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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 wolff@msu.edu 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
Michigan State University
wolff@msu.eduhttp://www.egr.msu.edu/~wolff
Question 1
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
seepage analyses considering multiple sections multiple conductivity assumptions
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?
QuestionsQuestions
Define purposeDefine purpose of analysis Select simplest reasonable approachsimplest reasonable approach
consistent with purpose Build an event treeevent tree Fill in probability values using whichever of whichever of
threethree approachesapproaches is appropriate to that node
Understand and admit relative vs absolute relative vs absolute probabilityprobability values
What Methods are Recommended for Reliability Assessments of Foundations and Structures ?
NeedsNeeds
A Lot of TrainingTraining Develop familarity and feeling for techniques
by practicing engineers ResearchResearch
Computer tools for practical probabilistic seepage and slope stability analysis for complex problems
Characterizing and using real mixed data sets, of mixed type and quality, on practical problems, including spatial correlation issues
Approaches and tools for Monte Carlo analysis
Four Case Histories
DeterministicDeterministic Alton to Gale Levee System
ProbabilisticProbabilistic Hodges Villages Dam Walter F. George Lock and Dam Herbert Hoover Dike
Deterministic Case HistoryAlton to Gale Levee System
200+ mile levee system on middle Mississippi River
Built in 40’s-50’s without seepage controls
Underseepage controls added in 50’s-60’s
Evaluated in ‘73 flood Tested in ‘93 flood
Deterministic Case HistoryAlton to Gale Levee System
zho
Clay
Sand
i o = h o / z
i c = (- w) / w
FS = i c / i o
Deterministic Case HistoryAlton to Gale Levee System
Based on predicted gradients at design flood, relief wells and seepage berms were constructed in critical locations
Piezometers were provided in marginal locations In 1973 flood, 20,000 piezometer readings were
made Generally indicated match to design assumptions
In 1993 flood system was loaded to top and overtopping
Again, generally matched design assumptions
Probabilistic Case HistoryHodges Village Dam
A dry reservoir
Notable seepage at high water events
Very pervious soils with no cutoff
Probabilistic Case HistoryHodges Village Dam
Required probabilistic analysis to demonstrate economic justification
Random variablesRandom variables horizontal conductivity conductivity ratio critical gradient
FASTSEEPFASTSEEP analyses using Taylor’s series to obtain probabilistic moments of FS
Probabilistic Case HistoryHodges Village Dam
Probabilistic Case HistoryHodges Village Dam
Pr (failure) = Pr (FS < 1)Pr (FS < 1)
This is a conditional conditional probabilityprobability, given the modeled pool, which has an annual probability of occurrence
Probabilistic Case HistoryHodges Village Dam
Annual Pr (failure)
= Pr [(FS < 1)|pool level] * Pr (pool level)
Integrated over all possible pool levels
Probabilistic Case HistoryHodges Village Dam
Probabilistic Case HistoryWalter F. George Lock and Dam
Probabilistic Case HistoryWalter F. George Lock and Dam
Has had several known seepage seepage eventsevents in 40 year history
From Weibull or Poisson frequency frequency analysisanalysis, can determine the probability distribution on the number of future events
Probabilistic Case HistoryWalter F. George Lock and Dam
Probabilistic Case HistoryWalter F. George Lock and Dam
Probabilistic Case HistoryHerbert Hoover Dike
128 mile long128 mile long dike surrounds Lake Okeechobee, FL
Built without cutoffs or filtered seepage control system
Boils and sloughing occur at high pool levels
Failure expectedFailure expected in 100 yr event (El 21)
Probabilistic Case HistoryHerbert Hoover Dike
Random variablesRandom variables hydraulic conductivities and ratio piping criteria
Seepage analysisSeepage analysis FASTSEEP
Probabilistic modelProbabilistic model Taylor’s series
Probabilistic Case HistoryHerbert Hoover Dike
Pr (failure) = Pr (FS < 1)Pr (FS < 1) Similar to Hodges Village, this is a
conditional probabilityconditional probability, given the occurrence of the modeled pool, which is has an annual probability
Consideration of length effectslength effects long levee is analogous to system of
discrete links in a chain; a link is hundreds of feet or meters
Workshop on Risk Assessment Workshop on Risk Assessment for Seepage and Piping for Seepage and Piping in Dams and Foundationsin Dams and Foundations
Thank You !Thank You !Thomas F. Wolff, Ph.D., P.E.
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