Riprap Sizing Methods — Reference
Sizing stone for channel, bank, and outlet protection. The design quantity is the median stone size D50, set by velocity or shear; gradation, layer thickness, and an underlying filter complete the design.
Velocity-Based D50 (Isbash)
| Term | Meaning / typical value |
|---|---|
| V | Design (local) velocity at the stone |
| Ss | Stone specific gravity, ~2.65 |
| C | Isbash coefficient: ~0.86 high-turbulence, ~1.20 low-turbulence |
| g | 32.2 ft/s² (9.81 m/s²) |
D50 Riprap Size Chart by Velocity (Isbash, Ss = 2.65)
| Velocity V (ft/s) | D50, high turbulence (C = 0.86) | D50, low turbulence (C = 1.20) |
|---|---|---|
| 4 | 0.20 ft (2.4 in) | 0.10 ft (1.3 in) |
| 6 | 0.46 ft (5.5 in) | 0.24 ft (2.8 in) |
| 8 | 0.81 ft (9.8 in) | 0.42 ft (5.0 in) |
| 10 | 1.27 ft (15.3 in) | 0.65 ft (7.8 in) |
| 12 | 1.83 ft (22.0 in) | 0.94 ft (11.3 in) |
| 14 | 2.49 ft (29.9 in) | 1.28 ft (15.4 in) |
| 16 | 3.26 ft (39.1 in) | 1.67 ft (20.1 in) |
SI: 1 m/s → 42 / 21 mm; 2 m/s → 167 / 86 mm; 3 m/s → 376 / 193 mm; 4 m/s → 668 / 343 mm (high / low turbulence). Computed from the equation above with g = 32.2 ft/s² (9.81 m/s²). D50 scales with V², so doubling velocity quadruples stone size.
FHWA HEC-11 (revetment) and HEC-23 (bridge/abutment countermeasures) give velocity- and depth-based D50 relations with bank-angle and specific-gravity corrections; use the method your reviewer requires.
Gradation Limits (Well-Graded Riprap)
| Ratio | Target |
|---|---|
| D85 / D15 (uniformity) | 1.5–2.5 (up to ~4.6 allowed) |
| D100 (max) / D50 | ≤ 2.0 |
| D50 / D15 | ~1.5–2.0 |
Well-graded stone interlocks and resists displacement; uniform (gap-graded) stone is unstable and prone to winnowing.
Layer Thickness & Filter
| Item | Rule |
|---|---|
| Blanket thickness | ≥ larger of 1.5·D50 or D100; increase for steep / submerged placement |
| Granular filter | Terzaghi: D15f/D85b < 4–5 < D15f/D15b |
| Geotextile filter | Alternative to granular; AOS sized to retain base soil |
Sources: FHWA HEC-11 Design of Riprap Revetment; FHWA HEC-23 Bridge Scour and Stream Instability Countermeasures; USACE EM 1110-2-1601; Isbash (1936). State DOT riprap classes (e.g., NCDOT Class A/B/1/2) define standard gradations — check the governing spec.
Worked example: culvert outlet apron
Outlet velocity 9 ft/s, high turbulence (C = 0.86), Ss = 2.65
Two things usually decide the job more than the D50 arithmetic. The first is which velocity you use. Outlet velocity from a culvert running partly full is higher than the full-barrel velocity, and the jet does not slow down right at the headwall. The second is the stone actually available. Most projects specify a standard state DOT class, so the calculation becomes “which class has a D50 at least this big,” and the class’s own gradation and thickness then apply.
Common mistakes
- Using the low-turbulence coefficient at an outlet. The jet from a pipe or a hydraulic jump is high turbulence by definition. C = 1.20 gives about half the stone size, 0.53 ft instead of 1.03 ft here.
- Using the average channel velocity on the outside of a bend or at a bridge pier. Local velocity there can be 1.3–1.7 times the average. Bend and pier methods in HEC-11, HEC-23 and EM 1110-2-1601 include that factor.
- Placing riprap with no filter. Without a filter, the base soil washes out through the voids and the blanket settles and unravels. That failure is common and avoidable.
- Specifying D50 without a gradation. Uniform stone with no smaller sizes leaves open voids and is less stable than a well-graded mix with the same D50.
When this card doesn’t apply
Isbash is a screening equation for velocity-dominated flows. Banks on steep slopes, channel bends, wave attack, overtopping flow on an embankment face and bridge piers each have their own methods with corrections the Isbash form lacks. Dam spillway channels and stilling-basin end protection are normally governed by agency criteria (USACE, USBR or the state dam safety program). Grouted riprap, gabions and articulated concrete blocks are separate products with their own design methods.
Related cheat sheets and tools
Get the design velocity from Manning's and the channel geometry card, then size stone in the riprap tool. Downstream of an energy dissipator, pair with the hydraulic-jump card. For erosion and sediment within a full watershed model, see HydroComplete. Scour at bridge piers and contracted openings follows a different equation set — see the bridge scour card.