Transcript The “Dam Safety Case” - Corps Risk Analysis Gateway

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Risk modeling
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Principles
• What is probabilistic risk analysis (PRA)?
– Structured approach to identifying failure
modes and analyzing their effects
– Accounting scheme for combining
uncertainties
– Approach to reasoning about uncertainties
using the math of probability.
• What it is not …
–Inherently different from traditional practice
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Risk models
Hazard
Vulnerability
Loss
Inventory
•Some of the hazards (perils) modeled:
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Earthquakes
Floods
Hurricanes
Fire, wildfire, conflagration
Tornados
Tsunamis
Landslides
Extreme weather
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Exceedance Probability
Annual exceedance probability (AEP)
AEP = Annual probability of an
event or consequence greater
than a given level.
p
L
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History
•The reason we use PRA is because we
don’t have enough data.
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History
•The reason we use PRA is because we
don’t have enough data.
•The reason we use PRA is because people
have (very) poor intuition about probability.
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Approaches to hazard modeling
1. Where most of the work is done for CAT models
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Seismic
Hurricane
Flood
Fire
Hazard
Vulnerability
Loss
Inventory
2. Approach
I. Spatial statistical model of occurrence
II. Historical frequency model of severity
III. Spatial model of effect at a particular site
• (Note: there may by a difference between
frequency of event and frequency of effect)
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Earthquake risk
Source: Jones, K. 2003 Willis Limited
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Wind risk
offset
wind speed
pressure
the USAID Office of Foreign
Disaster
Assistance
and the Caribbean Regional Program
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Wildfire outbreak risk
Virginia Department of Forestry
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Approaches to inventory modeling
• Geospatial databases (GIS)
• Biggest advance in recent years; changing quickly
• Mostly publicly available records (e.g., HAZUS)
– Impacted by DHS concerns
• Many web-based (free or cheap) tools
Hazard
Vulnerability
Inventory
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Loss
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Approaches to vulnerability
(reliability) modeling
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Failure modes and effects analysis (FMEA)
Event tree analysis
Fault tree analysis
Stochastic simulation (Monte Carlo)
Hazard
Vulnerability
Inventory
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Principles
•Levels of probabilistic reasoning
Ideal: theoretical
understanding
with many data
Model Completeness
Purely theoretical,
with few or no data
Little understanding,
few or no data
Theoretical
Assessment
Model-based
Assessment
Guess
Statistical
Assessment
Data Completeness
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Little understanding,
but many data
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FMEA
•Failure Modes and Effects Analysis
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FMEA
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FMEA
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FMEA
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Event trees
upstream shell
rip rap
core
filter
downstream shell
filter
Simple representation of earth dam system
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Dam Safety
•Reasons for Dam Failures
– OVERTOPPING ~ 35% of all failures
• Inadequate Spillway Design
• Debris Blockage of Spillway
• Settlement of Dam Crest
– FOUNDATION DEFECTS ~ 30% of all failures
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Differential Settlement
Sliding and Slope Instability
High Uplift Pressures
Uncontrolled Foundation Seepage
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Dam Safety
• Reason for Dam Failures
– PIPING AND SEEPAGE ~ 20% of all failures
• Internal Erosion Through Dam Caused by Seepage"Piping"
• Seepage and Erosion Along Hydraulic Structures Such as
Outlet
• Conduits or Spillways, or Leakage Through Animal
Burrows
• Cracks in Dam
– CONDUITS AND VALVES ~ 10% of all failures
• Piping of Embankment Material Into Conduit Through
Joints or Cracks
– OTHER ~ 5% of all failures
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Event trees
Generic event tree (US NRC 1975).
Initiating Event
S ys tem 1
S uc c es s S tate
(S 1)
Initiating Event
(I)
Failure S tate
(F 1)
S ys tem 2
A cc ident
S equenc es
S uc c es s S tate
(S 2)
(IS 1S 2)
Failure S tate
(F 2)
(IS 1F 2)
S uc c es s S tate
(S 2)
(IF 1S 2)
Failure S tate
(F 2)
(IF 1F 2)
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Event trees
Simple event tree for an embankment dam
Initiating Event
Foundation
liquefaction
None
(S 1 )
Earthquake
(I)
Liquefiable soil
(F 1 )
Embankment
cracking
Accident
Sequences
No cracking
(S 2 )
(IS 1 S 2 )
Cracking
(F 2 )
(IS 1 F 2 )
No cracking
(S 2 )
(IF 1 S 2 )
Cracking
(F 2 )
(IF 1 F 2 )
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Event Trees
Initiating Event
Foundation
liquefaction
Embankment
cracking
No cracking
0.95
None
Pr=0.9
Earthquake
Pr=0.01
Liquefied soil
Pr=0.1
Accident Sequence
Earthquake - no liquefied soil - no cracking
Pr = 0.01 x 0.9 x 0.95 = 8.55 E -03
Cracking
0.05
Earthquake - no liquefied soil - cracking
Pr = 0.01 x 0.9 x 0.05 = 0.45 E -03
No cracking
0.67
Earthquake - liquefied soil - no cracking
Pr = 0.01 x 0.1 x 0.67 = 0.67 E -03
Cracking
0.33
Earthquake - liquefied soil - cracking
Pr = 0.01 x 0.1 x 0.33 = 0.33 E -03
Dependence of Probabilities on earlier events
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Event trees
Annualized
initiating
ev ent
Probability of failure
Annualized
initiating
ev ent
Ev ent
Tree
Annualized initiating event generates input
Fragility
curv e
Load
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Event Trees
5
6
die 2
3 4
Sample space
Event trees = sample space
1
2
Simple event
die 1
1
2
3
4
5
6
earthquake
magnitude > m
soil liquefies
earthquake of
magnitude > m
soil
liquefies
soil does not
liquefy
earthquake
magnitude < m
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Event Trees
Initiating Event
Success State
(S1)
Leaf
  
States of Nature



Logic Tree
System 1
Initiating Event
(I)
Failure State
(F1)
System 2
Success State
(S2)
(IS 1S2)
Failure State
(F2)
(IS 1F2)
Success State
(S2)
(IF1S2)
Failure State
(F2)
(IF1F2)
Event Tree
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Accident
Sequences
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Event Trees
Event Tree
Consequence Tree
Logic Tree
States of Nature
Sys tem Events
Cons equenc es
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Event Trees
W ater level
above c res t
Overtopping
E xtrem e
s torm
< 50%
of c res t
Failure
P iping
oc c urs
S tringers
exis t
Duration
>week
No
Failure
No piping
oc c urs
S tringers
do not exist
50%-100%
of c res t
Duration
<week
High pore
pres s ure
S oft s oil
fill
Duration
>week
Geotec hnic al
Failure
No
Failure
Low pore
pres s ure
Good s oil
fill
50%-100%
of c res t
Duration
<week
Hydrologic, piping, and strength failure parts of the levee failure event trees
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Influence diagrams
river stage (water height)
Potential failure surface
Lev ee
Floodway
sand boil
flow path through lens
possible sand lens
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Event Trees
Ext reme
R ainfall
Piping
Flood
Duration
T
Influence diagram for levee
failure
Sand
Stringer s
Exist
Loss of
Containment
Pore
Pr essur e
Peak
Discharge
Q
Weak
Soil
Fill
Static
Strength
Failure
River
Stage
H
Overtopping
Levee
Floodway
sand boil
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Event Trees
Extreme
Rainfall
Piping
Flood
Duration
T
Influence diagram for levee
failure, including active
decision node
Sand
Stringer s
Exist
Loss of
Containment
Pore
Pr essur e
Peak
Discharge
Q
Weak
Soil
Fill
River
Stage
H
Static
Strength
Failure
Overtopping
Release
Water
Levee
Floodway
no
failure
sand boil
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Event Trees
debris 0m
dam overtopping
0-1m
1-2m
stilling basin
undermining
scour under
sheet piles
dam breach
none
stilling basin
collapse
intact
dam breach
none
slab uplift
dam breach
none
no scour
median
inflow
excess drain
inflow
spillway uplift
Partial event tree for
hydrologic failure at Alouette
Dam (Salmon 1995)
none
no excess
debris plugging
creek
creek scourng
bank erosion
splwy clps
none
none
none
sillway wall
overtopping
degris plugging
spillway channel
none
overtoping,
erodes slab
none
overtoping
erodes slab
none
dam breach
none
dam breach
none
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dam breach
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Dam Safety
•Different approaches of the various owners
and regulators
–Bureau of Reclamation
–US Army Corps of Engineers
–New South Wales (Austl)
–Canadian Electricity Association
• Dam Safety Interest Group
– BCHydro, OPG, HydroQuebec, Vattenfall,
Scottish & Southern Energy
• Ontario Ministry of Natural Resources & OPG
–Department of Environment and Rural Affairs (DEFRAUK)
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Glenmaggie Dam
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Fault tree analysis
TE
Top Ev ent
AND
S1
Sub-sy stem
S1
Sub-sy stem
OR
OR
T1
Sub-sy stem
A
T2
Sub-sy stem
C
AND
OR
B
C
A
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Fault tree analysis
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Fault trees
Dam
Breached
AND
Overtopping
Factor
Exceeded
Dam
Overtopped
OR
Water
Levek too
High
OR
Design
Flood
Exceeded
Crest Settles
Below Water
Level
Crest Eroded Below
Water Level
AND
Spillway
Fails
Crest
Eroded
AND
No A ction
Taken
Crest
Settles
OR
OR
Gates
Closed
Spillway
Blocked
OR
Operator
Error
Equipment
Malfunction
No A ction
Taken
Foundation
Settles
Foundation
Erodes
OR
Blocked
by Food
Debris
Fill
Consolidates
OR
Blocked
Prior to
Flood
Foundation
Erodes
Fault tree of dam failure (Fry 2001)
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Filter
Inadequate
Foundation
Cracks
Fill
Erodes
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Approaches to consequence
modeling
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Economics (NED)
Loss of life/property
Environmental
Historical
Hazard
Vulnerability
Inventory
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