Date post: | 25-Jun-2018 |
Category: |
Documents |
Upload: | trinhquynh |
View: | 233 times |
Download: | 0 times |
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
Erosion Model - Threshold Line
Erodibility Index Kh
StreamPower
Not Eroded
Eroded
Threshold Line
Erosion Model - Threshold Line
Erodibility Index (Kh)
Kh = Ms * Kb * Kd * Js
Ms = Material Strength NumberKb = Block Size NumberKd = Joint Shear Strength NumberJs = Joint Orientation Number
Erosion Model - Threshold Line
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
Ordinal Logistic Regression
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)
Ordinal Logistic Regression
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
Ordinal Logistic 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