Design for the Prediction of Peak Outflow of Embankment Breaching Due to Overtopping by Regression Technique and Modelling
Abstract
:1. Introduction
2. Breach Formation Models
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
4.2. Breach Process and Flow Parameters
4.2.1. Breach Flow Parameters
4.2.2. Breach Process
- Qp is the peak outflow at the time of failure (cm3/s);
- Vw is the reservoir volume at the time of failure (cm3);
- dw is the depth of water above the crest or sill of breach (cm);
- D50 is the median particle size of embankment fills material (mm);
- C is the cohesion of fill material (kg/cm2);
- Z is the side slope of the embankment model (tan θ);
- G is the acceleration due to gravity (m/s2).
5. Results and Discussion
5.1. Relation for Peak Outflow
5.2. Validation of Relation
5.3. Comparison with Other Researchers
- (a)
- (b)
- Chinnarasri et al. [26]
6. Conclusions
- Buckingham Pi theorem was used to obtain a relationship for non-dimensional peak outflow (Qp) corresponding to depth of water (dw) and volume of water (Vw). 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
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Fill Material (S) | Median Size, D50 (mm) | OMC (%) | Dry Density (gm/cc) | Cohesion, C (kg/cm2) | 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, D50 (mm) | Depth of Water, dw (cm) | Volume of Water, Vw (cm3) | Peak Outflow, Qp (cm3/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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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
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 StyleVerma, 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