isfd4 moellmann core
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8/3/2019 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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Case study Elbe river
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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Case study Elbe river
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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Case study Elbe river
Comparison to Elbe flood 2002 - dike failure statistics (Horlacher, 2005)
Overflow / Overtopping
Uplift / Piping
Slope instability
47 %
24 %
29 %
Overflow / Overtopping
Uplift / Piping
Slope instability
6 %
28 %
66 %
Relative failureprobability (PC-Ring)
29 %
24 %
47 %
Dike failurestatistics
Slope instability
Uplift / Piping
Overflow / Overtopping
Failure mode
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Case study Elbe river
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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Probabilistic Finite-Element Analysis
of embankment stability
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
Probabilistic Finite-Element Analysis
of embankment stability
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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Probabilistic Finite-Element Analysis
of embankment stability
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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Probabilistic Finite-Element Analysis
of embankment stability
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: axel.moellmann@igs.uni-stuttgart.de
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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