David S. Bowles Institute for Dam Safety Risk Management - Utah State University and RAC Engineers & Economists 2nd International Week on Risk Analysis as Applied to Dam Safety and Dam Security Theoretical-Practical Course Universidad Politecnica de Valencia Valencia, Spain 27 & 28 February 2008 Complete Dam Risk Analysis & Detailed Applications: L.6 - Hills Creek Dam Risk Assessment: Evaluation of Flood Risk Reduction Alternatives & Uncertainty Analysis RAC Engineers & Economists Outline 1) Engineering Assessment 2) Event Trees & Loadings 3) Consequences Inputs and Breach- Inundation Analyses 4) RA Results - Existing Dam 5) RA Results – Risk Reduction Alternatives 6) Uncertainty Analysis 7) Conclusions & Recommendations
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David S. BowlesInstitute for Dam Safety Risk Management - Utah State University
and RAC Engineers & Economists
2nd International Week on Risk Analysis as Applied to Dam Safety and Dam Security
Theoretical-Practical CourseUniversidad Politecnica de Valencia
Valencia, Spain27 & 28 February 2008
Complete Dam Risk Analysis & Detailed Applications:
L.6 - Hills Creek Dam Risk Assessment:
Evaluation of Flood Risk Reduction Alternatives & Uncertainty Analysis
RACEngineers & Economists
Outline
1) Engineering Assessment2) Event Trees & Loadings3) Consequences Inputs and Breach-
Inundation Analyses4) RA Results - Existing Dam5) RA Results – Risk Reduction Alternatives6) Uncertainty Analysis7) Conclusions & Recommendations
1) Engineering Assessment
Engineering Assessment
Assessment Factor RatingFLOODConcrete Gravity SectionExternal stability N/AInternal stability N/AFoundation Piping N/AAbutment Foundation Stability (Dam Structure) N/AOverall flood capacityPMF ANPOvertopping ANPSpillway and stilling basin systemStructural Stability PHydraulic capacity ANPWalls - overtopping ANPGates - structural capacity APGate piers - structural capacity PErodibility ANPMechanical Systems APElectrical Systems PObstructions Drift and Debris ANP Failed Slopes PSill POutlet WorksPiping N/AElectrical Systems APMechanical Systems PStability Intake P Tunnel/Conduit PObstructions PEmbankmentGeotech Piping P Stability PToe erosion ANPSurface Erosion PWave action PAbutments PFoundation Piping PReservoir RimStability PLoss Of Capacity PErodibility PMines N/AInstrumentation P
Assessment Factor RatingEARTHQUAKEConcrete Gravity SectionExternal stability N/AInternal stability N/AReservoirStability PLoss Of Capacity PMining N/ASpillway and stilling basin systemStructural Stability PGates - structural capacity PGate piers - structural capacity PAppurtenancesOutlet works PEmbankmentLiquefaction APStability (includes excessive deformation) APFoundationLiquefaction APStability APFault movement PInstrumentation PNORMAL OPERATING CONDITIONSConcrete Gravity SectionFoundation sliding N/AFoundation piping N/AStresses within dam body N/AReservoirReservoir rim stability PAppurtenancesOutlet works piping POutlet works gates PEmbankmentPiping PSlope stability PFoundationPiping PStability PInstrumentation PDeterioration of Materials P
Ratings No. %Number of P: 35 71%Number of AP: 7 14%Number of ANP: 7 14%Number of (ANP): 0 0%Number of NP: 0 0%Number of (NP): 0 0%Number of N/A: 12Total: 61Number of ANP+ NP: 7 14%Number of (ANP) + (NP): 0 0%
2) Event Trees & Loadings
AEP2 - AEP3
.
.
.
AEPn-1 - AEPn
> AEPn
.
.
.
Legend
AEP1 - AEP2
Overtopping Breach
SpillwayClear
No Failure No SpillwayErosion
No Breach
Breach
No Breach
Spillway ToeErosion
Spillwayplugged
.
.
.
All Gates Open
2 Gates Open
1 Gate Open
All Gates Closed
Flood Event Tree
• Embankment Failure Modes
- Overtopping- Spillway toe erosion
(+ loss of penstock control)
• Gate failure cases- Combinations of
individual gates- Common cause failure
of all gates• Spillway plugging by
debris• Consequences
- Life loss- Economic damages
Spillway Gate Plugging by Debris
Spillway Toe Erosion
AEP2 - AEP3
.
.
.
AEPn-1 - AEPn
> AEPn
.
.
.
LegendExpanded Chance Node
Collapsed Chance Node
Consequences Node
AEP1 - AEP2
Overtopping Breach
SpillwayClear
No Failure No SpillwayErosion
No Breach
Breach
No Breach
Spillway ToeErosion
Spillwayplugged
.
.
.
All Gates Open
2 Gates Open
1 Gate Open
All Gates Closed
Flood Loading intervals
PEAK STAGE – AEP: Existing Dam – Gates 100% reliable
• Single gate- 1 in 10: Preliminary fault tree estimate- 1 in 50: Used to allow for repairs (1 in 100 – 1 in 10)- 1 in 200: After Indicative Gate Reliability Fix (1 in
1,000 – 1 in 100)
• All gates – Common Cause- 1 in 100: Preliminary fault tree estimate- 1 in 50: Used to allow for repairs (1 in 100 – 1 in 10) - 1 in 200: After Indicative Gate Reliability Fix (1 in
Limit of tolerability Existing dam Limit of tolerability New Dam & Major Augmentations Existing - Base Case50 lives
1 in 5,000 /yr
Observations on Existing Dam• Does not meet Corps flood requirements (Engineering Assessment - ANPs)• “Apparently” meets all other Corps Earthquake and Normal Operating
requirements for dam safety– Investigations needed (ANP, AP ratings)
• Probability of failure not high, but not low– Needs to be considered in context of consequences
• Potential life loss is large– Non-structural opportunities for risk reduction?
• Potential economic consequences are large• “Apparently” meets
– USBR APF/ANCOLD Individual Risk/HSE Individual Risk Guidelines: Combination of all initiating events
– HSE Societal Risk Guideline: Combination of all initiating events• “Apparently” does not meet
– USBR ALL Guideline: Flood, Earthquake & Normal Operating – ANCOLD Societal Risk Guidelines: Combination of all initiating events
• Before Existing Dam RA is used for “sign off” decision making investigations needed to:
– test failure modes, improve strength parameter estimates, conduct in-depth analyses, etc.
• Intrinsic to RA and TA (SBA) • In RA “best estimates” plus sensitivity
analysis• Limited examples of uncertainty analysis
- USBR uses for more detailed RAs- Corps draft Tolerable Risk guidelines depend
on Uncertainty Analysis
Uncertainty
• Intrinsic to RA and TA (SBA) • In RA “best estimates” plus sensitivity
analysis• Limited examples of uncertainty analysis
- USBR uses for more detailed RAs - Corps drafted guidelines that depend on
Uncertainty Analysis
Best Estimate Inputs do not in general lead to Best Estimate Outputs
SystemResponses
Consequences
Risk AnalysisModelLoadings
Uncert aint y associat ed wit h:breach paramet ers, breach flow (dept h,
velocit y), inundat ion mapping, warningt imes,damages, life loss computat ions,efficiency of evacuat ion system, et c.
Uncertainty associated with:magnitude and AEP of floods,
precipit at ion, cat chment charact erist ics,rout ing methods, magnit ude-pga-AEP
relat ionship, et c.
Uncertainty associated with:performance of various componentsof dam under flood, and earthquakeloading, and under static condition,
etc.
RA Inputs
SystemResponses
Consequences
Risk AnalysisModelLoadings
Uncert aint y associat ed wit h:breach paramet ers, breach flow (dept h,
velocit y), inundat ion mapping, warningt imes,damages, life loss computat ions,efficiency of evacuat ion system, et c.
Uncertainty associated with:magnitude and AEP of floods,
precipit at ion, cat chment charact erist ics,rout ing methods, magnit ude-pga-AEP
relat ionship, et c.
Uncertainty associated with:performance of various componentsof dam under flood, and earthquakeloading, and under static condition,
etc.
Uncertainty input distribution on flood loading - peak reservoir stage
1540
1542
1544
1546
1548
1550
1552
1554
1556
1558
1560
1.9 2.3 2.7 3.1 3.5 3.9 4.3 4.7 5.1 5.5
Standardized z-variate
Res
ervo
ir Pe
ak S
tage
(ft M
SL)
0 gate available - Best estimate 1 gate available - Best estimate2 gates available - Best estimate 3 gates available -Best estimate3 gates available - Lower bound 3 gates available - Upper bound
Distributions
1540
1542
1544
1546
1548
1550
1552
1554
1556
1558
1560
1.9 2.3 2.7 3.1 3.5 3.9 4.3 4.7 5.1 5.5
Standardized z-variate
Res
ervo
ir Pe
ak S
tage
(ft M
SL)
0 gate available - Best estimate 1 gate available - Best estimate2 gates available - Best estimate 3 gates available -Best estimate3 gates available - Lower bound 3 gates available - Upper bound
Distributions
SystemResponses
Consequences
Risk AnalysisModelLoadings
Uncert aint y associat ed wit h:breach paramet ers, breach flow (dept h,
velocit y), inundat ion mapping, warningt imes,damages, life loss computat ions,efficiency of evacuat ion system, et c.
Uncertainty associated with:magnitude and AEP of floods,
precipit at ion, cat chment charact erist ics,rout ing methods, magnit ude-pga-AEP
relat ionship, et c.
Uncertainty associated with:performance of various componentsof dam under flood, and earthquakeloading, and under static condition,
etc.
RA Inputs
0.01
0.10
1.00
1 10 100 1,000 10,000
Annual Exceedance Probability (1 in N)
Peak
Gro
und
Acc
eler
atio
n (g
)
Best estimate Lower bound Upper bound
Distribution
0.01
0.10
1.00
1 10 100 1,000 10,000
Annual Exceedance Probability (1 in N)
Peak
Gro
und
Acc
eler
atio
n (g
)
Best estimate Lower bound Upper bound
Distribution
Uncertainty input distribution on earthquake loading - PGA
SystemResponses
Consequences
Risk AnalysisModelLoadings
Uncert aint y associat ed wit h:breach paramet ers, breach flow (dept h,
velocit y), inundat ion mapping, warningt imes,damages, life loss computat ions,efficiency of evacuat ion system, et c.
Uncertainty associated with:magnitude and AEP of floods,
precipit at ion, cat chment charact erist ics,rout ing methods, magnit ude-pga-AEP
relat ionship, et c.
Uncertainty associated with:performance of various componentsof dam under flood, and earthquakeloading, and under static condition,
etc.
RA Inputs
Upp
er b
ound
Lowe
r bou
nd
Best
Estim
ate
Ove
rtop
ping
sys
tem
resp
onse
pro
babi
lity
0.25
1.00
Overtopping depth (ft)
-0.5 0.5 1.5-1.5 2.50.00
Input Distributions
Uncertainty input distribution on flood overtopping failure SRP
SystemResponses
Consequences
Risk AnalysisModelLoadings
Uncert aint y associat ed wit h:breach paramet ers, breach flow (dept h,
velocit y), inundat ion mapping, warningt imes,damages, life loss computat ions,efficiency of evacuat ion system, et c.
Uncertainty associated with:magnitude and AEP of floods,
precipit at ion, cat chment charact erist ics,rout ing methods, magnit ude-pga-AEP
relat ionship, et c.
Uncertainty associated with:performance of various componentsof dam under flood, and earthquakeloading, and under static condition,
etc.
RA Inputs
0
1000
2000
3000
4000
5000
6000
7000
1400 1420 1440 1460 1480 1500 1520 1540 1560
Reservoir peak stage (ft MSL)
Life
loss
(liv
es)
Best estimate Lower bound Upper bound
Distribution
0
1000
2000
3000
4000
5000
6000
7000
1400 1420 1440 1460 1480 1500 1520 1540 1560
Reservoir peak stage (ft MSL)
Life
loss
(liv
es)
Best estimate Lower bound Upper bound
Distribution
RA Inputs - Uncertainty input distribution on dam failure life loss
1.0E-06
1.0E-05
1.0E-04
1.0E-03
0 10 20 30 40 50 60 70 80 90 100
Percentiles
Prob
abili
ty o
f Fai
lure
(/ye
ar)
Existing dam Widen spillway RCC spillwayUSBR Interim Tier2 Existing dam - deterministic Widen spillway - deterministicRCC spillway - deterministic
USBR APF (Tier 2)- Tot. Prob. Fail.
1x10-4 /yr
EXISTING DAM• Deterministic (Best Est
Inputs) 3.5x10-5 /yr• 25th percentile• Mean
7x10-5 /yrS/W FIXES• Widen • RCC
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
0 10 20 30 40 50 60 70 80 90 100
Percentiles
Ann
ualiz
ed In
crem
enta
l Life
Los
s(li
ves/
year
)
Existing dam Widen spillway RCC spillwayN-StrongL&S N-StrongL Existing dam - deterministicWiden spillway - deterministic RCC spillway - deterministic
USBR ALL (Tier 1) - Flood- Inc. Ann Life Loss
1x10-2 & 1x10-3 lives/yr
EXISTING DAM• Deterministic (Best Est
Inputs) 1.2x10-2 /yr• 20% confid. 1x10-2
• <1% confid. 1x10-3
S/W FIXES• Widen: 4th gate• 70% &
10% confid • RCC• 97% &
70% confid
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1 10 100 1000 10000
Incremental Number of Fatalities
Ann
ual E
xcee
danc
e Pr
obab
ility
of
Incr
emen
tal N
umbe
r of F
atal
ities
Limit of tolerability Existing dam Existing - Base Case Widen Spillway RCC Spillway
- 30% confid. that HSE guidelines would justify risk reduction
• Mean R:- Widen S/W (4th gate): - R = 25- RCC S/W:- R = 23
Divide R by 3 on plots
Widen S/W RCC S/W
Some thoughts on Uncertainty Analysis
• Best Estimate Inputs do not in general lead to Best Estimate Outputs
• Confidence in meeting Tolerable Risk Guidelines- Valuable insights into reality of uncertainty- Adds to challenge of interpretation and understanding- Corps of Engineers draft Tolerable Risk guidelines
based on confidence
• Guidelines for consistent uncertainty analysis• USBR using in detailed RAs
7) Conclusion & Recommendations
Observations on Risk Reduction Alternatives• Flood alternatives:
– Potential for risk increases• Flood “disbenefits”• Raise leads to increase in toe erosion probability
– Strength of risk-based justification:• ALARP strength of justification: very high – poor for individual
SCUPs• B/C > 1.0: Debris boom (1.4) and Indicative gate reliability (2.7)• HSE Disproportionality justifies Debris boom and Indicative gate
reliability• Residual Risk Evaluation
– Only RCC spillway “appears” to meet USBR ALL Guideline– Earthquake and Normal Operating “appear” not to meet USBR
ALL• Where to go from here?
1) Investigations (ANP, AP ratings)2) What structural OPTIONS to consider in ALARP evaluation for
Flood, EQ & NOC?3) What non-structural OPTIONS to consider in ALARP evaluation
for Flood, EQ & NOC?
Risk-informed Approach
Traditional Engineering Standards Approach
Risk Assessment Approach
Engineering Assessment – EA (TA – Traditional Approach to Reservoir Safety)