The rock sizes in the last column in Table 6.2 are used in the following equation (Stevens
1968) to find the representative grain size Dm. This effective grain size, Dm, of the mixture
corresponds to the D65 size of the riprap.
1/ 3
10 Di3
= i
≅ 1.25 D 50
Dm
(6.22)
10
When the bed material has a log-normal distribution, the representative size of the bed
material based on the weight of the particles is given by Mahmood (1973) as a function of the
gradation coefficient G:
3
Dm = D 50 exp (ln G)2
(6.23)
2
=
0.72 D50 and 1.81 D50 respectively.
G is
For gradation coefficients of 2 and 3, Dm
determined by Equation 3.9.
With a distributed size range, the interstices formed by the larger stones are filled with the
smaller sizes in an interlocking fashion, preventing formation of open pockets. Riprap
consisting of angular stones is more suitable than that consisting of rounded stones. Control of
the gradation of the riprap is almost always made by visual inspection. If it is necessary, poor
gradations of rock can be employed as riprap provided the proper filter is placed between the
riprap and the bank or bed material. Where available rock size is inadequate, wire enclosed
(gabion) riprap can be used.
Considering the practical problems of quarry production, a gradation band is usually specified
by the U.S. Army Corps of Engineers (1981) rather than a single gradation curve, and any
stone gradation within the limits is acceptable. The Corps criteria for establishing gradation
limits in terms of stone weight (W) for riprap are as follows:
Lower limit of W50 stone should not be less than the weight of stone required to withstand
the design shear forces.
Upper limit of W50 stone should not exceed five times the lower limit of W50 stone, the size
which can be obtained economically from the quarry, or the size that satisfies layer
thickness requirements.
Lower limit of W100 stone should not be less than two times the lower limit of W50 stone.
Upper limit of W100 stone should not exceed five times the lower limit of W50 stone, the size
which can be obtained economically from the quarry, or the size that satisfies layer
thickness requirements.
Lower limit of W15 stone should not be less than one-sixteenth the upper limit of W100 stone.
Upper limit of W15 stone should be less than the upper limit of the filter material.
6.29
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