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<br />FIGURE 4.4 DEFINITION SKETCH FOR CASE 1 ABUTMENT SCOUR <br /> <br />~ <br /> <br />.. <br />. <br />F <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br />. <br /> <br />SCOUR AT ABUTMENTS <br />CASE 1 ABUTMENTS PROJECT INTO CHANNEL, NO OVERBANK FUJII <br /> <br />Five equations apply to this case (equations 3, 5, 6, 7 and B): <br /> <br />Equation 3: live-bed scour at a spill through abutMnt. <br /> <br />According to the studies of liu, et al., (1961) the equilibrium scour depth <br />for local live-bed scour in sand at a stable spill slope when the flow is <br />subcritica1 is determined by Equation 3. (See also Figure 4.4). <br /> <br /> <br />Scour <br /> <br />~ = 1.1 (~1)0.40 Fr10.33 <br />i. = <br /> <br />(3) <br /> <br />Fr1= <br /> <br />equilibrium depth of scour (measured from the mean bed level <br />to the bottom of the scour hole) <br />average upstre.. flow depth in the aain channel <br />abutment and embankment length (measured at the top of the <br />water surface and normal to the side of the channel from <br />where the top of the design flood hits the bank to the outer <br />edge of the abutment) <br />upstream Froude number determined from equation 4 <br /> <br />V1 <br /> <br />19Y1)0. · <br /> <br />(4) <br /> <br />Y1 = <br />a = <br /> <br />Fr1 = <br /> <br />Equation 5: live bed scour at a vertical wall abument. <br /> <br />If the abutment terminates at a vertical wall and the wall on the upstream <br />side is also vertical, then the scour hole in sand calculated by equation 3 <br />nearly doubles (liu, 1961 and Gril" 1972). <br /> <br />~ = 2.15 (~1)0.40 Fr10.33 <br />30 <br /> <br />(5) <br />