# Evaluation of Local Scour along the Base of Longitudinal Training Walls

^{1}

^{2}

^{*}

## Abstract

**:**

_{u}) and the embedment of the longitudinal wall. This allows for a more robust identification of the scour behavior of longitudinal walls. This research enhances our comprehension of local scour in riverbeds. It provides engineers and researchers with a valuable tool for more accurate predictions, thereby contributing to the improved design and maintenance of river environment structures.

## 1. Introduction

_{u}) greater than 20, which indicates that the sediment is well-graded and homogeneous in composition [10,11].

## 2. Materials and Methods

#### 2.1. Experimental Setup

^{3}/s) and different slopes (0.5 and 2.5%) were analyzed to determine the changes in the maximum scour depth. Eleven measurement points were located along the experimental flume (Figure 1b). This configuration allowed obtaining information on scour depths from the initial point where the water interacts with the wall to its final edge.

#### 2.2. Riverbed Composition

_{u}) of 24.81 and 24.96, respectively [8,9,30], obtained through the d

_{60}/d

_{10}ratio corresponding to diameters for which 60% and 10% of the particles of the soil (in weight) are equal or less between each other. To establish a theoretical granulometric curve for sediments with a mean diameter of 7.75 mm within a well-graded granular bed while ensuring a Coefficient of uniformity (C

_{u}) significant than 20, we performed scaling on the curves derived from actual rivers [31,32]. Additionally, the proportions of each constituent of the bed (fine sand, coarse sand, and gravel) based on the sediment passing through specific laboratory sieves were calculated.

#### 2.3. Equations for Scour Depth Prediction

#### 2.4. Statistical Validation

## 3. Results and Discussion

#### 3.1. Riverbed Composition

_{u}) for the granulometric curves. The data showed values between 24.96 and 24.81 with a median diameter of 35.21 and 22.86 mm, respectively. These curves were scaled to generate the theoretical granulometric curve with a C

_{u}of 20.49 and an average diameter of 7.75 mm, obtained through the d

_{60}/d

_{10}ratio. According to the results, the necessary volumes of fine sand, coarse sand, and gravel were obtained (46, 26, and 28%, respectively).

#### 3.2. Experimental Results

^{3}/s reached 97.5 mm, observed in the second monitoring point. It is a significantly high value with which the instability of the longitudinal structure occurs. Table 1 compares the average depth change between the lowest proposed slope of 0.5% and the highest (2.5%), where differences that reach 83 mm were obtained. This is a significant difference and we can observe the direct effect of the slope on the maximum scour depth. It should be noted that there was no symmetry in the scour because, along the wall, there was sediment at the beginning of the channel and deposition at the end of it. However, the channel’s symmetry does not affect the equation proposed since it depends on the Froude number and the densimetric Froude number, which can vary and be measured at any point of the channel with well-graded granular material.

#### 3.3. Analysis of Existing Equations Used to Predict Scour

#### 3.4. Development of a New Mathematical Expression to Calculate Local Scour

^{2}closest to 1 was selected from the regression models of each equation. Lastly, a new Equation (11) was proposed to estimate the depth of local scour in longitudinal walls in rivers with well-graded granular bedding.

^{2}of 0.8567.

_{s}), relative to flow depth (Y

_{n}). This diagram facilitates the calculation of scour depth as a function of the Froude number, which was subsequently validated against experimental data obtained from physical models representing well-graded granular beds and longitudinal structures.

#### 3.5. Validation of the New Mathematical Expression to Calculate the Local Scour

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Cohesive Soils | Non-Cohesive Soils | ||||
---|---|---|---|---|---|

${\mathit{\gamma}}_{\mathit{m}}$(mm) | $\mathit{\chi}$ | $\mathbf{1}\mathbf{/}\left(\mathbf{1}\mathbf{+}\mathit{\chi}\right)$ | $\mathit{d}$(mm) | $\mathit{\chi}$ | $\mathbf{1}\mathbf{/}\left(\mathbf{1}\mathbf{+}\mathit{\chi}\right)$ |

0.80 | 0.52 | 0.66 | 0.05 | 0.43 | 0.70 |

0.83 | 0.51 | 0.66 | 0.15 | 0.42 | 0.70 |

0.86 | 0.50 | 0.67 | 0.50 | 0.41 | 0.71 |

0.88 | 0.49 | 0.67 | 1.00 | 0.40 | 0.71 |

0.90 | 0.48 | 0.67 | 1.50 | 0.39 | 0.72 |

0.93 | 0.47 | 0.68 | 2.50 | 0.38 | 0.72 |

0.96 | 0.46 | 0.68 | 4.00 | 0.37 | 0.73 |

0.98 | 0.45 | 0.69 | 6.00 | 0.36 | 0.74 |

1.00 | 0.44 | 0.69 | 8.00 | 0.35 | 0.74 |

1.04 | 0.43 | 0.70 | 10.00 | 0.34 | 0.75 |

1.08 | 0.42 | 0.70 | 15.00 | 0.33 | 0.75 |

1.12 | 0.41 | 0.71 | 20.00 | 0.32 | 0.76 |

1.16 | 0.40 | 0.71 | 25.00 | 0.31 | 0.76 |

1.20 | 0.39 | 0.72 | 40.00 | 0.30 | 0.77 |

1.20 | 0.38 | 0.72 | 60.00 | 0.29 | 0.78 |

1.28 | 0.37 | 0.73 | 90.00 | 0.28 | 0.78 |

1.34 | 0.36 | 0.74 | 140.00 | 0.27 | 0.79 |

1.40 | 0.35 | 0.74 | 190.00 | 0.26 | 0.79 |

1.46 | 0.34 | 0.75 | 250.00 | 0.25 | 0.80 |

1.52 | 0.33 | 0.75 | 310.00 | 0.24 | 0.81 |

1.58 | 0.32 | 0.76 | 370.00 | 0.23 | 0.81 |

1.64 | 0.31 | 0.76 | 450.00 | 0.22 | 0.83 |

1.71 | 0.30 | 0.77 | 570.00 | 0.21 | 0.83 |

1.80 | 0.29 | 0.78 | 750.00 | 0.20 | 0.83 |

1.89 | 0.28 | 0.78 | 1000.00 | 0.19 | 0.84 |

2.00 | 0.27 | 0.79 |

## References

- Czapiga, M.J.; Blom, A.; Viparelli, E. Efficacy of Longitudinal Training Walls to Mitigate Riverbed Erosion. Water Resour. Res.
**2022**, 58, e2022WR033072. [Google Scholar] [CrossRef] - Yan, G.; Cheng, H.; Jiang, Z.; Teng, L.; Tang, M.; Shi, T.; Jiang, Y.; Yang, G.; Zhou, Q. Recognition of Fluvial Bank Erosion Along the Main Stream of the Yangtze River. Engineering
**2022**, 19, 50–61. [Google Scholar] [CrossRef] - Sohrabi, M.; Keshavarzi, A.; Javan, M. Impact of Bed Sill Shapes on Scour Protection in River Bed and Banks. Int. J. River Basin Manag.
**2019**, 17, 277–287. [Google Scholar] [CrossRef] - Shahriar, A.R.; Ortiz, A.C.; Montoya, B.M.; Gabr, M.A. Bridge Pier Scour: An Overview of Factors Affecting the Phenomenon and Comparative Evaluation of Selected Models. Transp. Geotech.
**2021**, 28, 100549. [Google Scholar] [CrossRef] - Qi, H.; Yuan, T.; Zhao, F.; Chen, G.; Tian, W.; Li, J. Local Scour Reduction around Cylindrical Piers Using Permeable Collars in Clear Water. Water
**2023**, 15, 897. [Google Scholar] [CrossRef] - Le, T.B.; Crosato, A.; Uijttewaal, W.S.J. Long-Term Morphological Developments of River Channels Separated by a Longitudinal Training Wall. Adv. Water Resour.
**2018**, 113, 73–85. [Google Scholar] [CrossRef] - Toapaxi, J.; Galiano, L.; Castro, M.; Hidalgo, X.; Valencia, N. Análisis de La Socavación En Cauces Naturales. Rev. Politec.
**2015**, 35, 1–11. [Google Scholar] - Kokusho, T.; Hara, T.; Hiraoka, R. Undrained Shear Strength of Granular Soils with Different Particle Gradations. J. Geotech. Geoenvironmental Eng.
**2004**, 130, 621–629. [Google Scholar] [CrossRef] - Biron, P.M.; Robson, C.; Lapointe, M.F.; Gaskin, S.J. Three-Dimensional Flow Dynamics around Deflectors. River Res. Appl.
**2005**, 21, 961–975. [Google Scholar] [CrossRef] - Istanbulluoglu, E.; Tarboton, D.G.; Pack, R.T.; Luce, C. A Sediment Transport Model for Incision of Gullies on Steep Topography. Water Resour. Res.
**2003**, 39, 4. [Google Scholar] [CrossRef] - Attal, M.; Lavé, J. Pebble Abrasion during Fluvial Transport: Experimental Results and Implications for the Evolution of the Sediment Load along Rivers. J. Geophys. Res.
**2009**, 114, F04023. [Google Scholar] [CrossRef] - Barbosa Gil, S. Metodología Para Calcular La Profundidad de Socavación General En Ríos de Montaña (Lecho de Gravas). Ph.D. Thesis, Universidad Nacional de Colombia, Bogota, Colombia, 2013. [Google Scholar]
- Cañas, R. Estudio de La Socavación Local En Pilas Circulares de Puentes En Lechos No Cohesivos Con Modelación Física En Laboratorio. Master’s Thesis, Escuela Colombiana de Ingenieria Julio Garavito, Bogota, Colombia, 2018. [Google Scholar]
- Khosronejad, A.; Diplas, P.; Angelidis, D.; Zhang, Z.; Heydari, N.; Sotiropoulos, F. Scour Depth Prediction at the Base of Longitudinal Walls: A Combined Experimental, Numerical, and Field Study. Environ. Fluid Mech.
**2020**, 20, 459–478. [Google Scholar] [CrossRef] - Taha, N.; El-Feky, M.M.; El-Saiad, A.A.; Fathy, I. Numerical Investigation of Scour Characteristics Downstream of Blocked Culverts. Alex. Eng. J.
**2020**, 59, 3503–3513. [Google Scholar] [CrossRef] - Johnson, P.A.; Clopper, P.E.; Zevenbergen, L.W.; Lagasse, P.F. Quantifying Uncertainty and Reliability in Bridge Scour Estimations. J. Hydraul. Eng.
**2015**, 141, 04015013. [Google Scholar] [CrossRef] - Lacey, G. Stable channels in alluvium (includes appendices). Minutes Proc. Inst. Civ. Eng.
**1930**, 229, 259–292. [Google Scholar] [CrossRef] - Blench, T. A new theory of turbulent flow in liquids of small viscosity. (in abstract form). J. Inst. Civ. Eng.
**1939**, 11, 611–612. [Google Scholar] [CrossRef] - Lischtvan, L.; Lebediev, V. Gidrologia I Gidraulika v Mostovom Doroshnom, Straitielvie. In Hydrology and Hydraulics in Bridge and Road Building; Gidrometeoizdat: St. Petersburg, Russian, 1959. [Google Scholar]
- Laursen, E.M.; Toch, A. Bulletin no Scour around Bridge Piers and Abutments Iowa Institute of Hydraulic Research in Cooperation with Thl Iowa State Highway Commission and the Bureau of Public Roads; Iowa Highway Research Board: Ames, IA, USA, 1956. [Google Scholar]
- Straub, L.G. Report of Committee on Dynamics of Streams, 1937–1938. Trans. Am. Geophys. Union
**1938**, 19, 349. [Google Scholar] [CrossRef] - Komura, S. Equilibrium Depth of Scour in Long Constrictions. J. Hydraul. Div.
**1966**, 92, 17–37. [Google Scholar] [CrossRef] - Borges, M. Socavacion al Pie de Muros Longitudinales. Bachelor’s Thesis, Universidad de Merida, Merida, Mexico, 2008. [Google Scholar]
- Richardson, E.V.; Simons, D.B.; Julien, P.Y. Highways in the River Environment: Participant Notebook; Federal Highway Administration: Washington, DC, USA, 1990. [Google Scholar]
- Melville, B.W. Pier and Abutment Scour: Integrated Approach. J. Hydraul. Eng.
**1997**, 123, 125–136. [Google Scholar] [CrossRef] - Froehlich, D.C. Local Scour at Bridge Abutments. In Proceedings of the 1989 National Conference on Hydraulic Engineering, ASCE, New Orleans, LA, USA, 14 August 1989; pp. 13–18. [Google Scholar]
- Melville, B.W. Local Scour at Bridge Abutments. J. Hydraul. Eng.
**1992**, 118, 615–631. [Google Scholar] [CrossRef] - Mussetter, B.; Stoliker, D.; Foglesong, R.; Alsop, T.; Aguirre, F.; Stone, H.; Dodge, C.; Mortenson, J.; Carroll, R. Sediment and Erosion Design Guide Sscafca Sediment and Erosion Design Guide. 2008. Available online: https://sscafca.org/development/documents/sediment_design_guide/Sediment%20Design%20Guide%2012-30-08.pdf (accessed on 7 November 2023).
- Look, B.G. Handbook of Geotechnical Investigation and Design Tables; Taylor & Francis: Oxfordshire, UK, 2007; ISBN 9780429224379. [Google Scholar]
- Chachereau, Y.; Chanson, H. Free-Surface Fluctuations and Turbulence in Hydraulic Jumps. Exp. Therm. Fluid Sci.
**2011**, 35, 896–909. [Google Scholar] [CrossRef] - Guzmán, R.; Bezada, M.; Rodríguez-Santalla, I. Granulometric Characterization of Sediments in the Anastomosed System of the Apure River Venezuela. J. S. Am. Earth Sci.
**2021**, 109, 103274. [Google Scholar] [CrossRef] - Khan, U.A.; Valentino, R. Investigating the Granulometric Distribution of Fluvial Sediments through the Hybrid Technique: Case Study of the Baganza River (Italy). Water
**2022**, 14, 1511. [Google Scholar] [CrossRef] - Pereira, L.M. Erosión Local En Estribos. Master’s Thesis, Universidad de los Andes, Merida, Mexico, 1995. [Google Scholar]
- Gonzalez, J.R.P.; Escobar-Vargas, J.; Vargas-Luna, A.; Castiblanco, S.; Trujillo, D.; Guatame, A.C.; Corzo, G.; Santos, G.; Perez, L.A. Hydroinformatic Tools and Their Potential in the Search for Missing Persons in Rivers. Forensic Sci. Int.
**2022**, 341, 111478. [Google Scholar] [CrossRef] [PubMed] - Oliveto, G.; Hager, W.H. Temporal Evolution of Clear-Water Pier and Abutment Scour. J. Hydraul. Eng.
**2002**, 128, 811–820. [Google Scholar] [CrossRef] - Di Pietro, P.; Mahajan, R.R. Erosion Control Solutions with Case Studies; Springer: Berlin/Heidelberg, Germany, 2022; pp. 71–94. [Google Scholar]
- Radice, A.; Davari, V. Roughening Elements as Abutment Scour Countermeasures. J. Hydraul. Eng.
**2014**, 140, 06014014. [Google Scholar] [CrossRef] - Aguirre-Pe, J.; Olivero, M.L.; Moncada, A.T. Particle Densimetric Froude Number for Estimating Sediment Transport. J. Hydraul. Eng.
**2003**, 129, 428–437. [Google Scholar] [CrossRef]

**Figure 1.**A complete view of the experimental flume (

**a**) and the composition of the measurement points (

**b**).

**Figure 4.**Maximum scour measurements for the eleven control points for different discharges and slope configurations. slope = 0.5% (

**a**), slope = 1% (

**b**), slope = 1.5% (

**c**), slope = 2% (

**d**), and slope = 2.5% (

**e**).

**Figure 6.**Lineal regression of the results of the proposed equation and the experimental data to estimate the maximum local scour.

Slope (%) | Discharge (m ^{3}/s) | Maximum Scour Depth (mm) | ||||||||||

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | ||

0.5 | 0.008 | 10 | 10.6 | 3 | 5 | 4.4 | 7.8 | 8.2 | 8.8 | 2 | 2.4 | 6 |

0.017 | 2.5 | 6 | 8.2 | 0 | 5.5 | 5 | 10 | 10 | 2.7 | 2.1 | 5.6 | |

0.025 | 28 | 34.5 | 27.6 | 15.6 | 15 | 10 | 14.7 | 8.5 | 11.9 | 11.5 | 11.3 | |

0.03 | 28 | 40 | 36.1 | 26 | 19.5 | 12.5 | 14.8 | 15.5 | 15.2 | 16.9 | 14.4 | |

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | ||

2.5 | 0.008 | 29.7 | 28.2 | 21.9 | 26.9 | 17.9 | 12.9 | 16.9 | 17.7 | 18.2 | 10.8 | 12.3 |

0.017 | 56 | 57 | 56 | 38.9 | 37.6 | 23.9 | 24.1 | 27.1 | 19.2 | 18.9 | 23.2 | |

0.025 | 58.9 | 64 | 92 | 85 | 98 | 80 | 61.2 | 58.9 | 40 | 24.5 | 24.2 | |

0.03 | 62.1 | 97.5 | 83.5 | 80 | 83.9 | 68.7 | 74.5 | 27.8 | 24.9 | 22.8 | 29.8 |

**Table 2.**Statistical estimators were obtained by comparing experimental measurements with the prediction equations.

MNE | MPF | MSE (mm^{2}) | RMSE (mm) | Equation | Reference |
---|---|---|---|---|---|

63.03 | 4.67 | 0.0015 | 0.0381 | Lischtvan-Lebediev | [19] |

219.54 | 2.78 | 0.0024 | 0.0485 | Froehlich | [26] |

170.53 | 2.11 | 0.0012 | 0.0353 | Pereira | [33] |

110.41 | 2.93 | 0.0053 | 0.0690 | Borges | [23] |

1816.46 | 3.20 | 0.0038 | 0.0619 | Mussetter | [28] |

201.93 | 3.06 | 0.0023 | 0.0483 | Khosronejad et al. | [14] |

68.72 | 3.60 | 0.0010 | 0.0321 | Proposed equation | This research |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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**

Cely Calixto, N.J.; Galvis Castaño, A.; Carrillo Soto, G.A.
Evaluation of Local Scour along the Base of Longitudinal Training Walls. *Water* **2023**, *15*, 4001.
https://doi.org/10.3390/w15224001

**AMA Style**

Cely Calixto NJ, Galvis Castaño A, Carrillo Soto GA.
Evaluation of Local Scour along the Base of Longitudinal Training Walls. *Water*. 2023; 15(22):4001.
https://doi.org/10.3390/w15224001

**Chicago/Turabian Style**

Cely Calixto, Nelson Javier, Alberto Galvis Castaño, and Gustavo Adolfo Carrillo Soto.
2023. "Evaluation of Local Scour along the Base of Longitudinal Training Walls" *Water* 15, no. 22: 4001.
https://doi.org/10.3390/w15224001