th Annual Technical Forum th th 7 th Annual Technical Forum Annual Technical Forum 7 th th Annual Technical Forum Annual Technical Forum 7 Annual Technical Forum Geohazards Geohazards In Transportation In The Appalachian In Transportation In The Appalachian Geohazards Geohazards In Transportation In The Appalachian In Transportation In The Appalachian In Transportation In The Appalachian Geohazards Geohazards In Transportation In The Appalachian Region Region Region Region Region Region Session 4 Economic Session 4 Economic Session 4 Economic Session 4 Economic Impacts of a Impacts of a Karst Karst Karst Impacts of a Impacts of a Karst Foundation Wolf Foundation Wolf Foundation Wolf Foundation Wolf Creek Dam, Creek Dam, Creek Dam, Creek Dam, US Army Corps of US Army Corps of US Army Corps of US Army Corps of Engineers, Engineers, Engineers, Engineers, Nashville District Nashville District Nashville District Nashville District
Outline of Topics Outline of Topics Outline of Topics Outline of Topics • Project Description. • General Background. • Reliability Studies. • Interim Risk Reduction Measures. • Operating Restrictions. • Economic Impacts.
Project Location Project Location Project Location Project Location
Project Features Project Features Project Features Project Features
EMBANKMENT PLAN AND EMBANKMENT PLAN AND EMBANKMENT PLAN AND EMBANKMENT PLAN AND SECTION SECTION SECTION SECTION Cut Off Trench Drainage Blanket Toe of Random Fill
Foundation Treatment Foundation Treatment Problems Problems • Treatment techniques were inadequate for this geology • Most of the alluvium left in place • Except for cut-off trench, no embankment foundation treatment • Cutoff trench design and construction inadequate
Overhangs and loose rocks w ill only be removed w here Overhangs and loose rocks w ill only be removed w here they cross the line of the trench, since the earthfill they cross the line of the trench, since the earthfill in in the sides of the trench w ill have the function only of the sides of the trench w ill have the function only of stability and not of an absolutely uniform tight contact stability and not of an absolutely uniform tight contact w ith the trench w alls. Tamping w ill suppliment w ith the trench w alls. Tamping w ill suppliment the the regular rolling of the fill as required under the regular rolling of the fill as required under the overhangs and irregular salients overhangs and irregular salients. .
Foundation Treatment Foundation Treatment Cave Cave Solution Features
Sw itchyard 1968 Sinkhole Sinkhole
1960 ’ ’s and 70 s and 70 ’ ’s s 1960 Remedial Features Remedial Features Diaphragm Wall Sw itchyard Wall Concrete Dam Pow erhouse Diaphragm Wall Sw itchyar Earth Emb Wall Grout Lines Sw itchyard
Post Wall Performance Post Wall Performance – – Wet Areas Wet Areas et Areas Post Wall Performance Post Wall Performance Wet Areas March 2004 March 2004 March 2004 March 2004 3 2 1 Existing Diaphragm 1 Wall
Risk Risk Risk Risk � Risk is defined as the probability of unsatisfactory performance times the consequences of the unsatisfactory performance. � For Wolf Creek, based on a breach of the dam the estimated consequences are up to 350 lives lost and over $3 billion in damages. � How do we establish the probability of unsatisfactory performance? � It is especially difficult to predict the behavior in Karst.
Reliability Analysis for Dams and Reliability Analysis for Dams and Reliability Analysis for Dams and Reliability Analysis for Dams and Reliability Analysis for Dams and Reliability Analysis for Dams and Levees Levees Levees Levees Levees Levees Excerpts from a presentation by Thomas F. Wolff, Ph.D., P.E. Michigan State University Grand Rapids Branch ASCE September 2002
General Approaches: General Approaches: General Approaches: General Approaches: General Approaches: General Approaches: Event Tree Event Tree Event Tree Event Tree Event Tree Event Tree Close to levee given some water level : p = 0.6 0.09 Carries material p=0.3 Sand Boil p = 0.5 Not 0.06 close p = 0.4 Doesn’t p = 0.7 0.35 Most problems of interest involve or could be represented by an event tree..
Probabilities for the Probabilities for the Probabilities for the Probabilities for the Probabilities for the Probabilities for the Event Tree - - How ????? How ????? How ????? Event Tree - How ????? How ????? ow ????? Event Tree Event Tree Event Tree Event Tree � A) f (Uncertainty in parameter values) Reliability Index Methods ( β ) – Monte Carlo method – FOSM methods � point estimate � Taylor’s Series � Mean Value � Hasofer-Lind � B) Frequency Basis – Exponential, Weibull, or other lifetime distribution � C) Judgmental Values – Expert elicitation
A) A) Pr(f Pr(f) = Function of Pr(f ) = Function of ) = Function of A) Pr(f) = Function of A) Pr(f) = Function of A) A) Pr(f ) = Function of Parameter Uncertainty Parameter Uncertainty Parameter Uncertainty Parameter Uncertainty Parameter Uncertainty Parameter Uncertainty � Identify performance function and limit state , typically ln(FS) = 0 � Identify random variables , X i � Characterize random variables, – E[X], σ x , ρ � Determine E[FS], σ FS � Determine Reliability Index, β � Assume Distribution and calculate Pr(f) = f( β )
Pros and Cons of b, Pros and Cons of b, Pros and Cons of b, Pros and Cons of b, Pros and Cons of b, Pros and Cons of b, Pr(U) Pr(U) Pr(U) Pr(U) Pr(U) Pr(U) � Advantages � Disadvantages – Still need better – “Plug and Chug” practical tools for – fairly easy to complex problems understand with – Non-unique, can be some training seriously in error – provides some – No inherent time insight about the component problem – only accounts for uncertainties related to parameter values and models
B) Frequency B) Frequency- -based based based B) Frequency B) Frequency based B) Frequency-based B) Frequency-based Probabilities Probabilities Probabilities Probabilities Probabilities Probabilities � Represent probability of event per time period � Poisson / exponential model well- recognized in floods and earthquakes � Weibull model permits increasing or decreasing event rates as f(t), well developed in mechanical & electrical appliactions � Some application in material deterioration � Requires historical data to fit
Pros and Cons of Frequency Pros and Cons of Frequency Pros and Cons of Frequency Pros and Cons of Frequency Pros and Cons of Frequency Pros and Cons of Frequency Models Models Models Models Models Models � Advantages � Disadvantages – Can be checked – Need historical data against reality and – Uncertainty in extending history into future – Can obtain – Need “homogeneous” confidence limits or replicate data sets on the number of – Ignores site-specific events variations in structural – Is compatible with condition economic analysis
C) Judgmental C) Judgmental C) Judgmental C) Judgmental C) Judgmental C) Judgmental Probabilities Probabilities Probabilities Probabilities Probabilities Probabilities � Mathematically equivalent to previous two, can be handled in same way � Can be obtained by Expert Elicitation – a systematic method of quantifying individual judgments and developing some consensus, in the absence of means to quantify frequency data or parameter uncertainty
Pros and Cons of Judgmental Pros and Cons of Judgmental Pros and Cons of Judgmental Pros and Cons of Judgmental Pros and Cons of Judgmental Pros and Cons of Judgmental Probabilities Probabilities Probabilities Probabilities Probabilities Probabilities � Advantages � Disadvantages – Gives you a number – Distrusted by some when nothing else will (including some within Federal – May be better reality Agencies) check than parameter – Some consider values uncertainty approach “less accurate” than – permits consideration calculated ones of site-specific – Non-unique values information – Some experience in – Who is an expert? application to dams
1. Major Rehabilitation 1. Major Rehabilitation 1. Major Rehabilitation 1. Major Rehabilitation Report. Report. Report. Report. � 1. Analysis from Major Rehabilitation Report (MRR) – Based on analysis of stress indicators – Limit State defined as condition that would require operational restrictions. Limit State threshold selected by expert elicitation. – Damage accumulation based on projection of instrumentation data coupled with historical pool stages using a Monte Carlo simulation. – Reviewed by an independent panel of experts – Stress indicators show gradual change from 1984 to present – Considered risk to be high – Analysis based on engineering judgment
2. Screening Portfolio Risk 2. Screening Portfolio Risk 2. Screening Portfolio Risk 2. Screening Portfolio Risk Assessment Assessment Assessment Assessment � 2. Screening Portfolio Risk Assessment – In-house Corps expertise – Reviewed MRR and other data – Purpose to determine ranking in severity of Corps dams – Placed Wolf Creek in the “Urgent and Compelling” category
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