# Evaluation of the Effect of Surface Irregularities on the Hydraulic Parameters within Unlined Dam Spillways

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{UD}), water velocity (V), shear stress (τ

_{b}) applied to a rock surface, stress intensity (K

_{I}), and lifting force (F

_{L}) as important hydraulic erosive parameters (Table 1).

_{I}) is considered a hydraulic erosive parameter and is calculated based on the maximum pressure at the plunge pool bottom. Bollaert’s DI considers uplift force to be a hydraulic erosive parameter on the basis of impulsion and Newton’s second law of thermodynamics. This method ignores the geomechanical and geometric characteristics of the rock mass. In the DI approach, it is assumed that the shear force (F

_{sh}) is zero. Bollaert’s QSI method determines the forces applied to channel bottoms through the quasi-steady lift force (F

_{QSL}) on a protruding block, where the F

_{QSL}is dependent on uplift pressure and flow velocity.

_{UD})—initially developed using internal flow conditions. The concept of stress intensity (K

_{I}) was originally developed for metallurgical analysis [11] and is only used to estimate the probability of joint propagation in intact rocks, not rock masses. When the existing methods are compared (Table 1), the stream power dissipation parameter is the most commonly used; however, spillway geometry is not considered.

Hydraulic Erosive Parameter | Equation | |
---|---|---|

Parameter | Approach | |

Unit stream power dissipation (Π_{UD}) and Stream power dissipation (Π_{D})
| (Van Schalkwyk 1994) [10] | ${\mathsf{\Pi}}_{D}=\rho \xb7\mathrm{g}\xb7q\xb7S$ |

(Annandale 1995) [6] | ${\mathsf{\Pi}}_{D}=\gamma \xb7q\xb7\u2206E$ | |

(Pells 2016) [1] | ${\mathsf{\Pi}}_{UD}=\rho \xb7\mathrm{g}\xb7q\frac{dE}{dx}$ | |

Velocity (V) | (Weisbach 1845, Darcy 1857) [16,17] | $V=\sqrt{\frac{8\mathrm{g}}{f}}\sqrt{{R}_{H}{\xb7S}_{f}\mathrm{cos}\theta}$ |

(Manning et al., 1890) [18] | $V=\frac{1}{n}{{R}_{H}}^{2/3}{\xb7S}^{1/2}$ | |

Shear stress (τ_{b})
| (Yunus 2010) [19] | ${\overline{\tau}}_{b}=\rho \xb7\mathrm{g}\xb7{R}_{H}\xb7S\mathrm{cos}\beta $ |

${\overline{\tau}}_{b}=\rho \xb7\mathrm{g}\xb7{R}_{H}{\xb7S}_{f}\mathrm{cos}\beta $ | ||

MPM (Khodashenas and Paquier 1999) [20] | ${\tau}_{i}=\rho \xb7g\xb7{R\xb7J}_{f}$ | |

(Prasad and Russell 2000) [21] | $\frac{{\overline{\tau}}_{\left(b\right)}}{\rho gh{J}_{f}}=\left(1-0.01\%SFw\right)\left(1+\frac{{P}_{\left(w\right)}}{{P}_{\left(b\right)}}\right)$ | |

(Yang and Lim 2005) [22] | $\frac{{\overline{\tau}}_{\left(b\right)}}{\rho gh{J}_{f}}=1+\frac{h}{b}\frac{1}{\mathrm{tan}\beta}-\psi \frac{h}{b}\frac{1}{\mathrm{sin}\u03f4}$ | |

(Guo and Julien 2005) [23] | $\frac{{\overline{\tau}}_{\left(b\right)}}{\rho gh{J}_{f}}=\frac{4}{\pi}\mathrm{A}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{g}\left[\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{-\pi h}{b}\right)\right]+\frac{4}{\pi}\frac{h}{b}\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{-h}{b}\right)$ | |

(Seckin, Seckin et al., 2006) [24] | $\frac{{\overline{\tau}}_{\left(b\right)}}{\rho gR{S}_{f}}=\frac{a+b\left(B/H\right)}{1+c\left(B/H\right)+d{\left(B/H\right)}^{2}}$ | |

(Severy and Felder 2017) [25] | ${\tau}_{0}=\frac{1}{8}f\rho {V}^{2}$ | |

Stress intensity (K_{I})
| Bollaert and Schleiss 2002) [11] | ${K}_{I}={0.8\xb7P}_{max}\xb7F\xb7\sqrt{\pi \xb7{L}_{f}}$ |

Lifting force (F_{L})
| (Bollaert and Schleiss 2002) [11] | $I=\underset{0}{\overset{\mathsf{\Delta}tpulse}{\int}}\left({F}_{u}-{F}_{o}-{G}_{b}-{F}_{sh}\right)\xb7dt=m\xb7{V}_{\mathsf{\Delta}tpulse}$ |

(Bollaert 2010) [12] | ${F}_{QSL}={C}_{uplift}\xb7{L}_{block}\xb7\frac{{V}_{X,max}^{2}}{2g}$ |

- (1)
- Semitheoretical Approaches: Notably, Pells’ RMEI method among semitheoretical approaches showcased relatively lower errors compared to counterparts within the same category, despite inherent margins of error.
- (2)
- Semianalytical Methods: Among the array of semianalytical methods, Bollaert’s CSM approach emerged as a representative choice for evaluating hydraulic erodibility, particularly in scenarios involving plunge pool dynamics. The challenges associated with obtaining site-specific data were balanced by its applicability to channel flow situations, thereby suggesting its potential as a novel analytical technique tailored for unlined spillways.
- (3)
- Advancing Erosion Prediction Methods: The significance of developing new or refining existing erosion prediction methods was underscored as crucial for dam spillway design. This endeavor addressed the following pivotal aspects:
- Distinct Hydraulic Erosive Parameter: A foundational step involved defining a distinctive hydraulic parameter.
- Dam Spillway Geometry Influence: The influence of dam spillway geometry on the hydraulic erosive parameter.
- Impact of Rock Mass Geometry: Delving into the implications of rock mass geometry, including factors like block volume, joint characteristics, dip, and dip direction, on the hydraulic erosive parameter.
- Geomechanical Scrutiny: Definition of the effects of geomechanical factors on the hydraulic erosive parameter.

_{1}).

## 2. Materials and Methods

- Hydraulic parameters included total pressure, shear stress, flow velocity, force, stream power, and energy.
- Geomechanical parameters encompassed block volume, joint aperture, dip angle, and dip direction.
- Geometric parameters involved the shape of the rock surface, slope, and channel structure.

_{1}) of rock surface irregularities, impacted hydraulic parameters. With the value of l held constant (given its direct relationship with other geometrical parameters), the focus was exclusively directed towards h and α

_{1}. The investigation primarily centered on hydraulic parameters such as velocity, pressure, force, and energy. These parameters played a pivotal role, as they affected a range of other factors. By exploring the influence of h and α

_{1}on these hydraulic parameters, insights were gained into broader interactions.

#### 2.1. Determining Model Geometry

_{1}) are presented.

#### 2.1.1. Step 1: Blasting Effect on the Profile of Surface Irregularities

#### 2.1.2. Step 2: Selection of Geometries for Unlined Surface Profiles

_{1}) of the irregularities. It was assumed that the spillways’ geometric parameters remained constant. An irregularity angle ranging from 12° to 40° covered most irregularities, and the irregularity height varied between 10 and 30 cm. The irregularity length was proportional to the height and angles and generally fell between 1 and 2 m. A length of 1.5 m was selected for all the models.

_{1}, h, and l. The lengths of irregularity surfaces with and against water flow were represented by e

_{b}and e

_{f}, respectively (Figure 4). The irregularity angle in the flow direction, along with the spillway slope, was known as α

_{2}. This study considered several configurations, as shown in Figure 5.

#### 2.2. Numerical Modeling

#### 2.2.1. Step 1: Model Geometry and Boundary Conditions

_{1}) were identified based on the Pells data set. A total of 25 configurations were considered for this study (Figure 5).

#### 2.2.2. Step 2: Meshing and Convergence Analysis

_{1}= 12°. A meshing size of 10 cm was deemed optimal on the basis of outcomes of this grid convergence analysis (Table 3), considering the criteria of the time calculation and precision of the results. Finally, an approximately 48 m long portion of the channel (CC’ red line in Figure 3a) was analyzed.

#### 2.2.3. Step 3: Model Setup (VOF Method, Turbulence Model, Control Equation)

_{w}= 1, water fills every control unit in the calculation domain, and when a

_{a}= 1, it fills with air. Tracking the air–water interaction requires the following continuity equation [32]:

_{i}represents the coordinate and u

_{i}denotes the flow velocity. (For units of the various parameters, please refer to the included symbol notation table)

_{a}), and F

_{u}and F

_{v}are the forces of fluid particles in 2D directions.

_{k}denotes the turbulent kinetic energy production term, ${\mu}_{eff}$ represents the effective dynamic viscosity coefficient ${C}_{1\u03f5}$ and ${C}_{2\u03f5}$ denote the constants 1.42 and 1.68, respectively.

## 3. Results

_{D}) and total pressure (P

_{T}) extracted directly from Ansys_Fluent.

#### 3.1. Effect of Irregularities on Velocity

_{1}and height increased (Figure 8). Moreover, the effect of height on flow velocity was greater than the effect of α

_{1}. For instance, at a constant α

_{1}(α

_{1}= 12), maximum velocity decreased from approx. 11.5 m∙s

^{−1}at h = 10 cm to approx. 8 m∙s

^{−1}at h = 40 cm. At a constant height, however, velocity did not necessarily decrease as α

_{1}increased, the change often being minor and could be ignored. For instance, at a constant height (h = 10 cm), the maximum velocity for α

_{1}= 12 was approx. 11.5 m∙s

^{−1}and for α

_{1}= 40, it was approx. 9 m∙s

^{−1}. Flow velocity did not change significantly at a constant height (i.e, h = 30 cm) as α

_{1}increased. At greater heights (h), α

_{1}variations did not affect maximum velocity, and the height of the irregularity had a greater impact.

#### 3.2. Effect of Irregularities on Total Pressure (P_{T})

_{S}), and dynamic (P

_{D}) pressures are described in Equations (12)–(14), respectively.

_{T,max}represents maximum total pressure, P

_{S,channel bottom}represents the static pressure at the channel bottom, P

_{D,channel bottom}represents the dynamic pressure at the channel bottom, and P

_{D,water surface}is the dynamic pressure at the water surface, where it is at its maximum.

_{1}= 19°). To analyze these fluctuations, the most representative and appropriate lines, which represented the upper bound of each graph (e.g., red line of Figure 10), for each configuration were selected. These lines were then grouped into a single chart (Figure 11).

_{1}and h increased (Figure 11). For example, at a constant α

_{1}= 12°, the total pressure of flowing water at the channel bottom dropped with a higher h, from approx. 25 Pa at h = 10 cm to approx. 17 Pa at h = 40 cm. At a constant h, however, total pressure did not necessarily decrease as α

_{1}increased; often these changes were negligible and could be ignored. At greater heights (h), altering α

_{1}produced little effect on total pressure, whereas altering the height of the irregularity had a marked effect. The total pressure difference at the zero point occurred because the zero point on the X-axis (distance) did not match the model’s zero point (see Figure 11f). The analysis began 15 m from the model’s inlet; thus, the effect of irregularity height could already be observed, causing the initial pressure difference in the graphs.

_{1}and h increased (Figure 12). At greater heights (h), α

_{1}changes had minimal effect on the total pressure, whereas changes to irregularity height did produce a large effect.

#### 3.3. Effect of Irregularities on Shear Stress

_{1}= 12. Shear stress on the rock surface was negligible relative to the total, static, and dynamic pressures. Nonetheless, as irregularity height (h) increased, shear stress along the wall decreased; however, these values were so small that they could be ignored.

#### 3.4. Effect of Irregularities on the Energy Gradient

_{1}increased.

- In the first state, the velocity differential between upstream and downstream was close to zero; thus, the slope of the flow–distance relationship was zero;
- In the second state, the difference in velocity between the upstream and downstream was not zero, and flow velocity–distance relationship sloped upward.

_{P}was the same for both states, the negative relationship between the energy and distance decreased as the slope of the velocity increased for the second state, i.e., a greater velocity increased the amount of energy and decreased energy loss.

## 4. Discussion

- (1)
- Irregularities affected hydraulic parameters, despite existing approaches for determining hydraulic erosive parameters not considering these irregularities.
- (2)
- Velocity at a constant height did not continually decrease as α
_{1}increased, and these changes were often negligible. - (3)
- Changes in irregularity angle had a minimal effect on maximum flow velocity at greater heights; however, altering irregularity height had a marked effect.
- (4)
- Holding the irregularity angle constant, total pressure along the channel bottom decreased as h increased. At a constant h, however, total pressure did not consistently decrease as α
_{1}increased; these latter changes were typically negligible. At greater heights, changes in angle had a minimal impact on total pressure; however, altering irregularity height had a marked effect. - (5)
- Total pressure, using maximum dynamic pressure to determine the total pressure, increased 2.5–3× relative pressure along the channel bottom.
- (6)
- Along the water–rock interface, 70% of the energy was lost along the profile.
- (7)
- Energy at the water–rock interface increased by approx. 30% upstream and 250%–350% downstream.
- (8)
- Increased flow velocity increased energy and decreased energy loss.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Pells, S. Erosion of Rock in Spillways; University Of New South Wales: New South Wales, Sydney, 2016. [Google Scholar]
- Rock, A.J. Semi-Empirical Assessment of Plunge Pool Scour: Two-Dimensional Application of Annandale’s Erodibility Index Method on four Dams in British Columbia, Canada, A. Colorado School of Mines; Arthur Lakes Library: Golden, CO, USA, 2015. [Google Scholar]
- Jalili Kashtiban, Y.; Saeidi, A.; Farinas, M.-I.; Quirion, M. A Review on Existing Methods to Assess Hydraulic Erodibility Downstream of Dam Spillways. Water
**2021**, 13, 3205. [Google Scholar] [CrossRef] - Blake, W.; Hedley, D.G. Rockbursts: Case Studies from North American Hard-Rock Mines; SME: Southfield, MI, USA, 2003. [Google Scholar]
- Saeidi, A.; Eslami, E.; Quirion, M.; Seifaddini, M. Assessment of rock mass erosion in unlined spillways using developed vulnerability and fragility functions. Georisk Assess. Manag. Risk Eng. Syst. Geohazards
**2020**, 14, 280–292. [Google Scholar] [CrossRef] - Annandale, G. Erodibility. J. Hydraul. Res.
**1995**, 33, 471–494. [Google Scholar] [CrossRef] - Annandale, G.W. Current Technology to Predict Scour of Rock. In Golden Rocks 2006, The 41st US Symposium on Rock Mechanics (USRMS); OnePetro: Richardson, TX, USA, 2006. [Google Scholar]
- Kirsten, H.A.; Moore, J.S.; Kirsten, L.H.; Temple, D.M. Erodibility criterion for auxiliary spillways of dams. Int. J. Sediment Res.
**2000**, 15, 93–107. [Google Scholar] - Moore, J.S.; Temple, D.M.; Kirsten, H.A. Headcut advance threshold in earth spillways. Bull. Assoc. Eng. Geol.
**1994**, 31, 277–280. [Google Scholar] - Van Schalkwyk, A. Minutes—Erosion of rock in unlined spillways. ICOLD Q
**1994**, 71, 1056–1062. [Google Scholar] - Bollaert, E.; Schleiss, A. Transient Water Pressures in Joints and Formation of Rock Scour Due to High-Velocity Jet Impact; EPFL-LCH: Lausanne, Switzerland, 2002. [Google Scholar]
- Bollaert, E. The Comprehensive Scour Model: Theory and Feedback from Practice. In Proceedings of the 5th International Conference on Scour and Erosion, San Francisco, CA, USA, 7–10 November 2010. [Google Scholar]
- Carlotti, P. Two-point properties of atmospheric turbulence very close to the ground: Comparison of a high resolution LES with theoretical models. Bound. Layer Meteorol.
**2002**, 104, 381–410. [Google Scholar] [CrossRef] - Schmidt, H.; Schumann, U. Coherent structure of the convective boundary layer derived from large-eddy simulations. J. Fluid Mech.
**1989**, 200, 511–562. [Google Scholar] [CrossRef] - Townsend, A. The Structure of Turbulent Shear Flow; Cambridge university press: Cambridge, UK, 1976. [Google Scholar]
- Darcy, H. Recherches Expérimentales Relatives au Mouvement de l’eau Dans les Tuyaux; Mallet-Bachelier: Paris, France, 1857; Volume 1. [Google Scholar]
- Weisbach, J.L. Lehrbuch der Ingenieur-und Maschinen-Mechanik: Theoretische Mechanik; Druck und Verlag von Friedrich Vieweg und Sohn: Braunschweig, Gemary, 1845; Volume 1. [Google Scholar]
- Manning, R.; Griffith, J.P.; Pigot, T.; Vernon-Harcourt, L.F. On the Flow of Water in Open Channels and Pipes; Transaction of the Institution of Civil Engineers of Ireland: Dublin, Ireland, 1890; Volume 20. [Google Scholar]
- Yunus, A.C. Fluid Mechanics: Fundamentals And Applications (Si Units); Tata McGraw Hill Education Private Limited: New York, NY, USA, 2010. [Google Scholar]
- Khodashenas, S.R.; Paquier, A. A geometrical method for computing the distribution of boundary shear stress across irregular straight open channels. J. Hydraul. Res.
**1999**, 37, 381–388. [Google Scholar] [CrossRef] - Prasad, B.V.R.; Russell, M.J. Discussion of “Diffusional Mass Transfer at Sediment-Water Interface” by Nancy Steinberger and Midhat Hondzo. J. Environ. Eng.
**2000**, 126, 576. [Google Scholar] [CrossRef] - Yang, S.-Q.; Lim, S.-Y. Boundary shear stress distributions in trapezoidal channels. J. Hydraul. Res.
**2005**, 43, 98–102. [Google Scholar] [CrossRef] - Guo, J.; Julien, P.Y. Shear stress in smooth rectangular open-channel flows. J. Hydraul. Eng.
**2005**, 131, 30–37. [Google Scholar] [CrossRef] - Seckin, G.; Seckin, N.; Yurtal, R. Boundary shear stress analysis in smooth rectangular channels. Can. J. Civ. Eng.
**2006**, 33, 336–342. [Google Scholar] [CrossRef] - Severy, A.; Felder, S. Flow Properties and Shear Stress on a Flat-Sloped Spillway. In Proceedings of the 37th IAHR World Congress, Kuala Lumpur, Malaysia, 13–18 August 2017; pp. 13–18. [Google Scholar]
- Kashtiban, Y.J.; Shahriar, K.; Bakhtavar, E. Assessment of blasting impacts on the discontinuities in a salt stope and pillar mine using a developed image processing. Bull. Eng. Geol. Environ.
**2022**, 81, 1–14. [Google Scholar] [CrossRef] - Lopez Jimeno, C. Drilling and Blasting of Rocks; A.A. Balkema: Rotterdam, The Netherlands; Brookfield, VT, USA, 1995. [Google Scholar]
- Fluent, A. 12.0 Theory Guide. Ansys Inc
**2009**, 5, 15. [Google Scholar] - Hirt, C.W.; Nichols, B.D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys.
**1981**, 39, 201–225. [Google Scholar] [CrossRef] - Bombardelli, F.A.; Hirt, C.; García, M.H.; Matthews, B.; Fletcher, C.; Partridge, A.; Vasquez, S. Computations of curved free surface water flow on spiral concentrators. J. Hydraul. Eng.
**2001**, 127, 629–631. [Google Scholar] [CrossRef] - Lee, C.-H.; Xu, C.; Huang, Z. A three-phase flow simulation of local scour caused by a submerged wall jet with a water-air interface. Adv. Water Resour.
**2019**, 129, 373–384. [Google Scholar] [CrossRef] - Imanian, H.; Mohammadian, A. Numerical simulation of flow over ogee crested spillways under high hydraulic head ratio. Eng. Appl. Comput. Fluid Mech.
**2019**, 13, 983–1000. [Google Scholar] [CrossRef] - Li, Y.; Gao, Y.; Jia, X.; Sun, X.; Zhang, X. Numerical Simulations of Hydraulic Characteristics of A Flow Discharge Measurement Process with A Plate Flowmeter in A U-Channel. Water
**2019**, 11, 2382. [Google Scholar] [CrossRef]

**Figure 2.**Flowchart presenting the steps of modeling spillway for assessing the effect of irregularity geometry on hydraulic parameters.

**Figure 3.**(

**a**) Diagram of an unlined dam spillway; (

**b**) channel view from above; (

**c**) controlled-blasting pattern of the channel showing spacing and burden; and (

**d**) channel surface profile after blasting.

**Figure 4.**The assumed spillway geometry used in the model of irregularities along an unlined rock spillway.

**Figure 7.**(

**a**) The contour of volume fraction of water, (

**b**) dynamic pressure contour, and (

**c**) total pressure contour.

**Figure 8.**Maximum velocity profiles of the flow along the unlined spillway; (

**a**) α

_{1}= 12°; (

**b**) α

_{1}= 19°; (

**c**) α

_{1}= 26°; (

**d**) α

_{1}= 33°; (

**e**) α

_{1}= 40°.

**Figure 9.**Velocity profiles as a function of flow depth for various irregularity heights; a flow depth of 0 m refers to the channel bottom; (

**a**) α

_{1}= 12°; (

**b**) α

_{1}= 19°; (

**c**) α

_{1}= 26°; (

**d**) α

_{1}= 33°; (

**e**) α

_{1}= 40°; (

**f**) the analyzed section of the channel profile (red line).

**Figure 10.**Total pressure (sum of dynamic and static pressures) profile along the water–rock interface for the configuration α

_{1}= 19° and h = 10 cm; red line describes the upper bound of the graph.

**Figure 11.**Total pressure (static and dynamic pressure) profiles on water–rock interface as a function of spillway length for various irregularity heights and angles; (

**a**) α

_{1}= 12°; (

**b**) α

_{1}= 19°; (

**c**) α

_{1}= 26°; (

**d**) α

_{1}= 33°; and (

**e**) α

_{1}= 40°; (

**f**) the analyzed section of the channel profile (red line).

**Figure 12.**Total pressure profiles on the water surface as a function of spillway length for various irregularity heights; (

**a**) α

_{1}= 12°; (

**b**) α

_{1}= 19°; (

**c**) α

_{1}= 26°; (

**d**) α

_{1}= 33°; and (

**e**) α

_{1}= 40°.

**Figure 15.**Energy gradient profiles at the water–rock interface; (

**a**) α

_{1}= 12°; (

**b**) α

_{1}= 19°; (

**c**) α

_{1}= 26°; (

**d**) α

_{1}= 33°; and (

**e**) α

_{1}= 40°.

**Figure 16.**Energy gradient profiles along the water surface; (

**a**) α

_{1}= 12°; (

**b**) α

_{1}= 19°; (

**c**) α

_{1}= 26°; (

**d**) α

_{1}= 33°; and (

**e**) α

_{1}= 40°.

Parameters | Value | Description |
---|---|---|

Initial flow depth | 2 m | See point 3 in Figure 4 |

Initial flow velocity | 3 m∙s^{−1} | See point 1 in Figure 4 |

Inlet boundary condition | – | Velocity inlet (point 1 in Figure 4) |

Outlet boundary condition | – | Pressure outlet (point 4 in Figure 4) |

Unlined spillway length | 50 m | – |

No. of irregularities | 32 | – |

Irregularity height (h) | 10, 15, 20, 25, 30 cm | |

Irregularity angle (α_{1}) | 12°, 19°, 26°, 33°, 40° | |

Channel slope | 5° | – |

Boundary Conditions | Structural Schemes | ||||
---|---|---|---|---|---|

Maximum size of grid cell (cm) | 20 | 15 | 10 | 5 | 1 |

Maximum velocity (m∙s^{−1}) | 9.46 | 10.31 | 10.64 | 10.68 | 10.67 |

Water depth (cm) | 82.1 | 73.3 | 68.9 | 68.1 | 67.9 |

Maximum total pressure (kPa) | 52.63 | 60.16 | 63.18 | 63.52 | 63.6 |

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**

Jalili Kashtiban, Y.; Saeidi, A.; Farinas, M.-I.; Patarroyo, J.
Evaluation of the Effect of Surface Irregularities on the Hydraulic Parameters within Unlined Dam Spillways. *Water* **2023**, *15*, 3004.
https://doi.org/10.3390/w15163004

**AMA Style**

Jalili Kashtiban Y, Saeidi A, Farinas M-I, Patarroyo J.
Evaluation of the Effect of Surface Irregularities on the Hydraulic Parameters within Unlined Dam Spillways. *Water*. 2023; 15(16):3004.
https://doi.org/10.3390/w15163004

**Chicago/Turabian Style**

Jalili Kashtiban, Yavar, Ali Saeidi, Marie-Isabelle Farinas, and Javier Patarroyo.
2023. "Evaluation of the Effect of Surface Irregularities on the Hydraulic Parameters within Unlined Dam Spillways" *Water* 15, no. 16: 3004.
https://doi.org/10.3390/w15163004