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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