Breakwater Armor Stone Calculator

This calculator uses a simplified Hudson stability relationship to estimate the required single armor stone size. It is commonly used for preliminary sizing of rubble-mound breakwaters.

• Mass (t): m = W / g
• Nominal diameter: Dn50 = (W / gamma_r)^(1/3)
• Indicative gradation: 0.5*m to 2.0*m
• Layer thickness: t = (thickness factor) * Dn50
• Quantity estimate: mass per m^2 = rho_r * (1-n) * t / 1000

Design wave selection and scaling

The calculator sizes armor from an effective wave height H = Hs × wave factor. Use a project-defined design height (storm, return period, or limit state) and apply transformation factors consistently. Because Hudson uses H³, a 10% increase in H raises the required stone mass by roughly 33%, which is useful for sensitivity checks. For early feasibility, use a single governing Hs; for final design, check depth-limited breaking and spectral conditions. Record return period, transformation assumptions, and freeboard criteria.

Stability coefficient selection

Kd represents placement, unit shape, and hydraulic stability. Random quarry stone typically uses lower Kd than highly interlocking concrete units. If your specification provides Kd by trunk or head, select the more conservative value for preliminary sizing. Document the chosen Kd in your export for traceability during review. If you select Custom Kd, keep supporting references on file and note whether placement is random or patterned.

Slope, density ratio, and sensitivity

The term cot(theta) links slope steepness to stability; steeper slopes reduce cot(theta) and demand heavier armor. Density ratio Sr = rho_r / rho_w drives the (Sr − 1)³ term, so small density changes can materially affect weight. Check rock source density and seawater salinity assumptions early to avoid procurement surprises.

Layer thickness and quantity planning

Dn50 is derived from stone volume and provides a practical size metric for detailing and constructability. Layer thickness is estimated as (thickness factor) × Dn50; two-layer random placement is often near 2.0. Quantity uses porosity n to convert thickness to solid volume, producing tonnes per square meter for quick takeoffs.

Reporting, checks, and procurement notes

Use the detailed output table to compare alternatives: change slope, Kd, or rock density and record the effect on mass, Dn50, and total quantity. Validate the resulting gradation band against local quarry production limits. Export CSV for estimating and PDF for design submittals, then confirm final sizing with project standards and modeling. Include delivery tolerances, handling limits, and safety margins in quantities.

1) What does the wave factor change?

It scales Hs into the effective design height used in Hudson sizing. Use it to represent transformation, setup, or conservative amplification consistent with your design basis.

2) Should I use trunk or head Kd?

Heads usually require a lower Kd because they see more severe loading and multidirectional waves. If uncertain, use the conservative value until a detailed stability assessment is completed.

3) Why does slope affect stone size?

Steeper slopes reduce cot(theta), which increases the required armor weight in Hudson’s relationship. This reflects reduced stability and greater tendency for units to dislodge.

4) What is Dn50 used for on drawings?

Dn50 is a representative nominal diameter tied to stone volume. Designers use it to estimate layer thickness, filter compatibility, and placement practicality on the breakwater face.

5) How reliable is the quantity estimate?

It is a planning tool based on thickness, porosity, and density. Final quantities depend on construction tolerances, toe details, transitions, and specification gradation limits.

6) When should I verify with more detailed methods?

Verify when the site has complex bathymetry, oblique waves, overtopping constraints, or critical risk. Physical or numerical modeling and local standards provide higher confidence for final design.