isfd4 moellmann core

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Dipl.-Ing. Axel Moellmann, Prof. Dr.-Ing. Pieter A. Vermeer1

Prof. Dr.-Ing. habil. Bernhard Westrich2

1 University of Stuttgart, Germany, Institute of Geotechnical Engineering2 University of Stuttgart, Germany, Institute of Hydraulic Engineering

Reliability Analysis of River Embankments

--using analytical methods and finite elements--

4th International Symposium on Flood Defence,

6-8 May, 2008, Toronto, Canada

Funding Project Management Coordination

Presentation within the framework of the RIMAX-Project „PCRiver – Reliability and riskanalysis in river flood protection under consideration of geotechnical, hydrological andhydraulic factors”



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Benefits of reliability analysis

Aim of a reliability analysis in river flood protection

Systematic determination of flood risk as cost-benefit-analysis

Risk = Failure probability x Consequence

Not: „This is a potential weak spot!“

But: „Those are the sections to start improving theflood protection.“

And: „Those are the most cost-efficient measures.“



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Outline

• Introduction into reliability analysis

• Case study Elbe river

• Probabilistic Finite-Element Analysis of embankment stability

• Conclusions and Outlook



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µS µRσS σSσR σR

Introduction into reliability analysis

SRZ −= R: Resistance, S: Stress

Stress x, Resistance x

Failure probability p(Z<0)

P r o b a b i l i t y

d e n s i t y f (Resistance: R)f (Stress: S)

Z

Z

22

SR

SRσ

µ=

σ+σ

µ−µ=βReliability index for Gaussian (normally)

distributed variables and Z = R - S:

Limit state equation:



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Case study Elbe river

Torgau / Saxony



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Comparison to a 100-year flood only considering overflow (Dike stretch B)

99

87

9488

0

20

40

60

80

100

120

Validierung HQ100

R

e t u r n p e r i o d T [ a

Section 1 Section 2 Section 3 Section 4

100-year flood



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Computed failure probabilities for dike stretch B

461

463

448448 476

238

331

725

302

242

0

200

400

600

800

1000

Overflow /

Overtopping

Uplift / Piping Slope

instability

Damage of

the revetment

Combined

failure

probability

R e t u r n p e r i o d T

[ a ]

Section 1 Section 2 Section 3 Section 4

>>5000>>5000>>5000 1709 3759



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Comparison to Elbe flood 2002 - dike failure statistics (Horlacher, 2005)

Overflow / Overtopping

Uplift / Piping

Slope instability

47 %

24 %

29 %


Uplift / Piping

Slope instability

6 %

28 %

66 %

Relative failureprobability (PC-Ring)

29 %

24 %

47 %

Dike failurestatistics

Slope instability

Uplift / Piping


Failure mode



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Reliability water level and reliability freeboard

Design floodwater level

Reliability water level

Reliability freeboard Dike body

100 97 8377

94

46

91

53

0204060

80100

Section 1 Section 2 Section 3 Section 4 F r e e b o a r d f o r

H Q 1 0 0 / R e

l i a b i l i t y

f r e e b o a r d

[ c m ]

Freeboard for a HQ100 Reliability freeboard



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Probabilistic Finite-Element Analysis

of embankment stability

2.83 m4.06

HB = γ w· zB

1.44 m

1.70 m

15.99h

HA = γ w· zA

1

1.00 m

q = 0?

Total incremental displacements

→ Stability reserves due to transient seepage effects can be quantified.

→ Zoned dike structure can be taken into account.

Benefits:

N



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Stochastic input parameters

2 4 6 8 10 12 14c @kN•m²D

0.050.1

0.15

0.2p.d.f.

5.´10-8 k @m•sD

5´106

1´107

1.5´107

2´107

p.d.f.

15 18 21phi @°D

0.05

0.1

0.15

0.2

p.d.f.

ϕ‘

Friction angle ϕ‘→ normally

distributed

Effective cohesion c‘

→ lognormally distributed

Permeability k

→ lognormally distributed

µϕ’ = 17.1°σϕ’ = 1.76°

µc’ = 4.65 kN/m²σc’ = 3.72 kN/m²

µk = 5 · 10-5 m/sσk = 2.5 · 10-5 m/s

µϕ’µc

’

µk =

’

3 Scenarios:hmax,1 = 2.83 mhmax,2 = 2.40 mhmax,3 = 1.20 m

h

→ Correlated river water level h

and duration of the flood wave N



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0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0 2 4 6 8 10 12

Time [Days]

W

a t e r l e v e l a b o v e

l a n d w a r d d i k e t o e [ m ]

Water level h Factor of safety



Phase shift between maximum water level and minimum factor of safety

→ Factor of safety ? needs to be checked for various time steps

for various flow patterns

1.25

1.20

1.15

1.10

1.05

1.00

0.95

0.90

F

a c t o r o f s a f e t y ?

?crit

hmax



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First Order Reliability Method with Adaptive Response Surface (FORM-ARS)

Perform numerical simulations around mean value

Output: Factor of safety ? from a numerical stability analysis

Find best-fit Response Surface for ? = b0 + b1· f ‘ + b2· c‘+ b3· k

Find design point for Response Surface

Check design point with numerical results

IF ( ? ˜ 1 ) AND IF ( New design point = Old design point )

Determination of failure probability

then

Perform numericalsimulations around

the design point

else



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Response Surfaces for three different maximum water levels

Transformation into standard-normalized variables:

C o h e s

i o n u 2F ri c t i o n angl e u1

P e r m e a b i l i t y u 3

C o h e s

i o n u 2

hmax,1 = 2.83 m

hmax,2 = 2.40 m

hmax,3 = 1.20 m

Numericalresults β1 ˜ 3.18

x

xi

Xu

σ

µ−=

→ 240 Finite-Element calculations → Return period of failure: ˜ 40,000 years

β2 ˜ 3.41

β3 ˜ 4.01



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Conclusions and Outlook

• Reliability analysis as basis for a reliable flood riskmanagement

• Comparable tendency with dike failure statistics during the

flood in 2002

• Integration of a probabilistic FE-analysis for slope instabilitieswhich regards zoned dikes and transient seepage effects

• Provision of a tool for risk-based river flood protection

• Accompanying paper at ISFD4 2008 by Merkel and Westrich



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Thank you for your attention!

Questions?

4th International Symposium on Flood Defence6-8 May, 2008, Toronto, Canada

Dipl.-Ing. A. Moellmann

Institute of Geotechnical Engineering, University of Stuttgart

Pfaffenwaldring 35, 70569 Stuttgart

Tel. ++49/ (0)711 / 685 – 63779, Email: [email protected]

Financial support: Cooperation partners:

Dam Authority of Saxony, Pirna

Regional administrative authority Tübingen

Rijkswaterstaat, Dienst Weg-en Waterbouwkunde, Delft,The Netherlands

Forschungszentrum Karlsruhein der Helmholtz-GemeinschaftProjektträger Forschungszentrum Karlsruhe

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