COMRISK Workshop Norden 12./13. May 2004

COMRISK Workshop Norden12./13. May 2004

COMRISK Workshop Norden12./13. May 2004

Failure probability of the Ribe sea defence

Failure probability of the Ribe sea defence

Andreas Kortenhaus

Leichtweiß-Institut for Hydraulics (LWI)Dept. Hydromechanics and Coastal

EngineeringBeethovenstr. 51a

38106 Braunschweig

LWILWI

IntroductionLocationInput param.Det. calc.UncertaintiesProb. calc.Conclusions

ContentsContents

Introduction

Location of Ribe sea defence

Input parameter

Deterministic calculations

Uncertainties

Probabilistic calculations

Overall failure probability

Summary / concluding remarks

LWILWI


On the richness of English languageOn the richness of English language

Question: how is the German word “schräg”, Dutch: “”, Danish “” translated into English leaning (in terms of the tower of Pisa or the church in

Norden) oblique (in plan view for wave attack) diagonal sloping (in terms of slopes of a structure) inclining (in terms of walls) tilted (in terms of very large angles) at an angle (in terms you do not know exactly)

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Definition of riskDefinition of risk

Flooding risk Rfc = ( Pf )S ·E(D)Flooding risk Rf

c = ( Pf )S ·E(D)

Expected damage and consequences of

flooding E(D)Failure probability Pf

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Location of project areaLocation of project area

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Map of Ribe area and sea defencesMap of Ribe area and sea defences

Mandø

Ribe

Ribe-Å

Southern wing dike

Northern wing dike

Sluice Ribe-Å

Outlet V. Vedsted

Outlet Konge-Å

Outlet Darum

Potential flooding area

Main dike line Ribe

Contiguous dike line

NN

Ebb way

Contiguous dike line

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Standard dike profileStandard dike profile

0,00 m DVR90

hk= 6,88m

ht= 2,38m

Bk= 2,50m

d

DWL = + 5,22 m

Sandcore

1:31:10d fr

Clay layer

1:100

db

Parameter Value

Slope of foreland (length 100m) 1:100

Height of dikefoot ht 2,38 m

Height of crown hK 6,88 m

Width of crown BK 2,50 m

Seaward slope 1:n 1:10

Shoreward slope 1:m 1:3

Thickness clay layer outer slope dfr 1,0 m

Thickness clay layer inner slope db 0,5 m

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Ribe sluiceRibe sluice

Outer floodgates

0 mDVR90

DWL = 5,22 m

Outer flood gates (closed)

-3,60 m

Sole paving

5,78 m

5,88 m

Chamber walls

Inner floodgates

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Outlet Konge-Å Outlet Konge-Å

0 m DVR90

-2,00 m

5,22m DWL

6,88 m

Floodgate

Sandcore Grass

layer

Clay layer

Storm gate

Stone mattress

Berm

1:3 1:2

4,23 m

2,50 m1:7

Filter gravel

Drainage

Pavement

Sole (concrete)

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Location of profiles analysedLocation of profiles analysed

Wave rider Fanø

Fanø

Mandø

Ribe

N

3156

6644

9400

14499

8422

10403

Sluice Ribe-Å

Profile 270

Profile 1

Profile 250

Profile 290

Outlet Konge–Å

Outlet Darum

Outlet V. Vedstedt

Sluices / outlets

Dike profiles

Wind measurements

Water levelmeasurements

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Ribe Dike St. 3156

0.900.99

1.121.31 1.37 1.42 1.37

1.491.61

1.88

2.162.33

2.44 2.502.41

2.51 2.562.68

2.89

3.193.09

3.42

3.74

4.30

4.93

5.61

6.22

6.46

6.836.816.736.666.52

5.70

4.38

3.58

2.93

2.722.58

2.151.95

1.49

0.920.810.69

1.09

1.88

2.30

2.53

-3.00

-1.00

1.00

3.00

5.00

7.00

0 25 50 75 100 125 150 175 200 225

Distance [m]

Hei

ght (D

VR90

) [m

]

Adaption of profile data to model – profile 3156Adaption of profile data to model – profile 3156

Ribe

N

3156

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Ribe dike St. 6644

2.51 2.562.68

2.90

3.36

3.98

4.57

5.19

5.79

6.47

6.997.08

6.93

6.62

6.02

5.01

4.05

3.503.443.34

3.24

2.25

1.72

1.24

0.82

0.480.33

0.08

-0.84

-1.28-1.32

-1.58

-1.79

-0.94

-0.03

0.91

1.821.89

-3.00

-1.00

1.00

3.00

5.00

7.00

225 250 275 300 325 350

Distance [m]

Hei

ght (D

VR90

) [m

]


Ribe

N

6644

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Ribe dike St. 8422

2.232.23

2.50

2.752.91

3.83

4.76

6.15

6.726.736.71

5.89

4.51

3.43

2.53

2.26

1.941.811.791.86

1.962.062.05

-3.00

-1.00

1.00

3.00

5.00

7.00

850 875 900 925 950 975 1_000 1_025 1_050

Distance [m]

Hei

ght (D

VR90

) [m

]


Ribe

N

8422

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Ribe dike St. 9400

2.532.62

2.74

3.26

3.97

4.68

5.50

6.27

6.686.766.836.806.81

6.646.52

5.11

4.23

3.51

3.283.123.08 3.01

2.872.77

2.60

2.00

0.660.77

0.60

0.29

-0.80

-1.04

-1.40-1.27

-1.05

0.19

0.43

1.11

2.072.10

-3.00

-1.00

1.00

3.00

5.00

7.00

500 525 550 575 600 625

Distance [m]

Hei

ght (D

VR90

) [m

]


Ribe

N

9400

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Ribe dike St. 10403

1.75

2.43

2.682.652.83

3.403.603.75

4.09

5.62

6.646.656.49

5.72

4.37

3.03

2.542.50

2.25

2.031.88

1.681.59

-3.00

-1.00

1.00

3.00

5.00

7.00

850 875 900 925 950 975 1_000 1_025 1_050

Distance [m]

Hei

ght (D

VR90

) [m

]


Ribe

N10403

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Ribe dike St. 14499

2.45 2.442.55

2.632.74

3.24

3.61

4.03

4.50

4.94

5.42

5.94

6.26

6.67

6.876.896.926.85

6.22

5.61

5.03

4.57

3.96

3.683.503.363.323.293.26

3.17

2.83

2.36

1.67

1.231.09

1.20

0.88

0.65

0.38

-0.28-0.44

-0.56-0.65

-0.43-0.32

0.66

1.19

2.15

-3.00

-1.00

1.00

3.00

5.00

7.00

125 150 175 200 225 250

Distance [m]

Hei

ght (D

VR90

) [m

]


Ribe

N14499

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Typical input parameter for two sectionsTypical input parameter for two sections

0,00 m DVR90

hk= 6,73m

ht= 1,92m

Bk= 2,80m

dClay: K

, Kr

DWL = + 5,22 m Hs, Tp, θ

Sand: S, Sr, s

1:3,

1

1:20

1:11

d fr

km 8422

Hs = 1,47m dfr = 1,0 m cu = 15,0 [KN/m2]

Tp = 6,01 s K = 17,0KN/m3 dG = 0,05 [m]

θ = 20 ° Kr = 20,0KN/m3 S = 19,0 [KN/m3]

ts = 6,5 h cs = 35,0KN/m2 Sr = 22,0 [KN/m3]

d = 3,3 m css = 10,0KN/m2 s = 40,0 [°]

0,00 m DVR90

hk= 7,08m

ht= 2,66m

Bk= 2,00m

d Clay: K, Kr

1:12

1:10DWL = + 5,22 m

Hs, Tp, θ

Sand: S, Sr, s

1:2,

6

d fr

km 6644

Hs = 1,51 m dfr = 1,0 m cu = 15,0 [KN/m2]

Tp = 4,89 s K = 17,0KN/m3 dG = 0,05 [m]

θ = 20 ° Kr = 20,0KN/m3 S = 19,0 [KN/m3]

ts = 6,5 h cs = 35,0KN/m2 Sr = 22,0 [KN/m3]

d = 2,65 m css = 10,0KN/m2 s = 40,0 [°]

LWILWI


Failure modes for dike profilesFailure modes for dike profiles

CoreClay Layer

Global failure modes:Overflow

OvertoppingDike breachDike slid

Failure modes shoreward slope:Velocity overflowVelocity overtoppingGras erosionClay erosionInfiltrationKappensturzPhreatic lineClay upliftClay slidBishop shoreward slopeSand erosion

Failure modes seaward slope:

Revetment stabilityImpactRevetment uplift

Velocity wave run-upGras erosionClay erosionPhreatic lineCliff erosionBishop shoreward slope

Internal failure modes:PipingMatrix erosion

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Failure modes Ribe sluiceFailure modes Ribe sluice

Global failure modes:OvertoppingOverflow

Hydraulic uplift

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Results of deterministic calculationsResults of deterministic calculationsProfile

Failure modes 3156 6644 8422 9400 10403 14499

Global failure modesOverflow 999 999 999 999 999 999Overtopping 6,78 8,83 6,32 7,15 4,83 8,08Breach 999 999 999 999 999 999Dike slid 69,51 64,09 45,56 65,70 64,57 60,08Failure modes outer slopeImpact 34,95 36,18 31,51 35,75 34,05 34,82Velocity wave run-up 1,60 1,67 1,61 1,64 1,69 1,58Grass erosion 0,43 0,47 0,35 0,46 0,41 0,43Clay erosion 8,28 7,04 4,54 6,13 5,29 4,48Cliff erosion 999 999 999 999 999 999Bishop outer slope 1,63 1,55 1,77 1,58 1,80 1,56Failure modes inner slopeVelocity overflow 999 999 999 999 999 999Velocity overtopping 999 999 999 999 999 999Gras erosion 999 999 999 999 999 999Clay erosion 999 999 999 999 999 999Infiltration 999 999 999 999 999 999Kappensturz 1,87 1,56 1,94 1,67 2,09 999Phreatic Line 466,16 415,37 370,01 455,04 512,62 532,14Clay uplift 4,32 4,77 6,32 3,25 5,65 5,74Clay slid 4,55 4,40 5,14 3,96 5,14 4,84Bishop inner slope 2,74 2,31 3,14 2,25 2,13 2,12Sand erosion 999 999 999 999 999 999Failure modes inner erosionPiping 11,26 999 999 23,47 10,85 17,14Matrix erosion 1,70 1,41 1,88 1,88 2,42 3,64

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Results of sensitivity analysisResults of sensitivity analysis

Failure mode analysed Parameter influence on h

Grass erosion outer slope water level hw -quality of gras qG +

Velocity wave run-up material constant surface outer slope qM +wave period Tp -

Bishop outer slope cohesion of clay cu +saturated volume weight of sand gSr -

Kappensturz undrained cohesion of clay cu +percentage of sand in clay pk +volume weight of clay gK -

Overtopping water level hw +crown height hk -wave height Hs +

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Uncertainty analysis of water levelUncertainty analysis of water level

5,40 5,

54 5,77

5,62

5,05

5,47

5,41 5,

55

4,70

5,23

5,03

4,75

0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

Statistical distribution

Des

ign

wat

er le

vel

[m D

VR90

] (T

=20

0 ye

ars)

THRS= 3,38m, 20 Values



Statisticaldistribution

Mean[m]Standarddeviation

hw [T=200]

LogN 4,02 0,48 5,40Pearson III 4,02 0,48 5,63Log-Pearson III 3,99 0,46 5,54Gumbel 4,02 0,48 5,77Weibull 4,02 0,49 5,01Pareto 4,04 0,77 7,83

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Correlation of water level and wave heightsCorrelation of water level and wave heights

Wave height 50m in front of coast line (DHI Simulation)

0,8

0,9

1

1,1

1,2

1,3

1,4

1,5

1,6

1,7

1,8

0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50 4,00

Water depth d [m]

Wav

e he

ight

Hm

0 (5

0m)

[m]

Profile 3156

Profile 6644

Profile 8422

Profile 9400

Profile 10403

Profile 14449

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Uncertainties of input parameterUncertainties of input parameter

Parameter Uncertainty Restriction Remarks

Height of crown hk sdv = 0,06 m -Uncertainty of measurements made by Kystdirektorat

Water level hw CoV = 0,117 -Statistical characteristics based on 20 extreme values

Wave height Hs CoV = 0,125 Hs,max=0,5*d Breaker criterion

Wave period Tp CoV = 0,20 Tp,max=(Hs / 0,0938) 0̂,5 Limitation of wave steepness

Cohesion of clay cs CoV = 0,20 -Estimated as uncertainty due to in-situ measurements (CoV=0,76 in PRODEICH - model)

Undrained cohesion of clay cu

CoV = 0,20 -Estimated as uncertainty due to in-situ measurements (CoV=0,22 in PRODEICH - model)

Apparent cohesion of clay css

CoV = 0,20 -Estimated as uncertainty due to in-situ measurements (CoV=0,75 in PRODEICH - model)

Internal friction angle of sand phiS

CoV = 0,58 phiS > 0Angles < 0 phsysically make no sense

LWILWI


Fault tree calculationsFault tree calculations

Profile 10403= IF-gate

= OR-gate1

= AND-gate Pf =

2 T1

3 4 5 T2hW = [m] hk= [m]Hs = [m] Rc = [m]

7 T3 Tp = [s] NW = [-]vA= [m/s] ts = [h]vB= [m/s] qEAK= [l/sm]

vkrit A= [m/s] qT= [l/sm]

8 9 T4 vkrit B= [m/s]

T5

26 25 T13 21 20 T6

17 18 1927 T14 A B 13 T12

16 T730 29 T15

28 23 B2 T8 B3A

24B A2

32 31 T16

14 1542 T22 44 T23

33 34 T17

B4 T9A4 A3 T19 43 45

B6 T10 B7A6 A5 T20

B5 B8A7 T21

A8 A9

Phreatic line

- 0,0E+00

I

- 0,0E+00

I1,0E-11

Phreatic line0,0E+00

I0,0E+00

Flooding6,9E-05

7,1E-17

O6,9E-05

I

1,0E-11

O3,5E-07

1,0E-11

16O

12Partial breach

inner slope

- 0,0E+00

Velocitywave run-up

4,34

6,9E-04

I4,1E-06

Erosionouter slope

0,0E+00

0,00

1,1E-05

0,0E+00 1,4E-04-

O

O

0,0E+00-

Uplift clayinner slope

1,9E-04 - 0,0E+00

Infiltration

0,0E+00-

Phreatic line

I

O

A

Inner erosion

0,0E+00-

0,0E+00

6,50

Dike slid

3,5E-07

Bishopinner slope

0,002,13

1110

-

0,0E+00

2,0E-06 3,55 1,9E-04

1,0E-11

Velocityoverflow

Velocityovertopping

1,3E-07

4,61

IErosion grasinner slope

3,20

Erosion clayinner slope

3,79 7,6E-05

1,0E-11

7,0E-06

I4,2E-14

O

1,0E-11

0,000,00

O

2,744,61

2,645571

6,654,021,454,20

3,2E-04

1,35

Breach

8,9E-02

I3,1E-08

4,34

3,6E-092,64

Cliff erosion outer slope

I

4,1E-03O

1,1E-05

Partial breachouter slope

5,79 3,6E-09

Vandalism

Overflow

4,50 3,4E-06

ExplosionSabotage

Matrix erosion

Failure mode

Pf

Overtopping

3,82 6,6E-05

Kappensturzinner slope

0,44 3,3E-017,0E-06

3,37 3,7E-04

0,0E+00

-

Sliding clay layer

35

Erosioninner slope

O

Bishopouter slope

3,634,1E-06

3,4E-02

4,46

1,83

Erosion clayouter slope

PipingI I

Erosion grasouter slope

I 2,67 3,8E-03 0,0E+00 0,0E+00 4,74 1,1E-061,1E-02

Impact

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Probabilistic results (overview)Probabilistic results (overview)Profile

Failure modes 3156 6644 8422 9400 10403 14499P(f) P(f) P(f) P(f) P(f) P(f)

Global failure modesOverflow 1,0E-06 2,0E-07 2,3E-06 1,0E-06 3,4E-06 5,0E-07Overtopping 3,0E-05 9,0E-06 4,1E-05 3,5E-05 6,6E-05 9,0E-06Breach 4,3E-02 1,8E-02 7,4E-02 4,2E-02 8,9E-02 3,6E-02Dike slid 2,0E-07 6,0E-07 4,9E-07 6,0E-07 4,0E-07 7,3E-07Failure modes outer slopeImpact 8,0E-06 5,0E-06 2,0E-05 4,0E-06 7,0E-06 8,0E-06Velocity wave run-up 2,0E-02 1,8E-02 3,3E-02 1,8E-02 2,9E-02 3,1E-02Grass erosion 2,8E-01 2,4E-01 6,6E-01 2,5E-01 3,2E-01 2,9E-01Clay erosion 2,5E-05 6,5E-05 5,1E-04 9,5E-05 1,6E-04 5,5E-04Cliff erosion 4,7E-05 2,7E-04 4,8E-04 7,0E-05 6,3E-04 8,3E-04Bishop outer slope 0 0 0 0 0 0Failure modes inner slopeVelocity overflow 2,0E-06 3,0E-06 3,0E-06 2,0E-06 2,0E-06 0Velocity overtopping 2,6E-05 3,3E-05 1,4E-04 1,2E-05 1,9E-04 2,2E-05Gras erosion 1,6E-04 1,0E-04 5,7E-04 8,5E-05 6,9E-04 1,2E-04Clay erosion 6,3E-05 1,6E-05 6,6E-05 2,3E-05 7,6E-05 1,7E-05Infiltration 0 8,0E-06 2,1E-04 1,0E-06 0,0E+00 1,6E-04Kappensturz 1,4E-02 1,1E-02 7,6E-03 2,3E-02 4,1E-03 1,4E-02Phreatic Line 1,0E-06 1,0E-06 1,0E-06 2,0E-06 0 1,0E-06Clay uplift 1,0E-06 2,0E-06 1,0E-06 1,0E-06 0 0,0E+00Clay slid 4,1E-04 5,0E-04 1,3E-04 1,2E-03 1,3E-04 2,2E-04Bishop inner slope 0 0 9,6E-05 0 0 0Sand erosion 0 0 3,2E-05 3,0E-06 7,0E-06 0Failure modes inner erosionPiping 3,0E-06 2,0E-06 2,0E-06 2,0E-06 3,0E-06 3,0E-06Matrix erosion 2,7E-01 1,5E-01 2,7E-02 2,7E-02 4,0E-03 3,0E-04

Overall failure propability 3,1E-05 9,2E-06 4,3E-05 3,6E-05 7E-05 1E-05

LWILWI


Probabilistic results of scenario approach (sect. 10403)Probabilistic results of scenario approach (sect. 10403)

= IF- gate Pf =

= OR-gate

= AND-gate

1 T2

SZ I SZ II SZ X SZ XI

Impact

3,30 4,9E-04

Breach+

Cliff erosion

I3,4E-09

Breach+

Cliff erosion+

Clay erosion+

Grass erosion

3,98 3,4E-05

I1,1E-06

1,1E-06

Failureouter slope

4,96 3,5E-07

1,5E-06

1,5E-06

O

Failure througherosion

3,5E-07O

1,83 3,4E-02

4,34 7,0E-06

3,5E-07

Breach+

Sand erosioninner slope

+Piping

+Phreatic line

-

Dike slid

Overtopping

Breach+

Sand erosioninner slope

+Matrix erosion

+Phreatic line

- 0,0E+00- 0,0E+00

I

O

A 5,5E-05

Breach

4,67

Flooding

4,73 1,1E-06

O

Overflow

2,2E-06 3,82 5,2E-05

5,5E-05

O

4,50

Velocitywave run-up

Szenario tree Fault treeSZ I + velocity wave run-up

1,1E-06 1,2E-10

SZ II + impact 3,4E-09 2,0E-10SZ X 0 0SZ XI 0 0

Szenarios / failure modes

P(f)

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Probabilistic results (sensitivity analysis)Probabilistic results (sensitivity analysis)

LWILWI


Definition of sections of Ribe sea defenceDefinition of sections of Ribe sea defence

4,00

4,50

5,00

5,50

6,00

6,50

7,00

7,50

2000 4000 6000 8000 10000 12000 14000 16000 18000

Station [m]

Hei

gh

t o

f cr

ow

n h

k [m

DV

R90

]

Wave p

eriod

Tp [s]

3156Outlet 6644 8422

Sluice Ribe-Å

Outlet9400 10403 14499 Outlet

Section 2profile 3156


Section 4profile



Section 7sluice Ribe-Å



Section 10outlet 14499

Section 11outlet Konge Å



Section 14outlet Darum


Section 1outlet V. Vedsted

Tp

hk

LWILWI


Overall failure probability for Ribe sea defenceOverall failure probability for Ribe sea defence

Pf =

1,0E-051,0E-05

14OutletDarum

4,7E-01

13Dike

1449915

Dike14499

OutletKongeÅ

4,7E-01

12Dike6644

9,6E-06

10Dike

144991,7E-05

11Outlet

Vedsted5,6E-01

9Dike

104037,1E-05

3Dike6644

8,0E-06

2Dike6644

3,1E-05 3,7E-05

4 Dike

-

Dike6644

9,6E-06

6Dike8422

4,5E-05

9,5E-01

SluiceRibe-Å

6,3E-01

8Dike9410

Flooding

71

Section / Description

Pf

5

O9,5E-01

all sections all (modified) only dikes

Pf,max 6,3 10-1 6,2 10-3 7,1 10-5

section Ribe sluice Ribe sluice Dkm 10403

Pf,Ribe 9,5 10-1 2,6 10-2 2,5 10-4

LWILWI


ConclusionsConclusions

study of input parameters good representation of dike cross sections soil parameters taken from measurements if possible

deterministic calculations of all cross sections and sluices overtopping failure at sluice for design conditions grass erosion failure for all sea dikes

uncertainty analysis of input parameters detailed study of water level correlation of water levels and wave heights

probabilistic calculations of all cross sections and sluices reduction of scenario tree to most important elements overall failure probability for dikes in the range of Pf = 10-5

failure probability for sluice in the range of Pf = 10-1

Overall failure probability of sea defence sluice and outlets to be considered correctly overall probability governed by dike failure probability

LWILWI


Thank you very much for your attention

Andreas KortenhausLeichtweiß-Institut für WasserbauTechnische Universität BraunschweigTel.: 0531 / 391-3981E-mail: [email protected]

LWILWI

Documents

COMRISK Workshop Norden 12./13. May 2004