What is the Froehlich 2008 breach width equation?

Froehlich (2008) gives average breach width as B = 0.27·Ko·Vw^0.32·hb^0.04, where Vw is reservoir volume at the time of failure in cubic metres, hb is breach height in metres, and Ko is 1.3 for overtopping or 1.0 for piping. Failure time is tf = 63.2·sqrt(Vw/(g·hb²)) in seconds. Recommended side slopes are 1.0H:1V for overtopping and 0.7H:1V for piping.

Which dam breach parameter equation should I use?

Froehlich (2008) is the most widely used and is the current default in HEC-RAS for embankment dams, being based on the largest and most recent case-history dataset. Run Von Thun and Gillette (1990) and MacDonald and Langridge-Monopolis (1984) alongside it as a sensitivity check. Because breach parameters carry large uncertainty, standard practice is to bracket the result with several methods rather than rely on a single equation.

What is the Von Thun and Gillette breach equation?

Von Thun and Gillette (1990) give average breach width as B = 2.5·hw + Cb, where hw is depth of water above the breach invert in metres and Cb is an offset that depends on reservoir volume: 6.1 m below 1.23×10⁶ m³, 18.3 m to 6.17×10⁶ m³, 42.7 m to 1.23×10⁷ m³, and 54.9 m above that. Failure time is 0.02·hw + 0.25 hours for erosion-resistant fill and 0.015·hw hours for easily erodible fill.

How accurate are dam breach parameter predictions?

They are uncertain by design. Froehlich (2008) reports prediction uncertainty of roughly plus or minus one third on breach width and closer to a factor of two on failure time. Peak outflow is far more sensitive to failure time than to breach width, so failure time usually dominates the uncertainty in a dam-break study. This is why regulators expect a sensitivity analysis rather than one deterministic number.

What is the difference between overtopping and piping breach parameters?

Overtopping failures produce wider breaches and are assigned a larger multiplier: Ko = 1.3 in Froehlich 2008 and 1.4 in Froehlich 1995, versus 1.0 for piping in both. Side slopes are also flatter for overtopping, 1.0H:1V against 0.7H:1V for piping. A piping failure additionally requires a starting elevation for the pipe, which an overtopping failure does not.

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Dam Breach Parameters — Reference

By Michael Flynn, PE · water resources & dam safety engineer

The four regression equation sets used in practice to estimate breach width, side slope, and failure time for embankment dams. All equations below are metric — V in m³, h and B in m, g = 9.81 m/s². Convert before and after; these regressions are not unit-agnostic.

Notation

Symbol	Meaning	Units
B̄	Average breach width	m
V_w	Reservoir volume at time of failure	m³
V_out	Volume of water discharged through breach	m³
h_b	Breach height (invert to crest)	m
h_w	Depth of water above breach invert at failure	m
V_er	Volume of embankment material eroded	m³
K_o	Failure-mode factor (overtopping vs piping)	—
t_f	Breach formation (failure) time	s or hr

The Four Equation Sets

Froehlich (2008) — current default

B̄ = 0.27 · K_o · V_w^0.32 · h_b^0.04
t_f = 63.2 · √[ V_w / (g · h_b²) ] (seconds)

K_o = 1.3 overtopping, 1.0 piping. Side slope 1.0H:1V overtopping, 0.7H:1V piping. Based on 74 case histories — the largest dataset of the four, and the reason this set is the usual starting point.

Froehlich (1995)

B̄ = 0.1803 · K_o · V_w^0.32 · h_b^0.19
t_f = 0.00254 · V_w^0.53 · h_b^−0.90 (hours)

K_o = 1.4 overtopping, 1.0 piping. Side slope 1.4H:1V overtopping, 0.9H:1V piping. Superseded by the 2008 set but still cited and still offered in most software.

MacDonald & Langridge-Monopolis (1984)

V_er = 0.0261 · (V_out · h_w)^0.769 (earthfill)
t_f = 0.0179 · V_er^0.364 (hours)

Predicts eroded volume rather than width directly — breach geometry is then back-figured from the embankment section, assuming a trapezoid with 0.5H:1V side slopes. The distinct approach is exactly why it is a useful independent check.

Von Thun & Gillette (1990)

B̄ = 2.5 · h_w + C_b
t_f = 0.02 · h_w + 0.25 (erosion-resistant, hours)
t_f = 0.015 · h_w (easily erodible, hours)

The only set that keys failure time to erodibility rather than volume alone, which makes it the useful bracket when embankment materials are known.

Failure-Mode Factor K_o and Side Slopes

Method	K_o overtopping	K_o piping	Side slope z (H:1V)
Froehlich (2008)	1.3	1.0	1.0 OT / 0.7 piping
Froehlich (1995)	1.4	1.0	1.4 OT / 0.9 piping
MacDonald & L-M	—	—	0.5 (assumed)
Von Thun & Gillette	—	—	1.0 typical

Von Thun & Gillette Offset C_b

Reservoir volume V_w (m³)	V_w (ac-ft)	C_b (m)	C_b (ft)
< 1.23×10⁶	< 1,000	6.1	20
1.23×10⁶ – 6.17×10⁶	1,000 – 5,000	18.3	60
6.17×10⁶ – 1.23×10⁷	5,000 – 10,000	42.7	140
> 1.23×10⁷	> 10,000	54.9	180

Worked Comparison — All Four Methods

Small high-hazard embankment, overtopping failure. V_w = 500 ac-ft (616,800 m³), h_b = h_w = 30 ft (9.14 m), earthfill.

Method	B̄ (m)	B̄ (ft)	t_f (hr)
Froehlich (2008)	27.3	90	0.48
Froehlich (1995)	27.4	90	0.41
Von Thun & Gillette	29.0	95	0.43 resistant / 0.14 erodible
MacDonald & L-M	V_er = 4,060 m³	—	0.37

Breach widths cluster within about 6% here, but failure time spans 0.14 to 0.48 hours — a factor of 3.4. That spread is the whole point of running more than one method.

Failure time drives peak outflow, not breach width. Peak breach discharge is far more sensitive to t_f than to B̄, so the parameter with the widest prediction band is also the one the answer hinges on. Froehlich (2008) reports roughly ±⅓ uncertainty on width and closer to a factor of two on time. Run the range, not a single deterministic number, and state the range in the report.

Practice Notes

Issue	Guidance
Which method to lead with	Froehlich (2008) — largest dataset, HEC-RAS default for embankments
Concrete gravity / arch dams	These regressions do not apply. Use monolith-loss assumptions per FERC / USACE guidance
Very small dams	Case-history datasets thin out below about 6 m height; treat results as indicative
Regulatory submittals	Most state programs expect a sensitivity range across at least two methods
V_w definition	Volume at the moment of failure, not normal pool — for an overtopping case that is the routed peak

Sources: Froehlich, D.C. (2008), "Embankment Dam Breach Parameters and Their Uncertainties," J. Hydraulic Engineering 134(12), 1708–1721. Froehlich, D.C. (1995), "Embankment Dam Breach Parameters Revisited," ASCE Water Resources Engineering, 887–891. MacDonald, T.C. & Langridge-Monopolis, J. (1984), "Breaching Characteristics of Dam Failures," J. Hydraulic Engineering 110(5), 567–586. Von Thun, J.L. & Gillette, D.R. (1990), "Guidance on Breach Parameters," USBR. See also USACE HEC-RAS Hydraulic Reference Manual (dam breach chapter) and FERC Engineering Guidelines Chapter 2. Comparison values above were computed directly from the equations as written.

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Related cheat sheets and tools

Breach geometry from this card feeds the dam breach outflow and reservoir routing tools. Hazard class drives whether a breach study is required at all — see hazard classification and inflow design flood. For the erosion side of an overtopping failure, see embankment seepage and exit gradient.

Dam Breach Parameters — Reference

Notation

The Four Equation Sets

Froehlich (2008) — current default

Froehlich (1995)

MacDonald & Langridge-Monopolis (1984)

Von Thun & Gillette (1990)

Failure-Mode Factor Ko and Side Slopes

Von Thun & Gillette Offset Cb

Worked Comparison — All Four Methods

Practice Notes

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Failure-Mode Factor K_o and Side Slopes

Von Thun & Gillette Offset C_b