Probabilistic Risk Analysis for Dams

Martin McCann

Stanford University

& 

Jack R. Benjamin & Associates, Inc
Risk Analysis for Dam Systems

• In comparison to the nuclear industry, the state of PRA for dams is 

relatively new; maturing.

• In the nuclear business we are arguably in the second major 

generation of PRAs for all NPP.

• The nuclear industry has risk-informed regulation, a standard for 

PRAs, a PRA peer review process and regulatory oversight.
Risk Analysis for Dam Systems (cont.)

• With respect to external hazards (specifically seismic)

– Evaluation of aleatory and epistemic uncertainties is a requirement; 

evaluation of epistemic uncertainty is at the forefront, not an 

afterthought

– A SSHAC Level 3 or 4 is required

• In the dams business risk analysis is not as mature and not yet 

integrated into dam safety management and regulation; though as 

we heard it is getting there. 
Risk-Informed

• Work is going one now with a number of hydropower utilities and the 

FERC to develop risk-informed methods for the evaluation of dam 

systems. 

• The process is:

– Risk-informed (though risk analysis of a project may not be needed),

– Systems-based, and 

– Incorporates consideration of aleatory and epistemic uncertainties.

• The process is based on the assumption that the FERC is will have 

a tolerable risk criterion that must be satisfied.

• The process must be pragmatic, since all dams will not be required 

to do a PRA.
Systems-Based

• Dam systems are a comprised of:

– Structures (natural and man-made)

– Systems (control systems to operate gates, low level outlets, etc.),

– Mechanical & electrical components, and 

– Operators

• While dams are not as complex as nuclear power plants, there are 

numerous opportunities (combinations of events) that can lead to 

uncontrolled release.

• An objective of the seismic evaluation process is for the licensee to develop 

an understanding of:

– Seismic integrity/vulnerability of the structures, systems and components

– Accident sequences that may occur, and 

– System performance that supports risk-informed operator training, emergency 

action planning, and post-event operations.
Systems Based (cont.)

• Consider the following scenario for a hydro project:

– Earthquake occurs; dam survives but may be damaged

– The reservoir is maintained at a level above the spillway crest

– Gates have failed closed, offsite power and station power is lost

– The reservoir pool must be lowered to prevent failure, overtopping of the 

project embankments – at current (normal) inflows overtopping occurs 

in 12 hours

• Outflow capacity must be maintained in all cases, otherwise 

embankment overtopping will occur

• Potential modes of failure:

– Piping through the damaged embankment

– Overtopping the damaged or intact embankment
Embankment

Embankment
Systems Based (cont.)

Uncontrolled release of the reservoir

Reservoir retention structures are OK, but hydraulic 

control systems must operable to maintain outflows, 

otherwise embankment overtopping occurs leading 

to uncontrolled release of the reservoir.

Reservoir retention structures are damaged. Failure 

may occur unless the reservoir can be lower 

considerably (i.e., Lower San Fernando Dam). 

Hydraulic control systems must operable. 
Systems Based (cont.)

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PGA

Conditional Probability of Failure

Moderate Damage (Cracking)

Failure

Median Capacity for 

Performance

State 1; Moderate Damage

Median Capacity for 

Performance

State 2; Failure
Systems Based (cont.)

.....Less time to restore outflows/think Lower 

San Fernando Dam (1971)

Uncontrolled release of the reservoir
Consideration of Uncertainties

Taxonomy / Partitioning of Uncertainties

Element Epistemic Aleatory

Modeling Uncertainty about a model and the degree 

to which it can predict events. Model, 

epistemic uncertainty addresses the 

possibility that a model may systematically 

(but not necessarily predictably), over- or 

under-predict events/results of interest (i.e., 

deformations). 

Aleatory modeling variability is the 

variation not explained by a model. For 

instance, it is variability that is attributed 

to elements of the physical process that 

are not modeled and, therefore, 

represents variability (random differences) 

between model predictions and 

observations. 

Parametric Parametric epistemic uncertainty is 

associated with the estimate of model 

parameters given available data, indirect 

measurements, etc. 

This uncertainty is similar to aleatory 

modeling uncertainty. However, this is 

variability that may be due to factors that 

are random, but ave a systematic effect 

on model results.
Summary

• The seismic evaluation process is being prototype on a 

number of projects.

• Once this work is completed, final documentation of the 

methodology and implementation guidance will be 

prepared.