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6-98 <br />Appendix A <br />• ~ <br />This a:ample illustrates the armoring design concept. The uniform flow- <br />unit slice assumption was made for comenienee in computing the depth of <br />flow; it may not be valid for cost field applications. Furthermore, it <br />is not a conservative assumption, from a stability viewpoint, for sub- <br />critical but ;supernormal flows. Also, the choice of the numeric value <br />' for the modifying value (no), which accounts for energy loss due to fac- <br />tors other than boundary roughness, should be determined reach-Dy-reach <br />for each application. (See NEH-S, Supplement B, for guidance). The <br />smaller the no value, the ioore conservative the design from a stability <br />viewpoint. <br />Problem: A concrete emergency spillway is planned to discharge onto an <br />alluvial valley floor of at least 6 feet of homogeneous material. What <br />maximum steady-state unit discharge would limit scour by permitting <br />•• armoring to the dip size material? What would be the expected depth of <br />scour? The valley slope (So) is 0.00520 ft/ft, the duo is 110 milli- <br />meters, and the modifying value (no) is assumed to be 0.005. Assume <br />(• uniform flow-unit slice principles are applicable; therefore, the hy- <br />draulic radius is equal to the depth of flow (y = R), the rate of total <br />energy loss is equal to the valley slope (Se = So), and the actual trans- <br />verse tractive stress is uniformly distributed (Tact. ~ Tall.)' Use the <br />recommended allowable tractive stress formula from Report 108 that is <br />compatible with TR-59. Use Km = 0.0395. <br />Given: S = 0.00520 <br />0 <br />m 90 <br />dm duo 110 mm 0.3609 ft. <br />n 0.005 <br />0 <br />Required: (a) q~x for Tact. Tall. <br />(b) Dd for m = 90 <br />Solution: (a) nt = ~dml/s <br />• 0.0395(0.3609)1/s <br />= 0.0333 <br />