Post on 26-Apr-2020
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
150015051510151515201525153015351540154515501555156015651570
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5.0
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6.0
z-variate
Peak
Sta
ge (f
t MSL
)
Obs data Extrapolation Top of Dam Top of Parapet Wall
0G Fail 1G Fail 2G Fail 3G Fail
Raised_0G Fail Raised_1G Fail Raised_2G Fail Raised_3G Fail
WidenSp_w /o PP_0G Fail WidenSp_w ith PP_0G Fail RCCSp280ft_0G Fail RCCSp280ft_1G Fail
RCCSp280ft_2G Fail RCCSp280ft_3G Fail RCCSp455ft_0G Fail RCCSp455ft_1G Fail
RCCSp455ft_2G Fail RCCSp455ft_3G Fail
PMF 1 in 106Historical
Full PoolOvertopping
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
Gate failure to open cases
Per demand reliabilities
• 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
1,000 – 1 in 100)
PEAK STAGE – AEP: Existing Dam & 5 ft Raise
1540154115421543154415451546154715481549155015511552155315541555155615571558155915601561156215631564
2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0
z-variate
Peak
Sta
ge (f
t MSL
)
Extrapolation Top of Dam Top of Parapet Wall 0G Fail 1G Fail 2G Fail
3G Fail Raised_0G Fail Raised_1G Fail Raised_2G Fail Raised_3G Fail
0 F1 F2 F3 F
a1 - a2
.
.
.
.
.
.
LegendExpanded Chance N
a2 - a3
No Liquefaction
No Failure
Intervention -No Breach
No Intervention- Breach
Overtopping Breach
an-1 - an
> an
El1 - El2
.
.
.
PGA
ReservoirElevation
El2 - El3
Eln-1 - Eln
> Eln
No Failure
SlopeInstability
SEC failure(Seepage Erosionthrough Cracks)
Loss of CrestElevation
Liquefaction No FailureNo SlopeInstability
Earthquake Event Tree
• Embankment Failure Modes
- Liquefaction• Sudden Overtopping• Delayed Seepage
Erosion Through Cracks (SEC)
– Intervention?
• Consequences- Life loss- Economic damages
a1 - a2
.
.
.
.
.
.
LegendExpanded Chance Node
Collapsed Chance Node
Consequences Node
a2 - a3
No Liquefaction
No Failure
Intervention -No Breach
No Intervention- Breach
Overtopping Breach
an-1 - an
> an
El1 - El2
.
.
.
PGA
ReservoirElevation
El2 - El3
Eln-1 - Eln
> Eln
No Failure
SlopeInstability
SEC failure(Seepage Erosionthrough Cracks)
Loss of CrestElevation
Liquefaction No FailureNo SlopeInstability
Earthquake Loading intervals
Reservoir Loading intervals
Stage-Duration
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1400.00 1420.00 1440.00 1460.00 1480.00 1500.00 1520.00 1540.00 1560.00
Reservoir Stage (ft MSL)
Perc
ent D
urat
ion
Earthquake Loading
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
0.01 0.1 1 10
Peak Ground Acceleration
Ann
ual E
xcee
danc
e P
roba
bilit
y
Best estimate Low er bound Upper bound
3) Consequences Inputs and Breach-Inundation Analyses
Consequence Areas
Oakridge area
Lowell-Dexter-Jasper areas
Springfield-Eugene
Recreation & Isolated areas
Downstream areasGoshen –Creswell areas
NMiddle Fork
Coast Fork
Willamette
Hills Creek
DexterLookout Point
Summary of Economic Damages - Flood Overtopping Failure & No Failure
Failure/No Failure– Reservoir Level (No. gates failed)
Higher Projection($M)
Lower Projection($M)
DCF(0) - 1548 61,615 47,649DCF(0)nf 59,796 46,359
DCF(1) - 1548 90,063 69,087DCF(1)nf 56,810 44,065
DCF(2) - 1548 84,547 64,889DCF(2)nf 4,501 4,500
DCF(3) - 1548 75,186 57,693DCF(3)nf 3,034 3,033
Summary of Economic Damages- Flood, Normal Operating & Earthquake Failure
ModesFailure Mode
– Reservoir levelHigher Projection
($M)Lower Projection
($M)
Toe Erosion -1543
76,368 58,598
Piping - 1543 72,890 55,876Slope Stability -
154374,447 57,029
EQ(1) - 1541 72,704 55,725EQ(2) - 1500 47,401 36,710EQ(3) - 1450 35 28EQ(4) - 1425 27 21
Warning time• Warning time = Travel time +/– Warning Time Adjustment• Adjustment Time depends on failure timing-detection-
decision-notification-warning conditions - estimated by Engineering Team
Hills Creek Warning Time Adjustments
Event case Day Exposure Night Exposure
Dam Crest Flood > 200 minutes > 200 minutes
Earthquake -30 to -120 minutes -30 to -120 minutes
Normal Operating Condition
0 to 120 minutes -30 to -120 minutes
Life Loss Estimates – Graham Method Flood Overtopping Failure & No Failure
Failure/No Failure Event
Best Estimate
Lower Estimate
Higher Estimate
DCF(0) 2,229 370 4,457DCF(0)nf 2,188 363 4,376DCF(1) 3,100 516 6,201
DCF(1)nf 2,115 351 4,230DCF(2) 3,039 506 6,077
DCF(2)nf 215 35 430DCF(3) 2,667 444 5,334
DCF(3)nf 186 31 372
Life Loss Estimates – Graham MethodPiping, Slope Stability and Earthquake Failures
Event (WT Adjustment)
Best Estimate Event Case (WT Adjustment)
Best Estimate
TOE EROSION 2,843 SLOPE ST.: -120 NIGHT
2,954
PIPING: 0 DAY 2,577 EQ(1): -30 DAY OR NIGHT
2,595
PIPING:120 DAY 2,576 EQ(1): -120 DAY OR NIGHT
2,886
PIPING: -30 NIGHT 2,605 EQ(2): -30 DAY OR NIGHT
1,806
PIPING: -120 NIGHT 2,907 EQ(2): -120 DAY OR NIGHT
2,047
SLOPE ST.: 0 DAY 2,624 EQ(3): -30 DAY OR NIGHT
247
SLOPE ST.: 120 DAY 2,623 EQ(3): -120 DAY OR NIGHT
492
SLOPE ST.: -30 NIGHT
2,650 PIPING: -120-NIGHT REC. SEASON
2,939
4) Risk Assessment Results -Existing Dam
Existing Dam Results
(a) (b) (c) (d) (e) (f) (g)Risk Reduction Risk Reduction Total Benefit: Annualized Incremental
benefit cost economic Cost life losscost
(/yr) % ($/yr) % ($/yr) ($/yr) ($/yr) (-) (lives/yr) %E-B: Existing - Base Case
Flood 9.4E-06 27% 317,612$ 20% 317,612$ 0.012 18%Earthquake 1.6E-05 47% 646,653$ 41% 646,653$ 0.030 45%Normal Operating 9.3E-06 26% 605,469$ 39% 605,469$ 0.025 37%Total 3.5E-05 100% 1,569,733$ 100% 1,569,733$ 0.067 100%
Probability of failure Incremental risk cost
(j) (k) (l) (m) (n) (o) (p) (q)No Failure Reduction No Failure ReductionFlood Ann. in Flood Flood Ann. in Flood
Minimum Maximum Minimum Maximum Damages Benefits Life Loss Benefits($M) ($M) (lives) (lives) ($/yr) ($/yr) (lives/yr) (lives/yr)
222 75,476 4 2,893 3,897,565$ 0.21024 64,755 345 2,789
64,383 65,738 2,577 2,829 3,897,565$ 0.210
Life LossIncremental Damages Incremental
USBR APF USBR ALL
Existing Dam Hills
Creek Dam
ANCOLD (2003)
Societal Risk
Guideline (F-N)
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
Annu
al 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
Existing Dam – Risk Evaluation
• USBR ALL– Flood > 0.01 lives/yr– EQ > 0.01 lives/yr– NOC > 0.01 lives/yr
• USBR APF/ HSE & ANCOLD Individual < 1 in 10,000 /yr
• ANCOLD Societal above F-N limit line
• HSE Societal < 1 in 5,000 for > 50 lives
ANCOLD (2001) Revised Interim
Societal Risk Criteria
Limit of tolerability
Existing dam
Limit of tolerabilit
y New Dam & Major
Augmentations
CRF 0.062201563 0.01-$ 0.1 1.00E-03 1.00E-04
13
1030 1.00E-05 1.00E-06
100300 1.00E-05 1.00E-06
1000 1.00E-05 1.00E-0610000
ANCOLD (2001) Revised Interim Societal Risk Criteria
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 I
ncre
men
tal N
umbe
r of F
atal
ities
Limit of tolerability Existing dam Limit of tolerability New Dam & Major Augmentations Existing - Base Case
ANCOLD (2001) Revised Interim Societal Risk Criteria
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 I
ncre
men
tal N
umbe
r of F
atal
ities
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.
5) Risk Assessment Results –Risk Reduction Alternatives
Widen spillway –4th gate + 5 ft raise
280 ft RCC spillway + fuse plug + 5 ft raise
Toe channel Improved Gate
reliability
Debris control
92% PMF with full freeboard AEP of DCF: 1.6x10-6
Summary of Results & EvaluationsRisk
ReductionRisk
Reduction Benefit/ (ACSLS) Disproportionality ANCOLD HSE
Flood Earthquake Normal Operating Total Flood Earthquake Normal
Operating Total Flood Earthquake Normal Operating Total benefit cost Cost Ratio Ratio Societal Societal
USBR Tier 2
USBR Tier 1
USBR Tier 1
USBR Tier 1
E-B: Existing - Base Case 9.4E-06 1.6E-05 9.3E-06 3.5E-05 0.012 0.030 0.025 0.067 317,612$ 646,653$ 605,469$ 1,569,733$ -$ -$ N Y-ALARP?
E-SAEPLimit: Existing - Sensitivity 9.4E-06 2.0E-05 9.3E-06 3.9E-05 0.012 0.036 0.025 0.074 317,612$ 781,607$ 605,469$ 1,704,688$ (134,955)$ -$ N Y-ALARP?
BIToe: Toe channel 9.3E-06 1.6E-05 9.3E-06 3.5E-05 0.012 0.030 0.025 0.067 312,876$ 646,653$ 605,469$ 1,564,997$ 4,736$ 157,148$ 0.030 7.62E+08 381 N Y-ALARP?BIDebris: Debris boom 7.3E-06 1.6E-05 9.3E-06 3.3E-05 0.012 0.030 0.025 0.067 310,091$ 646,653$ 605,469$ 1,562,212$ 7,521$ 5,301$ 1.419 N Y-ALARP?BIGate: Gate reliability 5.5E-06 1.6E-05 9.3E-06 3.1E-05 0.004 0.030 0.025 0.059 93,743$ 646,653$ 605,469$ 1,345,864$ 223,869$ 83,435$ 2.683 N Y-ALARP?BIRaise: Raise 1.1E-05 1.6E-05 9.3E-06 3.6E-05 0.017 0.030 0.025 0.072 431,572$ 646,653$ 605,469$ 1,683,693$ (113,960)$ 72,635$ N Y-ALARP?BIWiden: Widen Spillway 7.2E-06 1.6E-05 9.3E-06 3.3E-05 0.011 0.030 0.025 0.066 280,470$ 646,653$ 605,469$ 1,532,592$ 37,142$ 1,038,079$ 0.036 7.67E+08 383 N Y-ALARP?BIRCC280: RCC Spillway 280ft & Raise 2.2E-06 1.6E-05 9.3E-06 2.8E-05 0.002 0.030 0.025 0.057 44,716$ 646,653$ 605,469$ 1,296,837$ 272,896$ 1,497,623$ 0.182 1.17E+08 58 N Y-ALARP?BIRCC455: RCC Spillway 455ft & Raise 8.7E-07 1.6E-05 9.3E-06 2.7E-05 0.000 0.030 0.025 0.056 12,381$ 646,653$ 605,469$ 1,264,502$ 305,231$ 2,274,296$ 0.134 1.67E+08 84 N Y-ALARP?
BCWiden: Widen Spillway Complete Fix 2.7E-06 1.6E-05 9.3E-06 2.8E-05 0.004 0.030 0.025 0.059 108,254$ 646,653$ 605,469$ 1,360,375$ 209,358$ 1,356,598$ 0.154 1.43E+08 71 N Y-ALARP?BCRCC280: RCC Spillway 280ft & Raise Complete Fix 9.3E-07 1.6E-05 9.3E-06 2.7E-05 0.000 0.030 0.025 0.055 9,001$ 646,653$ 605,469$ 1,261,123$ 308,611$ 1,743,507$ 0.177 1.20E+08 60 N Y-ALARP?BCRCC455: RCC Spillway 455ft & Raise Complete Fix 2.2E-07 1.6E-05 9.3E-06 2.6E-05 0.000 0.030 0.025 0.055 3,151$ 646,653$ 605,469$ 1,255,272$ 314,461$ 2,436,745$ 0.129 1.74E+08 87 N Y-ALARP?
Fix Description
Probability of failure Annualized Incremental life loss Incremental risk cost
No Failure Reduction No Failure Reduction
Flood Ann. in Flood Flood Ann. in Flood
Minimum Maxiimum Minimum Maxiimum Minimum Maxiimum Minimum Maxiimum Minimum Maxiimum Minimum Maxiimum Damages Benefits Life Loss Benefits
E-B: Existing - Base Case 222$ 75,476$ 24$ 64,755$ 64,383$ 65,738$ 4 2,893 345 2,789 2,577 2,829 3,897,565$ -$ 0.210 0.000
E-SAEPLimit: Existing - Sensitivity 222$ 75,476$ 24$ 64,755$ 64,383$ 65,738$ 4 2,893 345 2,789 2,577 2,829 3,897,565$ -$ 0.210 0.000
BIToe: Toe channel 222$ 75,476$ 24$ 64,755$ 64,383$ 65,738$ 4 2,893 345 2,789 2,577 2,829 3,903,103$ (5,538)$ 0.211 0.000BIDebris: Debris boom 222$ 76,532$ 24$ 64,755$ 64,383$ 65,738$ 4 2,914 345 2,789 2,577 2,829 4,014,464$ (116,899)$ 0.215 -0.005BIGate: Gate reliability 222$ 75,476$ 24$ 64,755$ 64,383$ 65,738$ 4 2,893 345 2,789 2,577 2,829 3,941,389$ (43,824)$ 0.212 -0.002BIRaise: Raise 222$ 70,409$ 24$ 64,755$ 64,383$ 65,738$ 4 2,828 345 2,789 2,577 2,829 3,917,236$ (19,672)$ 0.211 -0.001BIWiden: Widen Spillway 222$ 75,476$ 24$ 64,755$ 64,383$ 65,738$ 4 2,893 345 2,789 2,577 2,829 4,001,132$ (103,568)$ 0.215 -0.004BIRCC280: RCC Spillway 280ft & Raise 222$ 64,354$ 24$ 64,755$ 64,383$ 65,738$ 4 2,629 345 2,789 2,577 2,829 4,074,236$ (176,671)$ 0.218 -0.008BIRCC455: RCC Spillway 455ft & Raise 222$ 63,065$ 24$ 64,755$ 64,383$ 65,738$ 4 2,629 345 2,789 2,577 2,829 4,129,787$ (232,222)$ 0.220 -0.010
BCWiden: Widen Spillway Complete Fix 222$ 76,131$ 24$ 64,755$ 64,383$ 65,738$ 4 2,906 345 2,789 2,577 2,829 4,110,808$ (213,243)$ 0.219 -0.009BCRCC280: RCC Spillway 280ft & Raise Complete Fix 222$ 69,211$ 24$ 64,755$ 64,383$ 65,738$ 4 2,643 345 2,789 2,577 2,829 4,125,490$ (227,925)$ 0.220 -0.010BCRCC455: RCC Spillway 455ft & Raise Complete Fix 222$ 28,888$ 24$ 64,755$ 64,383$ 65,738$ 4 979 345 2,789 2,577 2,829 4,159,568$ (262,003)$ 0.221 -0.011
Fix Description
Incremental Life loss
Flood Earthquake Normal Operating Flood Earthquake Normal Operating
Incremental Damages
Divide R by 3
Benefit/Cost RatiosBenefit/Cost Ratios
0.000
0.500
1.000
1.500
2.000
2.500
3.000
BIToe: Toechannel
BIDebris:Debris boom
BIGate:Gate
reliability
BIRaise:Raise
BIWiden:Widen
Spillw ay
BIRCC280:RCC
Spillw ay280ft &Raise
BIRCC455:RCC
Spillw ay455ft &Raise
BCWiden:Widen
Spillw ayComplete
Fix
BCRCC280:RCC
Spillw ay280ft &Raise
CompleteFix
BCRCC455:RCC
Spillw ay455ft &Raise
CompleteFix
ALARP Strength of Justification Ratings for FixesAdjusted Cost per Statistical Life Saved
0.E+00
1.E+08
2.E+08
3.E+08
4.E+08
5.E+08
6.E+08
7.E+08
8.E+08
9.E+08
BIToe: T
oe ch
annel
BIDeb
ris: D
ebris
boom
BIGate
: Gate
relia
bility
BIWide
n: Wide
n Spil
lway
BIRCC28
0: RCC Spil
lway 28
0ft &
Rais
e
BIRCC45
5: RCC Spil
lway 45
5ft &
Rais
e
BCWide
n: Widen
Spillw
ay C
omplet
e Fix
BCRCC280:
RCC Spil
lway 28
0ft &
Rais
e Com
plete
Fix
BCRCC455:
RCC Spil
lway 45
5ft &
Rais
e Com
plete
Fix
$/St
atis
tical
Life
Sav
ed
Risk Reduction Measures$140M/statistical life saved$3M/statistical life saved
Poor > $140M/life
Very Strong < $3M/life
Moderate $30M -
$140M/life
Strong $3 - $30M/life
HSE Tolerability of Risk
-
5
10
15
20
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02
Probability of Life Loss before Risk Reduction Measure (Pb) (per year)
Disp
ropo
rtion
ality
Rat
io (R
)
HSE Disproportionality Ratios HSE Individual Risk Limit
R = 1.0 Strength of Tolerability Boundary
UNACCEPTABLE RISK – RISK REDUCTION REQUIRED
TOLERABLE RISK– OPTION MAY NOT
BE JUSTIFIED
INTOLERABLE RISK – OPTION
IS JUSTIFIED
Individual Risk Limit
HSE Disproportionality Ratios Disproportionality Ratios - Justification of Risk Reduction Measures
(Plots R values > 20 at R = 20)
-
5
10
15
20
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02
Probability of Life Loss before Risk Reduction Measure (Pb) (per year)
Dis
prop
ortio
nalit
y R
atio
(R)
HSE Disproportionality Ratios HSE Individual R
R = 1.0 Strength of ToleHills Creek Individual SCUPs Hills Creek - Co
Debris boom and Indicative gate reliability
Risk Reduction vs. Annualized CostReduction in Probability of Failure vs Annualized Cost
0.0E+00
1.0E-05
2.0E-05
3.0E-05
4.0E-05
5.0E-05
6.0E-05
7.0E-05
8.0E-05
9.0E-05
1.0E-04
$- $500,000 $1,000,000 $1,500,000 $2,000,000 $2,500,000
Annualized Cost of Risk Reduction ($/year)
Tota
l Pro
babi
lity
of F
ailu
re (/
year
)
IndividualFixes -SCUPs
CompletePMF Fixes
EQSensitivity - >MCE
USBR Tier 21 in 10,000per year
Reduction in Annualized Incremental Life Loss vs. Annualized Cost
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
0.080
$- $500,000 $1,000,000 $1,500,000 $2,000,000 $2,500,000
Annualized Cost of Risk Reduction ($/year)
Annu
aliz
ed In
crem
enta
l Life
Los
s (li
ves/
year
)
Total - Individual Fixes -SCUPs
Flood - Individual Fixes -SCUPs
USBR Tier 1: 0.01 lives/year
USBR Tier 1: 0.001 lives/year
Total - Complete PMF Fixes
Flood - Complete PMF Fixes
Risk Cost vs. Annualized Cost
$(300,000)
$(200,000)
$(100,000)
$-
$100,000
$200,000
$300,000
$400,000
$- $500,000 $1,000,000 $1,500,000 $2,000,000 $2,500,000 $3,000,000
Annualized Cost of Risk Reduction ($/year)
Ris
k C
ost (
$/ye
ar)
Risk CostReduction -Economic Benefit
Reduction in FloodBenefits (includedin Benefit)
Complete PMFFixes
Complete PMFFixes
Fix DescriptionAnnualized Cost of Risk Reduction
INDIVIDUAL FIXES- SCUPsE-B: Existing - Base Case -$ BIToe: Toe channel 157,148$ BIDebris: Debris boom 5,301$ BIGate: Gate reliability 83,435$ BIRaise: Raise 72,635$ BIWiden: Widen Spillway 1,038,079$ BIRCC280: RCC Spillway 280ft & Raise 1,497,623$ BIRCC455: RCC Spillway 455ft & Raise 2,274,296$ COMPLETE PMF FIXES:BCWiden: Widen Spillway Complete Fix 1,356,598$ BCRCC280: RCC Spillway 280ft & Raise Complete Fix 1,743,507$ BCRCC455: RCC Spillway 455ft & Raise Complete Fix 2,436,745$
6) Uncertainty Analysis
• 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
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 10 100 1000 10000
Incremental Number of Fatalities, N
Con
fiden
ce
Existing - Base Case Widen spillway RCC Spillway
DETERMINISTIC• Existing Dam & S/W
FixesDo not meet
UNCERTAINTYE.g. 50 lives• Existing:
5% confid meets• Widen S/W (4th gate):
20% confid meets• RCC S/W:
35% confid meets
ANCOLD Societal Risk(for Existing Dams)
0
1
10
100
1,000
10,000
0 10 20 30 40 50 60 70 80 90 100
Percentiles
Adj
uste
d C
ost p
er S
tatis
tical
Life
Sav
ed ($
M/li
fe)
Widen spillway RCC spillway
Poor
Moderate
Strong
Very Strong
0
1
10
100
1,000
10,000
0 10 20 30 40 50 60 70 80 90 100
Percentiles
Adj
uste
d C
ost p
er S
tatis
tical
Life
Sav
ed ($
M/li
fe)
Widen spillway RCC spillway
Poor
Moderate
Strong
Very Strong
DETERMINISTIC• Widen S/W (4th gate):
- US$143M- Moderate/Poor- 80th percentile
• RCC S/W:- US$120M- Moderate- 75th percentile
UNCERTAINTY• Widen & RCC S/W:- V. Strong: 30% confid- Strong: 20% confid- Moderate: 30% confid- Poor: 20% confid
ALARP Justification- Adjusted CSLS
-100200300400500600700800900
1,000
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02
Probability of Life Loss before Risk Reduction Measure (Pb) (per year)
Dis
prop
ortio
nalit
y R
atio
(R)
HSE Disproportionality Ratios HSE Individual Risk LimitR = 1.0 Strength of Tolerability BoundaryWiden Spillway Widen Spillway - Mean
Widen Spillway - Deterministic
-24
68
101214
161820
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02
Probability of Life Loss before Risk Reduction Measure (Pb) (per year)
Dis
prop
ortio
nalit
y R
atio
(R)
HSE Disproportionality Ratios HSE Individual Risk LimitR = 1.0 Strength of Tolerability BoundaryWiden Spillway
-100200300400500600700800900
1,000
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02
Probability of Life Loss before Risk Reduction Measure (Pb) (per year)
Dis
prop
ortio
nalit
y R
atio
(R)
HSE Disproportionality Ratios HSE Individual Risk LimitR = 1.0 Strength of Tolerability BoundaryRCC Spillway RCC Spillway - Mean
RCC Spillway - Deterministic
-2468
101214161820
1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02
Probability of Life Loss before Risk Reduction Measure (Pb) (per year)
Dis
prop
ortio
nalit
y R
atio
(R)
HSE Disproportionality Ratios HSE Individual Risk LimitR = 1.0 Strength of Tolerability BoundaryRCC Spillway
Disproportionality Ratio Justification
(UK HSE)
DETERMINISTIC• Widen S/W (4th gate):
- R = 24
• RCC S/W:- R = 20
• HSE guidelines would not justify risk reduction
UNCERTAINTY• Widen & RCC S/W
- 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)
InvestigationsRemedial measures
Risk Assessment – RA(Tolerable Risk Guidelines - Indicative)
InvestigationsRemedial measures
Engineering & Risk Assessments – EA (TA) & RA
Engineering & Risk Assessment – EA (TA) & RA
Investigations
Remedial measures
EQ & NOC
Gates & Debris
Flood - PMF
E-mail:David.Bowles@usu.edu
Home Page (including links to selected papers):
http://www.engineering.usu.edu/uwrl/www/faculty/bowles.html