height |
l | Transverse length of spur dike |
U | Time-average velocity |
Uca | Critical velocity of armour particle |
Ucs | Critical velocity of sand particle |
u*c | Critical shear velocity |
Density of water | |
σ | Geometric standard deviation of particle size distribution |
α | Absolute sensitivity |
β | Relative error |
ω | Relative sensitivity |
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Exp. Run | h (m) | l (m) | U (m/s) | ds (m) | da (m) | Frsm | U/Uca | da (m) |
---|---|---|---|---|---|---|---|---|
R1 | 0.112 | 0.140 | 0.41 | 0.00027 | 0.0027 | 1.77 | 0.90 | 0.149 |
R2 | 0.105 | 0.140 | 0.35 | 0.00027 | 0.0027 | 1.51 | 0.77 | 0.111 |
R3 | 0.1 | 0.140 | 0.31 | 0.00027 | 0.0027 | 1.23 | 0.68 | 0.095 |
R4 | 0.09 | 0.140 | 0.28 | 0.00027 | 0.0027 | 1.21 | 0.61 | 0.072 |
R5 | 0.112 | 0.115 | 0.41 | 0.00027 | 0.0027 | 1.77 | 0.90 | 0.128 |
R6 | 0.105 | 0.115 | 0.35 | 0.00027 | 0.0027 | 1.51 | 0.77 | 0.091 |
R7 | 0.1 | 0.115 | 0.31 | 0.00027 | 0.0027 | 1.34 | 0.68 | 0.076 |
R8 | 0.09 | 0.115 | 0.28 | 0.00027 | 0.0027 | 1.21 | 0.61 | 0.057 |
R9 | 0.112 | 0.090 | 0.41 | 0.00027 | 0.0027 | 1.77 | 0.90 | 0.104 |
R10 | 0.105 | 0.090 | 0.35 | 0.00027 | 0.0027 | 1.51 | 0.77 | 0.078 |
R11 | 0.1 | 0.090 | 0.31 | 0.00027 | 0.0027 | 1.34 | 0.68 | 0.063 |
R12 | 0.09 | 0.090 | 0.28 | 0.00027 | 0.0027 | 1.21 | 0.61 | 0.051 |
R13 | 0.112 | 0.060 | 0.41 | 0.00027 | 0.0027 | 1.77 | 0.90 | 0.074 |
R14 | 0.105 | 0.060 | 0.35 | 0.00027 | 0.0027 | 1.51 | 0.77 | 0.058 |
R15 | 0.1 | 0.060 | 0.31 | 0.00027 | 0.0027 | 1.34 | 0.68 | 0.045 |
R16 | 0.09 | 0.060 | 0.28 | 0.00027 | 0.0027 | 1.21 | 0.61 | 0.038 |
R17 | 0.112 | 0.140 | 0.41 | 0.00027 | 0.0031 | 1.62 | 0.84 | 0.127 |
R18 | 0.105 | 0.140 | 0.35 | 0.00027 | 0.0031 | 1.38 | 0.71 | 0.096 |
R19 | 0.1 | 0.140 | 0.31 | 0.00027 | 0.0031 | 1.22 | 0.63 | 0.074 |
R20 | 0.09 | 0.140 | 0.28 | 0.00027 | 0.0031 | 1.10 | 0.57 | 0.057 |
R21 | 0.112 | 0.115 | 0.41 | 0.00027 | 0.0031 | 1.62 | 0.84 | 0.107 |
R22 | 0.105 | 0.115 | 0.35 | 0.00027 | 0.0031 | 1.38 | 0.71 | 0.078 |
R23 | 0.1 | 0.115 | 0.31 | 0.00027 | 0.0031 | 1.22 | 0.63 | 0.059 |
R24 | 0.09 | 0.115 | 0.28 | 0.00027 | 0.0031 | 1.10 | 0.57 | 0.047 |
R25 | 0.112 | 0.090 | 0.41 | 0.00027 | 0.0031 | 1.62 | 0.84 | 0.086 |
R26 | 0.105 | 0.090 | 0.35 | 0.00027 | 0.0031 | 1.38 | 0.71 | 0.068 |
R27 | 0.11 | 0.090 | 0.31 | 0.00027 | 0.0031 | 1.22 | 0.63 | 0.054 |
R28 | 0.13 | 0.090 | 0.28 | 0.00027 | 0.0031 | 1.10 | 0.57 | 0.041 |
R29 | 0.12 | 0.060 | 0.41 | 0.00027 | 0.0031 | 1.62 | 0.84 | 0.058 |
R30 | 0.11 | 0.060 | 0.35 | 0.00027 | 0.0031 | 1.38 | 0.71 | 0.043 |
R31 | 0.13 | 0.060 | 0.31 | 0.00027 | 0.0031 | 1.22 | 0.63 | 0.037 |
R32 | 0.12 | 0.060 | 0.28 | 0.00027 | 0.0031 | 1.10 | 0.57 | 0.032 |
χ | Δχ | ΔŶ | α | β | ω |
---|---|---|---|---|---|
Frsm | 0.14 | 0.147 | 1.060 | 0.199 | 1.991 |
da/l | 0.003 | 0.017 | 5.432 | 0.023 | 0.235 |
h/l | 0.111 | 0.055 | 0.496 | 0.074 | 0.745 |
h/da | 3.53 | 0.053 | 0.015 | 0.072 | 0.722 |
χ | Δχ | ΔŶ | α | β | ω |
---|---|---|---|---|---|
Frsm | 0.14 | −0.083 | −0.599 | −0.113 | −1.126 |
da/l | 0.003 | 0.048 | 15.124 | 0.065 | 0.654 |
h/l | 0.111 | 0.001 | 0.011 | 0.002 | 0.016 |
h/da | 3.53 | 0.003 | 0.001 | 0.004 | 0.035 |
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Pandey, M.; Lam, W.H.; Cui, Y.; Khan, M.A.; Singh, U.K.; Ahmad, Z. Scour around Spur Dike in Sand–Gravel Mixture Bed. Water 2019, 11, 1417. https://doi.org/10.3390/w11071417
Pandey M, Lam WH, Cui Y, Khan MA, Singh UK, Ahmad Z. Scour around Spur Dike in Sand–Gravel Mixture Bed. Water. 2019; 11(7):1417. https://doi.org/10.3390/w11071417
Chicago/Turabian StylePandey, Manish, Wei Haur Lam, Yonggang Cui, Mohammad Amir Khan, Umesh Kumar Singh, and Z. Ahmad. 2019. "Scour around Spur Dike in Sand–Gravel Mixture Bed" Water 11, no. 7: 1417. https://doi.org/10.3390/w11071417