Incorporating Breach Parameter 

Estimation and Physically-Based Dam 

Breach Modeling into Probabilistic Dam 

Failure Analysis

Tony L. Wahl

USBR Hydraulics Laboratory

Denver, Colorado

Panel 4 - January 30, 2013
Issues

• How to evaluate failure probability?

• How to estimate breach parameters in a 

probabilistic way?

– Size of breach

– Shape of breach

– Time of failure (rate of erosion)

• Scope of this talk limited to embankment 

dams
Failure Probability

• Failure probability is a central question

Loading 

probability

Dam fails Consequences

Events progress 

toward failure

No failure

No progression
Hydrologic Failure Modes

• Is depth and duration of overtopping 

sufficient to produce unstoppable erosion?

• Can flood surcharge in the reservoir trigger a 

seepage-erosion sequence that progresses 

too quickly to stop?
Riley 1986

• First work discussing analysis of limited 

overtopping that might not cause dam failure

• Applied only to cohesive, erosion-resistant 

embankments protected by well maintained 

vegetation

• Suggested permissible duration-velocity 

limits for flow over crest and down the slope

• Also suggested permissible total volumes of 

flow in a given duration
Riley 1986

• Addressed the “will it fail?” question

– Suggested conservative thresholds for when 

failure would occur

• Did not address the probability of failure 

question

– When thresholds were exceeded, probability of 

failure was 1
Fragility Curves

• Attempt to estimate probability of failure 

based on engineering judgment of team 

members

– Depth of overtopping

– Velocity of flow

– Duration of overtopping / Volume of water

– Quality of slope protection (vegetation or riprap)

– Erodibility of embankment materials

• Very subjective...
New Tools

• Physically-based dam breach models

– WinDAM (USDA-ARS)

– HR BREACH (HR Wallingford)

– Others...
Dam Breach Models

• Inputs

– Hydraulic attack (overtopping depth, velocity, 

shear stress, stream power)

– Slope protection, threshold of failure

– Erodibility of embankment material (measured!)

• Estimate erosion rates

• Simulate mechanics of headcut development

– Simulate extent of erosion during duration of 

event
Submerged Jet Test - Erodibility
Compaction & Erodibility

0.01

0.1

1

10

100

1000

80

85

90

95

100

105

110

115

120

125

6% 8% 10% 12% 14% 16% 18% 20%

kd, ft/hr/psf

γd, pcf

Water Content

Dry unit weight

Erodibility

Test 1

Test 2

Test 3
Dam Breach Models

• Output

– Determine whether threshold for failure is reached

– Outflow hydrograph

– Time-history of breach development

• Probabilistic uses

– Models run quickly

– Can readily analyze variations in flood loading, 

slope protection and soil erodibility

Consequence analysis
Greg Hanson and Sherry Hunt – USDA-ARS

Soils used in breach widening tests
Effect of Wet or Dry Compaction is Dramatic
Compaction effort 

is also important

Dam Breach Model Status Today

• WinDAM B

– USDA-ARS (Stillwater, Oklahoma)

– Homogeneous embankments

– Vegetation or riprap slope protection

– Overtopping only

– Energy- and stress-based headcut erosion 

options

– Public domain

– Piping erosion module being developed...

– Zoned embankments envisioned for future...
Dam Breach Model Status Today

• HR BREACH

– HR Wallingford

– Homogeneous or zoned embankments

– Vegetation or riprap slope protection

– Overtopping and piping

– Energy-based headcut erosion

– Surface erosion option (for granular materials)

– Monte Carlo simulation option

– NOT Public domain

• Being used in consulting

• Being incorporated into other tools (InfoWorks RS 2D, AREBA 

rapid appraisal tool for homogeneous embankment breach)
Simplified Methods

• When physically-based erosion and dam 

breach modeling is not justified or practical:

– Breach parameters can be predicted using 

established regression equations

– Does not help address the “will it fail?” question

• Can we put probabilities on ranges of breach 

parameters?
Probabilistic Breach Parameters

• No work has been done that specifically 

assigns probabilities

• Three studies in last 10 years have 

addressed uncertainty of breach parameters

– Wahl (2004)

– Froehlich (2008)

– Xu & Zhang (2009)
Wahl (2004)

• Evaluated existing breach width and breach time 

equations to see how accurately they predicted 

observed values from case studies

• Uncertainties:

Breach width ± 1/3 order of magnitude

Breach time ± 1.0 order of magnitude

Peak outflow ± 0.5 to 1.0 order of magnitude

• USBR (1988), Von Thun & Gillette (1990) and 

Froehlich (1995) similar for breach width

• Froehlich (1995) peak flow and time equations were 

superior to competitors
Froehlich (2008)

• Revised breach parameter equations

– Breach width

– Time of failure

– Side slope of trapezoidal breach opening

• Presented case study of using a Monte 

Carlo-type stochastic dam breach flood 

model

– Inputs were breach parameters above, plus the 

critical overtopping head needed to trigger failure
Xu & Zhang (2009)

• Developed new equations using multiparameter nonlinear regression techniques 

and different input variables

– dam height, reservoir shape coefficient, dam type, 

failure mode, and dam erodibility (high, medium, 

low)

– dam erodibility was most significant factor

• Performed uncertainty analysis to compare 

their equations to others
Breach Parameters in Risk 

Assessment

• Use uncertainty estimates and assumed 

probability distributions

• It is only practical to treat many parameters 

this way if you have a flood model that 

supports Monte Carlo simulation or 

equivalent
Xu & Zhang (2009)

• Failure time equations should be used with 

caution

• Approx. 30 dam failure cases were used to 

develop their failure time equations

• 9 dams used in their analysis were also used 

by Froehlich (1995)

– Same failure time for 4 of the 9

– Dramatically longer failure times for 5 of the 9

(4x longer)

– No specific explanation of why they differ
Teton Dam

• Froehlich Tf = 1.25 hr

• Xu & Zhang, Tf = 4 hr
80% of volume released in 1.5 hrs
Questions?