Workshop on Risk Assessment for Seepage and Piping in Dams and Foundations

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

[email protected]://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


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


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


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


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


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


zho

Clay

Sand

i o = h o / z

i c = (- w) / w

FS = i c / i o


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


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



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


Annual Pr (failure)

= Pr [(FS < 1)|pool level] * Pr (pool level)

Integrated over all possible pool levels


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 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)


Random variablesRandom variables hydraulic conductivities and ratio piping criteria

Seepage analysisSeepage analysis FASTSEEP

Probabilistic modelProbabilistic model Taylor’s series


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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Workshop on Risk Assessment for Seepage and Piping in Dams and Foundations