Risk modeling

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Risk modeling
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Principles

• What is probabilistic risk analysis (PRA)?
• Structured approach to identifying failure modes
  and analyzing their effects
• Accounting scheme for combining uncertainties
• Approach to reasoning about uncertainties using
  the math of probability.
• What it is not
• Inherently different from traditional practice

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Risk models

• Some of the hazards (perils) modeled
• Earthquakes
• Floods
• Hurricanes
• Fire, wildfire, conflagration
• Tornados
• Tsunamis
• Landslides
• Extreme weather

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Annual exceedance probability (AEP)
AEP Annual probability of an event or
consequence greater than a given level.
Exceedance Probability
p
L
Loss
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History

• The reason we use PRA is because we dont have
  enough data.

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History

• The reason we use PRA is because we dont have
  enough data.
• The reason we use PRA is because people have
  (very) poor intuition about probability.

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Approaches to hazard modeling

• Where most of the work is done for CAT models
• Seismic
• Hurricane
• Flood
• Fire
• Approach
• Spatial statistical model of occurrence
• Historical frequency model of severity
• Spatial model of effect at a particular site
• (Note there may by a difference between
  frequency of event and frequency of effect)

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Earthquake risk
Source Jones, K. 2003 Willis Limited
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Wind risk
the USAID Office of Foreign Disaster Assistance
and the Caribbean Regional Program
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Wildfire outbreak risk
Virginia Department of Forestry
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Approaches to inventory modeling

• Geospatial databases (GIS)
• Biggest advance in recent years changing quickly
• Mostly publicly available records (e.g., HAZUS)
• Impacted by DHS concerns
• Many web-based (free or cheap) tools

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Approaches to vulnerability (reliability) modeling

• Failure modes and effects analysis (FMEA)
• Event tree analysis
• Fault tree analysis
• Stochastic simulation (Monte Carlo)

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Principles

• Levels of probabilistic reasoning

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FMEA

• Failure Modes and Effects Analysis

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FMEA
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FMEA
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FMEA
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Event trees
Simple representation of earth dam system
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Dam Safety

• Reasons for Dam Failures
• OVERTOPPING 35 of all failures
• Inadequate Spillway Design
• Debris Blockage of Spillway
• Settlement of Dam Crest
• FOUNDATION DEFECTS 30 of all failures
• Differential Settlement
• Sliding and Slope Instability
• High Uplift Pressures
• Uncontrolled Foundation Seepage

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Dam Safety

• Reason for Dam Failures
• PIPING AND SEEPAGE 20 of all failures
• Internal Erosion Through Dam Caused by
  Seepage-"Piping"
• Seepage and Erosion Along Hydraulic Structures
  Such as Outlet
• Conduits or Spillways, or Leakage Through Animal
  Burrows
• Cracks in Dam
• CONDUITS AND VALVES 10 of all failures
• Piping of Embankment Material Into Conduit
  Through Joints or Cracks
• OTHER 5 of all failures

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Event trees
Generic event tree (US NRC 1975).
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Event trees
Simple event tree for an embankment dam
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Event Trees
Dependence of Probabilities on earlier events
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Event trees
Annualized initiating event generates input
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Event Trees
Event trees sample space
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Event Trees
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Event Trees
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Event Trees
Hydrologic, piping, and strength failure parts of
the levee failure event trees
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Influence diagrams
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Event Trees
Influence diagram for levee failure
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Event Trees
Influence diagram for levee failure, including
active decision node
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Event Trees
Partial event tree for hydrologic failure at
Alouette Dam (Salmon 1995)
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Dam Safety

• Different approaches of the various owners and
  regulators
• Bureau of Reclamation
• US Army Corps of Engineers
• New South Wales (Austl)
• Canadian Electricity Association
• Dam Safety Interest Group
• BCHydro, OPG, HydroQuebec, Vattenfall, Scottish
  Southern Energy
• Ontario Ministry of Natural Resources OPG
• Department of Environment and Rural Affairs
  (DEFRA-UK)

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Glenmaggie Dam
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Fault tree analysis
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Fault tree analysis
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Fault trees
Fault tree of dam failure (Fry 2001)
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Approaches to consequence modeling

• Economics (NED)
• Loss of life/property
• Environmental
• Historical