Calculator Inputs
Example Data Table
| Scenario | Hm0 (m) | Tm-1,0 (s) | Rc (m) | Slope (V:H) | beta (deg) | gamma_f | gamma_b | gamma_V | q total (L/s/m) | Crest length (m) | Q total (L/s) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Baseline dike | 1.50 | 6.00 | 0.80 | 1:3 | 0 | 1.00 | 1.00 | 1.00 | Run the calculator | 50 | Run the calculator |
| Rough revetment | 2.00 | 7.00 | 0.90 | 1:4 | 15 | 0.60 | 1.00 | 1.00 | Compare impact | 80 | Compare impact |
| Overflow case | 1.20 | 5.50 | -0.15 | 1:3 | 0 | 1.00 | 1.00 | 1.00 | Includes weir overflow | 30 | Includes weir overflow |
Tip: Use the same wave climate and vary Rc, slope, and roughness to see which change reduces discharge most.
Formula Used
This tool estimates mean overtopping discharge per metre width using the dimensionless form Q* = q / sqrt(g*Hm0^3), then converts back to q in m^3/s/m. A breaker parameter is calculated as xi = tan(alpha) / sqrt(Hm0/L0) with L0 = g*T^2/(2*pi).
- Breaking-dominated (xi <= 2): Q* = (0.067/sqrt(tan(alpha)))*(gamma_b*xi)*exp(-k*Rc/(gamma*xi*Hm0))
- Non-breaking/surging (xi > 2): Q* = 0.2*exp(-k*Rc/(gamma*Hm0))
- Oblique wave attack uses gamma_beta = 1 - 0.0033|beta| with a cap for very oblique waves.
- When Rc is negative (water above crest), overflow is added using a broad-crested weir approximation q_overflow = Cd*(2/3)*sqrt(2g)*h^(3/2), where h = -Rc.
The conservative and mean coefficient sets follow widely used coastal guidance and implementation manuals. Always verify against project-specific standards and, where needed, physical or numerical modelling.
How to Use This Calculator
- Enter the wave climate at the structure toe: Hm0 and Tm-1,0.
- Set the crest freeboard Rc; use a negative value for overflow depth.
- Choose slope ratio and roughness; adjust gamma_b and gamma_V if applicable.
- Set beta for oblique wave attack; keep auto gamma_beta unless verified.
- Optionally set a target limit in L/s/m to get a pass/fail flag.
- Click Calculate; results will appear above the form.
- Use the CSV/PDF buttons to export the latest results.
Technical Article
1) What overtopping discharge represents
Overtopping discharge is the average water flow passing over a crest per unit width. It is commonly reported as q in m3/s/m or L/s/m. Small values can still create hazardous spray, ponding, and erosion behind the crest.
2) Why wave climate inputs matter
Wave height Hm0 and spectral period Tm-1,0 drive the energy scale sqrt(g·Hm03). Increasing Hm0 from 1.5 m to 2.0 m raises the scale by about (2.0/1.5)1.5 (≈1.54). Period affects deep-water wavelength L0 = g·T2/(2π), changing steepness and breaking behavior.
3) Freeboard Rc as the primary control
Freeboard Rc is the vertical difference between still water level and crest elevation. The calculator applies exponential decay with Rc/Hm0, so a modest increase in Rc can reduce discharge sharply in many cases. When Rc becomes negative, overflow is added using a broad-crested weir form where q grows with h3/2.
4) Slope and breaker parameter xi
The surf similarity parameter xi = tan(alpha)/sqrt(Hm0/L0) separates breaking-dominated and surging behavior. Steeper slopes (higher tan(alpha)) increase xi and may shift the response toward surging conditions. This calculator uses xi = 2 as a practical screening boundary between regimes.
5) Roughness and influence factors
Surface roughness is represented by a reduction factor gamma_f. Screening values often range from 1.00 for smooth faces down to 0.45 for very rough or stepped surfaces. Additional factors gamma_b and gamma_V help represent berm or wall influences in an auditable way.
6) Oblique wave attack and reduction
Oblique attack reduces the effective overtopping by a factor gamma_beta. The default approximation gamma_beta = 1 - 0.0033|beta| supports quick checks, while the custom option supports project-calibrated values. As beta increases, the reduction can be meaningful for long-crested seas.
7) Interpreting results against performance targets
Projects often define tolerable discharge targets in L/s/m for different receptor types. For screening, some teams use ranges such as 0.1–1 L/s/m for high public sensitivity and 5–20 L/s/m for robust backslopes with controlled access, but your project criteria always governs. Use the target field to flag whether a scenario appears within your chosen limit.
8) Using exports for design documentation
The CSV export records inputs and computed parameters such as L0, steepness, and xi. The PDF export supports quick sharing during design reviews and safety documentation. Treat outputs as preliminary estimates and confirm critical designs with suitable guidance and modelling.
FAQs
1) Which wave period should I enter?
Use Tm-1,0 when available. If you only have a peak period, apply your project conversion method, or enter a representative period and run sensitivity checks.
2) What does a negative Rc mean?
Negative Rc means water level is above the crest. The calculator adds overflow using a broad-crested weir approximation and reports both wave and overflow components.
3) How do I pick gamma_f?
Select the preset matching your revetment type. If you have tests or local guidance, use the custom input and keep the value between 0.40 and 1.00.
4) When should I adjust gamma_b and gamma_V?
Adjust them when berm geometry or a vertical element materially changes overtopping. If unsure, keep them at 1.00 and document the assumption for review.
5) What target limit should I use?
Targets depend on receptors and risk tolerance. Set your screening threshold in L/s/m, then compare scenarios to identify which design changes reduce discharge most.
6) Why do results change a lot with Rc?
Overtopping is sensitive to freeboard because relationships use exponential decay with Rc/Hm0. Small crest raises can produce large reductions in mean discharge.
7) Can this replace numerical or physical modelling?
No. This supports early design and option comparison. For critical assets, unusual geometries, or submissions, confirm with standards and appropriate modelling studies.