The Cross-Dike Failure Probability by Wave Overtopping over Grass-Covered and Damaged Dikes
Abstract
:1. Introduction
2. Framework for the Failure Probability by Wave Overtopping
2.1. Hydraulic Load
2.2. Analytical Grass-Erosion Model
3. Methods
3.1. Study Area
3.2. Cross-Dike Failure Probability
3.3. Additional Load at Damaged Spots
3.4. Failure Probability of Damages on the Landward Slope
4. Results
4.1. Cross-Dike Failure Probability
4.2. Additional Load at Damaged Spots
4.3. Failure Probabilities of Damaged Spots
5. Discussion
5.1. The Cross-Dike Failure Probability
5.2. The Effect of Damages on the Failure Probability
5.3. Additional Load at Damages
5.4. Comparison to Other Studies
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Convergence of the Failure Probability
Appendix B. The Depth-Averaged Relative Turbulence Intensity
References
- Scheres, B.; Schüttrumpf, H. Enhancing the ecological value of sea dikes. Water 2019, 11, 1617. [Google Scholar] [CrossRef] [Green Version]
- Hughes, S.A. Adaptation of the Levee Erosional Equivalence Method for the Hurricane Storm Damage Risk Reduction System (HSDRRS); Technical Report; U.S. Army Corps of Engineers: Vicksburg, MS, USA, 2011.
- Zhang, Y.; Chen, G.; Hu, J.; Chen, X.; Yang, W.; Tao, A.; Zheng, J. Experimental study on mechanism of sea-dike failure due to wave overtopping. Appl. Ocean Res. 2017, 68, 171–181. [Google Scholar] [CrossRef]
- Hoffmans, G.J.C.M. The Influence of Turbulence on Soil Erosion; Eburon Uitgeverij BV: Delft, The Netherlands, 2012. [Google Scholar]
- Van Bergeijk, V.M.; Warmink, J.J.; Hulscher, S.J.M.H. Modelling the Wave Overtopping Flow over the Crest and the Landward Slope of Grass-Covered Flood Defences. J. Mar. Sci. Eng. 2020, 8, 489. [Google Scholar] [CrossRef]
- Mazzoleni, M.; Dottori, F.; Brandimarte, L.; Tekle, S.; Martina, M.L. Effects of levee cover strength on flood mapping in the case of levee breach due to overtopping. Hydrol. Sci. J. 2017, 62, 892–910. [Google Scholar] [CrossRef]
- Hoffmans, G.; Akkerman, G.J.; Verheij, H.; Van Hoven, A.; Van Der Meer, J. The erodibility of grassed inner dike slopes against wave overtopping. Coast. Eng. 2009, 3224–3236. [Google Scholar]
- Thieu Quang, T.; Oumeraci, H. Numerical modelling of wave overtopping-induced erosion of grassed inner sea-dike slopes. Nat. Hazards 2012, 63, 417–447. [Google Scholar] [CrossRef]
- Oumeraci, H.; D’Eliso, C.; Kortenhaus, A. Breaching of Coastal Dikes: State of the Art; LWI Report Uumber: 910; TU Braunschweig: Braunschweig, Germany, 2005. [Google Scholar]
- Le, H.T.; Verhagen, H.J.; Vrijling, J.K. Damage to grass dikes due to wave overtopping. Nat. Hazards 2017, 86, 849–875. [Google Scholar] [CrossRef]
- Van der Meer, J.W.; Allsop, N.W.H.; Bruce, T.; De Rouck, J.; Kortenhaus, A.; Pullen, T.; Schüttrumpf, H.; Troch, P.; Zanuttigh, B. Manual on Wave Overtopping of Sea Defences and Related Structures. An Overtopping Manual Largely Based on European Research, but for Worldwide Application. EurOtop. 2018. Available online: www.overtopping-manual.com (accessed on 1 July 2020).
- Vuik, V.; van Vuren, S.; Borsje, B.W.; van Wesenbeeck, B.K.; Jonkman, S.N. Assessing safety of nature-based flood defenses: Dealing with extremes and uncertainties. Coast. Eng. 2018, 139, 47–64. [Google Scholar] [CrossRef] [Green Version]
- Marijnissen, R.; Kok, M.; Kroeze, C.; van Loon-Steensma, J. Re-evaluating safety risks of multifunctional dikes with a probabilistic risk framework. Nat. Hazards Earth Syst. Sci. 2019, 19, 737–756. [Google Scholar] [CrossRef] [Green Version]
- t Hart, R.; de Bruijn, H.; de Vries, G. Fenomenologische Beschrijving, Faalmechanismen WTI (in Dutch); Technical Report; Rijkswaterstaat Water, Verkeer en Leefomgeving: Lelystad, The Netherlands, 2016. [Google Scholar]
- Aguilar-López, J.P.; Warmink, J.J.; Bomers, A.; Schielen, R.M.J.; Hulscher, S.J. Failure of grass covered flood defences with roads on top due to wave overtopping: A probabilistic assessment method. J. Mar. Sci. Eng. 2018, 6, 74. [Google Scholar] [CrossRef] [Green Version]
- Van Bergeijk, V.M.; Warmink, J.J.; Frankena, M.; Hulscher, S.J.M.H. Modelling Dike Cover Erosion by Overtopping Waves: The Effects of Transitions. In Coastal Structures 2019; Goseberg, N., Schlurmann, T., Eds.; Bundesanstalt für Wasserbau: Karlsruhe, Germany, 2019; pp. 1097–1106. [Google Scholar] [CrossRef]
- Van Hoven, A. Residual Dike Strength after Macro-Instability, WTI2017; Technical Report; Deltares: Delft, The Netherlands, 2014. [Google Scholar]
- Van der Meer, J.W.; Hardeman, B.; Steendam, G.J.; Schüttrumpf, H.; Verheij, H. Flow depths and velocities at crest and landward slope of a dike, in theory and with the wave overtopping simulator. Coast. Eng. Proc. 2010, 1, 10. [Google Scholar] [CrossRef] [Green Version]
- Warmink, J.J.; Van Bergeijk, V.M.; Frankena, M.; Van Steeg, P.; Hulscher, S.J.M.H. Modelling Transitions in Grass Covers to Quantify Wave Overtopping Erosion. Coast. Eng. Proc. 2020, 1–8. [Google Scholar] [CrossRef]
- Steendam, G.J.; Van Hoven, A.; Van der Meer, J.W.; Hoffmans, G. Wave Overtopping Simulator Tests on Transitions and Obstacles At Grass-covered Slopes of Dikes. Coast. Eng. Proc. 2014, 1, 34. [Google Scholar] [CrossRef] [Green Version]
- Van Bergeijk, V.M.; Warmink, J.J.; Van Gent, M.R.A.; Hulscher, S.J.M.H. An analytical model of wave overtopping flow velocities on dike crests and landward slopes. Coast. Eng. 2019, 149, 28–38. [Google Scholar] [CrossRef] [Green Version]
- Bomers, A.; Aguilar-López, J.P.; Warmink, J.J.; Hulscher, S.J.M.H. Modelling effects of an asphalt road at a dike crest on dike cover erosion onset during wave overtopping. Nat. Hazards 2018, 93, 1–30. [Google Scholar] [CrossRef] [Green Version]
- Remmerswaal, G.; Hicks, M.A.; Vardon, P.J. Influence of Residual Dyke Strength on Dyke Reliability Using the Random Material Point Method. In Proceedings of the 7th International Symposiumon Geotechnical Safety and Risk (ISGSR), Taipei, Taiwan, 11–13 December 2019; pp. 775–780. [Google Scholar] [CrossRef]
- Van Der Krogt, M.G.; Schweckendiek, T.; Kok, M. Do all dike instabilities cause flooding? In Proceedings of the 13th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP 2019, Seoul, Korea, 26 May 2019. [Google Scholar] [CrossRef]
- Duits, M.T.; Kuijper, B. Hydra-NL–Systeemdocumentatie–Versie 2.4. HKV-Rapport PR3598; Technical Report; HKV: Lelystad, The Netherlands, 2018. [Google Scholar]
- Caires, S. Extreme Wind Statistics for the Hydraulic Boundary Conditions for the Dutch Primary Water Defences. SBW-Belastingen: Phase 2 of Subproject “Wind Modelling”; Technical Report, Deltares, 1200264-005; Deltares: Delft, The Netherlands, 2009. [Google Scholar]
- Rijkswaterstaat. Regeling Veiligheid Primaire Waterkeringen 2017: Bijlage II Voorschriften Bepaling Hydraulische Belasting Primaire Waterkeringen (in Dutch); Rijkswaterstaat: Utrecht, The Netherlands, 2016. [Google Scholar]
- Verdonk, V.A. The Impact of Overtopping on the Failure Probability of Slipped river dikes. Master’s Thesis, University of Twente, Water Engineering and Management, Enschede, The Netherlands, 2020. [Google Scholar]
- Breusers, H.N.C. Conformity and Time Scale in Two-Dimensional Local Scour; Technical Report; Delft Hydraulic Laboratory: Delft, The Netherlands, 1966. [Google Scholar]
- Breusers, H.N.C. Time Scale of Two Dimensional Local Scour. In Proceedings of the 12th Congress IAHR, Fort Collins, CO, USA, 11–14 September 1967; Volume 3, pp. 275–282. [Google Scholar]
- Van der Meulen, T.; Vinjé, J.J. Three-dimensional local scour in non-cohesive sediments. In Proceedings of the 16th IAHR-Congress, Sao Paulo, Brazil, 27 July–1 August 1975. [Google Scholar]
- Jorissen, R.E.; Vrijling, J.K. Local scour downstream hydraulic constructions. In Proceedings of the 23rd IAHR Conference Ottawa, Ottawa, ON, Canada, 21–25 August 1989. [Google Scholar]
- Hoffmans, G.; Verheij, H. Jet scour. Proc. Inst. Civ. Eng. Marit. Eng. 2011, 164, 185–193. [Google Scholar] [CrossRef] [Green Version]
- Frankena, M. Modelling the Influence of Transitions in Dikes on Grass Cover Erosion by Wave Overtopping. Master’s Thesis, University of Twente, Water Engineering and Management, Enschede, The Netherlands, 2019. [Google Scholar]
- Van Hoven, A.; Verheij, H.; Hoffmans, G.; Van der Meer, J. Evaluation and Model Development: Grass Erosion Test at the Rhine Dike; Technical Report; Deltares: Delft, The Netherlands, 2013. [Google Scholar]
- Verheij, H.J.; Meijer, D.G.; Kruse, G.A.M.; Smith, G.M.; Vesseur, M. Investigation of the Strength of a Grass Cover Upon River Dikes; Technical Report; Deltares: Delft, The Netherlands, 1995. [Google Scholar]
- Bakker, J.; Melis, R.; Mom, R.; Bakker. Factual Report: Overslagproeven Rivierenland; Technical Report; Infram: Maarn, The Netherlands, 2013. [Google Scholar]
- Actueel Hoogtebestand Nederland. Available online: https://www.ahn.nl/ahn-viewer (accessed on 1 September 2020).
- Natural Resources Conservation Service. Chapter 51 Earth Spillway Erosion Model and Chapter 52 Field Procedures Guide for the Headcut Erodability Index. In National Engineering Handbook Part 628 Dams, 210-vi-NEH ed.; Natural Resources Conservation Service: Washington, DC, USA, 1997. [Google Scholar]
- Valk, A. Wave Overtopping Impact of Water Jets on Grassed Inner Slope Transitions. Master’s Thesis, Technical University of Delft, Civil Engineering and Geosciences, Delft, The Netherlands, 2009. [Google Scholar]
- Ponsioen, L.; van Damme, M.; Hofland, B.; Peeters, P. Relating grass failure on the landside slope to wave overtopping induced excess normal stresses. Coast. Eng. 2019, 148, 49–56. [Google Scholar] [CrossRef]
- Scheres, B.; Schüttrumpf, H.; Felder, S. Flow Resistance and Energy Dissipation in Supercritical Air-Water Flows Down Vegetated Chutes. Water Resour. Res. 2020, 56, 1–18. [Google Scholar] [CrossRef] [Green Version]
- Felder, S.; Chanson, H. Simple Design Criterion for Residual Energy on Embankment Dam Stepped Spillways. J. Hydraul. Eng. 2015, 142, 04015062. [Google Scholar] [CrossRef] [Green Version]
- Bakker, J.; Mom, R.; Steendam, G. Golfoverslagproeven Zeeuwse Zeedijken-Factual Report (in Dutch); Technical Rport; Infram: Maarn, The Netherlands, 2008. [Google Scholar]
- Bakker, J.; Mom, R.; Steendam, G. Factual Report: Overslagproeven en Afschuifproef Afsluitdijk (in Dutch); Technical Report; Infram: Maarn, The Netherlands, 2009. [Google Scholar]
- Peeters, P.; de Vos, L.; Vandevoorde, B.; Taverniers, E.; Mostaert, F. Stabiliteit van de Grasmat bij Golfoverslag: Golfoverslagproeven Tielrodebroek (in Dutch); Technical Report; Waterbouwkundig Laboratorium, INBO en afdeling Geotechniek: Antwerp, Belgium, 2012. [Google Scholar]
- Pleijter, G.; van Steeg, P.; ter Horst, W.; van Hoek, M.; Pol, J. Data Analyse Golfoverslag en Overloop-Proeven Proeflocatie Wijmeers (in Dutch); Technical Report; HKV Lijn in Water & Deltares: Delft, The Netherlands, 2018. [Google Scholar]
- Bakker, J.; Mom, R.; Steendam, G.; Van der Meer, J.W. Factual Report: Overslagproeven en Oploopproef Tholen (in Dutch); Technical Report; Infram: Maarn, The Netherlands, 2011. [Google Scholar]
- Van Bergeijk, V.M.; Warmink, J.J.; Hulscher, S.J.M.H. Modelling of Wave Overtopping Flow over Complex Dike Geometries: Case Study of the Afsluitdijk. Coast. Eng. Proc. 2020, 1–9. [Google Scholar] [CrossRef]
- Kriebel, M. Quantification of Grass Erosion Due to Wave Overtopping at the Afsluitdijk. Master’s Thesis, University of Twente, Water Engineering and Management, Enschede, The Netherlands, 2019. [Google Scholar]
- Van Bergeijk, V.M.; Verdonk, V.A.; Warmink, J.J.; Hulscher, S.J.M.H. The Vulnerability of Damaged River and Lake Dikes to Wave Overtopping. In Proceedings of the FLOODrisk 2020-4th European Conference on Flood Risk Management, Budapest, Hungary, 21–25 June 2021. [Google Scholar]
- Warmink, J.J.; Van Bergeijk, V.M.; Kriebel, M.; Trul, H.; Kuiper, C.; Hulscher, S.J.M.H. The failure probability of grass erosion due to wave overtopping. A case study of the Afsluitdijk, The Netherlands. In Proceedings of the FLOODrisk 2020-4th European Conference on Flood Risk Management, Budapest, Hungary, 21–25 June 2020. [Google Scholar]
- Van der Meer, J.W.; Steendam, G.J.; Mosca, C.A.; Guzzo, L.B.; Takata, K.; Cheong, N.S.; Eng, C.K.; Lj, L.A.; Ling, G.P.; Wee, C. Wave Overtopping Test to Determine Tropical Grass Species and Topsoils for Polder Dikes in a Tropical Country. Coast. Eng. Proc. 2020, 1–15. [Google Scholar] [CrossRef]
- Klerk, W.J.; Roscoe, K.L.; Tijssen, A.; Nicolai, R.P.; Sap, J.; Schins, F. Risk based inspection of flood defence dams: An application to grass revetments. In Proceedings of the 6th International Symposium on Life-Cycle Civil Engineering, IALCCE 2018, Ghent, Belgium, 28–31 October 2018. [Google Scholar]
- Beltaos, S. Oblique Impingement of Circular Turbulent Jets. J. Hydraul. Res. 1976, 14, 17–36. [Google Scholar] [CrossRef]
- Stanczak, G. Breaching of Sea Dikes Initiated from the Seaside by Breaking Wave Impacts. Ph.D. Thesis, University of Braunschweig, Braunschweig, Germany, University of Florence, Florence, Italy, 2008. [Google Scholar]
- Scheres, B.; Schüttrumpf, H. Investigating the Erosion Resistance of Different Vegetated Surfaces for Ecological Enhancement of Sea Dikes. J. Mar. Sci. Eng. 2020, 8, 519. [Google Scholar] [CrossRef]
Parameter | Relation | Method |
---|---|---|
Turbulence parameter | Calibration using the measured erosion depth at 7 field tests [19,34] | |
Determined from measured pressure fluctuations at Millingen a/d Rijn [35] | ||
Determined from measured pressure fluctuations at Millingen a/d Rijn [35] | ||
Threshold velocity | Calibration using the measured erosion depth at 7 field tests [19,34] |
Grass | Clay | |||||
---|---|---|---|---|---|---|
Good | Average | Poor | Good | Source | ||
[m/s] | 6.5 | 4 | 2.5 | 0.85 | Aguilar-López et al. [15] | |
[-] | 0.3 | 0.3 | 0.3 | 0.1 | Aguilar-López et al. [15] | |
[s/m] | 1 | 2 | 3 | 50 | Verheij et al. [36] |
Test Section | [m] | [m/s] | q [L/s/m] | [h] | Source |
---|---|---|---|---|---|
Afsluitdijk 2 | 2.8 | 4.0 | 1, 10 | 6 | Bakker et al. [45] |
Tielrodebroek 1 | 1.9 | 1.2 | 1, 10, 30() | 2 | Peeters et al. [46] |
Tielrodebroek 2 | 1.9 | 1.6 | 1, 10, 30() | 2 | Peeters et al. [46] |
Wijmeers 1 | 1.7 | 3.5 | 1, 5, 25 | 2 | Pleijter et al. [47] |
Wijmeers 3 | 1.3 | 3.0 | 25 | 2 | Pleijter et al. [47] |
Kattendijke 2 | 6.6 | 6.5 | 30, 50 | 6 | Bakker et al. [44] |
St. Philipsland | 6.5 | 6.5 | 0.1, 1, 10, 30, 50 | 6 | Bakker et al. [44] |
Tholen 3 | 6.5 | 0.0 | 1, 5 () | 6 | Bakker et al. [48] |
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van Bergeijk, V.M.; Verdonk, V.A.; Warmink, J.J.; Hulscher, S.J.M.H. The Cross-Dike Failure Probability by Wave Overtopping over Grass-Covered and Damaged Dikes. Water 2021, 13, 690. https://doi.org/10.3390/w13050690
van Bergeijk VM, Verdonk VA, Warmink JJ, Hulscher SJMH. The Cross-Dike Failure Probability by Wave Overtopping over Grass-Covered and Damaged Dikes. Water. 2021; 13(5):690. https://doi.org/10.3390/w13050690
Chicago/Turabian Stylevan Bergeijk, Vera M., Vincent A. Verdonk, Jord J. Warmink, and Suzanne J. M. H. Hulscher. 2021. "The Cross-Dike Failure Probability by Wave Overtopping over Grass-Covered and Damaged Dikes" Water 13, no. 5: 690. https://doi.org/10.3390/w13050690