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Design of Roadside Channels with Flexible Linings
Hydraulic Engineering Circular Number 15, Third Edition

Appendix F: Shear Stress Relationship for RECPS

The general relationship for the transmission of shear to soil surface beneath a manufactured unvegetated lining is given by (Cotton, 1993; Gharabaghi, et al., 2002; Robeson, et al., 2003):

tau sub e equals m times the quantity (tau sub d minus tau sub c) (F.1)


τe= effective shear stress on the soil surface, N/m2 (lb/ft2)
m= rate of shear transmission
τd= applied (design) shear at the surface of the lining, N/m2 (lb/ft2)
τc= shear at which the soil surface is first mobile (i.e. critical shear), N/m2 (lb/ft2)

The critical shear value, τc, 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.

Illustration of the linear relationship between applied shear and effective soil shear presented in equation F.1
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, τl. (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 τl.

comparison of the measured and estimated shear in support of equation F.4 (F.2)


τl= applied shear (lining shear) at a cumulative erosion of 12.7 mm (0.5 in), N/m2 (lb/ft2)

Likewise, the rate of shear transmission correlates to:

m equals alpha divided by tau sub l (F.3)


α= unit conversion constant, 6.5 (SI), 0.14 (CU)

Combining Equation F.2 and Equation F.3 with Equation F.1 gives:

tau sub e equals the quantity (tau sub d minus tau sub l divided by 4.3) times alpha divided by tau sub l (F.4)

Comparison to data presented in Robeson, et al. is shown in Figure F.2.

comparison of the measure and estimated shear
Figure F.2. Effective Shear on the Soil for Four RECP Linings

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Dan Ghere
Resource Center (Matteson)

Updated: 04/07/2011

United States Department of Transportation - Federal Highway Administration