annual probability of exceedance - the city of nanaimo
TRANSCRIPT
Colliery Dam (Nanaimo BC) Risk Assessment by Dr. Bill Roberds
21 Jan 2014 1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1 10 100 1000 10000
An
nu
al P
rob
abili
ty o
f Ex
cee
dan
ce
Number of Fatalities
unacceptable bound
acceptable bound
Societal Safety Criteria (ref. CDA, 2013)
unacceptable
acceptable
examples of a complementary cumulative probabilitydistribution for a facility (considering all scenarios)
Develop Colliery Dams (Nanaimo BC) Plan
13 Dec 2013 Meeting Objectives - identify optimal dam rehab option plan Criteria - including (but not limited to) safety and
financial performance
Process - conduct risk assessment to appropriately evaluate potential performance (rather than worst-case scenario) of any plan, per recent dam safety guidelines
Risk assessment performance model translates inputs outputs
inherent uncertainties in inputs and in model result in uncertainties in outputs
quantify uncertainty in terms of probability
assess probability objectively or subjectively 21 Jan 2014 2
People/property/critical functions/etc. might exist within each element, but especially “downstream”
Outflow from Lower Dam can cause inundation downstream that might affect those people/property/critical functions/etc. outflow from Lower Dam consequences (safety and financial) of Lower Dam
outflow
Colliery Dam System: Elements
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Middle Reservoir
Lower Reservoir
Middle Res Watershed
Lower Res Watershed
Middle Dam
Lower Dam
Precipitation Event
Down- stream
Seismic Event
Lower Dam Release
Lower Dam outflow model
Lower Dam reservoir level Lower Dam reservoir inflow
Lower Dam res. watershed Precipitation Runoff
Middle Dam release Lower Dam storage capacity /
spillway release / overtopping release Undamaged Damaged
Breach by overtopping Seismic collapse Other (e.g., piping)
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Middle Dam outflow model
Middle Dam reservoir level Middle Dam reservoir inflow
Middle Dam res. Watershed Precipitation Runoff
Middle Dam storage capacity /
spillway release / overtopping release Undamaged Damaged
Breach by overtopping Seismic collapse Other (e.g., piping)
Safety / financial consequences
Inundation from Lower Dam release
Consequences (fatalities/damage) of inundation
Downstream Consequences
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# Peo. by Type Exp. in Area
# Peo. by Type Norm. in Area
#Fatalities (by Type, by Area)
P[Ind Fatal For Peo. Type
In Area]
Fatality Func- tions (by Type)
Depth&Velo- city in Area
Warning/Evac/ Prep in Area
Ind. Structure Values in Area
Structures by Type in Area
Timing of Failure
Damage (by Type, by Area)
p[% Damage for Struct. Type
in Area]
Damage Func- tions (by Type)
Depth&Velocity in each Area
by Downstream
Areas
Lower Dam Release
Downstream Hydro. Char.
Risk Inputs (1 of 10)
Precipitation/Hydrology/Reservoir Inflow Exceedance Frequency – Magnitude (flow rate/duration) for inflow
Middle Dam reservoir inflow Lower Dam reservoir inflow (excl Middle Dam reservoir inflow)
Status: We have precipitation frequency and hydrographs from previous studies, but will refine hydrographs (e.g., considering Nanaimo Parkway culvert) and subjectively assess uncertainties.
Reservoir Storage/Hydraulics/Outflow Storage(m3)—depth (m) – spillway (+ leakage) release (flow
rate/duration) – overtopping release (flow rate/duration) relationships Middle Dam Lower Dam
Status: We have these relationships (rating curves) from previous studies, but will refine them (e.g., considering Nanaimo Parkway culvert and spillway hydraulics) and subjectively assess uncertainties.
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Hypothetical Example Inputs
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1
10
100
1000
10000
1 10 100 1000 10000
Ave
rage
re
turn
pe
rio
d (
year
s)
Peak flood flow (m3/s)
Middle Dam flood flow
Lower Dam peak flood flow (excl Middle Dam)
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 2000 4000 6000 8000 10000
Pe
ak O
vert
op
pin
g Fl
ow
(m
3/s
)
Peak Flood Flow (m3/s)
Middle Dam
Lower Dam
Risk Inputs (2 of 10)
Seismic Load Exceedance Frequency – Magnitude (pga) relationship Status: We have this relationship from previous studies, but need to
develop site-specific seismic inputs and subjectively assess uncertainties. Dam “Failure”
Dam failure – seismic (pga) relationship Middle Dam Lower Dam
Status: We have “performance” of each dam for several pga values from previous studies. However, we will collect additional geotechnical data from the ongoing investigation (geophysics & drilling), which will be used to develop parameters for re-analysis. We need performance at several pga’s for each dam (also considering previous results) in order to subjectively develop the complete relationship (by interpolation/extrapolation), and subjective assessments of: a) the uncertainty in modeled performance; and b) the probability of failure - performance relationship and the uncertainty in that relationship. Note: not differentiating degree of dam failure.
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Hypothetical Example Inputs
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1
10
100
1000
10000
0.01 0.1 1
Ave
rage
re
turn
pe
rio
d (
year
s)
Peak seismic event (pga)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 1 2 3 4 5
Pro
bab
ility
of
Failu
re
Peak Ground Acceleration (g)
Middle Dam
Lower Dam
Risk Inputs (3 of 10)
Dam “Failure” (cont.) Dam failure/breach – overtopping (flow rate/duration) relationship
Middle Dam Lower Dam
Status: We do not have any overtopping “breach” analyses for either dam from previous studies. We need breach analyses at several overtopping values for each dam in order to subjectively develop the complete relationship (by interpolation/extrapolation), and subjective assessment of the uncertainty in that relationship.
Dam failure/breach – other causes (e.g., piping) relationship Middle Dam Lower Dam
Status: We do not have any other failure analyses for either dam from previous studies nor reliable models to do such analyses. We need subjective assessment of probability of dam failure by other causes (not seismic or overtopping, e.g., piping).
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Hypothetical Example Inputs
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0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2000 4000 6000 8000 10000
Pro
bab
ility
of
Ove
rto
pp
ing
Failu
re
Peak Overtopping Flow (m3/s)
Middle Dam
Lower Dam
Risk Inputs (4 of 10)
Lower Dam Release Magnitude (flow rate/duration) for no Lower Dam failure in
combination with No Middle Dam failure Middle Dam overtopping failure Middle Dam seismic failure Middle Dam failure by other causes (e.g., piping)
Status: We have the magnitude of releases for each dam in the absence of dam failure from previous studies, but will confirm and need subjective assessments of the uncertainties in those releases (done elsewhere).
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Risk Inputs (5 of 10)
Lower Dam Release (cont.) Magnitude (flow rate/duration) for Lower Dam overtopping failure in
combination with No Middle Dam failure Middle Dam overtopping failure Middle Dam seismic failure Middle Dam failure by other causes (e.g., piping)
Status: We do not have any overtopping “breach” analyses to determine the magnitude of release for either dam if breached, from previous studies. We need breach analyses at several overtopping values for each dam (done elsewhere) in order to subjectively develop the complete relationship (by interpolation/extrapolation) of dam release magnitude to overtopping value, and subjective assessment of the uncertainty in that relationship, for each dam.
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Risk Inputs (6 of 10)
Lower Dam Release (cont.) Magnitude (flow rate/duration) for Lower Dam seismic failure in
combination with No Middle Dam failure Middle Dam overtopping failure NA Middle Dam seismic failure Middle Dam failure by other causes (e.g., piping) NA
Status: We do not have any analyses to determine the magnitude of release for either dam if it fails due to a seismic event, from previous studies. We need to subjectively assess dam release magnitude if the dam fails due to a seismic event and the uncertainty in that release, for each dam.
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Risk Inputs (7 of 10)
Lower Dam Release (cont.) Magnitude (flow rate/duration) for Lower Dam failure by other causes
(e.g., piping) in combination with No Middle Dam failure Middle Dam overtopping failure NA Middle Dam seismic failure NA Middle Dam failure by other causes (e.g., piping) NA
Status: We do not have any analyses to determine the magnitude of release for either dam if it fails due to some other cause besides overtopping or seismic event (e.g., piping), from previous studies. We need to subjectively assess dam release magnitude if the dam fails due to some other cause besides overtopping or seismic event (e.g., piping), and the uncertainty in that release, for each dam.
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Risk Inputs (8 of 10)
Downstream Inundation Downstream inundation (depth/velocity/location) – Lower Dam
release (flow rate/duration) relationship Status: We can get downstream inundation values at relevant locations for
several Lower Dam releases from previous studies, but we need additional analyses for other Lower Dam releases in order to subjectively develop the complete relationship (by interpolation/extrapolation), and subjective assessment of the uncertainty in that relationship.
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Hypothetical Example Inputs
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0
1
2
3
4
5
6
7
8
9
10
0 2000 4000 6000 8000 10000
Inu
nd
atio
n (
de
pth
an
d v
elo
vcit
y)
Lower Dam Release (m3/s)
Location XXX
Location YYY
Risk Inputs (9 of 10)
Downstream consequences Downstream consequences – downstream inundation
(depth/velocity/location) - warning (failure mode related) relationship Properties/facilities
Downstream properties and facilities (type, location, value, and occupant type/number)
Damage (% of value) – inundation (depth/velocity) – warning relationship by type
Individual casualty (occupant probability) – damage (% of value) – warning relationships by type
Population (outside of property/facilities) Downstream populations (type, location and number) Individual casualty (by type) – inundation (depth/velocity) – warning
by type
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Risk Inputs (10 of 10)
Downstream consequences (cont.) Status: We can get relatively current inventory (type, location, value,
number) of downstream property/facilities and populations from previous studies, but we need to confirm and project into future when a failure might occur, and subjectively assess uncertainties in those values. We have the damage – inundation and individual casualty – inundation relationships from previous studies, but still need to subjectively assess effectiveness of warning and individual casualty – damage relationship, and the uncertainty in all those relationships.
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Hypothetical Example Inputs
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0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 2 4 6 8 10 12
% o
f va
lue
Inundation (depth and velocity)
Structure Type AA
Structure Type BB
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 2 4 6 8 10 12
Pro
b o
f in
div
id f
atal
ity
Inundation (depth and velocity)
Person Type aa
Person Type bb
Risk Model
Algorithms (outputs from inputs in chains) implemented in MS Excel with @Risk (commercial add-in) to do probabilistic analysis: Inputs expressed probabilistically (representing their uncertainties) Outputs calculated probabilistically (representing their uncertainties)
via Monte Carlo simulation (many possible sets of input values are generated, each with known probability, from which outputs with known probability are generated)
Simulation Sequence: Maximum precipitation and seismic events Dam(s) failure mode (each with particular lower dam release, timing and
warning/no warning) Downstream inundation and downstream population/property Downstream damage and casualties
Status: In development
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Colliery Dam Risk Assessment
Thank you! Questions?
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