# Temporal Scour Variations at Permeable and Angled Spur Dikes under Steady and Unsteady Flows

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}equal to 0.94) is introduced to predict the time-dependent scour depth due to the passage of a flood wave. The model suggests that the main independent dimensionless variables which control local scour processes are: the densimetric Froude number, the time t normalized to the hydrograph base-time, the degree of permeability, and the orientation angle. These dimensionless variables would generalize the laboratory results to the real-world scenarios, although caution should always be taken because of possible scale effects.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experiments

_{50}equal to 0.8 mm. The gradation of the sediment mixture that can be described by the standard deviation σ

_{g}= (d

_{84}/d

_{16})

^{0.5}was equal to 1.22 which would imply an almost uniform sediment [26]. d

_{84}and d

_{16}are the particle sizes for which 84% and 16% of the sediment mixture are finer, respectively. In the present study, a single unsubmerged spur dike was considered with three levels of permeability, namely 0% (i.e., impermeable spur dike), 33%, and 66%. Moreover, three spur dike orientation angles θ equal to 60° (repelling alignment), 90° (deflecting alignment), and 120° (attractive alignment) were considered. θ is the angle between the spur dike and the upstream wall. A Plexiglas plate 0.5 m high and 10 mm thick was employed to simulate an impermeable spur dike. Brass rods with a height of 0.5 m and a diameter of 4 mm, which were fixed to two Plexiglas plates at the top and bottom, were used to simulate a permeable spur dike. The effective length of the spur dike for the repelling, deflecting, and attractive alignments was always equal to 20% of the flume width. Figure 1 shows a view of the flume with an impermeable spur dike looking from upstream.

_{C}at the incipient sediment motion was estimated using the following well-known equation V

_{C}/u*

_{C}= 5.75log[h/(2d

_{50})] + 6 in which the shear velocity u*

_{C}was computed according to the Shields’ diagram and h is the approach flow depth. Local scour processes did not occur around the spur dike when the flow rates were less than 15 L/s and the flow depth was 13.7 cm. As a result, the hydrographs began with a 15 L/s base flow. Consistently with the experimental facilities, the hydrograph base times were 15, 30, or 60 min.

_{s}at the given time t. In addition, 9 runs under steady flow conditions were performed to allow a comparison with the findings from unsteady flow conditions and hydrograph base-time equal to 60 min. In this case 54 datasets were collected. Then, a total of 36 runs were carried out in this study. The rationality behind this number of runs is as follows. In case of unsteady flows our intention was to investigate: (i) the effect of the spur dike orientation angle considering the typical (and equidistant) angle values of 60° (repelling alignment), 90° (deflecting alignment), and 120° (attractive alignment); (ii) the effect of the degree of permeability considering the three equidistant values of 0%, 33%, and 66%; (iii) the effect of the hydrograph base-time considering the three values of 15, 30, and 60 min. Therefore, the combination of all the possible values of these variables leads to a total of 3

^{3}= 27 runs. Likewise in case of steady flows our intention was to compare the maximum scour depths observed for unsteady flows and hydrograph base-time equal to 60 min to the maximum scour depths observed for steady flow runs of duration equal to 60 min and approach flow conditions corresponding to those at the hydrograph peak flow. Therefore, all the possible combinations lead to a total of 3

^{2}·1 = 9 runs. All the experimental data are provided in a supplementary file associated with this article. The scour depth around the nose of the spur dike was monitored over the time, this being the region in which the maximum scour depth occurred, at least for runs of short duration, as in this study. Moreover, the discharge and the flow depth over the time were measured for the purposes of characterization of the approach flow conditions.

_{b}, Q

_{p}, h, F, F

_{d}, V/V

_{C}, t

_{b}, θ, and φ are the: hydrograph base discharge, hydrograph peak discharge, approach flow depth, approach Froude number, approach densimetric Froude number, approach flow intensity, hydrograph base-time, spur dike orientation angle, and spur dike degree of permeability, respectively. V is the approach flow velocity and V

_{C}is the approach flow velocity at the bed particles incipient motion. The densimetric Froude number F

_{d}will be defined later.

_{50}was equal to 0.80 mm.

#### 2.2. Dimensional Analysis

_{s}as the maximum scour depth around the spur dike at the time t, one can assume the following functional relationship

_{s}, d

_{50}, σ

_{g}, V

_{c}, g, L, θ, φ, t

_{b}, and t represent: average approach flow velocity, approach flow depth, water density, kinematic viscosity of water (= 10

^{−6}m

^{2}/s), sediment density, sediment median grain size, sediment gradation, threshold velocity for particle entrainment, gravitational acceleration, spur dike length, spur dike orientation angle, spur dike degree of permeability, base-time of hydrograph, and time, respectively. In sediment-water interaction it is appropriate to represent the independent parameters g, ρ, and ρ

_{s}as a combined parameter Δg where Δg = s − 1 and s relative density of sediment that is ρ

_{s}/ρ [26,29]. Moreover, the influence of the kinematic viscosity n can be considered negligible under a fully turbulent flow over a rough bed [29] as in this study. Using the dimensional analysis with repeating variables V and L, and rearranging the nondimensional parameters logically [29], yields

_{d}is the densimetric Froude number defined as V/[(s = 1)gd

_{50}]

^{0.5}. The role of F

_{d}in local scour processes was well emphasized by Oliveto and Hager [26], who also show that the effect of L on d

_{s}is preponderant compared to the approach flow depth h. It should be noted that d

_{50}/L and σ

_{g}were kept constant in this study.

^{2}), defined in Equations (3)–(5), respectively [30]:

_{s}/L, respectively, and N is the total number of the experimental data collected in this study. Actually, in case of unsteady flow conditions N was equal to 317 and not only 162 because additional observations were acquired during the runs outside of the default monitoring times.

## 3. Results

#### 3.1. Impact of the Spur Dike Orientation Angle on the Temporal Scour Development

_{s}is the observed scour depth in millimeters.

#### 3.2. Impact of the Spur Dike Permeability on the Temporal Scour Development

#### 3.3. Impact of the Duration of the Hydrograph on the Temporal Scour Development

#### 3.4. Comparison of the Scouring Conditions under Steady and Unsteady Flows

#### 3.5. A New Empirical Model for Temporal Scour Development under Unsteady Flows

_{s}under unsteady flows were used for calibration and validation, respectively (e.g., [30]). For t/t

_{b}> 0.63 the experimental observations revealed that d

_{s}/L remained constant while for t/t

_{b}≤ 0.63 the experimental data were analyzed by nonlinear regression, which implies a nonlinear combination of the model parameters. Therefore,

_{s}which were observed at the hydrograph peak. Moreover, the coefficient of determination, R

^{2}, was found equal to 0.94, indicating a satisfactory fitting effect.

^{2}for the proposed model were 0.052, 0.034, and 0.94 when considering all the data, confirming a satisfactory scour depth prediction. More specifically the values of RMSE, MAE, and R

^{2}were 0.047, 0.032, and 0.935, respectively, in case of calibration and 0.069, 0.042, and 0.91, respectively, in case of validation.

## 4. Discussion

_{d}, should be more investigated on larger ranges of approach flow conditions and sediment characteristics. However, Equations (6) and (7) clearly demonstrate the strong impact of the degree of permeability of spur dikes on local scour processes.

## 5. Conclusions

- The orientation angle θ of the spur dike had not relevant effect on the scour depth especially in case of impermeable spur dikes. The impact of θ was increasingly evident although always restricted with increasing the degree of permeability;
- The spur dike permeability had a consistent effect on the scour depth around the spur dike with the scouring process reducing significantly as the degree of permeability increases. The differences in percentage between the maximum scour depth for impermeable spur dikes and the maximum scour depths for various degrees of spur dike permeability were found ranging from 44% (at φ = 33% and θ = 60°) up to 88% (at φ = 66% and θ = 120°);
- By quadrupling the hydrograph base-times, keeping constant the peak and base flood discharges, the maximum scour depths increased by about 29%, 42%, and 25% in case of impermeable spur dike, spur dike with 33% degree of permeability, and spur dike with 66% degree of permeability, respectively;
- The results from steady flow experiments were significantly different in comparison to those for unsteady flows, as expected. The maximum percentage differences in terms of maximum scour depths were observed for spur dikes with an orientation angle of 90° and this for various degrees of permeability;
- Finally, a new empirical formula was developed based on the experimental data collected in this study. The ranges of applications are those related to this experimental work.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Pinter, N.; Jemberie, A.A.; Remo, J.W.F.; Heine, R.A.; Ickes, B.S. Cumulative impacts of river engineering, Mississippi and Lower Missouri rivers. River Res. Appl.
**2010**, 26, 546–571. [Google Scholar] [CrossRef] - Cao, X.-M.; Gu, Z.-H. Three classification criteria and their comparison impact scale between double non-submerged spur dikes. J. Zhejiang Univ.
**2015**, 49, 200–207. [Google Scholar] - Pandey, M.; Valyrakis, M.; Qi, M.; Sharma, A.; Lodhi, A.S. Experimental assessment and prediction of temporal scour depth around a spur dike. Int. J. Sediment Res.
**2021**, 36, 17–28. [Google Scholar] [CrossRef] - Shampa; Hasegawa, Y.; Nakagawa, H.; Takebayashi, H.; Kawaike, K. Three-dimensional flow characteristics in slit-type permeable spur dike fields: Efficacy in riverbank protection. Water
**2020**, 12, 964. [Google Scholar] [CrossRef] [Green Version] - Gu, Z.; Cao, X.; Gu, Q.; Lu, W.-Z. Exploring proper spacing threshold of non-submerged spur dikes with ipsilateral layout. Water
**2020**, 12, 172. [Google Scholar] [CrossRef] [Green Version] - Ahmad, M. Experiments on design and behavior of spur dikes. In Proceedings of the International Hydraulics Convention; University of Minnesota: Minneapolis, MN, USA, 1953; pp. 145–159. [Google Scholar]
- Chen, F.-Y.; Ikeda, S. Horizontal separation flows in shallow open channels with spur dikes. J. Hydrosci. Hydraul. Eng.
**1997**, 15, 15–30. [Google Scholar] - Diplas, P.; Dancey, C.L.; Celik, A.O.; Valyrakis, M.; Greer, K.; Akar, T. The role of impulse on the initiation of particle movement under turbulent flow conditions. Science
**2008**, 322, 717–720. [Google Scholar] [CrossRef] [Green Version] - Valyrakis, M.; Diplas, P.; Dancey, C.L.; Greer, K.; Celik, A.O. Role of instantaneous force magnitude and duration on particle entrainment. J. Geophys. Res. Earth
**2010**, 115, F02006. [Google Scholar] [CrossRef] - Valyrakis, M.; Diplas, P.; Dancey, C.L. Entrainment of coarse particles in turbulent flows: An energy approach. J. Geophys. Res. Earth
**2013**, 118, 42–53. [Google Scholar] [CrossRef] [Green Version] - 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] [Green Version] - Valyrakis, M.; Michalis, P.; Zhang, H. A new system for bridge scour monitoring and prediction. In Proceedings of the 36th IAHR World Congress, The Hague, The Netherlands, 28 June–3 July 2015. [Google Scholar]
- Liu, D.; Valyrakis, M.; Williams, R. Flow hydrodynamics across open channel flows with riparian zones: Implications for riverbank stability. Water
**2017**, 9, 720. [Google Scholar] [CrossRef] [Green Version] - Kothyari, U.C.; Ranga Raju, K.G. Scour around spur dikes and bridge abutments. J. Hydraul. Res.
**2001**, 39, 367–374. [Google Scholar] [CrossRef] - Ezzeldin, M.M.; Saafan, T.A.; Rageh, O.S.; Nejm, L.M. Local scour around spur dikes. In Proceedings of the Eleventh International Water Technology Conference, IWTC11, Sharm El-Sheikh, Egypt, 15–18 March 2007; pp. 779–795. [Google Scholar]
- Cao, Y.; Liu, P.; Enhui, J. The design and application of permeable groynes. Appl. Mech. Mat.
**2013**, 353–356, 2502–2505. [Google Scholar] [CrossRef] - Li, Z.; Michioku, K.; Maeno, S.; Ushita, T.; Fujii, A. Hydraulic characteristics of a group of permeable groins constructed in an open channel flow. J. Appl. Mech.
**2005**, 8, 773–782. [Google Scholar] [CrossRef] - Fukuoka, S.; Watanabe, A.; Kawaguchi, H.; Yasutake, Y. A study of permeable groins in series installed in a straight channel. Proc. Hydraul. Eng.
**2000**, 44, 1047–1052. [Google Scholar] [CrossRef] - Kang, J.; Yeo, H.; Kim, S.; Ji, U. Permeability effects of single groin on flow characteristics. J. Hydraul. Res.
**2011**, 49, 728–735. [Google Scholar] [CrossRef] - Zhang, H.; Nakagawa, H. Scour Around Spur Dyke: Recent Advances and Future Researches; Annuals of Disaster Prevention Research Institute, No. 51B; Kyoto University: Kyoto, Japan, 2008; pp. 633–652. [Google Scholar]
- Pandey, M.; Ahmad, Z.; Sharma, P.K. Estimation of maximum scour depth near a spur dike. Can. J. Civil. Eng.
**2016**, 43, 270–278. [Google Scholar] [CrossRef] [Green Version] - Teraguchi, H.; Nakagawa, H.; Kawaike, K.; Baba, Y.; Zhang, H. Morphological Change Induced by River Training Structures: Bandal-like and Groins; Annuals of Disaster Prevention Research Institute, No. 51B; Kyoto University: Kyoto, Japan, 2010. [Google Scholar]
- Link, O.; Castillo, C.; Pizarro, A.; Rojas, A.; Ettmer, B.; Escauriaza, C.; Manfreda, S. A model of bridge pier scour during flood waves. J. Hydraul. Res.
**2017**, 55, 310–323. [Google Scholar] [CrossRef] - Raikar, R.V.; Hong, J.-H.; Deshmukh, A.R.; Guo, W.-D. Parametric study on abutment scour under unsteady flow. Water
**2022**, 14, 1820. [Google Scholar] [CrossRef] - Melville, B.W.; Chiew, Y.-M. Time scale for local scour at bridge piers. J. Hydraul. Eng. ASCE
**1999**, 125, 59–65. [Google Scholar] [CrossRef] - Oliveto, G.; Hager, W.H. Temporal evolution of clear-water pier and abutment scour. J. Hydraul. Eng. ASCE
**2002**, 128, 811–820. [Google Scholar] [CrossRef] - Graf, W.H.; Altinakar, M.S. Fluvial Hydraulics-Flow and Transport Processes in Channels of Simple Geometry; John Wiley & Sons Inc.: Chichester, UK, 1998; pp. 10–12. [Google Scholar]
- Özyaman, C.; Yerdelen, C.; Eris, E.; Daneshfaraz, R. Experimental investigation of scouring around a single spur under clear water conditions. Water Supply
**2022**, 22, 3484. [Google Scholar] [CrossRef] - Dey, S.; Raikar, R.V. Scour in long contractions. J. Hydraul. Eng. ASCE
**2005**, 131, 1036–1049. [Google Scholar] [CrossRef] - Niazkar, M.; Afzali, S.H. Developing a new accuracy-improved model for estimating scour depth around piers using a hybrid method. Iran J. Sci. Technol. Trans. Civ. Eng.
**2019**, 43, 179–189. [Google Scholar] [CrossRef] - Lu, J.-Y.; Shi, Z.-Z.; Hong, J.-H.; Lee, J.-J.; Raikar, R.V. Temporal Variation of Scour Depth at Nonuniform Cylindrical Piers. J. Hydraul. Eng. ASCE
**2011**, 137, 45–56. [Google Scholar] [CrossRef] [Green Version] - Chang, W.-Y.; Lai, J.-S.; Yen, C.-L. Evolution of scour depth at circular bridge piers. J. Hydraul. Eng. ASCE
**2004**, 130, 905–913. [Google Scholar] [CrossRef] - Oliveto, G.; Hager, W.H. Further results to time-dependent local scour at bridge elements. J. Hydraul. Eng. ASCE
**2005**, 131, 97–105. [Google Scholar] [CrossRef] - Raikar, R.V.; Dey, S. Clear-water scour at bridge piers in fine and medium gravel beds. Can. J. Civil. Eng.
**2005**, 32, 775–781. [Google Scholar] [CrossRef]

**Figure 2.**Schematic view of the flume used in this study and the physical models simulating spur dikes of different permeability.

**Figure 3.**Hydrographs with different base times t

_{b}(i.e., t

_{b}= 15, 30, and 60 min) used in the present experimental work.

**Figure 4.**Observed scour depths over the time at spur dikes with different orientation angle θ and different base-times t

_{b}. Panel (

**a**) refers to the runs for impermeable spur dikes, panel (

**b**) to the runs for spur dikes with 33% permeability, and panel (

**c**) to the runs for spur dikes with 66% permeability.

**Figure 5.**Observed scour depths over the time at spur dikes with different degree of permeability φ and different orientation angle θ. Panel (

**a**) refers to the runs with base-time equal to 60 min, panel (

**b**) to the runs with base-time equal to 30 min, and panel (

**c**) to the runs with base-time equal to 15 min.

**Figure 6.**Observed scour depths over the time at spur dikes for hydrographs with different base-times and with different degree of permeability. Panel (

**a**) refers to the runs with orientation angle θ equal to 60°, panel (

**b**) to the runs with orientation angle θ equal to 90°, and panel (

**c**) to the runs with orientation angle θ equal to 120°.

**Figure 7.**Comparison of the temporal development of the scour depth under a 60-min hydrograph and corresponding steady flow conditions for different angles θ. (

**a**) Impermeable spur dikes, (

**b**) spur dikes with 33% permeability, and (

**c**) spur dikes with 66% permeability.

**Figure 8.**Comparison between observed and computed values of the maximum scour depths at spur dikes under unsteady flows. The full line is the line of perfect agreement and the dashed lines are the ±30% deviation lines with respect to the line of perfect agreement.

**Table 1.**Flow conditions and spur dike characteristics for the runs of the present experimental work.

h | F | F_{d} | V/V_{C} | t_{b} | θ | φ | |
---|---|---|---|---|---|---|---|

(m) | (-) | (-) | (-) | (min) | (°) | (%) | |

Q_{b} = 15 L/s | 0.137 | 0.12 | 1.30 | 0.48 | 15, 30, 60 | 60, 90, 120 | 0, 33, 66 |

Q_{p} = 50 L/s | 0.202 | 0.24 | 2.93 | 0.95 | 15, 30, 60 | 60, 90, 120 | 0, 33, 66 |

**Table 2.**Differences in percentage between the maximum scour depth and the scour depth at the hydrograph peak for various degrees of spur dike permeability (φ) and spur dike orientation angles (θ). Differences are divided by the maximum scour depth.

φ (%) | t_{b} (min) | θ = 60° | θ = 90° | θ = 120° |
---|---|---|---|---|

0% | 60 | 13% | 11% | 14% |

30 | 21% | 20% | 21% | |

15 | 25% | 23% | 26% | |

33% | 60 | 26% | 28% | 25% |

30 | 24% | 26% | 21% | |

15 | 28% | 25% | 29% | |

66% | 60 | 29% | 31% | 25% |

30 | 33% | 30% | 31% | |

15 | 33% | 36% | 33% |

**Table 3.**Differences in percentage between the maximum scour depth for impermeable spur dikes and the maximum scour depths for various degrees of spur dike permeability (φ) and spur dike orientation angles (θ). Differences are divided by the maximum scour depth for impermeable spur dikes.

t_{b} [min] | φ [%] | θ = 60° | θ = 90° | θ = 120° |
---|---|---|---|---|

60 | 33% | 44% | 49% | 51% |

66% | 87% | 89% | 89% | |

30 | 33% | 52% | 56% | 57% |

66% | 86% | 88% | 89% | |

15 | 33% | 51% | 56% | 54% |

66% | 85% | 87% | 88% |

**Table 4.**Differences in percentage between the maximum scour depths for hydrographs with the base time of 60 min and the maximum scour depths for hydrographs with base time of 15 and 30 min for various degrees of spur dike permeability (φ) and spur dike orientation angles (θ). Differences are divided by the maximum scour depth for hydrographs with base time of 60 min.

φ [%]-θ [°] | t_{b} = 15 min | t_{b} = 30 min |
---|---|---|

0%-60° | 27% | 15% |

0%-90° | 23% | 7% |

0%-120° | 29% | 15% |

33%-60° | 37% | 32% |

33%-90° | 42% | 34% |

33%-120° | 34% | 28% |

66%-60° | 14% | 7% |

66%-90° | 15% | 8% |

66%-120° | 25% | 17% |

**Table 5.**Differences in percentage between the maximum scour depth under steady flows of duration 60 min and the corresponding hydrographs with the base time of 60 min for various degrees of spur dike permeability (φ) and spur dike orientation angles (θ). Differences are divided by the maximum scour depth under steady flow.

φ (%) | θ = 60° | θ = 90° | θ = 120° |
---|---|---|---|

0% | 31% | 33% | 29% |

33% | 35% | 43% | 38% |

66% | 13% | 24% | 20% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Farshad, R.; Kashefipour, S.M.; Ghomeshi, M.; Oliveto, G.
Temporal Scour Variations at Permeable and Angled Spur Dikes under Steady and Unsteady Flows. *Water* **2022**, *14*, 3310.
https://doi.org/10.3390/w14203310

**AMA Style**

Farshad R, Kashefipour SM, Ghomeshi M, Oliveto G.
Temporal Scour Variations at Permeable and Angled Spur Dikes under Steady and Unsteady Flows. *Water*. 2022; 14(20):3310.
https://doi.org/10.3390/w14203310

**Chicago/Turabian Style**

Farshad, Reza, Seyed Mahmood Kashefipour, Mehdi Ghomeshi, and Giuseppe Oliveto.
2022. "Temporal Scour Variations at Permeable and Angled Spur Dikes under Steady and Unsteady Flows" *Water* 14, no. 20: 3310.
https://doi.org/10.3390/w14203310