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FHWA > Engineering > Hydraulics > HEC 15 
Design of Roadside Channels with Flexible Linings

(F.1) 
where,
τ_{e}  = effective shear stress on the soil surface, N/m^{2} (lb/ft^{2}) 
m  = rate of shear transmission 
τ_{d}  = applied (design) shear at the surface of the lining, N/m^{2} (lb/ft^{2}) 
τ_{c}  = shear at which the soil surface is first mobile (i.e. critical shear), N/m^{2} (lb/ft^{2}) 
The critical shear value, τ_{c}, is for the soil type described in testing procedure ASTM D 6460.
Laboratory testing (McWhorter et al., 1968; Sanders, et al., 1990; Israelsen, et al., 1991; Northcutt, 1996; Robeson, et al. 2003) has shown that the rate of soil loss remains nearly constant and does not change with increasing shear stress over a wide range of applied shear stress. Data from Robeson, et al. (2003) is presented in Figure F.1 and shows this linear relationship for four lining types.
Figure F.1. Soil Shear versus Applied Shear to the Manufactured Lining
For a wide range of product types, the critical shear and the rate of shear transmission is directly related to the applied shear on the lining at cumulative soil erosion of 12.7 mm (0.5 in) over 30 minutes for a specified soil type in accordance with the ASTM D 6460. This shear value is referred to as the lining shear, τ_{l}. (Note, the lining shear should be determined by testing under the same conditions as recommended by the manufacturer, i.e. stapling pattern, check slots, etc.)
As would be expected the critical shear on the lining is just a linear extrapolation from τ_{l}.
(F.2) 
where,
τ_{l}  = applied shear (lining shear) at a cumulative erosion of 12.7 mm (0.5 in), N/m^{2} (lb/ft^{2}) 
Likewise, the rate of shear transmission correlates to:
(F.3) 
where,
α  = unit conversion constant, 6.5 (SI), 0.14 (CU) 
Combining Equation F.2 and Equation F.3 with Equation F.1 gives:
(F.4) 
Comparison to data presented in Robeson, et al. is shown in Figure F.2.
Figure F.2. Effective Shear on the Soil for Four RECP Linings