Complete Dam Risk Analysis & Detailed Applications: L.6 ... BOWLES... · L.6 - Hills Creek Dam Risk Assessment: Evaluation of Flood Risk Reduction Alternatives & Uncertainty Analysis

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 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

.

.

.



Consequences Node

AEP1 - AEP2

Overtopping Breach

SpillwayClear


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

.

.

.

.

.

.



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


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


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


BCWiden:Widen

Spillw ayComplete

Fix

BCRCC280:RCC


CompleteFix

BCRCC455:RCC


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


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


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


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








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








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

)


Distribution

Uncertainty input distribution on earthquake loading - PGA

SystemResponses

Consequences








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








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)


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)


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


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


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


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


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


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:[email protected]

Home Page (including links to selected papers):

http://www.engineering.usu.edu/uwrl/www/faculty/bowles.html

Documents

Complete Dam Risk Analysis & Detailed Applications: L.6 ... BOWLES... · L.6 - Hills Creek Dam Risk Assessment: Evaluation of Flood Risk Reduction Alternatives & Uncertainty Analysis