What are Froehlich 2008 breach parameters?

Froehlich (2008) estimates average breach width as 0.27 times Ko times reservoir volume to the 0.32 power times breach height to the 0.04 power, in SI units, with Ko of 1.3 for overtopping and 1.0 for piping. Failure time is 63.2 times the square root of volume divided by g times breach height squared.

How wide is the breach in a 22-foot earthfill dam holding 145 acre-feet?

Using Froehlich 2008, average breach width is about 59 feet for an overtopping failure and about 46 feet for a piping failure, with a breach formation time near 23 minutes and a peak discharge around 7,150 cfs.

How accurate are dam breach parameter regressions?

Reported uncertainty on breach width is roughly plus or minus 50 percent. Standard practice is to run several parameter sets and carry the more conservative inundation extent onto the emergency action plan map rather than relying on a single estimate.

Dam safety worked examples

Breach Parameters for a 22-ft Earthfill Dam

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

Froehlich (2008) average breach width and failure time, and the Froehlich (1995) peak discharge regression, worked end to end in SI and reported in customary units — the numbers that feed an inundation map, and the ones a reviewer will check first. Sources: Froehlich, D.C. (2008), Embankment Dam Breach Parameters and Their Uncertainties, ASCE J. Hydraulic Engineering; Froehlich (1995a), Embankment Dam Breach Parameters Revisited.

The structure

Type	Homogeneous earthfill embankment, recreation impoundment
Dam height	22 ft
Normal storage	145 acre-ft
Breach height, h_b	20 ft (breach cuts to near original ground)
Depth of water above breach invert, h_w	20 ft at the moment of failure
Failure mode	Overtopping (also run as piping for comparison)

Step 1 · Convert to SI

The Froehlich regressions are metric

Both Froehlich sets are fitted in SI. Converting first and reporting back out is safer than hunting for a customary-unit restatement, which is where most spreadsheet errors in this calculation come from.

V_w = 145 ac-ft × 1,233.48 m³/ac-ft = 178,855 m³
h_b = 20 ft × 0.3048 = 6.096 m
h_w = 20 ft × 0.3048 = 6.096 m

Why this matters more than it looks: check the dimensions of each equation before you trust it in any unit system.

Equation	Length dimension	Homogeneous?	Consequence
B̄ = 0.27·K_o·V_w^0.32·h_b^0.04	L^3(0.32)+0.04 = L^1.00	Yes	Unit-invariant — works in ft or m
t_f = 63.2√(V_w/(g·h_b²))	√(L³/L³T⁻²) = T	Yes	Unit-invariant, with g in matching units
Q_p = 0.607·V_w^0.295·h_w^1.24	L^{3(0.295)+1.24} = L^2.125	No — Q needs L³T⁻¹	SI only

The peak-discharge regression is dimensionally inhomogeneous, and that is not a typo in the source. Its coefficient 0.607 carries hidden units, so the equation is only valid in the units it was fitted in. Feed it cubic feet and feet and it returns 2,530 — a perfectly plausible-looking number that is wrong by a factor of about three. The two Froehlich 2008 equations are homogeneous and would survive the same abuse; this one will not. Convert first, every time.

Step 2 · Average breach width

Froehlich (2008): B̄ = 0.27·K_o·V_w^0.32·h_b^0.04

K_o = 1.3 (overtopping) | 1.0 (piping)

V_w^0.32 = 178,855^0.32 = 47.95
h_b^0.04 = 6.096^0.04 = 1.0750

Overtopping: B̄ = 0.27 × 1.3 × 47.95 × 1.0750 = 18.09 m = 59.4 ft
Piping: B̄ = 0.27 × 1.0 × 47.95 × 1.0750 = 13.92 m = 45.7 ft

Note how weakly breach width depends on breach height: the exponent on h_b is 0.04, so doubling the breach height moves the width by under 3%. Storage volume, at exponent 0.32, does essentially all the work. Getting the stage-storage curve right matters far more than refining the breach elevation.

Step 3 · Failure time

t_f = 63.2·√(V_w / (g·h_b²))

g·h_b² = 9.81 × 6.096² = 364.6
V_w / (g·h_b²) = 178,855 / 364.6 = 490.5
√490.5 = 22.15
t_f = 63.2 × 22.15 = 1,400 s = 0.39 hr ≈ 23 minutes

23 minutes is the entire warning budget. That is the formation time of the breach, not the travel time to the first structure — and it is why the notification procedures in an emergency action plan are written as a call tree with named roles rather than a general instruction to alert downstream residents. A plan that assumes someone will drive the road and knock on doors has already failed the arithmetic.

Step 4 · Peak breach discharge

Froehlich (1995): Q_p = 0.607·V_w^0.295·h_w^1.24

V_w^0.295 = 178,855^0.295 = 35.44
h_w^1.24 = 6.096^1.24 = 9.407
Q_p = 0.607 × 35.44 × 9.407 = 202.4 m³/s = 7,150 cfs

For scale: this 22-foot recreation dam releases roughly seven thousand cubic feet per second at the breach — comparable to a substantial river in flood, out of a pond most neighbours would call small. This is the single most useful number for explaining to an owner why their dam is regulated.

Step 5 · Summary

What goes on the calc sheet

Parameter	Overtopping	Piping	Source
Average breach width B̄	59.4 ft	45.7 ft	Froehlich 2008
Side slopes (H:V)	1.0:1	0.7:1	Froehlich 2008
Failure time t_f	0.39 hr	0.39 hr	Froehlich 2008
Peak discharge Q_p	7,150 cfs	7,150 cfs	Froehlich 1995

These are regressions, not physics. Froehlich's own reported uncertainty on breach width is roughly ±50%, and the dataset behind it is dominated by dams unlike any specific one you are analysing. Standard practice is to run more than one parameter set — Froehlich 2008, Froehlich 1995, MacDonald & Langridge-Monopolis — and carry the more conservative inundation extent onto the EAP map. Do not present a single breach width to three significant figures as though it were measured.

Tools used

Breach Parameters

Froehlich 2008 / 1995 / MLM side by side

Dam Breach Peak Discharge

Peak Q regressions and envelope comparison

Breach Parameter Card

Reference values at a glance

The rest of this series

These four examples follow one structure through the whole decision chain, because in practice that is how the questions actually arrive:

Breach parameters for a 22-ft earthfill dam — produces the failure hydrograph everything else depends on.
Class B or Class C? The 1.5-foot flood rise test — turns that hydrograph into a hazard classification.
Does an 18-ft farm pond dam need a permit? — the classification decides whether the size exemption survives.
Spillway design flood for a Class C dam — and the classification sets the storm the spillway must pass.

Breach Parameters for a 22-ft Earthfill Dam

The structure

The Froehlich regressions are metric

Froehlich (2008): B̄ = 0.27·Ko·Vw0.32·hb0.04

tf = 63.2·√(Vw / (g·hb²))

Froehlich (1995): Qp = 0.607·Vw0.295·hw1.24