Transcript Workshop on Risk Assessment for Seepage and Piping in Dams

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

Describe your preferred approach,
methodology and procedure 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
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Develop a set of detailed foundation profiles
from boring and testing data
Assign hydraulic conductivity values
Perform a set of finite-element
seepage analyses considering
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multiple sections
multiple conductivity assumptions
Compare predicted gradients to
piping criteria
Question 1—Preferred approach
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However, I would perform the analysis
probabilistically. Not to determine the
absolute probability of failure, but to recognize
inherent uncertainty in the modeled
parameter values
Question 1—Preferred approach
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Deterministic approach
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k = 400 x 10-4 cm/s
Probabilistic approach
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E[k] = 400 x 10-4 cm/s
k = 100 x 10-4 cm/s
Question 1—Preferred approach
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Deterministic approach
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i = 0.65
FS = 1/0.65 = 1.54
Probabilistic
approach
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E[i - icrit] = 0.35
(i -i c) = 0.15
Question 2

In this conventional evaluation, what
information, factors, practices and
considerations have the greatest
influence on establishing the potential of a
seepage and piping problem developing?
What are the significant unknowns in
this process?
Question 2
information, factors, practices and considerations
Foundation stratigraphy
 Relative conductivity of various
materials in various directions
 Homogeneity or non-homogeneity of
materials
 internal stability of materials, filter
capabilities of one material to the next
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Question 2
information, factors, practices and considerations
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Piping criteria
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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 defense -reliability through redundancy
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Question 2—Unknowns
Hydraulic conductivity of materials
 Degree of anisotropy
 Piping criteria
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Questions 3
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In performing a risk assessment for a project
with an embankment dam, what are the
important considerations, cautions and
best methodology for the Corps to use in
establishing the probability of failure of the
dam for seepage and piping?
How important is sound engineering
judgment?
Questions 3
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Probability of failure ?
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Do we know what we really mean here?
What is the denominator?
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Per annum ?
Per design ?
Uncertainty in parameters is unique to the
structure considered, but is per design
per annum requires some input regarding
observed frequency
Questions 3

Considerations and Cautions

Do you know the question you are trying to
answer?

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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
sophistication in the analysis?
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Accuracy of answer may be much more important than
precision -- do we end up at the correct decision?
Questions 3
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Best Methodology - Pr(f) per design
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Characterize uncertainty in parameters
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Use FOSM methods, or if practical,
simulation methods
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requires a mix of statistics and judgment
Uncertainty in parameters
 uncertainty in performance measure
Use results as comparison to a common criteria
for acceptable risk (also requires judgment)
Questions 3
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Best Methodology - Pr(f) per annum
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Estimate annual probability of failure for a class of
structures based on historical data fit to Weibull
distribution
This is problematical because events are few,
making confidence limits wide
Somehow adjust results for a specific structure
based on its characteristics, performance and
uncertainties within its class.
Question 4
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What approach would you recommend
to obtain the final results (i.e. Probability
of Failure = 4.65 x 10-4) -- an
analytical evaluation of the data and
information, or a subjective
evaluation of the data and information,
or somewhere in between?
Question 4—Same answer !
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Probability of failure ?
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Do we know what we really mean here?
What is the denominator?
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Per annum ?
Per design ?
Uncertainty in parameters is unique to the
structure considered, but is per design
per annum requires some input regarding
observed frequency
Question 4
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Approach
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Best estimates of parameter values and
their uncertainties, based on both
statistics and judgment
A probabilistic analysis to determine
expected performance and its inherent
uncertainty
Comparison of the results to some
common criteria of acceptability
Questions
Has the theory developed sufficiently
for use in practical applications?
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Yes
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Comparative reliability
problems
Water vs. Sand vs. Clay
pressures on walls,
different b for same FS
Event tree for
identifying relative risks
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No
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Tools for complex geometries
Absolute reliability
Spatial correlation where
data are sparse
Time-dependent change in
geotechnical parameters
Accurate annual risk costs
Questions
When and where are the theories
used most appropriately?
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FOSM Reliability Index
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Reliability Comparisons
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structure to structure
component to component
before and after a repair
relative to desired target value
Insight to Uncertainty Contributions
Questions
When and where are the theories
used most appropriately?
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Frequency - Based Probability
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Earthquake and Flood recurrence, with
conditional geotechnical probability values
attached thereto
Recurring random events where good
models are not available: scour, throughseepage, impact loads, etc.
Wearing-in, wearing-out, corrosion, fatigue
Questions
When and where are the theories
used most appropriately?
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Expert Elicitation
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“Hard” problems without good frequency
data or analytical models
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seepage in rock
likelihood of finding seepage entrance
likelihood of effecting a repair before distress is
catastrophic
Questions
Are time-dependent reliability analysis
possible for geotechnical problems? How?
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YES
 Conditional probability values tied to timedependent events such as earthquake acceleration
or water level
NO
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variation of strength, permeability, geometry
(scour), etc; especially within resource constraints
of planning studies
Questions
What Methods are Recommended for Reliability
Assessments of Foundations and Structures ?
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Define purpose of analysis
Select simplest reasonable approach consistent
with purpose
Build an event tree
Fill in probability values using whichever of three
approaches is appropriate to that node
Understand and admit relative vs absolute
probability values
Needs
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A Lot of Training
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Develop familarity and feeling for techniques by
practicing engineers
Research
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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
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Deterministic
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Alton to Gale Levee System
Probabilistic
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Hodges Villages Dam
Walter F. George Lock and Dam
Herbert Hoover Dike
Deterministic Case History
Alton to Gale Levee System
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200+ mile levee
system on middle
Mississippi River
Built in 40’s-50’s
without seepage
controls
Underseepage
controls added in 50’s60’s
Evaluated in ‘73 flood
Tested in ‘93 flood
Deterministic Case History
Alton to Gale Levee System
ho
Clay
Sand
z
io=ho/z
i c = ( - w) / w
FS = i c / i o
Deterministic Case History
Alton to Gale Levee System
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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
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Generally indicated match to design assumptions
In 1993 flood system was loaded to top and
overtopping
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Again, generally matched design assumptions
Probabilistic Case History
Hodges Village Dam
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A dry reservoir
Notable
seepage at
high water
events
Very pervious
soils with no
cutoff
Probabilistic Case History
Hodges Village Dam
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Required probabilistic analysis to
demonstrate economic justification
Random variables
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horizontal conductivity
conductivity ratio
critical gradient
FASTSEEP analyses using Taylor’s series
to obtain probabilistic moments of FS
Probabilistic Case History
Hodges Village Dam
Probabilistic Case History
Hodges Village Dam
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Pr (failure)
= Pr (FS < 1)
This is a
conditional
probability, given
the modeled pool,
which has an annual
probability of
occurrence
Probabilistic Case History
Hodges Village Dam
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Annual Pr (failure)
= Pr [(FS < 1)|pool level] * Pr (pool level)
Integrated over all possible pool levels
Probabilistic Case History
Hodges Village Dam
Probabilistic Case History
Walter F. George Lock and Dam
Probabilistic Case History
Walter F. George Lock and Dam
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Has had several known
seepage events in 40
year history
From Weibull or Poisson
frequency analysis,
can determine the
probability distribution
on the number of future
events
Probabilistic Case History
Walter F. George Lock and Dam
Probabilistic Case History
Walter F. George Lock and Dam
Probabilistic Case History
Herbert Hoover Dike
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128 mile long dike
surrounds Lake
Okeechobee, FL
Built without cutoffs
or filtered seepage
control system
Boils and sloughing
occur at high pool
levels
Failure expected in
100 yr event (El 21)
Probabilistic Case History
Herbert Hoover Dike
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Random variables
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Seepage analysis
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hydraulic conductivities and ratio
piping criteria
FASTSEEP
Probabilistic model
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Taylor’s series
Probabilistic Case History
Herbert Hoover Dike
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Pr (failure) = Pr (FS < 1)
Similar to Hodges Village, this is a
conditional probability, given the
occurrence of the modeled pool, which is has
an annual probability
Consideration of length effects
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long levee is analogous to system of discrete links
in a chain; a link is hundreds of feet or meters
Workshop on Risk Assessment
for Seepage and Piping
in Dams and Foundations
Thank You !
Thomas F. Wolff, Ph.D., P.E.