May 6-8, 2008

1

PROBABILISTIC SENSITIVITY ANALYSIS OF DUNE EROSION CALCULATIONS

4th International Symposium on Flood Defence, Toronto, Canada

Kees den Heijer, Jan van de Graaff and Pieter van Gelder

Section of Hydraulic Engineering

May 7, 2008 2

Contents

• Introduction• Model description• Probabilistic model• Dune erosion model

• Approach• Results• Conclusions

May 7, 2008 3

Introduction

• approximately 350 km Dutch coastline• 254 km dunes• 34 km sea dikes• 38 km beach flats• 27 km of boulevards, beach walls etc.

• Design conditions very extreme (10-5 year-1)• No prototype data for these extreme situations• Policy to maintain coastline of 1990

May 7, 2008 4

Introduction

Current method for Dutch dune safety assessment:

• Empirical model• Applied in semi-deterministic way• Conditions based on probabilistic investigations

(WL | Delft Hydraulics, 2007)

May 7, 2008 5

Objective

• This study aims at more insight in the sensitivity of the rate of dune erosion for the stochastic characteristics of various variables, currently taken into account.

Remarks:• 10-5 year-1 probability of exceedance• DUROS-plus dune erosion model• Simple cross-shore profile

May 7, 2008 6

Model descriptionProbabilistic model

Prob2B (former 'Probox'; Courage & Steenbergen, 2007)•FORM method•Easy to couple with other software

Input:Stochastic characteristics

Limit state function

Probabilistic model Dune erosion model

Generate set of input values based on stochasts and

results so farCalculation

Result:Retreat distance

Process results of calculation

If result ≠ design point

Result:Probability of failure

Parameter values in design point

May 7, 2008 7

Model descriptionDune erosion model (DUROS-plus)

-200 0 200 400 600 800 1000 1200

-3

0

3

5

15

Cross-shore distance [m]

Le

vel w

.r.t. MS

L [m

]

1 : 2

.51 : 16.7

1 : 58.3

1 : 150

-200 0 200 400 600 800 1000 1200

-3

0

3

5

15

Cross-shore distance [m]

Le

vel w

.r.t. MS

L [m

]

Computational water level

-200 0 200 400 600 800 1000 1200

-3

0

3

5

15

Cross-shore distance [m]

Le

vel w

.r.t. MS

L [m

]

Computational water level

1 : 1

1 : 12.5

Parabolic shape depends on: WL, Hs, T

p, D

50 and profile fluctuation

-200 0 200 400 600 800 1000 1200

-3

0

3

5

15

Cross-shore distance [m]

Le

vel w

.r.t. MS

L [m

]

Computational water level

A

-200 0 200 400 600 800 1000 1200

-3

0

3

5

15

Cross-shore distance [m]

Le

vel w

.r.t. MS

L [m

]

Computational water level

AA A includes a contribution for storm duration and model accuracy

-200 0 200 400 600 800 1000 1200

-3

0

3

5

15

Cross-shore distance [m]

Le

vel w

.r.t. MS

L [m

]

Computational water level

AA A includes a contribution for storm duration and model accuracy

Retreat distance

May 7, 2008 9

Approach

• Stochastic characteristics of reference situation are mainly based on the probabilistic investigation of WL | Delft Hydraulics (2007)

• The stochastic characteristics have been changed one by one, keeping the others the same

May 7, 2008 10

OverviewReference situation

Parameter Mean value Uncertainty/variance Distribution type

Water level Related to Pexceedance - Conditional Weibull

Wave height Related to water level 0.6 m Normal

Wave period Related to wave height 1 s Normal

Grain size 225 m 10% of mean (22.5 m) Normal

Profile fluctuation 0 60 m3/m1 Normal

Surge duration 0 10 % * A Normal

Model accuracy 0 15 % * A Normal

May 7, 2008 11

Reference situation

10-6

10-5

10-4

10-3

10-2

10-1

20

30

40

50

60

70

80

90

100

Probability of exceedance [year-1]

Re

trea

t dista

nce

[m]

33.6

45.6

60.3

78.8

May 7, 2008 13

Overview of investigations

Variable Mean value Uncertainty/variance

Water level Reference situation + [-0.5, -0.25, 0, 0.25, 0.5] m -

Wave height Reference situation + [-0.5, -0.25, 0, 0.25, 0.5] m [0, 0.3, 0.6, 0.9 and 1.2] m

Wave period Reference situation + [0, 1 and 2] s [0, 0.5, 1.0, 1.5 and 2.0] s

Grain size [200, 225, 250, 275 and 300] m [0, 5, 10 and 15] % of 225 m

Profile fluctuation [-20, 0 and 20] m3/m1 [0, 30, 60, 90 and 120] m3/m1

Surge duration [0, 5 and 10] % * A [0, 5, 10, 15 and 20] % * A

Model accuracy [0, 5 and 10] % * A [0, 5, 10, 15 and 20] % * A

May 7, 2008 14

Results: Sensitivity water level

-0.5 -0.25 0 0.25 0.560

65

70

75

80

85

90

Re

trea

t dista

nce

[m]

Water level change [m] w.r.t. reference situation

Reference case

May 7, 2008 15

Sensitivity mean grain size

200 225 250 275 30060

65

70

75

80

85

90

Re

trea

t dista

nce

[m]

D

50

[m]

Reference case

May 7, 2008 16

Standard deviation grain size

0 11.25 22.5 33.7560

65

70

75

80

85

90

Re

trea

t dista

nce

[m]

D

50

[m]

Reference case

May 7, 2008 17

Standard deviation peak wave period

0 0.5 1 1.5 260

65

70

75

80

85

90

Re

trea

t dista

nce

[m]

Tp

[s]

Reference case

May 7, 2008 18

Conclusions

• Water level and grain size distribution are the most important variables in current safety assessment method for the Dutch dune coast

• Proper field data of these variables are crucial• The other variables do have their contribution,

but changing their stochastic char. does not have so much influence