Chickamauga Lock and Dam Lock Addition Cofferdam Height ... · Curve as Independent Predictor of...
28
August 4, 2005 Chickamauga Lock and Dam Lock Addition Cofferdam Height Optimization Study Leon A. Schieber, P.E. (KS) Project Engineer/Structural Engineer
Transcript of Chickamauga Lock and Dam Lock Addition Cofferdam Height ... · Curve as Independent Predictor of...
August 4, 2005
Chickamauga Lock and DamLock Addition
Cofferdam Height Optimization Study
Leon A. Schieber, P.E. (KS)Project Engineer/Structural Engineer
08/04/05Page - 2
Cofferdam Height Optimization StudyAgenda
Background - Lock Replacement Study
Cofferdam Risk and Uncertainty (R&U)Approach – EM1605 (hand method)vs. Monte Carlo Simulation
R&U Inputs
R&U Results
08/04/05Page - 3
Background - Lock Replacement Study
Nashville District and Tennessee ValleyAuthority Performed Feasibility Study andDetermined In-The-Dry Construction for
Lock Replacement
08/04/05Page - 4
Chickamauga Lock ReplacementBackground
USACE NashvilleDistrict and theTennessee ValleyAuthority PerformedLock ReplacementStudy
Lock is to beReplaced Due toExisting Lock StabilityConcerns
Determined that in theDry Construction isMost Desirable
08/04/05Page - 5
Cofferdam Height
TO WHAT HEIGHT SHOULDCOFFERDAM BE CONSTRUCTED?
WHAT METHOD SHOULD BE USEDTO ANSWER THIS QUESTION?
08/04/05Page - 6
Cofferdam Starting Parameters
100661.825658.510655.2
Equivalent Return Period(years)
Top of Cofferdam(feet)
Given Information Regarding CofferdamHeight Optimization
Three different construction periods for lockaddition were considered: 5, 7, & 10 years.
08/04/05Page - 7
Cofferdam Risk and Uncertainty (R&U)Approach – EM 1110-2-1605 (hand
method) vs. Monte Carlo Simulation
EM 1605 (Hand Method) is Limited inPrediction of Risk Costs, While Monte
Carlo Simulation Allows for MoreVersatility in Prediction of Risk Costs
08/04/05Page - 8
Risk Cost Equation
Cofferdam Height Optimization Equation Canbe Simplified Into:
Risk Cost = RC = P * Flood Damage Costs
+ Construction Cost
The Derivation or Determination of P is WhereMonte Carlo Simulation Allows for GreaterAdvantage Over the EM 1605 (Hand Method)
08/04/05Page - 9
EM 1110-2-1605 – Derivation of P
Risk of Flooding is Defined as:
Where:
� N = Construction Period
� i = Number of Occurrences of Specific Flood Return Period
� P = Probability of Obtaining During Construction Period Exactly iEvents of Specific Flood Return Interval Having a Probability of pOccurring in a Single Trial.
Problem is There is no Reasonable “HandMethod” for Determining “i”.
PN! pi⋅ 1 p−( )N i−
⋅
i! N i−( )!⋅
08/04/05Page - 10
EM 1110-2-1605 – Simplification of P
Solution - Use Statistics to Simplify Equation
Solve Opposite Question – What is ProbabilityNo Floods Occur? i.e. i = 0
Where:
� P = probability of obtaining during construction period no floodevents having a probability of p
Now 1 - P = Probability of Obtaining at LeastOne Event of Probability p During ConstructionPeriod.
The result does not define how many events(i.e. Could be More Than 1)
P 1 p−( )N
08/04/05Page - 11
Monte Carlo Simulation – Prediction of P
Monte Carlo Simulation Allows for Predictionof “i”.
“i” is Predicted by Treating Annual FrequencyCurve as Independent Predictor of FloodEvents for Each Year of Construction Period
This is Accomplished by Fitting a ProbabilityDistribution to Annual Frequency Curve
08/04/05Page - 12
Monte Carlo Simulation – Prediction of P
Thus the Monte Carlo Simulation Model canProvide One or More Tailwater ElevationsAbove the Cofferdam Height During aConstruction Period
Cost Equations were Then Adjusted to Allowfor Flooding Costs that Result From MoreThan One Event to be Added to the Total RiskCost (Construction + Flooding Costs).
RC = Sum (Flood Costi + Construction Cost)� Where i = number of floods
08/04/05Page - 13
R&U Inputs
Identification of Uncertainty andAssignment of Probability Distributions
08/04/05Page - 14
Monte Carlo Simulation – Prediction of P
The inputs include:� cofferdam cell height (constant),
� construction duration (entered as discrete values),
� tailwater frequency curve (cumulative/beta general distributions),
� tailwater duration curve (constant per specific flood event),
� flooding costs (triangular distribution),
� construction costs (triangular distribution).
The output includes:� total risk cost (triangular distribution).
08/04/05Page - 15
Annual Tailwater Frequency Curve DataFrom 1958 to 1999
648.09( 2- year )50652.63( 5 - year )20655.16( 10 - year )10657.35( 20 - year )5659.96( 50 - year )2661.79( 100 - year )1665.75( 500 - year )0.2
( Elevation in feet )Expected Probability
( Return Intervalin Years )
PercentChance
Exceedance
08/04/05Page - 16
Corrected Flood Probabilities ForEM 1605 (Hand Method)
99.9%99.2%96.9%648.09( 2- year )5089.3%79.0%67.2%652.63( 5 - year )2065.1%52.2%41.0%655.16( 10 - year )1040.1%30.2%22.6%657.35( 20 - year )518.3%13.2%9.6%659.96( 50 - year )29.6%6.8%4.9%661.79( 100 - year )12.0%1.4%1.0%665.75( 500 - year )0.2
10 yrs7 yrs5 yrs
Probability of at leastone or more flood
events duringconstruction period( Elevation in feet )
Expected Probability( Return Interval in
Years )
PercentChance
Exceedance
08/04/05Page - 17
Cofferdam Construction Cost –Probability Distribution
$35,652,531$33,612,552$31,582,069$27,261,317661.8 (100 yr)
$33,835,602$31,890,153$29,953,783$25,835,790658.5 (25 yr)
$31,594,681$29,763,812$27,940,842$24,072,499655.2 (10 yr)
(w/oContingency)
MAX%AVG %MIN %BASE
Construction Cost w/Contingencies
ConstructionCost
T.O.COFFERDAMELEVATION
08/04/05Page - 18
Cofferdam Construction Cost –Measurement of Uncertainty
302315Cofferdam Removal9503520Miscellaneous8503520Instrumentation7403530Dewatering6403020Flooding Facility5604530Tie-Ins4252015Ramp Cells3252015Cofferdam Cells2532Mob/Prepatory1
Max %Avg %Min %DescriptionNo.% of ContingencyItem
08/04/05Page - 19
Cofferdam Construction Cost –Mitigation of Bias
604530Selected Values
M. LedbetterParticipated in
discussion
J. Koontz504030
L. Schieber302520
G. Hicks432Tie-ins to Existing
Facilities4
Max%
Avg%
Min%
TeamMember
% of Contingency
DescriptionItemNo.
08/04/05Page - 20
Cofferdam Flood Cost –Probability Distribution
$6,660,811$6,195,062$5,729,313$4,865,427661.8 (100 yr)
$6,605,389$6,141,266$5,677,143$4,682,352658.5 (25 yr)
$6,235,746$5,794,580$5,353,413$4,533,977655.2 (10 yr)
(w/oContingency)ELEVATION
MAX%AVG %MIN %BASE
T.O.COFFERDAM
Total Fixed Flood Costs w/Contingencies
Total Fixed FloodCost
08/04/05Page - 21
Cofferdam Flood Cost –Measurement of Uncertainty
503520Damage4
403020Downtime3
503520Cleanup2
201510Pumping1
Max %Avg %Min %
% of Contingency
DescriptionItemNo.
08/04/05Page - 22
R&U Results
EM 1110-2-1605 Results Suggest The OptimumCofferdam Height is the Lowest Elevation,
The Monte Carlo Simulation Results Suggest theOptimum Cofferdam Height is the Middle to TallestElevation Depending Upon Construction Duration
08/04/05Page - 23
Distribution for Estimated Cost of Construction andFlooding:/G28
M ean = 3.270646E+07
X <=3831526495%
X <=306243765%
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
28 31.5 35 38.5 42
Values in Millions
Val
ues
in 1
0^ -7
Distribution for Estimated Cost of Construction andFlooding:/G28
M ean = 3.366506E+07
X <=3507306895%
X <=322018885%
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
30 34 38 42
Values in Millions
Val
ues
in 1
0^ -7
EM 1605 – Risk Cost ResultsDistribution for Estimated Cost of Construction and
Flooding:/G28
M ean = 3.206013E+07
X <=3661774495%
X <=286797925%
0
0.5
1
1.5
2
2.5
3
3.5
27 29.75 32.5 35.25 38
Values in Millions
Val
ues
in 1
0^ -7
Cell Height 658.5
Cell Height 661.8
Cell Height 655.2
08/04/05Page - 24
Monte Carlo Simulation – Risk CostResults
Distribution for Estimated Cost of Construction andFlooding:/G27
M ean = 4.256498E+07
X <=5465214895%
X <=300078285%
0
1
2
3
4
5
6
7
8
9
25 38.75 52.5 66.25 80
Values in Millions
Val
ues
in 1
0^ -8
Distribution for Estimated Cost of Construction andFlooding:/G27
M ean = 3.5145E+07
X <=4428278895%
X <=307683665%
0
0.5
1
1.5
2
2.5
3
30 40 50 60
Values in Millions
Val
ues
in 1
0^ -7
Distribution for Estimated Cost of Construction andFlooding:/G27
Mean = 3.395146E+07
X <=3836193295%
X <=322434605%
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
30 36 42 48
Values in Millions
Val
ues
in 1
0^ -7
Cell Height 655.2
Cell Height 658.5
Cell Height 661.8
08/04/05Page - 25
Comparison of Risk Cost
350262443222741433625169350055123223422033608618009451.18353100661.8
3437524030618184321852563319728230577972318848832475259.750292081.07225658.5
3485277228680974311172433101849628521360297671144867541.501350796.7410655.2
95%5%95%5%95%5%
90% ConfidenceInterval for Mean ofTotal Risk Cost ($)
TotalRiskCost,
Mean ($)
90% Confidence Intervalfor Mean Total
Construction Cost Mean($)
TotalConstructio
n Cost,Mean ($)
90% ConfidenceInterval for TotalFlooding Cost
Mean ($)Total FloodingCost, Mean
($)
EquivalentRetur
nPeriod
(yr)
TopElevation
ofCofferda
m (ft)
Cofferdam Height Optimization Results for EM 1605-10 Year Construction Period
3836193232243460339514613500643632221876336153285867248.50336133.295100661.8
4428278830768366351449943321558630560092318983791235133703246614.7525658.5
54652148300078284256497631012780285194402976696523954028012798011.610655.2
95%5%95%5%95%5%
90% ConfidenceInterval for Mean ofTotal Risk Cost ($)
TotalRiskCost,
Mean ($)
90% Confidence Intervalfor Mean of Total
Construction Cost Mean($)
TotalConstructio
n Cost,Mean ($)
90% ConfidenceInterval for Mean ofTotal Flooding Cost
($)Total
FloodingCost, Mean
($)
EquivalentRetur
nPeriod
(yr)
TopElevation
ofCofferda
m (ft)
Cofferdam Height Optimization Results for Alternate Method-10 Year Construction Period
08/04/05Page - 26
Summary of Risk Cost
Cofferdam Risk Cost
654655656657658659660661662663
3E+07 3.2E+07
3.4E+07
3.6E+07
3.8E+07
4E+07 4.2E+07
4.4E+07
Cost ($)
Elev
atio
n
EM 1605 - 5yrEM 1605 - 7yrEM 1605 - 10yrMonte Carlo - 5yrMonte Carlo - 7yrMonte Carlo - 10yr
08/04/05Page - 27
Questions ?
Used Monte Carlo Simulation as a Tool to Predict Risk Costand Provide Information Regarding Risk Management.
Compared this with EM 1110-2-1605 (Hand Method).
08/04/05Page - 28
Contact Information
Leon A. Schieber, P.E.Black & Veatch Special Projects Corp.
Phone: 913-458-6546E-mail: [email protected]
