Objective:

1

• Objective
• Develop a simplified probabilistic model for risk
  assessment of concrete gravity dam-foundation
  system. Evaluate sliding, overtopping,
  overturning, and internal stability as failure
  modes. Fit it within overall Frameworks.

2

• Current Progress
• The probability of failure for a specific hazard
  can be depicted by its fragility.
• This work unit will demonstrate the use of
  fragility modeling as tool for risk assessment of
  concrete gravity dams present quantitative
  methods to evaluate failure probabilities of
  these dams due to extreme events.

3

• 2-D structural fragility model application to a
  concrete gravity dam, based on work of Dr. Bruce
  Ellingwood.
• Extreme postulated hydrologic event
  considered.

4

• Fragility analysis requires probabilistic models
  and supporting statistics for all parameters that
  play a significant role in dam performance and
  safety.
• Ideally, one could develop a fragility for each
  of several progressively more severe states of
  damage.

5

• Primary load condition affecting concrete gravity
  dams arises from the differential hydrostatic
  head that occurs during hydrologic events up to
  and including the PMF.

6

7

• Limit states included in application
• LS1- resultant outside of kern (rigid body)or
  tension at the heel (FEM)
• LS2- resultant outside of middle-half of base
• LS3- resultant outside the base
• LS4- pool elevation above the dams top height
• LS5- material failure (foundation at toe)
• LS6- material failure (concrete at toe)
• LS7- sliding failure at the dam/foundation
  interface
• LS8- material failure (at the dams neck) (FEM
  only)
• LS9- deflection at top of dam relative to heel
  0.1m (FEM only)

8

9

• Statistical distributions of parameters
• Normal Concrete compressive strength
• Uniform for max uncertainty
• Drain effectiveness (0-100)
• Tail water elevation (1360-1400 ft)
• Effective uplift area (33-100)
• Angle of friction (40-52)
• Cohesion (24-32 psi)
• Compressive strength of intact rock (6000-15000
  psi)

10

• Loads included
• Horizontal hydrostatic pressure on the upstream
  (from the impounded water) downstream (from the
  tail water)
• Uplift force at the base of the dam
• Weight of the dam
• Vertical weights of water upstream downstream
  of the dam
• Ice pressure of 292 kN/m applied at pool
  elevation of the reservoir
• No interaction between adjacent monoliths is
  included in this sample

11

• Probability of achieving various limit states for
  a given pool height is obtained by simulating the
  performance of 1000 dams (defined by the random
  variables)

12

• Limit state probability is expressed as
• PLS ? PLS Y y P Y y
• PYy hazard (annual probability)
• PLS Y y conditional probability of
  structural failure given that Y y
• Fragility PLS Y y, ? conditional
  probability of LS given demand y and ? vector
  of fragility parameters

13

• FEM

14

15

• Future work
• Fragility translated to failure probability for
  inclusion into both frameworks.
• Representatives cases for use with portfolio
  analysis
• Placeholders for hydrologic, uplift, etc.
• 2D model to 3D model in order demonstrate effect
  on fragility.