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

sand clay

sand

failure block

revetment grass on clay

block revetment

failure

clay layer

failure dike

resid

ual

str

en

gth

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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 hourt = 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

tan0.063e s

m

op

V Hc

t s

220,8

,2 1,3

0,15tan 135 1500 exp 0,0091e s t

m op

p op s

V H Bc s

t T s H

0.25

,3 min 0.4 0.7; 2et m s

s

Vd c H

H

(Klein Breteler et al., 2012)

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Numerical model

0 10 20 30 40 50 60 700

1

2

3

4

5

6

7

8

9

10

Width [m]

He

igh

t [m

+N

AP

]

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

dcSand 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]

wa

ter

leve

l [m

+N

AP

] • 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

Example h

eig

ht [m

+N

AP

]

dike geometry

water level

erosion profile

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Questions?

Thank you for attending my presentation!

0 10 20 30 40 50 60 700

1

2

3

4

5

6

7

8

9

10

Width [m]

He

igh

t [m

+N

AP

]

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.