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increase beyond bank-full disch3fge: but sometimes back- water effects or loss of flow into the overbanks results in velocities that are less than those at bank-full. Riprap at channel bends is designed conservatively for the point having the maximum force or velocity. For braided chan- nels, bank-full discharges may nOt be the most severe condition. At lesser flows, now is often divided into multiple channels. Flow in these channels often impinges abruptly on banks or levees at sharp angles. Guidance is lacking in defining design flow conditions for braided channels. 3-7. Stone Size This method for determining stone size uses depth- averaged local velocity. The method is based on the idea that a designer will be able to estimate local velocity bet- ter than local boundary shear. Velocity and flow depth are used in this procedure to quantify the imposed forces. Riprap size and unit weight quantify the resisting force of the riprap. This method is based on a large body of lab- oratory data and has been compared to available prototype data (Maynard 1988). It defIDes the stability of a wide range of gradations if placed to a thickness of lDloo<max). Guidance is provided for thickness greater than lDloo<max) for riprap gradations similar to grada- tions given in Table 3.1. This method is applicable to side slopes of IV on LSH or flatter. a. Velociry eSlimiltion. The ch3r:lcteristic velocity for side slopes V 55 is the depth-averaged local velocity over the slope at a point 20 percent of the slope length from the toe of slope. Plate 33 presents the ratio V 5sfY A YO were V A YO is the average channel velocity at the upstre:lm end of the bend as a function of the chan- nel geomeay, which is described by R/W, where R is the center-line radius of bend and W is the water-surface width. For straight channels sufficiently far (>5W) from upstream bends. large values of R/W should be used. resulting in constant values of V ssfY A YO' Plate 34 describes V 55 and Plate 35 shows the location in a trapezoidal channel bend of the maximum V 55 . Plate 36 shows the variation in velocity over the side slope in a channel bend. Plates 35 and 36 are presented to ilIUSlrale concepts; the designer should consider the specific geomeay. Other parameters, such as side slope angle. ratio of bed and bank roughness. and aspect ratio (channel width/depth), are probably important in defining V 5sfY A YO ' but data do not exist to defme these effects. For equal cross-sectional areas. steep side slopes tend to move the maximum velocities away from the side slope whereas mild side slopes allow the maximum velocities to occur over the side slope. A.n alternate means of velocity EM 1110-2.1601 1 Jul 91 estimation based on field observation is discussed in Appendix G. The alpha method (Appendix q, or velocities resulting from subsections of a water-surface prof1le computation, should be used only in straight reaches. When the alpha method is used, velocity from the subsection adjacent to the bank subsection should be used as V 55 in design of bank riprap. b. Slone size relations. The basic equation for the representative SlOne size in straight or curved channels is 030 s SrCsCvC-rd rr y" J/2 ~Ys - y" V ]2.5 /Klgd (3-3) where D30 = riprap size of which 30 percent is finer by weight. length Sf = safety factor (see c below) c. = stability coefficient for incipient failure. thickness '" lDlOO(max) or 1.5D50(max), whichever is greater, DgsID15 " 1.7 to 5.2 = 0.30 for angular rock = 0.36 for rounded rock Cy = vertical velocity distribution coefficient = 1.0 for straight channels. inside of bends = 1.283 . 0.2 log (RNl), outside of bends (1 for (RIW) > 26) = 1.25, downsa-eam of concrete channels = 1.25. ends of dikes Cr "thickness coefficient (see del) below) d = local depth of flow, length Y., " unit weight of water. weight/volume V = local average velocity. usually V 55 ' length/time 3-5