Robinson, Rice & Kadavy (1998) developed two empirical equations for median rock lining size D50 based on steep channel slope and unit discharge. Equation 1 applies for mild slopes (S0 < 0.10); Equation 2 applies for steep slopes (0.10 ≤ S0 ≤ 0.40). Both equations require qt in m²/s and return D50 in mm. The validated range is 0.02 ≤ S0 ≤ 0.40.
Unit Discharge
qt is the total unit discharge at the steep channel crest (total flow per unit width). For a channel of bottom width B carrying total flow Q, approximate qt ≈ Q / B, or compute it from the critical-depth condition at the steep channel inlet.
Flow Through the Rock Mantle
A fraction of the total flow moves through the pores of the rock lining (mantle flow qm); the remainder flows over the rock surface (qs = qt − qm). The flow depth d is computed from Manning’s equation applied to the surface flow qs using the steep channel roughness n. Default porosity np = 0.45 is typical for angular crushed rock.
Valid Rock Size Range
The equations were developed using a D50 range of 15 mm to 278 mm. Results outside this range are extrapolated and should be used with additional engineering judgement.
Outlet Apron Elevation
The elevation of the top of the rock lining in the outlet reach should be at or below the downstream channel bed elevation. If it is higher, the outlet rock will be unstable.
Inlet Ponding
When the normal depth in the inlet channel is less than the weir head (Hp) required to pass qt, restricted flow or ponding occurs upstream of the steep channel inlet. This is generally acceptable — ponding reduces velocity and prevents erosion upstream. To check: use a weir flow calculator to find Hp for the given qt and crest width, and compare it to the inlet channel normal depth. If Hp exceeds normal depth, ponding will occur.
Reference
Robinson, K.M., Rice, C.E., and Kadavy, K.C. (1998). “Design of rock chutes.” Transactions of the ASAE, 41(3), 621–626. USDA ARS also publishes an Excel spreadsheet based on the same method.