Download Report

Fragility Curves
Jonathan Simm
Flood Management Group, HR Wallingford
Practitioner workshop on asset management
Questions/topics addressed in presentation
1. What is a fragility curve (and how do
fragility curves relate to design thinking)?
2. Why are fragility curves important in FRM?
3. Generalised fragility curves (with ref. to
asset types and condition grades)
4. Challenging accuracy of generic curves.
5. Generating bespoke fragility curves
6. Conclusions
Page 2
1
1. What is a fragility curve?
Answer:
A curve which expresses the probability of
failure of a defence as a function of the loading
Page 3
Estimating fragility curves (Simm et al, 2008)
Standard of protection
provided by defence
Probability of
defence failure
Difference relates to
factor of safety in design
100%
1.0
Typically
assumed fragility
curve
‘True’ fragility
50%
5% to 10%
0
0
Severity of load event
Page 4
2
Establishing fragility different from design
Strength
Rrep
R
Load
  S S rep
partial load factors
Statistical variability reflected by setting design values
a certain number of standard deviations away from the
mean:
R  k 
rep
R
R
R
S rep   S  k S  S
To generate fragility curves we must change approach
and use the mean values. (Otherwise, for example, we
would not get pf = 50% when FS=1)
Page 5
Fragility curve - uncertainty
Page 6
3
Better data/models reduce uncertainty
Increasing
certainty in
defence
performance
Pf
load
Pf
load
Increased
defence data
and analysis
Pf
load
Page 7
Questions/topics addressed in presentation
1. What is a fragility curve (and how do
fragility curves relate to design thinking)?
2. Why are fragility curves important in FRM?
3. Generalised fragility curves (with ref. to
asset types and condition grades)
4. Challenging accuracy of generic curves.
5. Generating bespoke fragility curves
6. Conclusions
Page 8
4
Fragility curves in flood system analysis
Pathway
(e.g. beach, raised/non-raised
Receptor
defence and floodplain)
(e.g. people and property)
Source
(River or sea)
Page 9
Fragility curves importance in FRM
• In flood systems analysis
• In determining flood risk attributable to individual
defences
• In providing a rigorous discipline for understanding
our flood defences
Page 10
5
Questions/topics addressed in presentation
1. What is a fragility curve (and how do
fragility curves relate to design thinking)?
2. Why are fragility curves important in FRM?
3. Generalised fragility curves (with ref. to
asset types and condition grades)
4. Challenging accuracy of generic curves.
5. Generating bespoke fragility curves
6. Conclusions
Page 11
Asset typology
Asset typology:
Flood
defences
Fluvial
Type 1
Vertical
wall
Type 2
Slope or
embankment
Type 3
High
ground
Coastal
Type 4
Culverts
Type 5
Vertical
seawall
Type 6
Sloping
seawall /
dyke
Type 7
Beach
Within this framework there are 61 asset types.
For each type, a generic fragility curves is
available for each of 5 condition grades.
Page 12
6
Example generic fragility curves
(cf. presentation on condition assessment)
HLM+ Fragility curve - Condition Grades 1 to 5
(Central estimates)
1.0
P (breaching¦feeboard)
0.9
0.8
0.7
Condition grade1
Condition grade2
Condition grade 3
Condition grade4
Condition grade 5
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Overflow head (Water level - crest level)
WL < CL
WL > CL
Page 13
Example generic fragility curves
(cf. presentation on deterioration)
HLM+ Fragility curve - Condition Grades 1 to 5
(Central estimates)
1.0
P (breaching¦feeboard)
0.9
0.8
0.7
Condition grade1
Condition grade2
Condition grade 3
Condition grade4
Condition grade 5
0.6
0.5
Structure 0.4
Deterioration0.3
0.2
0.1
0.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Overflow head (Water level - crest level)
WL < CL
WL > CL
Page 14
7
Questions/topics addressed in presentation
1. What is a fragility curve (and how do
fragility curves relate to design thinking)?
2. Why are fragility curves important in FRM?
3. Generalised fragility curves (with ref. to
asset types and condition grades)
4. Challenging accuracy of generic curves.
5. Generating bespoke fragility curves
6. Conclusions
Page 15
New science to improve fragility curves
• FloodProBE workpackage 3 addressing:
− Internal erosion (piping etc)
− External erosion of grass cover (riverine)
- Asset Performance Tools
− Extension of RELIABLE fragility curve generation tool to
cover most asset types and most failure modes
− Overtopping research to look at coastal grass cover erosion
− Guidance for practitioners
Page 16
8
Questions/topics addressed in presentation
1. What is a fragility curve (and how do
fragility curves relate to design thinking)?
2. Why are fragility curves important in FRM?
3. Generalised fragility curves (with ref. to
asset types and condition grades)
4. Challenging accuracy of generic curves.
5. Generating bespoke fragility curves
6. Conclusions
Page 17
How to create a specific fragility curve?
BASIC STEPS:
1. Identify and analyse all relevant failure modes (key issue
emerging in production of International Levee Handbook)
2. Identify Limit State Equations (LSE) or models for all
failure modes and recast them in reliability format:
Z (reliability) = R (strength) – S (loading)
3. Prepare schedule of engineering parameters and their
uncertainties.
4. Prepare fault trees that specify the logical sequence of all
possible mechanisms leading to defence failure.
5. Perform many reliability analyses, for a single hydraulic
loading across range of parameter uncertainties (MonteCarlo sampling). For each loading analysed, probability of
failure is proportion of times that Z < 1 . Repeat for other
hydraulic loadings and draw the resulting fragility curve.
Page 18
9
Variation in Ave Factor of Safety with River Level.
TE2100
embankment
example
(SLOPE-W)
Average Factor of Safety
2.9
2.4
1.9
1.4
0.9
0.4
Variation in Probability of Failure with River Level
3.0
4.0
5.0
Probability of Failure (%)
90.0
80.0
6.0
7.0
8.0
9.0
10.0
River Level (mOD)
100.0
With Surcharge
Without Surcharge
Existing Crest Level
Critical PWP under Virgin Marsh
Design Water Level
Deterministic With Surcharge
Critical PWP under Berm
Deterministic Without Surcharge
70.0
60.0
50% failure probability
for FOS = 1.0
50.0
40.0
30.0
20.0
10% failure probability
at design extreme event
10.0
0.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
River Level (mOD)
Page 19
With Surcharge
Without Surcharge
Existing Crest Level
Critical PWP under Virgin Marsh
Design Water Level
Deterministic Analysis
Critical PWP under Berm
Reliability analysis – multiple failure modes
Can combine using De Morgan’s Law
Pr( f )  1  {[1  Pr( f r )]  [1  Pr( f s )]}
if failure modes are independent
Example: embankment
High water breach
If not, better to use RELIABLE tool
generated under FLOODsite and UK
FRMRC projects
Erosion of embankment
surface by overflow
(Ba 1.1)
SLOPEW
Page 20
10
Combined fragility curve
High water breach
EX8 All condition Grades
1.2
Erosion of embankment
surface by overflow
(Ba 1.1)
CG1
CG2
CG3
CG4
CG5
1
SLOPEW
P(failure¦freeboard)
0.8
0.6
0.4
0.2
0
-1.5
-1
-0.5
0
0.5
1
Freeboard (m)
Page 21
Intermediate way to generate fragility curves
• Thames estuary (TE2100) studies adopted this approach
rather than using generic curves:
− Higher than national average defences
− Composite structural defence forms
− Complex geology with artesian pressures
• Adaptation of ‘exemplar’ curves to other sites based on:
− Comparisons of forms of defences around estuary
− National defence categories for exemplar and other defences
Elevation (mOD)
30
25
20
15
10
5
10
0
1
9
4
5
-5
2
7
3
6
8
-10
-15
Page 22
80
100
120
140
160
180
200
220
240
260
280
11
Questions/topics addressed in presentation
1. What is a fragility curve (and how do
fragility curves relate to design thinking)?
2. Why are fragility curves important in FRM?
3. Generalised fragility curves (with ref. to
asset types and condition grades)
4. Challenging accuracy of generic curves.
5. Generating bespoke fragility curves
6. Conclusions
Page 23
Who can use fragility curves?
• Engineers and researchers
− who create generic and bespoke fragility curves
− who use the curves in flood risk systems modelling
− who want to enhance conventional analysis of asset failure
modes by providing information about uncertainty in
deterministic factors of safety (Duncan, 2000)
• Operational flood risk management personnel
− need to understand the basic concept
− will use the curves indirectly because of their embedment
within operational tools (UK example ‘RAFT’)
– next presentation by Marta Roca will explain this
− and within systems analysis tools
– presentations in final session will explain this
Page 24
12
Conclusions
• Fragility curves are a fundamental tool in flood risk
management. They
− express the varying probability of breach of levees with load
− allow flood systems analysis to properly include the effect of
defences
− can be generalised for broad scale analysis of bespoke for local
system or project analysis
• Demystifying the basic concept for non-experts is
worthwhile so that they can be used in operational tools
• Contributions of shared experiences on fragility and more
generally on the performance, design, and management
of levees are sought for the International Levee Handbook
www.leveehandbook.net
Page 25
References
• Simm, J., Gouldby, B., Sayers, P., Flikweert, J, Wersching,
S. and Bramley, M. (2008) Representing fragility of flood and
coastal defences: getting into the detail. Proc. Eur, Conf. on
Flood Risk Management: Research into Practice
(FLOODrisk 2008). London: Taylor & Francis, 621-631.
• Flikweert, J. and Simm J. (2008) Improving performance
targets for flood defence assets. J Flood Risk Management
1, 201–212.
• Simm, J. and Flikweert, J. (2009) PAMS (Performance-based
Asset Management System) – Phase 2: Development of
fragility curves for use in management of flood defence
assets. Report SC040018/SR5. Environment Agency
• Schultz, M., Gouldby, B., Simm, J. and Wibowo, J. (2010)
Beyond the factor of safety: developing fragility curves to
characterize system reliability. USACE ‘white paper’ ERDC
SR-10-1.
Page 26
13
The Use of Fragility Curves for UK Flood
Defences and their Implications for Flood Risk
Management
Jonathan Simm
Flood Management Group, HR Wallingford
14