1. 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

2. Question 1 approach, methodologyprocedure n 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.

3. Question 1—Preferred approach profiles n Develop a set of detailed foundation profiles from boring and testing data conductivity n Assign hydraulic conductivity values finite-element n Perform a set of finite-element seepage analyses considering l multiple sections l multiple conductivity assumptions gradients criteria n Compare predicted gradients to piping criteria

4. Question 1—Preferred approach n However probabilistically n 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

5. Question 1—Preferred approach n Deterministic approach l k = 400 x 10 -4 cm/s n Probabilistic approach l E[k] = 400 x 10 -4 cm/s l  k = 100 x 10 -4 cm/s

6. Question 1—Preferred approach n Deterministic approach l i = 0.65 l FS = 1/0.65 = 1.54 n Probabilistic approach l E[i - i crit ] = 0.35 l  (i -i c) = 0.15

7. Question 2 information, factors, practices and considerations unknowns n 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?

8. information, factors, practices and considerations Question 2 information, factors, practices and considerations stratigraphy n Foundation stratigraphy n Relative conductivity n Relative conductivity of various materials in various directions n Homogeneity n Homogeneity or non-homogeneity of materials n internal stability n internal stability of materials, filter capabilities of one material to the next

9. information, factors, practices and considerations Question 2 information, factors, practices and considerations n Piping criteria l Corps’ criteria have traditionally been derived on gradient only, and not particle size or tractive shear stress n All of the above have inherent uncertainty multiple lines of defense n Presence of multiple lines of defense -- reliability through redundancy

10. Question 2—Unknowns conductivity n Hydraulic conductivity of materials anisotropy n Degree of anisotropy n Piping criteria

11. Questions 3 considerations, cautions best methodology probability of failure n 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? judgment n How important is sound engineering judgment?

12. Questions 3 n Probability of failure ? l Do we know what we really mean here? l What is the denominator? s Per annum ? s Per design ? per design l Uncertainty in parameters is unique to the structure considered, but is per design l per annum l per annum requires some input regarding observed frequency

13. Questions 3 n Considerations and Cautions question l Do you know the question you are trying to answer? s Probability of this dam failing in a given time span s Relative reliability of this dam with regard to other dams sophisticationanalysis l What are the incremental benefits of increasing sophistication in the analysis? s Accuracy of answer may be much more important than precision -- do we end up at the correct decision?

14. Questions 3 n Best Methodology - Pr(f) per design uncertainty in parameters l Characterize uncertainty in parameters judgment s requires a mix of statistics and judgment FOSM methods l Use FOSM methods, or if practical, simulation methods s Uncertainty in parameters  uncertainty in performance measure comparison to a common criteria judgment l Use results as comparison to a common criteria for acceptable risk (also requires judgment)

15. Questions 3 n Best Methodology - Pr(f) per annum historical data l Estimate annual probability of failure for a class of structures based on historical data fit to Weibull distribution problematical l This is problematical because events are few, making confidence limits wide adjust results l Somehow adjust results for a specific structure based on its characteristics, performance and uncertainties within its class.

16. Question 4 approach analytical evaluation subjective evaluation in between n 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?

17. Question 4—Same answer ! n Probability of failure ? l Do we know what we really mean here? l What is the denominator? s Per annum ? s Per design ? per design l Uncertainty in parameters is unique to the structure considered, but is per design l per annum l per annum requires some input regarding observed frequency

18. Question 4 n Approach parameter values uncertainties l Best estimates of parameter values and their uncertainties, based on both statistics and judgment probabilistic analysis l A probabilistic analysis to determine expected performance and its inherent uncertainty l Comparison common criteria of acceptability l Comparison of the results to some common criteria of acceptability

19. Questions n Yes l Comparative reliability problems Water vs. Sand vs. Clay pressures on walls, different  for same FS l Event tree for identifying relative risks n No l Tools for complex geometries l Absolute reliability l Spatial correlation where data are sparse l Time-dependent change in geotechnical parameters l Accurate annual risk costs Has the theory developed sufficiently for use in practical applications ?

20. Questions n FOSM Reliability Index l Reliability Comparisons s structure to structure s component to component s before and after a repair s relative to desired target value l Insight to Uncertainty Contributions When and where are the theories used most appropriately?

21. Questions n Frequency - Based Probability l Earthquake and Flood recurrence, with conditional geotechnical probability values attached thereto l Recurring random events l Recurring random events where good models are not available: scour, through- seepage, impact loads, etc. l Wearing-in, wearing-out, corrosion, fatigue When and where are the theories used most appropriately?

22. Questions n Expert Elicitation l “Hard” problems without good frequency data or analytical models s seepage in rock s likelihood of finding seepage entrance s likelihood of effecting a repair before distress is catastrophic When and where are the theories used most appropriately?

23. Questions n YES l Conditional probability values tied to time- dependent events such as earthquake acceleration or water level n NO l variation of strength, permeability, geometry (scour), etc; especially within resource constraints of planning studies Are time-dependent reliability analysis possible for geotechnical problems? How?

24. Questions n Define purpose n Define purpose of analysis simplest reasonable approach n Select simplest reasonable approach consistent with purpose event tree n Build an event tree whichever of three approaches n Fill in probability values using whichever of three approaches is appropriate to that node relative vs absolute probability n Understand and admit relative vs absolute probability values What Methods are Recommended for Reliability Assessments of Foundations and Structures ?

25. Needs Training n A Lot of Training l Develop familarity and feeling for techniques by practicing engineers n Research l Computer tools for practical probabilistic seepage and slope stability analysis for complex problems l Characterizing and using real mixed data sets, of mixed type and quality, on practical problems, including spatial correlation issues l Approaches and tools for Monte Carlo analysis

26. Four Case Histories n Deterministic l Alton to Gale Levee System n Probabilistic l Hodges Villages Dam l Walter F. George Lock and Dam l Herbert Hoover Dike

27. Deterministic Case History Alton to Gale Levee System n 200+ mile levee system on middle Mississippi River n Built in 40’s-50’s without seepage controls n Underseepage controls added in 50’s-60’s n Evaluated in ‘73 flood n Tested in ‘93 flood

28. Deterministic Case History Alton to Gale Levee System z hoho Clay Sand i o = h o / z i c = (  -  w ) /  w FS = i c / i o

29. Deterministic Case History Alton to Gale Levee System n Based on predicted gradients at design flood, relief wells and seepage berms were constructed in critical locations n Piezometers were provided in marginal locations n In 1973 flood, 20,000 piezometer readings were made l Generally indicated match to design assumptions n In 1993 flood system was loaded to top and overtopping l Again, generally matched design assumptions

30. Probabilistic Case History Hodges Village Dam n A dry reservoir n Notable seepage at high water events n Very pervious soils with no cutoff

31. Probabilistic Case History Hodges Village Dam n Required probabilistic analysis to demonstrate economic justification n Random variables l horizontal conductivity l conductivity ratio l critical gradient n FASTSEEP n FASTSEEP analyses using Taylor’s series to obtain probabilistic moments of FS

32. Probabilistic Case History Hodges Village Dam

33. Pr (FS < 1) n Pr (failure) = Pr (FS < 1) conditional probability n This is a conditional probability, given the modeled pool, which has an annual probability of occurrence

34. Probabilistic Case History Hodges Village Dam n Annual Pr (failure) = Pr [(FS < 1)|pool level] * Pr (pool level) Integrated over all possible pool levels

35. Probabilistic Case History Hodges Village Dam

36. Probabilistic Case History Walter F. George Lock and Dam

37. seepage events n Has had several known seepage events in 40 year history frequency analysis n From Weibull or Poisson frequency analysis, can determine the probability distribution on the number of future events

38. Probabilistic Case History Walter F. George Lock and Dam

40. Probabilistic Case History Herbert Hoover Dike n 128 mile long n 128 mile long dike surrounds Lake Okeechobee, FL n Built without cutoffs or filtered seepage control system n Boils and sloughing occur at high pool levels n Failure expected n Failure expected in 100 yr event (El 21)

41. Probabilistic Case History Herbert Hoover Dike n Random variables l hydraulic conductivities and ratio l piping criteria n Seepage analysis l FASTSEEP n Probabilistic model l Taylor’s series

42. Probabilistic Case History Herbert Hoover Dike Pr (FS < 1) n Pr (failure) = Pr (FS < 1) conditional probability n Similar to Hodges Village, this is a conditional probability, given the occurrence of the modeled pool, which is has an annual probability length effects n Consideration of length effects l long levee is analogous to system of discrete links in a chain; a link is hundreds of feet or meters

43. Workshop on Risk Assessment for Seepage and Piping in Dams and Foundations Thank You ! Thomas F. Wolff, Ph.D., P.E.