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<br />w = Ys (K + cot 8) <br /> <br />(:1 ) <br /> <br />where <br />W = <br />ys = <br />K = <br />0 = <br /> <br />top width of the scour hole from the side of the pier <br />or footing <br />scour depth <br />bottom width of the scour hole as a fraction of scour <br />depth <br />Angle of repose of the bed material (it ranges from <br />about 30 to 44 degrees) (7) <br /> <br />If the bottom width of the scour hole is equal to the depth of <br />scour "Ys" (K = 1), an unlikely condition, then the top width in <br />cohesionless sand would vary from 2,07 to 2.80 y. At the other <br />extreme if K = 0 then the top width would vary f~om 1,07 to 1.8 <br />Ys' Thus, the range in top width would probably be from 1.0 to <br />2.8 Ys' <br /> <br />G. STEP 7. PLOT TOTAL SCOUR DEPTHS AND EVALUATE DESIGN <br /> <br />. <br /> <br />1. Plot the Total Scour Deoths, <br /> <br />On the cross-section of the stream channel and floodplain at the <br />bridge crossing, plot the estimate of 1) long-term bed elevation <br />change, 2) contraction scour, and 3) local scour at the piers and <br />abutments. Use a distorted scale so that the scour <br />determinations will be easy to evaluate, Make a sketch of any <br />plan form changes (lateral stream channel movement due to meander <br />migration, etc,) that might be reasonably expected to occur. <br /> <br />o Long-term elevation changes may be either aggradation <br />or degradation. <br /> <br />o Contraction scour is then plotted from and below the <br />long-term aggradation or degradation lines. <br /> <br />o Local scour is then plotted from and below the <br />contraction scour line. <br /> <br />o Plot not only the depth of scour at each pier and <br />abutment, but also the scour hole width. The width can <br />be determined by assuming the bottom of the scour hole <br />is 5 feet wider than the pier or footing and using the <br /> <br />57 <br />