Workshop on Risk Assessment Workshop on Risk Assessment for Seepage and Piping for Seepage and Piping in Dams and Foundations in Dams and Foundations Virginia Tech / U.S. Army Corps of Engineers March 21-22, 2000 Thomas F. Wolff, Ph.D., P.E. Associate Dean, College of Engineering Michigan State University [email protected]http://www.egr.msu.edu/~wolff
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Workshop on Risk Assessment for Seepage and Piping in Dams and Foundations
Workshop on Risk Assessment for Seepage and Piping in Dams and Foundations. Virginia Tech / U.S. Army Corps of Engineers March 21-22, 2000 Thomas F. Wolff, Ph.D., P.E. Associate Dean, College of Engineering Michigan State University [email protected] http://www.egr.msu.edu/~wolff. Question 1. - PowerPoint PPT Presentation
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Workshop on Risk Assessment Workshop on Risk Assessment for Seepage and Piping for Seepage and Piping in Dams and Foundationsin Dams and Foundations
Virginia Tech / U.S. Army Corps of EngineersMarch 21-22, 2000
Thomas F. Wolff, Ph.D., P.E.Associate Dean, College of Engineering
Describe your preferred approachapproach, , methodologymethodology and procedureprocedure for making a conventional analysis of the potential for a seepage and piping problem to develop at an embankment dam and/or foundation where applicable.
Question 1—Preferred approach
Develop a set of detailed foundation profilesprofiles from boring and testing data
Assign hydraulic conductivityconductivity values Perform a set of finite-elementfinite-element
Compare predicted gradientsgradients to piping criteriacriteria
Question 1—Preferred approach
HoweverHowever, I would perform the analysis probabilisticallyprobabilistically. Not to determine the absolute probability of failure, but to recognize inherent uncertainty in the modeled parameter values
Question 1—Preferred approach
Deterministic approach k = 400 x 10-4 cm/s
Probabilistic approach E[k] = 400 x 10-4 cm/s k = 100 x 10-4 cm/s
0
5
10
15
20
25
30
0 0.02 0.04 0.06 0.08 0.1 0.12
k
Question 1—Preferred approach
Deterministic approach i = 0.65 FS = 1/0.65 = 1.54
Probabilistic approach E[i - icrit] = 0.35 (i -i c) = 0.15
0
0.5
1
1.5
2
2.5
3
-0.5 0 0.5 1
i - icrit
Question 2
In this conventional evaluation, what information, factors, practices information, factors, practices and considerationsand considerations have the greatest influence on establishing the potential of a seepage and piping problem developing? What are the significant unknownsunknowns in this process?
Question 2 information, factors, practices and considerationsinformation, factors, practices and considerations
Foundation stratigraphystratigraphy Relative conductivityRelative conductivity of various
materials in various directions HomogeneityHomogeneity or non-homogeneity of
materials internal stabilityinternal stability of materials, filter
capabilities of one material to the next
Question 2 information, factors, practices and considerationsinformation, factors, practices and considerations
Piping criteriaPiping criteria Corps’ criteria have traditionally been derived
on gradient only, and not particle size or tractive shear stress
All of the above have inherent uncertainty Presence of multiple lines of defensemultiple lines of defense --
reliability through redundancy
Question 2—Unknowns
Hydraulic conductivityconductivity of materials Degree of anisotropyanisotropy Piping criteriaPiping criteria
Questions 3
In performing a risk assessment for a project with an embankment dam, what are the important considerations, considerations, cautionscautions and best methodologybest methodology for the Corps to use in establishing the probability of failureprobability of failure of the dam for seepage and piping?
How important is sound engineering judgmentjudgment?
Questions 3
Probability of failure ?Probability of failure ? Do we know what we really mean here? What is the denominator?
Per annum ? Per design ?
Uncertainty in parameters is unique to the structure considered, but is per designper design
per annumper annum requires some input regarding observed frequency
Questions 3
Considerations and CautionsConsiderations and Cautions Do you know the questionquestion you are trying to
answer? Probability of this dam failing in a given time span Relative reliability of this dam with regard to
other dams What are the incremental benefits of
increasing sophisticationsophistication in the analysisanalysis? Accuracy of answer may be much more important
than precision -- do we end up at the correct decision?
Questions 3
Best Methodology - Pr(f) per designBest Methodology - Pr(f) per design Characterize uncertainty in parametersuncertainty in parameters
requires a mix of statistics and judgmentjudgment Use FOSM methodsFOSM methods, or if practical,
simulation methods Uncertainty in parameters
uncertainty in performance measure Use results as comparison to a common comparison to a common
criteriacriteria for acceptable risk (also requires judgmentjudgment)
Questions 3
Best Methodology - Pr(f) per annumBest Methodology - Pr(f) per annum Estimate annual probability of failure for a
class of structures based on historical datahistorical data fit to Weibull distribution
This is problematicalproblematical because events are few, making confidence limits wide
Somehow adjust resultsadjust results for a specific structure based on its characteristics, performance and uncertainties within its class.
Question 4
What approachapproach would you recommend to obtain the final results (i.e. Probability of Failure = 4.65 x 10-
4) -- an analytical evaluationanalytical evaluation of the data and information, or a subjective evaluationsubjective evaluation of the data and information, or somewhere in in betweenbetween?
Question 4—Same answer !
Probability of failure ?Probability of failure ? Do we know what we really mean here? What is the denominator?
Per annum ? Per design ?
Uncertainty in parameters is unique to the structure considered, but is per designper design
per annumper annum requires some input regarding observed frequency
Question 4
ApproachApproach Best estimates of parameter valuesparameter values
and their uncertaintiesuncertainties, based on both statistics and judgment
A probabilistic analysisprobabilistic analysis to determine expected performance and its inherent uncertainty
ComparisonComparison of the results to some common criteria of acceptabilitycommon criteria of acceptability
QuestionsQuestions
YesYes Comparative
reliability problems Water vs. Sand vs.
Clay pressures on walls, different for same FS
Event tree for identifying relative risks
NoNo Tools for complex
geometries Absolute reliability Spatial correlation where
data are sparse Time-dependent change
in geotechnical parameters
Accurate annual risk costs
Has the theory developed sufficiently for use in practical applications?
QuestionsQuestions
FOSM Reliability IndexFOSM Reliability Index Reliability Comparisons
structure to structure component to component before and after a repair relative to desired target value
Insight to Uncertainty Contributions
When and where are the theories used most appropriately?
QuestionsQuestions
Frequency - Based ProbabilityFrequency - Based Probability Earthquake and Flood recurrence, with
conditional geotechnical probability values attached thereto
Recurring random eventsRecurring random events where good models are not available: scour, through-seepage, impact loads, etc.
Wearing-in, wearing-out, corrosion, fatigue
When and where are the theories used most appropriately?
QuestionsQuestions
Expert ElicitationExpert Elicitation “Hard” problems without good
frequency data or analytical models seepage in rock likelihood of finding seepage entrance likelihood of effecting a repair before
distress is catastrophic
When and where are the theories used most appropriately?
QuestionsQuestions
YESYES Conditional probability values tied to time-
dependent events such as earthquake acceleration or water level
NONO variation of strength, permeability, geometry
(scour), etc; especially within resource constraints of planning studies
Are time-dependent reliability analysis possible for geotechnical problems? How?