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<br />(5) island or bar formations upstream or downstream of the bridge <br />opening, (6) debris, and (7) the growth of vegetation in the <br />channel or flood plain. <br /> <br />In a natural channel, the depth of flow is always greater on the <br />outside of a bend. In fact there may well be deposition on the <br />inner portion of the bend, If a bridge is located on or close to <br />a bend, the contraction scour will be concentrated on the outer <br />part of the bend. Also, in bends the thalweg (the part of the <br />stream where the flow is deepest and, typically, the velocity is <br />the greatest) may shift toward the center of the stream as the <br />flow increases, This can increase scour and the nonuniform <br />distribution of the scour in the bridge opening. <br /> <br />1. contraction Scour Eauations. Contraction scour equations are <br />based on a single principle of conservation of sediment <br />transport. It simply means that the fully developed scour in <br />the bridge cross-section reaches equilibrium when sediment <br />transported into the contracted section equals sediment <br />transported out in the case of live-bed scour or the shear <br />stress in the contracted section has been decreased by scour <br />increasing the area so that it is equal to the critical shear <br />stress of the sediment at the bottom of the contracted cross <br />section. <br /> <br />There are two forms of contraction scour depending upon the <br />competence of the uncontracted approach flow to transport bed <br />material into the contraction. Live-bed scour occurs when <br />there is sediment being transported into the scour hole, <br />Clear-water scour is the case when the sediment transport in <br />the uncontracted approach flow is zero. In this case the <br />scour hole reaches equilibrium when the average bed shear <br />stress is the critical required for incipient motion of the <br />bed material. Clear-water and live-bed scour are discussed <br />further in another section in this chapter. <br /> <br />Laursen (8) derived the following live-bed contraction scour <br />equation based on his simplified transport function and <br />several other simplifying assumptions: <br /> <br />Q 6 W <br />Y2 = ( mel)"" ( ---1.) K, ( n2 ) K, <br />Y1 Qme2 W2 n1 <br /> <br />(1) <br /> <br />ys = yz - y, (Average scour depth) <br /> <br />Where: <br /> <br />y, <br /> <br />= average depth in the main channel <br /> <br />11 <br />