2013-05-28_REVISION - M1977311 (3)

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when the tractive force exerted by the flowing water exceeds the riprap materials ability to resist motion. It is this process that the riprap design relationships presented in this section were developed for. Two methods or approaches have been used historically to evaluate a materials resistance to particle erosion. These methods are: 1. Permissible velocity approach: Under the permissible velocity approach the channel is assumed stable if the computed mean velocity is lower than the maximum permissible velocity. 2. Permissible tractive force (shear stress) approach. The tractive force (boundary shear stress) approach focuses on stresses developed at the interface between flowing water and materials forming the channel boundary. By Chow's definition, permissible tractive force is the maximum unit tractive force that will not cause serious erosion of channel bed material from a level channel bed (9) . Permissible tractive force methods are generally considered to be more academically correct; however, critical velocity approaches are more readily embraced by the engineering community. 4.1.1.1 Design Relationship A riprap design relationship that is based on tractive force theory yet has velocity as its primary design parameter is presented in Equation 6. The design relationship in Equation _6 is based on the assumption of uniform, gradually varying flow. The derivation of Equation 6 along with a comparison with other methods is presented in Appendix D. Chart 1 in Appendix C presents a graphical solution to Equation 6. Equation 7 can be solved using Chart 3 and Chart 4 of Appendix C. The following form can be used to calculate D50: D50 = 0.00594 Va3 /(davg0.5 K11-5) where: D50 = the median riprap particle size (m); C = correction factor (described below); Va = the average velocity in the main channel (m /s); dav9 = the average flow depth in the main flow channel (m); and K1 is defined as: (6)