# Scour around Spur Dike in Sand–Gravel Mixture Bed

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{ca}), water depth-armour particle ratio (h/d

_{a}), Froude number for sediment mixture (

**F**

_{r}_{sm}), water depth-spur dike length ratio (h/l), and decreases with increase in armour particle-spur dike length ratio (d

_{a}/l). The maximum scour depth is proportional to dimensionless parameters of U/U

_{ca}, h/d

_{a},

**F**

_{r}_{sm}, h/l, but the scour depth is inverse proportional to d

_{a}/l. Scour around spur dike in a sand–gravel mixture is mainly influenced by the property of the sediment mixture. The scour increases with decrease in non-uniformity of the sediment mixture. A non-linear empirical equation is proposed to estimate the maximum scour depth at an upstream nose of rectangular spur dike with a maximum error of 15%. The sensitivity analysis indicates that the maximum non-dimensional equilibrium scour depth depends on

**F**

_{r}_{sm}, followed by the secondary sensible parameters d

_{a}/l, h/l, and h/d

_{a}.

## 1. Introduction

_{84}and d

_{16}are particle sizes at 84% and 16% finer, respectively. In non-uniform sediment mixtures, finer particles are being removed first, followed by the coarser particles trying to act as a protective layer near the bridge elements due to the complex sediment transport processes [5]. This protective layer of coarser particles is known as armour layer. The median diameter (d

_{a}) of the armour layer is usually larger than the parent median diameter (d) of the streambed [15]. After the formation of an armour layer around a spur dike, further removal of sediment particles under the same hydraulic condition is very difficult. Kothyari et al. [6] stated that the armour layers of concern to calculate the scour depths around the bridge elements, are those where the bridge element is fixed in a streambed of relatively fine sediment covered by a coarser sediment layer (armour layer), developed due to the sorting of non-uniform sediments. The scour phenomenon at equilibrium scour stage is analysed by the approach flow parameters, the characteristics of armour particles along with parent bed material [16]. Most of the previous studies are limited to uniform sediment and therefore, in this research, the effect of non-uniformity of sediment on maximum scour depth was studied by performing 32 experiments.

_{sa}) around a rectangular spur dike in a sediment mixture can be written as,

_{sa}is the maximum scour depth at equilibrium condition; ${d}_{s},{d}_{a},d,\sigma ,{U}_{ca},{U}_{cs}$ are sediment parameters; $\rho ,$ U, h are flow parameters, and l is the spur dike geometry parameters. Where d

_{s}is a median diameter of sand, d

_{a}is a median diameter of armour or gravel particles, d is an effective median diameter of sediment mixture, $\sigma $ is a standard deviation of sediment mixture, U

_{cs}and U

_{ca}are critical velocities of sand and armour particles, respectively.

**F**= U/{(S−1)gd}

_{rd}^{0.5}is densimetric particle Froude number and ${F}_{rsm}={\sigma}^{-1/3}{F}_{rd}$ is densimetric Froude number of the sediment mixture [15]. U is time-averaged approach velocity, S is relative density, $\rho $ is the density of water, g is gravitational acceleration, l is transverse length of spur dike.

## 2. Experimental Setup and Procedure

_{s}= 0.27 mm and σ = 1.22) and 50% gravel (d

_{a}= 2.7 mm and σ = 1.21), and (ii) 50% sand (d

_{s}= 0.27 mm and σ = 1.22) and 50% gravel (d

_{a}= 3.1 mm and σ = 1.18). These sediment mixtures were filled up to the longitudinal level of the flume bed. A 2-D profiler was used to level the working section. Four different rectangular spur dikes having transverse lengths (l) of 6.0 cm, 9.0 cm, 11.5 cm, and 14.0 cm were used for the experiments. The water supply into the flume was regulated by a valve, which was provided in the inlet pipe. An ultrasonic flow meter was provided at the flume entrance pipe to measure the flow rate. Approach flow depth was adjusted using the tailgate, which was located at the downstream end of the flume. A wave regulator was facilitated at flume entrance to produce a uniform or near-uniform flow condition in the experimental flume. The maximum equilibrium scour depth was measured with a Vernier point gauge. The scour depth was measured at upstream nose of the spur dike and the upstream wall-junction of the spur dike with different time intervals. Figure 2b shows the variation of temporal scour depth (d

_{st}) at upstream spur dike’s nose and spur dike’s wall-junction. All experiments were completed for 20 h. However, experimentally, we saw that the equilibrium scour stage was reached within 10–14 h, as can be seen Figure 2b. After the equilibrium time of scour, the scour depth at upstream nose and wall-junction of the spur dike was the same at every 30 min interval. At the equilibrium scour condition, the maximum scour depth always occurred at the upstream nose of the spur dike. In the present study, the maximum equilibrium scour depth (d

_{sa}) at the nose of spur dike was only considered for analysis. Before the start of each experiment, the test-section of flume was perfectly levelled with respect to the flume bed and covered with a thin Perspex sheet. Once pre-set flow conditions were achieved, the Perspex sheet was separated very sensibly to avoid the undesirable scour around the pier. Table 1 illustrates the maximum scour depth along with flow and sediment properties.

_{*}) to study the maximum equilibrium scour depth. The critical shear velocity of flume bed particles and armour layer particles was calculated by Shield’s curve. The corresponding values of critical velocities (U

_{ca}) were calculated using Lauchlan and Melville [20] in Equation (2).

_{s}is the height of roughness.

## 3. Results and Discussion

#### 3.1. Maximum Scour Depth and Location

_{sa}). The equilibrium condition of scour strongly depends on the approach flow parameters, characteristics of the armour bed, and the dimension of the spur dike. The estimation of d

_{sa}around the spur dike is an important function for the safe and efficient design of the spur dikes.

_{sa}) at equilibrium condition is a key factor for a non-dimensional analysis. Experimentally, it was observed that d

_{sa}always occurs at the upstream nose of the spur dike. Distribution of high bed shear stresses in armour beds around the bridge elements is responsible for the maximum scour depth [16]. It was observed that the scour depth at spur dike nose in equilibrium stage was comparatively more as compared to the spur dike wall-junction, as shown in Figure 2b and Figure 3. Figure 3 illustrates the position of maximum depth of scour and scour depth variation in equilibrium condition.

#### 3.2. Influence of Different Parameters on Maximum Scour

_{sa}) variations with time-averaged velocity (U) for different transverse lengths (l) of spur dike along with different sediment sizes are shown in Figure 4a. It can be seen that larger armour particles show less variation in scour depth with time-averaged velocity, while smaller armour particle beds with a larger transverse length of spur dike show higher scour depth variation. The maximum depth of scour (d

_{sa}) increases with the increase in time-averaged velocity for any sizes of armour particle, as referred in Figure 4a. Scour depth variation increases with an increase in U/U

_{ca}. For a particular range of U/U

_{ca}, d

_{sa}increases with increase in l, as shown in Figure 4b.

_{sa}/l vs. h/l, d

_{sa}/l vs. d

_{a}/l, d

_{sa}/l vs.

**F**

_{r}_{sm}, and d

_{sa}/l vs. h/d

_{a}. The organised variation between non-dimensional scour depth and flow shallowness ratio (h/l) clearly states that the variation of maximum scour depth in non-dimensional form increases with a decrease in l. For a particular spur dike, d

_{sa}/l increases with increase in the flow shallowness ratio, as can be seen in Figure 5a. The results indicate that the rate of maximum scour depth variation in the sand–gravel mixture is found to be at a maximum for the longest spur dike, as shown in Figure 5a.

_{a}/l with respect to the non-dimensional scour depth (d

_{sa}/l). It is clearly visible from Figure 5b, the magnitude of d

_{sa}/l increases with a decrease in d

_{a}/l. For a particular spur dike, the maximum scour depth variation increases with decrease in armour particle size (Figure 5b). For the constant value of armour particle, the maximum scour depth variation decreases with a decrease in transverse length of spur dike. This implies that the variation of maximum non-dimensional scour depth increases with a decrease in armour particle and an increase in the transverse length of spur dike.

_{sa}) in terms of sediment mixture Froude number (

**F**

_{r}_{sm}= σ

^{−1/3}

**F**

_{r}_{d}). Figure 5c illustrates the effect of

**F**

_{r}_{sm}on maximum scour depth. It was observed that the non-uniformity factor of sediment plays a significant role in scour processes for non-uniform sediment’s case. For a constant dimension of spur dike, the maximum scour depth in non-dimensional form increases with

**F**

_{r}_{sm}(Figure 5c). It means that the maximum scour depth increases with a decrease in non-uniformity of sediment. It was also observed that the development of armour layer in the scoured region results in the exposure of coarser gravel size due to washing out of the finer gravel particles.

_{sa}/l vs. h/d

_{a}with different dimensions of spur dike. The pattern of trend lines indicates that the d

_{sa}/l increases with the increase in h/d

_{a}, as can be seen in Figure 5d. The influence of h/d

_{a}was more visible for a particular spur dike’s case. The rate of maximum scour depth variation increases with the length of spur dike.

#### 3.3. Maximum Scour Depth

#### 3.4. Sensitivity Analysis

**F**

_{r}_{sm}, d

_{a}/l, h/l, and h/d

_{a}for the datasets used in this analysis are 1.4, 0.032, 1.11, and 35.25, respectively.

_{sa}/l and input χ =

**F**

_{r}_{sm}, d

_{a}/l, h/l, and h/d

_{a}. The error also can be expressed in a relative form β = ΔŶ/Ŷ. The error ΔŶ in output is fundamentally the deviation sensitivity with Δχ being the error. The relative sensitivity can be expressed ω = (χ.ΔŶ)/(Ŷ.Δχ) [21].

**F**

_{r}_{sm}is the most sensitive parameter followed by d

_{a}/l, h/l, and h/d

_{a}. For 10% increase in χ, the relative sensitivity of

**F**

_{r}_{sm}is nearly 8.5, 2.7, and 2.8 times of d

_{a}/l, h/l, and h/d

_{a}, respectively. However, for a 10% decrease in χ, the relative sensitivity of

**F**

_{r}_{sm}is nearly 1.7, 70.4, and 30.2 times of d

_{a}/l, h/l, and h/d

_{a}, respectively. Hence, it must be said that the accuracy of Equation (4) significantly depends on

**F**

_{r}_{sm}, followed by d

_{a}/l, h/l, and h/d

_{a}.

_{sa}/l, the discrepancy ratio is defined in Equation (5) as:

_{sa}/l are identical to the experimental values of d

_{sa}/l. For negative/positive values of discrepancy ratio, the calculated values of d

_{sa}/l is smaller/greater than the experimental values. Accuracy is described as the frequency of cases for which the discrepancy ratio is within a suitable range for the total number of data, as can be seen in Figure 7. Data frequency within DR = ±0.01 is 23 out of total 32 datasets. Discrepancy ratio analysis shows good agreements between calculated and experimental values of maximum scour depth, as can be seen in Figure 7.

## 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/U
_{ca}, h/d_{a},**F**_{r}_{sm}, h/l, and decreases with increase in d_{a}/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 d
_{a}/l, h/l, and h/d_{a}in Table 2 and Table 3.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## List of Notations

d | Median diameter of sediment mixture |

d_{a} | Median diameter of armour or gravel particle |

d_{s} | Median diameter of sand |

d_{16} | Particle size at 16% finer |

d_{84} | Particle size at 84% finer |

d_{sa} | Maximum equilibrium scour depth |

d_{st} | Scour depth at time t |

F_{r}_{d} | Densimetric Froude number |

F_{r}_{sm} | Froude number of sediment mixture |

g | Acceleration due to gravitational |

h | Flow depth |

k_{s} | Roughness height |

l | Transverse length of spur dike |

U | Time-average velocity |

U_{ca} | Critical velocity of armour particle |

U_{cs} | Critical velocity of sand particle |

u_{*c} | Critical shear velocity |

$\rho $ | Density of water |

σ | Geometric standard deviation of particle size distribution |

α | Absolute sensitivity |

β | Relative error |

ω | Relative sensitivity |

## References

- Zhang, H.; Nakagawa, H.; Mizutani, H. Bed morphology and grain size characteristics around a spur dyke. Int. J. Sediment Res.
**2012**, 27, 141–157. [Google Scholar] [CrossRef] - Zhang, L.; Wang, H.; Zhang, X.; Wang, B.; Chen, J. The 3-D morphology evolution of spur dike scour under clear-water scour conditions. Water
**2018**, 10, 1583. [Google Scholar] [CrossRef] - Pandey, M.; Ahmad, Z.; Sharma, P.K. Estimation of maximum scour depth near a spur dike. Can. J. Civ. Eng.
**2016**, 43, 270–278. [Google Scholar] [CrossRef] [Green Version] - Pandey, M.; Ahmad, Z.; Sharma, P.K. Scour around impermeable spur dikes: A review. ISH J. Hydraul. Eng.
**2017**, 24, 25–44. [Google Scholar] [CrossRef] - Kothyari, U.C.; Hager, W.H.; Oliveto, G. Generalized approach for clear-water scour at bridge foundation elements. J. Hydraul. Eng.
**2007**, 133, 1229–1240. [Google Scholar] [CrossRef] - Kothyari, U.C.; Ranga Raju, K.G. Scour around spur dikes and bridge abutments. J. Hydraul. Res.
**2001**, 39, 367–374. [Google Scholar] [CrossRef] - Aamir, M.; Ahmad, Z. Review of literature on local scour under plane turbulent wall jets. Phys. Fluids
**2016**, 28, 105102. [Google Scholar] [CrossRef] - Cui, Y.; Lam, W.H.; Zhang, T.; Sun, C.; Hamill, G. Scour Induced by Single and Twin Propeller Jets. Water
**2019**, 11, 1097. [Google Scholar] [CrossRef] - Ghodsian, M.; Vaghefi, M. Experimental study on scour and flow field in a scour hole around a T-shape spur dike in a 90° bend. Int. J. Sediment Res.
**2009**, 24, 145–158. [Google Scholar] [CrossRef] - Kuhnle, R.; Alonso, C. Flow near a model spur dike with a fixed scoured bed. Int. J. Sediment Res.
**2013**, 28, 349–357. [Google Scholar] [CrossRef] - Koken, M.; Gogus, M. Effect of spur dike length on the horseshoe vortex system and the bed shear stress distribution. J. Hydraul. Res.
**2015**, 53, 196–206. [Google Scholar] [CrossRef] - Mostafa, M.M.; Ahmed, H.S.; Ahmed, A.A.; Abdel-Raheem, G.A.; Ali, N.A. Experimental study of flow characteristics around floodplain single groyne. J. Hydro-Environ. Res.
**2019**, 22, 1–13. [Google Scholar] [CrossRef] - Ezzeldin, R.M. Numerical and experimental investigation for the effect of permeability of spur dikes on local scour. J. Hydroinform.
**2019**, 21, 335–342. [Google Scholar] [CrossRef] - Pandey, M.; Sharma, P.K.; Ahmad, Z.; Karna, N. Maximum scour depth around bridge pier in gravel bed streams. Nat. Hazards
**2018**, 91, 819–836. [Google Scholar] [CrossRef] - Oliveto, G.; Hager, W.H. Temporal evolution of clear-water pier and abutment scour. J. Hydraul. Eng.
**2002**, 128, 811–820. [Google Scholar] [CrossRef] - Sui, J.; Afzalimehr, H.; Samani, A.K.; Maherani, M. Clear-water scour around semi-elliptical abutments with armored beds. Int. J. Sediment Res.
**2010**, 25, 233–245. [Google Scholar] [CrossRef] - Qi, M.; Li, J.; Chen, Q. Applicability analysis of pier-scour equations in the field: Error analysis by rationalizing measurement data. J. Hydraul. Eng.
**2018**, 144, 04018050. [Google Scholar] [CrossRef] - Fazli, M.; Ghodsian, M.; Neyshabouri, S.A.A.S. Scour and flow field around a spur dike in a 90° bend. Int. J. Sediment Res.
**2008**, 23, 56–68. [Google Scholar] [CrossRef] - Melville, B.W. Local scour at bridge abutments. J. Hydraul. Eng.
**1992**, 118, 615–631. [Google Scholar] [CrossRef] - Lauchlan, C.S.; Melville, B.W. Riprap protection at bridge piers. J. Hydraul. Eng.
**2001**, 127, 412–418. [Google Scholar] [CrossRef] - Ahmad, Z. Prediction of longitudinal dispersion coefficient using laboratory and field data: Relationship comparisons. Hydrol. Res.
**2013**, 44, 362–376. [Google Scholar] [CrossRef]

**Figure 2.**Experiments. (

**a**) Photometric view. (

**b**) Scour depth variations with time at upstream nose and wall-junction of the spur dike.

**Figure 4.**Maximum scour depth of spur dike (

**a**) Depth with time-averaged velocity, and (

**b**) Depth with transverse lengths.

**Figure 5.**Influence of parameters on maximum non-dimensional scour depth. (

**a**) d

_{sa}/l vs. h/l. (

**b**) d

_{sa}/l vs. d

_{a}/l. (

**c**) d

_{sa}/l vs.

**F**

_{r}_{sm}. (

**d**) d

_{sa}/l vs. h/d

_{a}.

**Figure 6.**Experimental vs. computed maximum non-dimensional scour depths. (

**a**) 70% training datasets. (

**b**) 30% validation datasets. (

**c**) Comparison between percentage data frequency and percentage error.

Exp. Run | h (m) | l (m) | U (m/s) | d_{s} (m) | d_{a} (m) | F_{rsm} | U/U_{ca} | d_{a} (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 |
---|---|---|---|---|---|

F_{rsm} | 0.14 | 0.147 | 1.060 | 0.199 | 1.991 |

d_{a}/l | 0.003 | 0.017 | 5.432 | 0.023 | 0.235 |

h/l | 0.111 | 0.055 | 0.496 | 0.074 | 0.745 |

h/d_{a} | 3.53 | 0.053 | 0.015 | 0.072 | 0.722 |

χ | Δχ | ΔŶ | α | β | ω |
---|---|---|---|---|---|

F_{rsm} | 0.14 | −0.083 | −0.599 | −0.113 | −1.126 |

d_{a}/l | 0.003 | 0.048 | 15.124 | 0.065 | 0.654 |

h/l | 0.111 | 0.001 | 0.011 | 0.002 | 0.016 |

h/d_{a} | 3.53 | 0.003 | 0.001 | 0.004 | 0.035 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Pandey, 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