Embankment Dam Breach

What is modelled

Water running over the crest of an earth embankment erodes a notch. A deeper, wider notch passes more water, which erodes faster: the outflow grows until the reservoir level falls to the breach invert.

Equations

• Weir flow: Q = Cw b Hw3/2, Cw = √g (2/3)3/2 ≈ 1.7 (critical flow at the crest).
• Reservoir: As dh/dt = Qin - Q.
• Erosion closure (lumped): dzb/dt = -Kz Hw, db/dt = Kb Hw.
• Fixed notch: h-1/2 = h0-1/2 + Cw b t/(2 As).

Checks run in the page

• Released volume equals storage drop.
• Analytic drawdown of a non-eroding notch.
• Weir coefficient derived from critical flow.
• Peak flow within a factor 3 of Froehlich (1995) Qp = 0.607 V0.295 H1.24.

Honest simplifications

The erosion law is a lumped linear closure with two calibration constants, not a sediment-transport model; real breaches depend on soil, compaction, seepage and headcut migration. The reservoir has vertical walls (constant area) and the downstream flood wave is not routed. Educational only: never use it to assess a real dam.

• Compare "Compacted clay" and "Sandy fill": same dam, very different hydrographs.
• Set K_z and K_b to the lowest values: the dam survives much longer.
• Enlarge the reservoir area and watch the peak and the duration grow.