Type1 Type2

which describes Airy′s. law stated in paragraph 2.


4. Experimental Results. 

Experimental data on stone movement in flowing water from the early (1786) work of DuBuat (5) to the more recent Bonneville Hydraulic Laboratory tests (6) have been shown to confirm Airy’s law and Isbash′s stability coefficients (7). The published experimental data are generally defined in terms of bottom velocities. However, some are in terms of average flow velocities and some are not specified. The Isbash coefficients are from tests with essentially no boundary layer development and the average flow velocities are representative of the velocity against stone. When the stone movement resulted by sliding, a coefficient of 0.86 was obtained. When movement was effected by rolling or overturning, a Coefficient of 1.20 resulted. Extensive U. S. Army Engineer Waterways Experiment Station laboratory testing for the design of riprap below stilling basins indicates that the coefficient of 0.86 should be used with the average flow velocity over the end sill for sizing stilling basin riprap because of the excessively high turbulence level in the flow. For impact type stilling basins, the Bureau of Reclamation (8) has adopted a riprap design curve based on field and laboratory experience and on a study by Mavis and Laushey (9). The Bureau curve specifies rock weighing 165 lb/ft^3 and is very close to the Isbash curve for similar rock using a stability coefficient of 0.86.

5. Application. 

The curves given in Chart 712-1 are applicable to specific stone weights of 135 to 205 lb/ft^3. The use of the average flow velocity is desirable for conservative design. The solid-line curves are recommended for stilling basin riprap design and other high-level turbulence conditions. The dashed line curves are recommended for river closures and similar low-level turbulence conditions. Riprap bank and bed protection in natural and artificial flood-control channels should be designed in accordance with reference 10.

6. Stilling Basin Riprap.

a. Size. 
  The W50 stone weight and the D50 stone diameter for establishing riprap size for stilling basins can be obtained using Chart 712-1 in the manner indicated by the heavy arrows thereon. The effect of specific weight of the rock on the required size is indicated by the vertical spread of the solid line curves.

b. Gradation. 
  The following size criteria should serve as guidelines for stilling basin riprap gradation.

  (1) The lower limit of W50 stone should not be less than the weight of stone determined using the appropriate “Stilling Basins” curve in Chart 712-1.
  (2) The upper limit of W50 stone should not exceed the weight that can be obtained economically from the quarry or the size that will satisfy layer thickness requirements as specified in paragraph 6c.
  (3) The lower limit of W100 stone should not be less than two times the lower limit of W50 stone.
  (4) The upper limit of W100 stone should not be more than five times the lower limit of W50 stone, nor exceed the size that can be obtained economically from the quarry, nor exceed the size that will satisfy layer thickness requirements as specified in paragraph 6c.
  (5) The lower limit of W15 stone should not be less than one-sixteenth the upper limit of W100 stone.
  (6) The upper limit of W15 stone should be less than the upper limit of W50 stone as required to satisfy criteria for graded stone filters specified in EM 1110-2-1901.
  (7) The bulk volume of stone lighter than the W15 stone should not exceed the volume of voids in the revetment without this lighter stone.
  (8) W0 to W25 stone maybe used instead of W15 stone in criteria (5), (6), and (7) if desirable to better utilize available stone sizes.

c. Thickness. 
  The thickness of the riprap protection should be 2D50max or 1.5D100max, whichever results in the greater thickness.

d. Extent. 
  Riprap protection should extend downstream to where nonerosive channel velocities are established and should be placed sufficiently high on the adjacent bank to provide protection from wave wash during maximum discharge. The required riprap thickness is determined by substituting values for these relations in equation 2.

7. References.

(1) Shelford, W., “On rivers flowing into tideless seas, illustrated by the river Tiber.” Proceedings, Institute of Civil Engineers, VOl 82 (1885).

(2) Hooker, E. H., “The suspension of solids in flowing water.” Transactions, American Society of Civil Engineers, vol 36 (1896),pp 239-340.

(3) Isbash, S. V., Construction of Dams by Dumping Stones in Flowing Water, Leningrad, 1932. Translated by A. Drijikov, U. S. Army Engineer District, CE, Maine, 1935.

(4) _________, “Construction of dams by depositing rock in running water.” Transactions, Second Congress on Large Dams, VOl 5 (1936), pp 123-136.

(5) DuBuat, P. L. G., Traite d’Hydraulique. Paris, France, 1786.

(6) U. S. Army Engineer District, Portland, CE, McNary Dam - Second Step Cofferdam Closure. Bonneville Hydraulic Laboratory Report No. 51-1, 1956.

(7) U. S. Army Engineer Waterways Experiment Station, CE, Velocity Forces on Submerged Rocks. Miscellaneous Paper No. 2-265, Vicksburg, Miss., April 1958.

(8) U. S. Bureau of Reclamation, Stilling Basin Performance; An Aid in Determining Rinran Sizes, by A. J. Peterka. Hydraulic Laboratory Report No. HYD-409, Denver, Colo., 1956.

(9) Mavis, F. T. and Laushey, L. M., “A reappraisal of the beginning of bed movement - competent velocity.” Second Meeting, International Association for Hydraulic Structure Research. Stockholm, Sweden, 1948. See also Civil Engineering, vol 19 (January 1949), pp 38, 39, and 72.

(10) U. S. Army, Office, Chief of Engineers, Engineering and Design; Hydraulic Design of Flood Control Channels. EM 1110-2-1601. Washington, D. C., 1 July 1970.