IAHR 2015 - Numerical model to predict the erosion of a dike using time dependent boundary conditions, Kaste, Deltares, 02072015
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This document presents a numerical model to predict erosion of dikes with time-dependent boundary conditions such as varying water levels and wave conditions. The model divides the dike into horizontal sections and distributes the erosion volume within each time step over the sections. Empirical formulas are used to calculate erosion rates in clay and sand based on large-scale physical model tests. The model was adapted to account for time-varying boundary conditions by storing the erosion volume and depth per section. An example application to a dike with eroding clay under varying water level and wave conditions is presented.
![IAHR Congress July 2nd 201511
Numerical model
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Width [m]
Height[m+NAP]
Dike geometry
Sand core
t = 0.5 h
t = 5.0 h
t = 10.0 h
t = 15.0 h
t = 20.0 h
t = 25.0 h
t = 28.5 h
Water level
• Calculation of the erosion volume over the duration of the storm
divided in time steps
• Determination of the erosion profile in each time step
erosion depth, progress of erosion
(Kaste & Klein Breteler, 2014)](https://image.slidesharecdn.com/iahr2015-numericalmodeltopredicttheerosionofadikeusingtimedependentboundaryconditionskastedeltares02-150709155403-lva1-app6892/85/IAHR-2015-Numerical-model-to-predict-the-erosion-of-a-dike-using-time-dependent-boundary-conditions-Kaste-Deltares-02072015-11-320.jpg)
![IAHR Congress July 2nd 201514
water level course
with tide
water level course
during a storm
(HR2006)
time t [h]
waterlevel[m+NAP]
• Recent enhancement with PBZ: adaptation for varying boundary
conditions
• Replacing erosion rate formula for clay with new formula (Mourik, 2015)
Adaption numerical model](https://image.slidesharecdn.com/iahr2015-numericalmodeltopredicttheerosionofadikeusingtimedependentboundaryconditionskastedeltares02-150709155403-lva1-app6892/85/IAHR-2015-Numerical-model-to-predict-the-erosion-of-a-dike-using-time-dependent-boundary-conditions-Kaste-Deltares-02072015-14-320.jpg)
![IAHR Congress July 2nd 201518
Example of the erosion of clay with a varying water level and varying
wave conditions
Exampleheight[m+NAP]
dike geometry
water level
erosion profile](https://image.slidesharecdn.com/iahr2015-numericalmodeltopredicttheerosionofadikeusingtimedependentboundaryconditionskastedeltares02-150709155403-lva1-app6892/85/IAHR-2015-Numerical-model-to-predict-the-erosion-of-a-dike-using-time-dependent-boundary-conditions-Kaste-Deltares-02072015-18-320.jpg)
![IAHR Congress July 2nd 201519
Questions?
Thank you for attending my presentation!
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Width [m]
Height[m+NAP]
Dike geometry
Sand core
t = 0.5 h
t = 5.0 h
t = 10.0 h
t = 15.0 h
t = 20.0 h
t = 25.0 h
t = 28.5 h
Water level
dorothea.kaste@deltares.nl](https://image.slidesharecdn.com/iahr2015-numericalmodeltopredicttheerosionofadikeusingtimedependentboundaryconditionskastedeltares02-150709155403-lva1-app6892/85/IAHR-2015-Numerical-model-to-predict-the-erosion-of-a-dike-using-time-dependent-boundary-conditions-Kaste-Deltares-02072015-19-320.jpg)
IAHR 2015 - Numerical model to predict the erosion of a dike using time dependent boundary conditions, Kaste, Deltares, 02072015
- 1. Numerical model to predict the erosion of a dike using time dependent boundary conditions Dorothea Kaste - Deltares Mark Klein Breteler - Deltares Yvo Provoost - Projectbureau Zeeweringen IAHR Congress - The Hague - July 2nd 2015
- 2. IAHR Congress July 2nd 20152 Contents • Introduction • Derivation of the numerical model • Adaption for time dependant boundary conditions • Example
- 3. IAHR Congress July 2nd 20153 Why do we need this model? Typical dike in the Netherlands with a block revetment
- 4. IAHR Congress July 2nd 20154 Residual strength of a dike sandclay sand failure block revetment grass on clay block revetment failure clay layer failure dike residual strength
- 5. IAHR Congress July 2nd 20155 Simulating a whole storm
- 6. IAHR Congress July 2nd 20156 Contents • Introduction • Derivation of the numerical model • Adaption for time dependant boundary conditions • Example
- 7. IAHR Congress July 2nd 20157 Large scale experiments in the Deltaflume (Wolters & Klein Breteler, 2011) - Scale 1:1 - Dike is built with a sand core and a clay layer made from clay blocks (2 x 2 m, 80 cm thick) - Block revetment below the berm and grass on the upper slope Large scale model tests
- 8. IAHR Congress July 2nd 20158 Large scale experiments in the Deltaflume - Scale 1:1 - Dike is built with a sand core and a clay layer made from clay blocks (80 cm thick) - Block revetment below the berm and grass above Large scale model tests
- 9. IAHR Congress July 2nd 20159 Large scale model tests Erosion of the clay layer and the sand core by waves Large scale experiments in the Deltaflume
- 10. IAHR Congress July 2nd 201510 Analysis of the physical model tests Z (m) X (m) Original profile t = 1.0 hour t = 2.6 hour t = 5.3 hour t = 8.7 hour t = 3.1 hour t = 0.4 hour Hs = 1.6 m; Tp = 5.4 s; sop = 0.035 schematized erosion profile Measurements of the erosion formulas to calculate the erosion rate in clay and sand 2 ,1 tan 0.063e s m op V H c t s 22 0,8 ,2 1,3 0,15 tan 135 1500 exp 0,0091e s t m op p op s V H B c s t T s H 0.25 ,3 min 0.4 0.7; 2e t m s s V d c H H (Klein Breteler et al., 2012)
- 11. IAHR Congress July 2nd 201511 Numerical model 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 7 8 9 10 Width [m] Height[m+NAP] Dike geometry Sand core t = 0.5 h t = 5.0 h t = 10.0 h t = 15.0 h t = 20.0 h t = 25.0 h t = 28.5 h Water level • Calculation of the erosion volume over the duration of the storm divided in time steps • Determination of the erosion profile in each time step erosion depth, progress of erosion (Kaste & Klein Breteler, 2014)
- 12. IAHR Congress July 2nd 201512 Input Bb Bc ) u b a i ) ) ( zc zb 0m+NAP dc Sand core SWL h schematized dike geometry hydraulic boundary conditions
- 13. IAHR Congress July 2nd 201513 Contents • Introduction • Derivation of the numerical model • Adaption for time dependant boundary conditions • Example
- 14. IAHR Congress July 2nd 201514 water level course with tide water level course during a storm (HR2006) time t [h] waterlevel[m+NAP] • Recent enhancement with PBZ: adaptation for varying boundary conditions • Replacing erosion rate formula for clay with new formula (Mourik, 2015) Adaption numerical model
- 15. IAHR Congress July 2nd 201515 • Split the dike into horizontal sections • Distribute erosion volume of the current time step over the sections • Store erosion volume and erosion depth per section Approach for a varying water level (Kaste & Klein Breteler, 2015)
- 16. IAHR Congress July 2nd 201516 • Split the dike into horizontal sections • Distribute erosion volume of the current time step over the sections • Store erosion volume and erosion depth per section Approach for a varying water level dike geometry erosion profile water level (Kaste & Klein Breteler, 2015)
- 17. IAHR Congress July 2nd 201517 Contents • Introduction • Derivation of the numerical model • Adaption for time dependant boundary conditions • Example
- 18. IAHR Congress July 2nd 201518 Example of the erosion of clay with a varying water level and varying wave conditions Exampleheight[m+NAP] dike geometry water level erosion profile
- 19. IAHR Congress July 2nd 201519 Questions? Thank you for attending my presentation! 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 7 8 9 10 Width [m] Height[m+NAP] Dike geometry Sand core t = 0.5 h t = 5.0 h t = 10.0 h t = 15.0 h t = 20.0 h t = 25.0 h t = 28.5 h Water level dorothea.kaste@deltares.nl
- 20. IAHR Congress July 2nd 201520 References • Kaste & Klein Breteler, 2014: Sensitivity study into residual strength of dikes after block revetment failure, given as preliminary safety factor – WTI 2017. Deltares, rapport 1207811-010. • Kaste & Klein Breteler, 2015: Rekenmodel voor kleierosie bij variërende waterstand. Deltares, report 1209832-010. • Klein Breteler et al., 2012: Erosie van een dijk na bezwijken van de steenzetting door golven - SBW reststerkte; analyse Deltagootproeven. Deltares, report 1204200-008. • Mourik, 2015: Prediction of the erosion velocity of a slope of clay due to wave attack – WTI2017. Deltares, report 1209437-017. • Wolters & Klein Breteler, 2011: Reststerkte van een dijk met steenzetting op een kleilaag - Meetverslag Deltagootproeven SBW-Reststerkte. Deltares, report 1202122.002.