# Design for the Prediction of Peak Outflow of Embankment Breaching Due to Overtopping by Regression Technique and Modelling

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## Abstract

**:**

_{p}) by correlating with other independent embankment breach parameters for cohesive as well as non-cohesive embankments. The model is validated with historical and laboratory data compiled in the past. For the validation of current investigational work, the experimental data of the present study are compared with the model already developed by other researchers. From the study and analysis, it is observed that breach peak outflow depends upon hydraulic, geometric, and geotechnical parameters of embankments. Being a phenomenon that is active for a short duration only, the manual measurement of various parameters of the modeling process poses some limitations under laboratory conditions.

## 1. Introduction

## 2. Breach Formation Models

_{p}) with depth of water behind the dam at the time of breach (d

_{w}). MacDonald and Langride-MonoPiolis [13] studied 42 data failures and related breach formation factor with the volume of breach outflow and the depth of water above the breach. Von Thun and Gillette [14] studied 57 case studies of dam failures and proposed methods for estimating breach formation time. Froehlich [17] revised his previous papers [15,16] using data of 63 dam failures and developed a new dimensional equation for average breach width and time of failure by assuming a constant breach side slope factor for overtopping failure. After that, other researchers also developed regression models by using dam failure data. Wu [10] summarized the different relations proposed by researchers MacDonald et al. [13], Von Thun and Gillette [14], Froehlich [15,16,17], and Pierce et al. [19]. Many researchers developed a relationship to estimate peak outflow by correlating different parameters. The accuracy of these models depends upon the database of dam failures which is used to derive regression equations rather than physical processes. Thus, there might be a lot of uncertainties in the prediction of breach parameters, and these uncertainties are described by Wahl [20]. Additionally, to correlate a relationship among different breach parameters, an experimental study is more accurate. In the last decade, different researchers conducted laboratory tests, small-scale as well as large-scale tests, and field tests to predict breach parameters. Recently, experimental investigation of breaching of embankments was studied in a large flume by Zhao [21] and in a small flume by Verma et al. [22]. Furthermore, Vanani and Ostad-Ali-Askari [23] described the correct path to use flumes in water resources management. Additionally, Verma et al. [24,25] studied two fuse plug embankment models by conducting laboratory experiments in a flume and observed three phase erosion profile. They observed that breach growth largely relies on fuse plug dimensions, fill material, reservoir storage, and inflow intensity. Chinnarasri et al. [26] proposed a relationship between dimensionless peak outflow and reservoir depth using experimental investigation as well as historical data. Wahl [27] described that predictions of peak outflow generally have uncertainties of about ±0.5 to ±1 order of magnitude.

## 3. Design Parameter for the Embankment Models

#### 3.1. Layout of Hydraulic Channel

#### 3.2. Material Characteristics Used in Modeling

## 4. Design and Modeling Procedure

#### 4.1. Design of Embankment Models

_{b}) and depth (D

_{b}) were observed at short time intervals using point gauges. The process of breach growth was videotaped with a high-speed digital video camera (Fastec Imaging Inline Gigabyte Ethernet Camera). Additionally, photographs at different points in time were taken with digital cameras.

#### 4.2. Breach Process and Flow Parameters

#### 4.2.1. Breach Flow Parameters

#### 4.2.2. Breach Process

_{f}= height of embankment model; h

_{r}= water level in reservoir; h

_{cf}= d

_{w}= water level above crest; h

_{cs}= height of crest sediment; h

_{b}= height of downstream at any instant during embankment breaching; L = longitudinal dimension of embankment model; and h

_{cf}= h

_{r}− h

_{cs}. Here, h

_{cf}means the depth of water above crest level (d

_{w}). In the literature, d

_{w}is generally used; so, in the present study, d

_{w}is used. The water level above the crest affects the breach formation time and subsequently the time of breach failure (t

_{f}). As the breach widens due to overtopping, the discharge through the breach channel increases. The outflow (discharge) increases with time, reaches its peak (maximum value), and then further decreases. As the experiments were conducted under falling reservoir conditions, the reservoir became empty, and the breaching process was completed. These experiments provided an insight into the breach mechanism obtained with the embankment breach profile and different breach parameters.

_{p}) corresponding to dimensionless geotechnical and embankment parameters. The important identified parameters associated with the phenomenon are:

_{p}, V

_{w}, d

_{w}, D

_{50},c, Z, g)

- Q
_{p}is the peak outflow at the time of failure (cm^{3}/s); - V
_{w}is the reservoir volume at the time of failure (cm^{3}); - d
_{w}is the depth of water above the crest or sill of breach (cm); - D
_{50}is the median particle size of embankment fills material (mm); - C is the cohesion of fill material (kg/cm
^{2}); - Z is the side slope of the embankment model (tan θ);
- G is the acceleration due to gravity (m/s
^{2}).

## 5. Results and Discussion

#### 5.1. Relation for Peak Outflow

^{b}, where ‘a’ is coefficient and ‘b’ is power index, which matches most of the points in the figure. The values of coefficients ‘a’ and ’b’ for the present data were employed and these values for mean correlation were found as 0.335 and 1.21. The data points yielded a best fit equation: y = 0.335 x

^{1.21}where x = $\frac{{d}_{w}}{{V}_{w}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}$, y = $\frac{{Q}_{P}}{\sqrt{g{V}_{w}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}$. Therefore, the equation may be written as:

#### 5.2. Validation of Relation

_{p}) using small-scale tests (similar to the present study), but considered only non-cohesive homogeneous embankment models.

_{w}’ and ‘V

_{w}’. The dimensionless term ‘d

_{w}/V

_{w}’ as shown in the equation is characterized as reservoir shape characteristic. Chinnarasri et al. [26] had also used the power regression analysis for laboratory data and observed the values of coefficients ‘a’ and ‘b’ as 0.209 and 1.6, respectively, for upper curve and 0.02 and 1.714 for the lower enveloping curve, respectively. Hence, by summarizing these values, the confidence limits for ‘a’ and ‘b’ are 0.02 to 0.21 and 0.9 to 1.72. The values of coefficient ‘a’ and ‘b’ are also compared and tabulated below in Table 3.

_{p}= f(V

_{w}, d

_{w,}D

_{50}, Z, g). Another significant dimensionless group obtained from Buckingham Pi theorem is $\left(\frac{{d}_{w}{}^{2}{D}_{50}Z}{{V}_{w}}\right)$ and so obtained the relationship as:

_{50}and Z. The equation fitted to the combined data (present data and Chinnarasri et al. [26]) with correlation coefficient (CC) as 0.9086, which results in the form of an equation as:

#### 5.3. Comparison with Other Researchers

- (a)
- (b)
- Chinnarasri et al. [26]:$$\frac{{Q}_{P}}{\sqrt{g{V}_{w}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}=0.0021ln\left[\frac{{d}_{w}^{2}{D}_{50}S}{{V}_{w}}\right]+0.32$$

- (a)

_{w}‘ is more important which affects the peak outflow.

- (b)
- Chinnarasri et al. [26]

## 6. Conclusions

- Buckingham Pi theorem was used to obtain a relationship for non-dimensional peak outflow (Q
_{p}) corresponding to depth of water (d_{w}) and volume of water (V_{w}). Through a combination of present data and laboratory as well as field data of other investigators, upper and lower envelope lines were defined for developing a universal relationship (Equation (3)). - A relationship was developed for determining peak outflow using depth of water, median particle size, side slope, and downstream slope (Equation (6)). From the graph, it is concluded that all data lie in a common cluster with coefficient of correlation as 0.9086.
- Furthermore, for the validation of present data, the experimental data were compared with two different equations (Equations (7) and (8)) developed by other investigators for predicting peak outflow. It is concluded that predicted values yield results that are closer to those of the present data, which validates the present data.
- Relationships developed in the present work are likely to be valuable for correlating other parameters.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Ge, W.; Wang, X.; Li, Z.; Zhang, H.; Guo, X.; Wang, T.; Gao, W.; Lin, C.; van Gelder, P. Interval Analysis of the Loss of Life Caused by Dam Failure. J. Water Resour. Plan. Manag.
**2021**, 147, 04020098. [Google Scholar] [CrossRef] - Hatje, V.; Pedreira, R.M.A.; de Rezende, C.E.; Schettini, C.A.F.; De Souza, G.C.; Marin, D.C.; Hackspacher, P.C. The environmental impacts of one of the largest tailing dam failures worldwide. Sci. Rep.
**2017**, 7, 10706. [Google Scholar] [CrossRef] [PubMed][Green Version] - Adamo, N.N.; Al-Ansari, N.; Sissakian, V.; Laue, J.; Knutsson, S. Dam Safety Problems Related to Seepage. J. Earth Sci. Geotech. Eng.
**2020**, 10, 191–239. [Google Scholar] - International Commission on large dams (ICOLD). In Lessons from Dam Incidents; ICOLD: Paris, France, 1978.
- Viseu, T.; de Almeida, A.B. Dam-break risk management and hazard mitigation. State Art Sci. Eng.
**2009**, 36, 211–239. [Google Scholar] - Ge, W.; Li, Z.; Liang, R.Y.; Li, W.; Cai, Y. Methodology for Establishing Risk Criteria for Dams in Developing Countries, Case Study of China. Water Resour. Manag.
**2017**, 31, 4063–4074. [Google Scholar] [CrossRef] - Wu, M.; Ge, W.; Li, Z.; Wu, Z.; Zhang, H.; Li, J.; Pan, Y. Improved Set Pair Analysis and Its Application to Environmental Impact Evaluation of Dam Break. Water
**2019**, 11, 821. [Google Scholar] [CrossRef][Green Version] - Cui, P.; Zhou, G.G.; Zhu, X.; Zhang, J. Scale amplification of natural debris flows caused by cascading landslide dam failures. Geomorphology
**2013**, 182, 173–189. [Google Scholar] [CrossRef] - Psomiadis, E.; Tomanis, L.; Kavvadias, A.; Soulis, K.; Charizopoulos, N.; Michas, S. Potential Dam Breach Analysis and Flood Wave Risk Assessment Using HEC-RAS and Remote Sensing Data: A Multicriteria Approach. Water
**2021**, 13, 364. [Google Scholar] [CrossRef] - Wu, W. Earthen Embankment Breaching. J. Hydraul. Eng.
**2011**, 137, 1549–1564. [Google Scholar] [CrossRef] - Gaagai, A.; Aouissi, H.A.; Krauklis, A.E.; Burlakovs, J.; Athamena, A.; Zekker, I.; Boudoukha, A.; Benaabidate, L.; Chenchouni, H. Modeling and Risk Analysis of Dam-Break Flooding in a Semi-Arid Montane Watershed: A Case Study of the Yabous Dam, Northeastern Algeria. Water
**2022**, 14, 767. [Google Scholar] [CrossRef] - Gaagai, A.; Boudoukha, A.; Benaabidate, L. Failure simulation of Babar dam—Algeria and its impact on the valley downstream section. J. Water Land Dev.
**2020**, 44, 75–89. [Google Scholar] [CrossRef] - MacDonald, T.C. and Langridge-Monopolis, J. Breaching Characteristics of Dam Failures. J. Hydraul. Eng.
**1989**, 110, 567–586. [Google Scholar] [CrossRef] - Von Thun, J.L.; Gillette, D.R. Guidance on Breach Parameters, Unpublished Internal Document; U.S. Bureau of Reclamation: Denver, CO, USA, 1990; p. 17.
- Froehlich, D.C. Embankment-Dam Breach Parameters. In Proceedings of the 1987 ASCE National Conference on Hydraulic Engineering, Williamsburg, VA, USA, 3–7 August 1987; pp. 570–575. [Google Scholar]
- Froehlich, D.C. Peak Outflow from Breached Embankment Dam. J. Water Resour. Plan. Manag.
**1995**, 121, 90–97. [Google Scholar] [CrossRef] - Froehlich, D.C. Embankment Dam Breach Parameters Revisited. In Proceedings of the 1995 ASCE Conference on Water Resources Engineering, San Antonio, TX, USA, 14–18 August 1995; pp. 887–891. [Google Scholar]
- Kirkpatrick, G.W. Evaluation Guidelines for Spillway Adequacy. In Proceedings of the Evaluation of Dam Safety, Engineering Foundation Conference, Pacific Grove, CA, USA; ASCE: Reston, VA, USA, 1976; pp. 395–414. [Google Scholar]
- Pierce, M.W.; Thornton, C.I.; Abt, S.R. Predicting Peak Outflow from Breached Embankment Dams. J. Hydrol. Eng.
**2010**, 15, 338–349. [Google Scholar] [CrossRef][Green Version] - Wahl, T.L. Predicting of Embankment Dam Breach Parameters: A Needs Assessment; USBR, Water Resources Research Laboratory, PAP-735: Denver, CO, USA, 2007.
- Zhao, G. Breach Growth in Cohesive Embankments due to Overtopping. Ph. D. Thesis, Delft University of Technology, Delft, The Netherlands, 2016. [Google Scholar]
- Verma, D.; Setia, B.; Arora, V.K. Mechanism of embankment dam breach. In Proceedings of the International Conference on Fluvial Hydraulics, Lausanne, Switzerland, 3–5 September 2014; pp. 1655–1659. [Google Scholar]
- Vanani, H.R.; Ostad-Ali-Askari, K. Correct path to use flumes in water resources management. Appl. Water Sci.
**2022**, 12, 187. [Google Scholar] [CrossRef] - Verma, D.; Setia, B.; Arora, V.K. Experimental study on breaching of embankments. In Proceedings of the 9th International Conference on Scour and Erosion, ICSE, Taipei, Taiwan, 5–8 November 2018; pp. 255–261. [Google Scholar]
- Verma, D.K.; Setia, B. Two dimensional unsteady dam breach analysis using fuse plug models. Disaster Adv.
**2021**, 14, 74–82. [Google Scholar] - Chinnarasri, C.; Jirakitlerd, S.; Wongwises, S. Embankment dam breach and its outflow characteristics. Civ. Eng. Environ. Syst.
**2004**, 21, 247–264. [Google Scholar] [CrossRef] - Wahl, T.L. Uncertainty of Predictions of Embankment Dam Breach Parameters. J. Hydraul. Eng.
**2004**, 130, 389–397. [Google Scholar] [CrossRef] - Alhasan, Z.; Jandora, J.; Říha, J. Study of Dam-break Due to Overtopping of Four Small Dams in the Czech Republic. Acta Univ. Agric. Silvic. Mendel. Brun.
**2015**, 63, 717–729. [Google Scholar] [CrossRef][Green Version] - Verma, D.K.; Setia, B.; Arora, V.K. Experimental Study of Breaching of an Earthen Dam using a Fuse Plug Model. Int. J. Eng. Trans. A Basics
**2017**, 30, 479–485. [Google Scholar] - Hasson, M.; Morris, M.; Hanson, G.; Lakhal, K. Breach Formation: Laboratory and Numerical Modeling of Breach Formation; Association of State Dam Safety Officials: Phoenix, AZ, USA, 2004. [Google Scholar]
- Kruse, E.; Eslamian, S.; Ostad-Ali-Askari, K.; Hosseini-Teshnizi, S.H. Borehole Investigations. In Encyclopedia of Engineering Geology, Encyclopedia of Earth Sciences Series; Bobrowsky, P., Marker, B., Eds.; Springer: Cham, Switzerland, 2018. [Google Scholar] [CrossRef]
- Ashraf, M.; Soliman, A.H.; El-Ghorab, E.; El Zawahry, A. Assessment of embankment dams breaching using large scale physical modeling and statistical methods. Water Sci.
**2018**, 32, 362–379. [Google Scholar] [CrossRef][Green Version] - Wang, B.; Chen, Y.; Wu, C.; Peng, Y.; Song, J.; Liu, W.; Liu, X. Empirical and semi-analytical models for predicting peak outflows caused by embankment dam failures. J. Hydrol.
**2018**, 562, 692–702. [Google Scholar] [CrossRef] - Tabrizi, A.A.; Elalfy, E.; Elkholy, M.; Chaudhry, M.H.; Imran, J. Effects of compaction on embankment breach due to overtopping. J. Hydraul. Res.
**2016**, 55, 236–247. [Google Scholar] [CrossRef] - Pickert, G.; Weitbrecht, V.; Bieberstein, A. Breaching of overtopped river embankments controlled by apparent cohesion. J. Hydraul. Res.
**2011**, 49, 143–156. [Google Scholar] [CrossRef] - Dhiman, S.; Patra, K.C. Studies of dam disaster in India and equations for breach parameter. Nat. Hazards
**2019**, 98, 783–807. [Google Scholar] [CrossRef] - Aamir, M.; Khan, M.A.; Ahmad, Z. Soft-computing approach to scour depth prediction under wall jets. In Current Directions in Water Scarcity Research; Elsevier: Amsterdam, The Netherlands, 2022; Volume 7, pp. 71–82. [Google Scholar]
- Aamir, M.; Ahmad, Z.; Pandey, M.; Khan, M.A.; Aldrees, A.; Mohamed, A. The Effect of Rough Rigid Apron on Scour Downstream of Sluice Gates. Water
**2022**, 14, 2223. [Google Scholar] [CrossRef] - Pandey, M.; Pu, J.H.; Pourshahbaz, H.; Khan, M.A. Reduction of scour around circular piers using collars. J. Flood Risk Manag.
**2022**, 15, e12812. [Google Scholar] [CrossRef] - Pu, J.; Wallwork, J.; Khan, A.; Pandey, M.; Pourshahbaz, H.; Satyanaga, A.; Hanmaiahgari, P.; Gough, T. Flood Suspended Sediment Transport: Combined Modelling from Dilute to Hyper-Concentrated Flow. Water
**2021**, 13, 379. [Google Scholar] [CrossRef]

**Figure 1.**Major dam failures in the world. (

**a**) Collapse of Banqiao Dam in China; (

**b**) Teton Dam Breach in US.

**Figure 7.**Variation of $\frac{{Q}_{P}}{\sqrt{g{V}_{w}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}$ with $\left[\frac{{d}_{w}}{{V}_{w}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}\right]$ using present data.

**Figure 11.**Variation of $\frac{{Q}_{P}}{\sqrt{g{V}_{w}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}$ corresponding to $\left[\frac{{\mathrm{d}}_{\mathrm{w}}{}^{2}{\mathrm{D}}_{50}\mathrm{Z}}{{\mathrm{V}}_{\mathrm{w}}}\right]$.

**Figure 12.**Variation of $\frac{{Q}_{P}}{\sqrt{g{V}_{w}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}$ corresponding to $\left[\frac{{\mathrm{d}}_{\mathrm{w}}{}^{2}{\mathrm{D}}_{50}\mathrm{Z}}{{\mathrm{V}}_{\mathrm{w}}}\right]$ [26].

**Figure 14.**Variation of observed peak outflow with predicted peak outflow using Chinnarsari et al. [26] Equation (8).

Fill Material (S) | Median Size, D_{50} (mm) | OMC (%) | Dry Density (gm/cc) | Cohesion, C (kg/cm^{2}) | Angle of Shearing Resistance, Φ (degree) | Type of Soil |
---|---|---|---|---|---|---|

S1 | 0.600 | 9.8 | 1.76 | 0.062 | 25.5° | Poorly graded sand (SP) |

S2 | 0.250 | 10.7 | 1.82 | 0.055 | 26° | Well-graded sand (SW) |

S7 | 0.095 | 15.2 | 1.81 | 0.025 | 27° | Silty sand (SM) |

S8 | 0.056 | 16.8 | 1.64 | 0.385 | 15° | Clay with low compressibility (CL) |

Expt. No. | Soil | Flow Chart at Time of Breach | |||
---|---|---|---|---|---|

Side Slope, Z (tan θ) | Fill Size, D_{50} (mm) | Depth of Water, d_{w} (cm) | Volume of Water, V_{w} (cm^{3}) | Peak Outflow, Q_{p} (cm^{3}/s) | |

1 | 1 | 0.6 | 9.1 | 35,262.5 | 14,854 |

2 | 1 | 0.095 | 8 | 31,000 | 13,254 |

3 | 1 | 0.056 | 6.2 | 24,025 | 7853 |

4 | 0.67 | 0.6 | 9.1 | 35,262.5 | 14,586 |

5 | 0.67 | 0.095 | 8.8 | 34,100 | 14,232 |

6 | 0.67 | 0.056 | 5.3 | 20,537.5 | 5956 |

7 | 1 | 0.6 | 7.2 | 27,900 | 10,125 |

8 | 1 | 0.095 | 6 | 23,250 | 6585 |

9 | 1 | 0.056 | 4 | 15,500 | 3852 |

10 | 0.67 | 0.25 | 5.4 | 20,925 | 4852 |

11 | 0.67 | 0.095 | 4.5 | 17,437.5 | 3958 |

12 | 0.67 | 0.056 | 5 | 19,375 | 4015 |

13 | 1 | 0.6 | 8.5 | 32,937.5 | 12,692 |

14 | 1 | 0.095 | 7.4 | 28,675 | 9228 |

15 | 1 | 0.056 | 5.3 | 20,537.5 | 4282 |

16 | 0.67 | 0.25 | 8.2 | 31,775 | 11,685 |

17 | 0.67 | 0.056 | 4.2 | 16,275 | 4521 |

18 | 1 | 0.6 | 7.2 | 27,900 | 8664 |

19 | 1 | 0.095 | 7.3 | 28,287.5 | 8954 |

20 | 1 | 0.056 | 4.2 | 16,275 | 4508 |

21 | 0.67 | 0.6 | 8.4 | 32,550 | 12,351 |

22 | 0.67 | 0.25 | 7.4 | 28,675 | 9227 |

23 | 0.67 | 0.056 | 2.4 | 9300 | 4012 |

24 | 0.67 | 0.6 | 6.2 | 24,025 | 7021 |

25 | 0.67 | 0.095 | 6.8 | 26,350 | 7597 |

26 | 1 | 0.25 | 9.2 | 35,650 | 14,586 |

27 | 0.67 | 0.25 | 9 | 34,875 | 14,952 |

28 | 1 | 0.25 | 7.3 | 28,287.5 | 9885 |

29 | 1 | 0.25 | 8.6 | 33,325 | 13,038 |

30 | 0.67 | 0.6 | 8.5 | 32,937.5 | 12,692 |

31 | 1 | 0.25 | 8.5 | 32,937.5 | 12,692 |

32 | 1 | 0.25 | 23.8 | 685,440 | 58,321 |

33 | 1 | 0.095 | 20.4 | 587,520 | 43,545 |

34 | 1 | 0.056 | 19.5 | 561,600 | 39,546 |

35 | 0.67 | 0.6 | 23.5 | 676,800 | 52,654 |

36 | 1 | 0.25 | 20.5 | 590,400 | 43,584 |

37 | 1 | 0.095 | 18.5 | 532,800 | 37,852 |

38 | 1 | 0.056 | 17.6 | 506,880 | 34,215 |

39 | 0.67 | 0.6 | 17.4 | 501,120 | 32,012 |

40 | 0.67 | 0.095 | 20.7 | 596,160 | 42,541 |

Author (s) | Enveloping Curve | Values of Coefficient (a) and Power Index (b) | |
---|---|---|---|

A | b | ||

Present study | Upper | 0.43 | 0.91 |

Lower | 0.15 | 1.08 | |

Chinnarasri et al. [19] | Upper | 0.209 | 1.6 |

Lower | 0.02 | 1.714 |

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**MDPI and ACS Style**

Verma, D.; Berwal, P.; Khan, M.A.; Alharbi, R.S.; Alfaisal, F.M.; Rathnayake, U.
Design for the Prediction of Peak Outflow of Embankment Breaching Due to Overtopping by Regression Technique and Modelling. *Water* **2023**, *15*, 1224.
https://doi.org/10.3390/w15061224

**AMA Style**

Verma D, Berwal P, Khan MA, Alharbi RS, Alfaisal FM, Rathnayake U.
Design for the Prediction of Peak Outflow of Embankment Breaching Due to Overtopping by Regression Technique and Modelling. *Water*. 2023; 15(6):1224.
https://doi.org/10.3390/w15061224

**Chicago/Turabian Style**

Verma, Deepak, Parveen Berwal, Mohammad Amir Khan, Raied Saad Alharbi, Faisal M. Alfaisal, and Upaka Rathnayake.
2023. "Design for the Prediction of Peak Outflow of Embankment Breaching Due to Overtopping by Regression Technique and Modelling" *Water* 15, no. 6: 1224.
https://doi.org/10.3390/w15061224