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Wave Runup & Freeboard Calculator

Reservoir wave-runup analysis for embankment dams: wind setup, significant wave height (SPM 1984 shallow-water formulas), wave period, Iribarren breaker classification, and runup R per Hunt/Saville with surface-roughness reduction. Returns total required freeboard above maximum design pool.

mph
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ft
— typical 2.5–3.5
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s
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Wind setup S = U²·F/(1400·d) per Sibul / Saville (US units, mph, mi, ft → ft). Wave height and period from SPM 1984 shallow-water formulas. Runup uses Hunt's R/Hs = ξ for plunging waves with surface-type reduction γ_r.

$$ S = \frac{U^2 F}{1400\,d_{\text{avg}}} \quad(\text{US}) $$
$$ H_s, T_p \;\;\text{from SPM 1984 shallow-water formulas} $$
$$ \xi = \tan\alpha\,/\,\sqrt{H_s/L_0}, \quad R = \gamma_r\,\xi\,H_s\;(\xi<2.5) $$
U design wind speed at 10 m · F fetch · d mean depth · α slope angle · γ_r surface roughness factor · ξ Iribarren (surf-similarity) parameter.

Wind setup formulas

Sibul / Saville's empirical relation S = U²·F/(1400·d) gives wind setup in feet for U in mph, F in miles, and d_avg in feet. In SI: S = U²·F·c, with c = 1.16×10⁻⁶ for U in m/s, F in km, d in m, S in m. Both reduce to S ≈ τ·F/(γw·d) with the wind shear stress τ proportional to U². For very deep reservoirs (d > 100 ft) wind setup is negligible.

Wave height and period (SPM 1984)

The Shore Protection Manual shallow-water relations:

$$ \frac{gH_{m0}}{U^2} = 0.283\,\tanh\!\left[0.530\!\left(\frac{gd}{U^2}\right)^{0.75}\right]\,\tanh\!\left[\frac{0.00565\,(gF/U^2)^{0.5}}{\tanh[0.530(gd/U^2)^{0.75}]}\right] $$

$$ \frac{gT_p}{U} = 7.54\,\tanh\!\left[0.833\!\left(\frac{gd}{U^2}\right)^{0.375}\right]\,\tanh\!\left[\frac{0.0379\,(gF/U^2)^{1/3}}{\tanh[0.833(gd/U^2)^{0.375}]}\right] $$

Surface-roughness reduction γ_r

USACE EM 1110-2-1420 — surface roughness factor for runup
Slope surfaceγ_r
Smooth concrete, asphalt-paved1.00
Single-layer cellular concrete blocks0.65
Two-layer riprap on granular filter0.55
Single-layer riprap, dumped0.65
Grass-lined embankment0.85
Asphalt or fabric mat0.85

Worked example

Example — small high-hazard embankment dam

Given: U = 60 mph, F = 2 mi, d = 20 ft, slope 1V:3H, two-layer riprap, safety margin 2 ft.
Wind setup S = 60²·2/(1400·20) = 7200/28000 = 0.26 ft
SPM gives Hs ≈ 2.6 ft, Tp ≈ 3.5 s
L0 = 32.2·3.5²/(2π) = 62.8 ft
tan α = 1/3 = 0.333; ξ = 0.333/√(2.6/62.8) = 0.333/0.203 = 1.64 → plunging
R = 0.55·1.64·2.6 = 2.35 ft
FBrequired = 0.26 + 2.35 + 2.0 = 4.6 ft above max routed pool

References: USACE EM 1110-2-1420 (1997). Hydrologic Engineering Requirements for Reservoirs. USACE EM 1110-2-1100 (2002). Coastal Engineering Manual. Saville, T. (1962). Wave Runup on Composite Slopes. ASCE Trans. Hunt, I.A. (1959). Design of Sea-Walls and Breakwaters. ASCE J. Waterways & Harbors Div. Sibul, O.J. (1955). Laboratory Study of the Generation of Wind Waves in Shallow Water. USACE BEB Tech. Memo 72.

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