Wave Run-Up on Mortar-Grouted Riprap Revetments
Abstract
:1. Introduction
1.1. Motivation
1.2. Wave Run-Up
- they are the most widely used models for design purposes
- they are easy to use and comprehensible
- full-scale hydraulic model tests on MGRRs have been conducted, thus, the number of experiments is not suited for machine learning techniques
- we test the ability of different parameters for describing wave run-up for different roughnesses, porosities, and permeabilities, as these parameters vary considerably for MGRRs.
- To analyze the wave run-up process in the presence of partially or fully mortar-grouted riprap
- To determine the appropriate influence factors in the framework of the EurOtop equations
2. Materials and Methods
2.1. Revetment Configurations
2.2. Instrumentation
2.3. Experimental Program
2.4. Detection of the Wave Run-Up Height
2.5. Error Evaluation of Different Equations and Parameters
3. Results
3.1. Relative Wave Run-Up Height as a Function of Surf Similarity Parameter ξm−1,0
3.2. Relative Wave Run-Up Height as a Function of the Momentum Flux Parameter MF
3.3. Relative Wave Run-Up Height as a Function of the Modified Surf Similarity Parameter ϕ
3.4. Relative Wave Run-Up Height as a Function of the Reflection Coefficient Cr
4. Discussion
4.1. 2D-LIDAR Measurements
4.2. Comparison of Models and Corresponding Parameters
4.3. Further Discussion
5. Conclusions
- The wave run-up heights on MGRRs are generally lower than for smooth impermeable revetments and higher than for non-grouted riprap revetments. Partially grouted MGRRs, due to their roughness, porosity, and permeability, reduce wave run-up heights from 21% to 28%, and fully grouted MGRRs, due to their roughness, reduce wave run-up heights from 12% to 14% compared to smooth impermeable revetments.
- Influence factors for the state-of-the-art design guideline EurOtop have been determined for four widely used revetment configurations, which can now be used for design purposes.
- For the results acquired in the model tests, wave run-up for all MGRR configurations is best described by the state-of-the-art EurOtop equation, which describes wave run-up as a function of the surf similarity parameter ξm−1,0. The model of Hughes [27], which describes wave run-up as a function of the momentum flux parameter MF, also gives very good results. Models describing wave run-up as a function of the modified surf similarity parameter ϕ or the reflection coefficient Cr give poorer results for MGRRs.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Configuration Nr. | Hm0 [m] | Tm−1,0 [s] | Tp [s] | Lm−1,0 [m] | Ru2% [m] | Ru2%/Hm0 [-] | Ru2%/h [-] | ξm−1,0 [-] | MF/(ρgh2) [-] | Φ [-] | Cr [-] | Hm0/Lp [-] | tan(α)/(Hm0/h) [-] |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.375 | 2.73 | 3.01 | 11.60 | 0.80 | 2.14 | 0.201 | 1.85 | 0.021 | 0.639 | 0.24 | 0.027 | 3.56 |
1 | 0.389 | 6.14 | 7.08 | 58.92 | 0.92 | 2.36 | 0.230 | 4.10 | 0.048 | 0.279 | 0.58 | 0.005 | 3.43 |
1 | 0.383 | 3.53 | 4.01 | 19.48 | 0.90 | 2.35 | 0.225 | 2.38 | 0.028 | 0.488 | 0.32 | 0.015 | 3.48 |
1 | 0.577 | 6.14 | 6.58 | 58.78 | 1.32 | 2.29 | 0.330 | 3.36 | 0.075 | 0.229 | 0.55 | 0.009 | 2.31 |
1 | 0.759 | 6.13 | 6.85 | 58.57 | 1.72 | 2.27 | 0.431 | 2.93 | 0.112 | 0.200 | 0.51 | 0.010 | 1.76 |
1 | 0.765 | 7.84 | 9.24 | 95.87 | 2.10 | 2.74 | 0.525 | 3.73 | 0.139 | 0.156 | 0.63 | 0.006 | 1.74 |
1 | 0.389 | 4.39 | 4.89 | 30.06 | 0.94 | 2.42 | 0.236 | 2.93 | 0.035 | 0.390 | 0.43 | 0.010 | 3.43 |
1 | 0.579 | 8.36 | 10.10 | 109.07 | 1.47 | 2.54 | 0.367 | 4.57 | 0.105 | 0.168 | 0.70 | 0.004 | 2.30 |
1 | 0.659 | 9.04 | 12.18 | 127.54 | 2.03 | 3.08 | 0.508 | 4.64 | 0.141 | 0.145 | 0.71 | 0.003 | 2.02 |
1 | 0.667 | 3.97 | 4.27 | 24.61 | 1.46 | 2.19 | 0.364 | 2.02 | 0.067 | 0.329 | 0.31 | 0.023 | 2.00 |
1 | 0.764 | 4.41 | 5.08 | 30.41 | 1.65 | 2.15 | 0.411 | 2.10 | 0.092 | 0.277 | 0.34 | 0.019 | 1.75 |
1 | 0.853 | 4.87 | 5.30 | 36.97 | 1.90 | 2.22 | 0.474 | 2.19 | 0.112 | 0.237 | 0.38 | 0.019 | 1.56 |
1 | 0.765 | 4.11 | 4.44 | 26.32 | 1.65 | 2.16 | 0.413 | 1.96 | 0.084 | 0.297 | 0.31 | 0.025 | 1.74 |
1 | 0.580 | 4.85 | 5.36 | 36.68 | 1.35 | 2.33 | 0.338 | 2.65 | 0.065 | 0.289 | 0.43 | 0.013 | 2.30 |
1 | 0.572 | 4.05 | 4.47 | 25.63 | 1.30 | 2.28 | 0.326 | 2.23 | 0.055 | 0.348 | 0.34 | 0.018 | 2.33 |
1 | 0.580 | 4.85 | 5.36 | 36.76 | 1.35 | 2.33 | 0.338 | 2.65 | 0.065 | 0.289 | 0.43 | 0.013 | 2.30 |
2 | 0.375 | 2.73 | 3.01 | 11.60 | 0.83 | 2.21 | 0.207 | 1.85 | 0.021 | 0.639 | 0.24 | 0.027 | 3.56 |
2 | 0.389 | 6.14 | 7.08 | 58.92 | 0.99 | 2.54 | 0.247 | 4.10 | 0.048 | 0.279 | 0.58 | 0.005 | 3.43 |
2 | 0.383 | 3.53 | 4.01 | 19.48 | 0.91 | 2.37 | 0.227 | 2.38 | 0.028 | 0.488 | 0.32 | 0.015 | 3.48 |
2 | 0.577 | 6.14 | 6.58 | 58.78 | 1.50 | 2.61 | 0.376 | 3.36 | 0.075 | 0.229 | 0.55 | 0.009 | 2.31 |
2 | 0.759 | 6.13 | 6.85 | 58.57 | 1.90 | 2.51 | 0.476 | 2.93 | 0.112 | 0.200 | 0.51 | 0.010 | 1.76 |
2 | 0.765 | 7.84 | 9.24 | 95.87 | 2.21 | 2.89 | 0.552 | 3.73 | 0.139 | 0.156 | 0.63 | 0.006 | 1.74 |
2 | 0.389 | 4.39 | 4.89 | 30.06 | 0.95 | 2.44 | 0.237 | 2.93 | 0.035 | 0.390 | 0.43 | 0.010 | 3.43 |
2 | 0.579 | 8.36 | 10.10 | 109.07 | 1.58 | 2.74 | 0.396 | 4.57 | 0.105 | 0.168 | 0.70 | 0.004 | 2.30 |
2 | 0.659 | 9.04 | 12.18 | 127.54 | 2.15 | 3.26 | 0.537 | 4.64 | 0.141 | 0.145 | 0.71 | 0.003 | 2.02 |
2 | 0.667 | 3.97 | 4.27 | 24.61 | 1.56 | 2.34 | 0.390 | 2.02 | 0.067 | 0.329 | 0.31 | 0.023 | 2.00 |
2 | 0.764 | 4.41 | 5.08 | 30.41 | 1.82 | 2.38 | 0.454 | 2.10 | 0.092 | 0.277 | 0.34 | 0.019 | 1.75 |
2 | 0.853 | 4.87 | 5.30 | 36.97 | 1.99 | 2.33 | 0.497 | 2.19 | 0.112 | 0.237 | 0.38 | 0.019 | 1.56 |
2 | 0.765 | 4.11 | 4.44 | 26.32 | 1.78 | 2.32 | 0.445 | 1.96 | 0.084 | 0.297 | 0.31 | 0.025 | 1.74 |
2 | 0.580 | 4.85 | 5.36 | 36.68 | 1.48 | 2.55 | 0.370 | 2.65 | 0.065 | 0.289 | 0.43 | 0.013 | 2.30 |
2 | 0.572 | 4.05 | 4.47 | 25.63 | 1.35 | 2.36 | 0.337 | 2.23 | 0.055 | 0.348 | 0.34 | 0.018 | 2.33 |
2 | 0.580 | 4.85 | 5.36 | 36.76 | 1.45 | 2.50 | 0.362 | 2.65 | 0.065 | 0.289 | 0.43 | 0.013 | 2.30 |
Configuration Nr. | Hm0 [m] | Tm−1,0 [s] | Tp [s] | Lm−1,0 [m] | Ru2% [m] | Ru2%/Hm0 [-] | Ru2%/h [-] | ξm−1,0 [-] | MF/(ρgh2) [-] | Φ [-] | Cr [-] | Hm0/Lp [-] | tan(α)/(Hm0/h) [-] |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3 | 0.768 | 4.11 | 4.44 | 26.36 | 1.76 | 2.29 | 0.439 | 1.95 | 0.085 | 0.296 | 0.36 | 0.025 | 1.74 |
3 | 0.856 | 4.87 | 5.43 | 37.08 | 2.07 | 2.42 | 0.518 | 2.19 | 0.114 | 0.237 | 0.43 | 0.019 | 1.56 |
3 | 0.760 | 6.12 | 6.85 | 58.42 | 1.98 | 2.61 | 0.496 | 2.92 | 0.112 | 0.200 | 0.59 | 0.010 | 1.75 |
3 | 0.386 | 3.52 | 3.68 | 19.38 | 1.17 | 3.04 | 0.293 | 2.36 | 0.027 | 0.488 | 0.43 | 0.018 | 3.45 |
3 | 0.390 | 4.39 | 4.53 | 30.09 | 0.99 | 2.54 | 0.248 | 2.93 | 0.033 | 0.389 | 0.56 | 0.012 | 3.42 |
3 | 0.582 | 6.13 | 7.06 | 58.59 | 1.57 | 2.69 | 0.392 | 3.34 | 0.080 | 0.228 | 0.65 | 0.007 | 2.29 |
3 | 0.763 | 7.83 | 8.47 | 95.67 | 2.21 | 2.90 | 0.553 | 3.73 | 0.131 | 0.156 | 0.71 | 0.007 | 1.75 |
3 | 0.664 | 9.04 | 12.18 | 127.65 | 2.25 | 3.40 | 0.564 | 4.62 | 0.142 | 0.145 | 0.79 | 0.003 | 2.01 |
3 | 0.393 | 6.14 | 6.57 | 58.90 | 1.11 | 2.82 | 0.277 | 4.08 | 0.046 | 0.277 | 0.71 | 0.006 | 3.39 |
3 | 0.576 | 4.05 | 4.55 | 25.63 | 1.52 | 2.64 | 0.380 | 2.22 | 0.056 | 0.347 | 0.41 | 0.018 | 2.31 |
3 | 0.584 | 8.37 | 9.36 | 109.46 | 1.74 | 2.98 | 0.435 | 4.56 | 0.100 | 0.167 | 0.79 | 0.004 | 2.28 |
3 | 0.752 | 3.59 | 3.90 | 20.10 | 1.83 | 2.43 | 0.457 | 1.72 | 0.075 | 0.343 | 0.29 | 0.032 | 1.77 |
3 | 0.727 | 3.34 | 3.79 | 17.45 | 1.76 | 2.43 | 0.441 | 1.63 | 0.070 | 0.374 | 0.28 | 0.033 | 1.83 |
3 | 0.941 | 4.26 | 4.77 | 28.31 | 2.32 | 2.47 | 0.580 | 1.83 | 0.121 | 0.258 | 0.32 | 0.027 | 1.42 |
3 | 0.929 | 3.87 | 4.42 | 23.32 | 2.18 | 2.35 | 0.545 | 1.67 | 0.113 | 0.286 | 0.29 | 0.030 | 1.44 |
3 | 0.908 | 3.66 | 4.10 | 20.87 | 2.05 | 2.26 | 0.513 | 1.60 | 0.104 | 0.306 | 0.27 | 0.035 | 1.47 |
3 | 0.722 | 3.16 | 3.43 | 15.61 | 1.70 | 2.36 | 0.426 | 1.55 | 0.064 | 0.397 | 0.26 | 0.039 | 1.85 |
4 | 0.768 | 4.11 | 4.44 | 26.36 | 1.89 | 2.46 | 0.472 | 1.95 | 0.085 | 0.296 | 0.36 | 0.025 | 1.74 |
4 | 0.856 | 4.87 | 5.43 | 37.08 | 2.21 | 2.58 | 0.552 | 2.19 | 0.114 | 0.237 | 0.43 | 0.019 | 1.56 |
4 | 0.760 | 6.12 | 6.85 | 58.42 | 2.08 | 2.74 | 0.520 | 2.92 | 0.112 | 0.200 | 0.59 | 0.010 | 1.75 |
4 | 0.386 | 3.52 | 3.68 | 19.38 | 1.17 | 3.02 | 0.291 | 2.36 | 0.027 | 0.488 | 0.43 | 0.018 | 3.45 |
4 | 0.390 | 4.39 | 4.53 | 30.09 | 1.03 | 2.63 | 0.257 | 2.93 | 0.033 | 0.389 | 0.56 | 0.012 | 3.42 |
4 | 0.582 | 6.13 | 7.06 | 58.59 | 1.65 | 2.83 | 0.412 | 3.34 | 0.080 | 0.228 | 0.65 | 0.007 | 2.29 |
4 | 0.763 | 7.83 | 8.47 | 95.67 | 2.19 | 2.88 | 0.548 | 3.73 | 0.131 | 0.156 | 0.71 | 0.007 | 1.75 |
4 | 0.664 | 9.04 | 12.18 | 127.65 | 2.25 | 3.38 | 0.562 | 4.62 | 0.142 | 0.145 | 0.79 | 0.003 | 2.01 |
4 | 0.393 | 6.14 | 6.57 | 58.90 | 1.12 | 2.84 | 0.279 | 4.08 | 0.046 | 0.277 | 0.71 | 0.006 | 3.39 |
4 | 0.576 | 4.05 | 4.55 | 25.63 | 1.62 | 2.81 | 0.405 | 2.22 | 0.056 | 0.347 | 0.41 | 0.018 | 2.31 |
4 | 0.584 | 8.37 | 9.36 | 109.46 | 1.82 | 3.11 | 0.454 | 4.56 | 0.100 | 0.167 | 0.79 | 0.004 | 2.28 |
4 | 0.752 | 3.59 | 3.90 | 20.10 | 1.91 | 2.54 | 0.477 | 1.72 | 0.075 | 0.343 | 0.29 | 0.032 | 1.77 |
4 | 0.727 | 3.34 | 3.79 | 17.45 | 1.80 | 2.47 | 0.450 | 1.63 | 0.070 | 0.374 | 0.28 | 0.033 | 1.83 |
4 | 0.941 | 4.26 | 4.77 | 28.31 | 2.23 | 2.37 | 0.557 | 1.83 | 0.121 | 0.258 | 0.32 | 0.027 | 1.42 |
4 | 0.929 | 3.87 | 4.42 | 23.32 | 2.10 | 2.26 | 0.525 | 1.67 | 0.113 | 0.286 | 0.29 | 0.030 | 1.44 |
4 | 0.908 | 3.66 | 4.10 | 20.87 | 2.04 | 2.25 | 0.510 | 1.60 | 0.104 | 0.306 | 0.27 | 0.035 | 1.47 |
4 | 0.722 | 3.16 | 3.43 | 15.61 | 1.73 | 2.39 | 0.431 | 1.55 | 0.064 | 0.397 | 0.26 | 0.039 | 1.85 |
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Type of Revetment | Influence Factor γf | Equation Nr. in This Work | Revetment Characteristics | Reference | ||
---|---|---|---|---|---|---|
Rough | Porous | Permeable | ||||
Grass | 0.9–1.0 | (2) | (x) | [8] | ||
Polyurethane bonded gravel | ≈0.75 | mod. (2) | (x) | x | x | [22,23] |
Basalt | 0.9 | (2) | (x) | (x) | (x) | [8] |
Stepped revetments | 0.4–0.9 | (4) | x | [26] | ||
Two layers of rock | 0.55 | (2) | x | x | x | [8] |
Two layers of rock | 0.51 | (10) | x | x | x | [27] |
Pattern placed revetments with enhanced roughness | 0.65–0.85 | (4) | x | (x) | (x) | [28] |
Partially Grouted | Fully Grouted | |||
---|---|---|---|---|
Section | North | South | North | South |
Configuration Nr. | 1 | 2 | 3 | 4 |
Top layer thickness t [m] | 0.6 | 0.4 | 0.6 | 0.4 |
Amount of mortar vg [l/m2] | 80 | 80 | 80+100 | 180 |
Estimated porosity n before grouting [-] | 0.45 | 0.45 | 0.45 | 0.45 |
Porosity n after grouting [-] | 0.32 | 0.25 | 0.16 | 0 |
Pore volume Vp after grouting [l/m2] | 190 | 100 | 90 | 0 |
Partially Grouted | Fully Grouted | ||||||
---|---|---|---|---|---|---|---|
Section | North | South | North | South | |||
Equation | Nr. | 1 (▲) | 2 (●) | 3 (■) | 4 (▼) | ||
(2) | γf | 0.72 | 0.79 | 0.86 | 0.88 | ||
bias | −0.02 | 0 | 0 | 0 | |||
RMSE | 0.09 | 0.08 | 0.11 | 0.10 | |||
SI | 6.27 | 5.51 | 6.00 | 5.56 | |||
(10) | γf,M | 0.65 | 0.70 | 0.76 | 0.77 | ||
bias | 0.01 | 0.02 | 0.01 | 0 | |||
RMSE | 0.11 | 0.11 | 0.13 | 0.12 | |||
SI | 7.86 | 7.38 | 7.22 | 6.68 | |||
(11) | a | 1.87 | 1.90 | 2.07 | 2.13 | ||
b | −0.18 | −0.22 | −0.18 | −0.18 | |||
bias | 0.01 | 0.02 | 0.03 | 0.05 | |||
RMSE | 0.12 | 0.10 | 0.16 | 0.19 | |||
SI | 8.17 | 6.84 | 9.26 | 10.29 | |||
(12) | a [-] | 1.63 | 1.73 | 1.77 | 1.81 | ||
bias | 0 | −0.01 | −0.01 | 0 | |||
RMSE | 0.09 | 0.07 | 0.11 | 0.10 | |||
SI | 6.11 | 4.72 | 6.37 | 5.68 |
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Kreyenschulte, M.; Schürenkamp, D.; Bratz, B.; Schüttrumpf, H.; Goseberg, N. Wave Run-Up on Mortar-Grouted Riprap Revetments. Water 2020, 12, 3396. https://doi.org/10.3390/w12123396
Kreyenschulte M, Schürenkamp D, Bratz B, Schüttrumpf H, Goseberg N. Wave Run-Up on Mortar-Grouted Riprap Revetments. Water. 2020; 12(12):3396. https://doi.org/10.3390/w12123396
Chicago/Turabian StyleKreyenschulte, Moritz, David Schürenkamp, Benedikt Bratz, Holger Schüttrumpf, and Nils Goseberg. 2020. "Wave Run-Up on Mortar-Grouted Riprap Revetments" Water 12, no. 12: 3396. https://doi.org/10.3390/w12123396