τ

D

= 8.52 V* = 8.52 o

Vr = 2.5 V* ln 30.2 50

(6.14)

ρ

D50

Thus, the relation between Vr and τo is:

ρ Vr2

τo =

(6.15)

72

The relation is valid only for uniform flow in wide prismatic channels in which the flow is fully

turbulent. For the purpose of riprap design, Equation 6.15 can be used when the flow is

accelerating such as on the tip of spur dikes or abutments. The equation should not be used in

areas where the flow is decelerating or below energy dissipating structures. In these areas,

the shear stress is larger than calculated for Equation 6.15.

One can also demonstrate (Richardson et al. 1975) that the reference velocity Vr is related to

_ 1.4 V ).

the velocity against the stone Vs (Vr

s

In summary the following expressions for η are equivalent:

21 τo

η=

(6.5)

(S s - 1) γD s

0.30 Vr2

η=

(6.16)

(S s - 1) gD s

0.60 Vs2

η=

(6.17a)

(S s - 1) gD s

2

V2

3.4

η = 0.30

(6.17b)

(S s - 1) gD s

y

ln

(12.3 o )

Ds

U.S. Army Corps of Engineers design equations are based on local depth-averaged velocity

(V), local depth of flow (y), and coefficients for a factor of safety (Sf ), stability (Cs), vertical

velocity distribution (Cv ), blanket thickness (CT ), and side slope (K1). The principal equation

determines the riprap size of which 30 percent is finer by weight (D30) (U.S. Army Corps of

Engineers EM 1110-2-1601, 1991 and 1994a and Maynord 1988). The equation is:

6.25

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