Unlined Spillway Erosion Risk Assessment

Transcription

1 Unlined Spillway Erosion Risk Assessment Johannes Wibowo Don Yule Evelyn Villanueva U.S. Army COE ERDC Darrel Temple USDA Tuttle Creek, KS

2 Introduction Canyon Dam Spillway, Texas Date: July 6, 2002 Flow: 66,000 cfs, 250 yr flood Duration: 2 days Spillway Width: 260 ft Material: Limestone

3 Introduction Problem Statements: Spillway erosion analysis encounters variable nature of geometry, geologic material, and unpredictable flood events. Dam Safety Port Folio Analysis needs a tool to determine the probability of spillway damages. Painted Rock, AZ

4 Introduction RESEARCH OBJECTIVES: Develop a tool to assess the probability of damages on unlined spillway erosion Saylorville, IA

5 Risk Assessment Process of Answering Three Questions: What can go wrong? 2 What is the likelihood it will go wrong? 3 What are the consequences if it does go wrong?

6 Risk Assessment What Can Go Wrong? Local Scouring Spillway Breach Headcut Erosion Dam Breach

7 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

8 Risk Assessment 3 What Are the Consequences If It Does Go Wrong? Spillway Partial Damage Lightly Damaged Moderately Damaged Severely Damaged Spillway Breach Population at Risk Loss of Economic Value

9 Spillway Erosion Models REMR (WES, 998) USDA (Temple et al., 994) Annandale (995) Bollaert (2002)

10 Spillway Erosion Models Rock Phases of Erosion Top Soil Original Surface Vegetal Detachment Head-cut Development Head-cut Advancement

11 Erosion Process Event Tree Spillway Flow Erosion Occurred Intact Headcut Developed Local Scour Big Pot Hole Headcut Advanced Local Damages Spillway Breach Spillway Breach Partial Damages Dam Breach Dam Breach Partial Damages

12 Erosion Model - Threshold Line Erosion Model - Threshold Line Stream Power Eroded Threshold Line Not Eroded Erodibility Index Kh

13 Erosion Model - Threshold Line Erodibility Index (K h ) K h = M s * K b * K d * J s M s K b K d J s = Material Strength Number = Block Size Number = Joint Shear Strength Number = Joint Orientation Number

14 Erosion Model - Threshold Line Stream Power P = * q * S f P = Stream Power = Unit weight of water q = Unit discharge S f = Energy Slope

15 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, 988)

16 Logistic Regression Odds ratio p p Logit transformation p Ln p p = + exp = b 0 + b x [ ( b + b x) ] 0 p = probability of occurrence b 0, b = regression parameters x = independent variable

17 Logistic Regression Multiple Logistic Regression p = + exp [ ( b + b x + b x )] b n x n p = probability of occurrence b 0, b, b 2,.., b n = regression parameters x, x 2,.., x n, = independent variables

18 Logistic Regression Multiple Logistic Regression for Spillway Erosion p = + exp [ ( b + b K + b qh )] 0 h 2 K h = Erosion Index, Material Resistance qh = Hydraulic Attack

19 Logistic Regression Result of Multiple Logistic Regression p e = + exp [ ( K qh )] h Nagelkerke s R 2 = p e = probability of erosion K h = Erosion Index, Material Resistance qh = Maximum qh, Hydraulic Attack

20 Logistic Regression E+6 E+5 E+4 ERODED ERODED NON ERODED PE=50% PE=30% PE=20% PE=0% Threshold Maximum qh, cfs E+3 E+2 E+ PE=99% PE=90% PE=80% PE=70% PE=% NON ERODED E+0 E- E-2 E- E+0 E+ E+2 E+3 E+4 E+5 Erodibility Index Logistic Regression for ERDC Threshold

21 Logistic Regression E+004 ERODED STREAM POWER (KW/M2) E+003 E+002 E+00 E+000 PE = 50% PE = 99% PE = % PE = % PE = 99% E-00 Threshold NON ERODED E-002 E-00 E+000 E+00 E+002 E+003 E+004 EROSION INDEX Logistic Regression for Annandale Threshold

22 Ordinal Logistic Regression Independent Variables Hydrograph Peak unit discharges (cfs/ft) Flood durations (hrs) Spillway Geometry Lengths (ft) Slopes (degrees) Material Index Erosion Indexes

23 Ordinal Logistic Regression Sj = F (Material, Peak Discharge, Duration, Average_Slope, and Length) Data: Case Histories (USDA and COE) Damage Levels Percent of Erosion No Damage % Light Damage % Moderate Damage 6 40% Severe Damage 4 75% Breach 76 00%

24 Ordinal Logistic Regression Sj = -.55 Log_Kh Log_q.58Log_Dura Slope_av Log_Length Nagelkerke s R 2 = Probability Formulation: No Damage Light Damage Moderate Damage Severe Damage Breach = /(+ exp(sj-k)) = /(+ exp(sj-k2)) - /(+ exp(sj-k)) = /(+ exp(sj-k3)) - /(+ exp(sj-k2)) = /(+ exp(sj-k4)) - /(+ exp(sj-k3)) = /(+ exp(sj-k4)) k,k2, k3, and k4 = boundary parameters from regression

25 Ordinal Logistic Regression Input Tuttle Creek KS Ls-Sh Painted Rock AZ Felsite Tuff Saylorville IA Ss-Sh Buck_Doe MO Clay Unit Disch. (cfs/ft) Duration (hours) Erosion Index, K h Ave. Slope (deg) Length (ft) Probability Output No Damage Light Moderate Severe Breach

26 Logistic Regression The Dalles, OR The Dalles, OR Bluestone. WV Q=2,290,000 cfs Q=430,000 cfs Bluestone, WV Erosion Index (Kh) Stream Power (Kw/m2) Probability of Erosion

27 Unlined Spillway Erosion Risk Assessment Prioritizing Process Ranking the outcome: Risk = P occurrence * P failure * Consequences

28 Summary Two Risk Assessment tools were developed for Port Folio analysis: Logistic Regression Formulation for calculating the probability of erosion Ordinal Logistic Regression for calculating the probability of erosion of different levels of damages These tools will be useful for prioritizing the maintenance of earth and rock surface unlined spillway