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Unlined Spillway ErosionRisk Assessment

Johannes WibowoDon YuleEvelyn VillanuevaU.S. Army COE ERDC

Darrel Temple USDA

Tuttle Creek, KS

Introduction

Canyon Dam Spillway, TexasDate: July 6, 2002Flow: 66,000 cfs, 250 yr floodDuration: 12 daysSpillway Width: 1260 ftMaterial: Limestone

Introduction

• Spillway erosion analysis encounters variable natureof geometry, geologic material, and unpredictableflood events.

• Dam Safety Port Folio Analysis needs a tool todetermine the probability of spillway damages.

Problem Statements:

Painted Rock, AZ

Introduction

• Develop a tool to assess the probability of damageson unlined spillway erosion

RESEARCH OBJECTIVES:

Saylorville, IA

Risk Assessment

Process of Answering Three Questions:

1 What can go wrong?2 What is the likelihood it will go wrong?3 What are the consequences if it does go wrong?

Risk Assessment

1 What Can Go Wrong?

Spillway Breach

Local Scouring Headcut Erosion

Dam Breach

Risk Assessment

2 What Is the Likelihood It Will Go Wrong?

♦ Uncertainty of Flood Event♦ Uncertainty of Material Parameters♦ Uncertainty of Performance of the Unlined

Spillway

Risk Assessment

3 What Are the ConsequencesIf It Does Go Wrong?

♦ Spillway Partial Damage• Lightly Damaged• Moderately Damaged• Severely Damaged

♦ Spillway Breach• Population at Risk• Loss of Economic Value

Spillway Erosion Models

♦ REMR (WES, 1998)♦ USDA (Temple et al., 1994)♦ Annandale (1995)♦ Bollaert (2002)

Spillway Erosion Models

Phases of Erosion

Head-cut Development Head-cut Advancement

Original Surface Vegetal Detachment

Top Soil

Rock

Erosion Process

Event Tree

SpillwayFlow

ErosionOccurred

HeadcutDeveloped

HeadcutAdvanced

Intact

SpillwayBreach

LocalScour

BigPot Hole

PartialDamages

LocalDamages

DamBreach

PartialDamages

SpillwayBreach

DamBreach

Erosion Model - Threshold Line


Erodibility Index Kh

StreamPower

Not Eroded

Eroded

Threshold Line


Erodibility Index (Kh)

Kh = Ms * Kb * Kd * Js

Ms = Material Strength NumberKb = Block Size NumberKd = Joint Shear Strength NumberJs = Joint Orientation Number


Stream Power

P = γ * q * Sf

P = Stream Powerγ = Unit weight of waterq = Unit dischargeSf = Energy Slope

Logistic Regression

♦ Regression for Binary Outcomes• Occurrence (Erosion)• Non-Occurrence (No Erosion)

♦ User of Logistic Regression Method• Medical• Business

♦ Probabilistic Liquefaction Analysis (Liao et al, 1988)

Logistic Regression

♦Odds ratio

♦Logit transformation

pp−1

( )[ ]xbbp

xbbppLn

10

10

exp11

1

+−+=

+=

−

p = probability of occurrence

b0, b1 = regression parameters

x = independent variable

Logistic Regression

Multiple Logistic Regression

( )[ ]nn xbxbxbbp

++++−+=

..exp11

22110

p = probability of occurrence

b0, b1, b2, .., bn = regression parameters

x1, x2, .., xn, = independent variables

Logistic Regression

Multiple Logistic Regression for Spillway Erosion

( )[ ]qHbKbbp

h 210exp11

++−+=

Kh = Erosion Index, Material ResistanceqH = Hydraulic Attack

Logistic Regression

Result of Multiple Logistic Regression

( )[ ]qHKp

he 364.39.3171.1exp1

1+−−+

=

pe = probability of erosionKh = Erosion Index, Material ResistanceqH = Maximum qH, Hydraulic Attack

Nagelkerke’s R2 = 0.763

Logistic Regression

Logistic Regression for ERDC Threshold1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 1E+4 1E+5

Erodibility Index

1E-1

1E+0

1E+1

1E+2

1E+3

1E+4

1E+5

1E+6

Max

imum

qH

, cfs

ERODED

NON ERODED

ERODED

NON ERODED

Threshold

PE=50%

PE=99%

PE=1%

PE=10%

PE=90%

PE=30%PE=20%

PE=70%PE=80%

Logistic Regression

Logistic Regression for Annandale Threshold

1E-002 1E-001 1E+000 1E+001 1E+002 1E+003 1E+004

EROSION INDEX

1E-001

1E+000

1E+001

1E+002

1E+003

1E+004

STR

EAM

POW

ER(K

W/M

2) PE = 1%

PE = 99%

PE = 50%

Threshold

ERODED

NON ERODED

PE = 1%

PE = 99%

Ordinal Logistic Regression

Independent Variables

♦ Hydrograph• Peak unit discharges (cfs/ft)• Flood durations (hrs)

♦ Spillway Geometry• Lengths (ft)• Slopes (degrees)

♦ Material Index• Erosion Indexes


Sj = F (Material, Peak Discharge, Duration, Average_Slope, and Length)

Damage Levels Percent of Erosion

No Damage 0 - 0.05%Light Damage 0.06 – 15%Moderate Damage 16 – 40%Severe Damage 41 – 75%Breach 76 – 100%

Data: Case Histories (USDA and COE)


Sj = -1.515 Log_Kh + 8.635 Log_q – 1.581Log_Dura+ 0.807 Slope_av + 3.975 Log_Length

Nagelkerke’s R2 = 0.727

Probability Formulation:No Damage = 1/(1+ exp(Sj-k1))Light Damage = 1/(1+ exp(Sj-k2)) - 1/(1+ exp(Sj-k1))Moderate Damage = 1/(1+ exp(Sj-k3)) - 1/(1+ exp(Sj-k2))Severe Damage = 1/(1+ exp(Sj-k4)) - 1/(1+ exp(Sj-k3))Breach = 1 – 1/(1+ exp(Sj-k4))

k1,k2, k3, and k4 = boundary parameters from regression


5201.325340

23014.04

28576

41.8

Painted RockAZ

Felsite Tuff

15513402200Length (ft)7.211.4Ave. Slope (deg)0.0110317Erosion Index, Kh

3216120Duration (hours)

163.5104.4112.1Unit Disch. (cfs/ft)

Buck_DoeMOClay

SaylorvilleIA

Ss-Sh

Tuttle CreekKS

Ls-Sh

Input

0.0000.0000.0010.0090.990

0.3120.6390.0470.0020.000

0.9970.0020.046Breach0.0030.0850.629Severe0.0000.6090.305Moderate0.0000.2750.019Light0.0000.0290.001No Damage

Probability Output

Logistic Regression

22.3125.4Stream Power(Kw/m2)

0.0000.012Probability ofErosion

27341960Erosion Index(Kh)

Bluestone. WVQ=430,000 cfs

The Dalles, ORQ=2,290,000 cfs

Bluestone, WV

The Dalles, OR

Unlined Spillway ErosionRisk Assessment

Prioritizing Process

Ranking the outcome:

Risk = Poccurrence * Pfailure * Consequences

Summary

• Two Risk Assessment tools were developedfor Port Folio analysis:

– Logistic Regression Formulation forcalculating the probability of erosion

– Ordinal Logistic Regression for calculatingthe probability of erosion of different levelsof damages

• These tools will be useful for prioritizing themaintenance of earth and rock surfaceunlined spillway

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