Numerical model to predict the erosion of a dike using time dependent boundary conditions

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

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Contents
• Introduction
• Derivation of the numerical model
• Adaption for time dependant boundary
conditions
• Example

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Why do we need this model?
Typical dike in the Netherlands with a block revetment

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Residual strength of a dike
sandclay
sand
failure block
revetment
grass on clay
block revetment
failure
clay layer
failure dike
residual
strength

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Simulating a whole storm

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Contents
• Introduction
• Derivation of the numerical model
• Adaption for time dependant boundary
conditions
• Example

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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

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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

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Large scale model tests
Erosion of the clay layer and the sand core by waves
Large scale experiments in the Deltaflume

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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)

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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)

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Input
Bb
Bc
) u
b
a
i
)
)
(
zc zb
0m+NAP
dc
Sand core
SWL
h
schematized dike geometry
hydraulic boundary conditions

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Contents
• Introduction
• Derivation of the numerical model
• Adaption for time dependant boundary
conditions
• Example

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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

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• 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)

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• 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)

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Contents
• Introduction
• Derivation of the numerical model
• Adaption for time dependant boundary
conditions
• Example

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Example of the erosion of clay with a varying water level and varying
wave conditions
Exampleheight[m+NAP]
dike geometry
water level
erosion profile

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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

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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.