Probabilistic Assessment of Overtopping Reliability of a Dam

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Probabilistic Assessment of Overtopping
Reliability of a Dam

• Melih YANMAZ and M. Engin GÜNINDI
• Middle East Technical University
• Civil Engineering Department
• Ankara-Turkey

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Probabilistic Design/Analysis

• Assessment of various reliability levels under
  different combinations of random design
  parameters.
• Probability-based safety levels of existing dams
  may be evaluated against various tendencies.
• The adequacy of old dams needs to be checked with
  respect to the current safety and conformity
• degree of measures to be implemented

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Probabilistic Analysis of Existing Dams

• Important if pronounced variations occur in
• aging and deterioration of constructional
  materials
• deficiencies due to structural, hydraulic, and
  geotechnical aspects
• changes in watershed characteristics
• alteration of operational policies
• inability of old design methods to consider
  random nature of loading and resistance
  parameters
• Probabilistic design and operation approaches
  provide more realistic information for
  site-specific conditions.

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Multivariate Flood Frequency Analysis
Accurate flood modelling by the joint
consideration of flood peaks, volumes, and
durations Foundations of the modelling Sackl
and Bergmann (1987), Goel et al. (1998),
Escalante-Sandoval and Raynal-Villaseñor (1998),
Yue (2000), Yue (2001), Yue et al. (2001), Yue
(2002), Yue and Rasmussen (2002), Michele et al.
(2005), Smith et al. (1982)
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Five-parameter bivariate gamma distribution

• A good distribution for hydrologic events having
  skewed distributions, such as flood peak
  discharge and flood volume

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gM2/S2 (Scale parameter of marginal gamma
distribution) ßM/S2 (Shape parameter of marginal
gamma distribution) Mmean Sstandard deviation
The PDFs of marginal distributions of X and Y
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Case Study- Fol Creek Basin in Turkey
Frequent floods loss of lives and damage to
facilities It is an elongated basin A219.6 km2
and hmax2340 m. Existing structural measures
be supplemented by an upstream flood detention
dam at 2511 m upstream of the Black Sea
shoreline Design of the dam Check its adequacy
against overtopping induced by flood action
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Flood Frequency Analysis

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Uni-variate Flood Frequency Analysis

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Bi-variate Flood Frequency Analysis

Gamma marginals are used for Qp and V
KolmogorovSmirnov test is applied. The
critical value 0.290 at a 0.05. The KS test
statistics 0.198 for Qp

O.K. 0.204 for V
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Multivariate Analysis of Fol Creek Data
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Limits for the Data to be Generated

• Definition of rmVD/QD

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Generation of Equal Return Period Curves

• Achieved by a code written in MS Excel medium

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rmin
A
B
C
D
E
rmax
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Comparison of Qp values
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Generation of hydrographs

• Aldama and Ramirez (1999) technique

tp2V/3Qp tb3tp
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Generated hydrographs for Cases A-E
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• The cases A and E represent two extreme
  conditions within the limits of upper and lower
  bounds of Qp and V pairs under the return period
  of 100 years.
• Hydrograph A has a high Qp but small tb
• Hydrograph E has a small Qp but large V and tb.
• Greater overtopping risk
• Release of high outflows during a long duration.
  
• Duration of downstream inundation increases as
  the outflow experiences the cases from A to E.

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Computation of Overtopping Reliability
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• Overtopping reliabilityP(hcgthm)
• K3 m, D1 m, L40 m hs25 m hi3.2 m
• Hydrograph shapes are expressed by Eq. (14)

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• Reservoir routing is carried out using Monte
  Carlo technique with 20000 cycles

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Stage hydrographs
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Deterministic versus probabilistic stage
hydrographs
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Variation of the deterministic SF against VV/Vd
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Variation of reliability against VV/Vd
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Conclusions

• a of an earth-fill flood detention dam is
  investigated.
• The design Qp and V are determined using a
  bivariate gamma distribution with five
  parameters.
• Equal return period curves (Qp vs V) are
  generated.
• A number of hydrographs under Tr 100 years are
  obtained using the technique proposed by Aldama
  and Ramirez to observe their effects on a
• An overflow spillway 25 m high and 40 m long is
  proposed. Flood frequency analyses are performed
  for univariate and bivariate cases.

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Conclusions-contd.

• The average Qp of different PDFs in univariate
  analysis lt the lower limits of Qp ranges of the
  bivariate analysis for all return periods.
• This result implies that the deterministic
  approach yield underestimates in the design
  compared to the probabilistic approach.
• Various possible hydrographs tested under
  Tr100-year yielded relatively high values of a
• Therefore, the flood detention dam is effective.
• The effects hi, cov, PDF on h and various
  relevant dimensions of the dam on a may also be
  examined