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<br />If a large number of alternatives are being considered, it is expedient to <br />determine the overtopping discharges by interpolating betweeen water <br />surface elevations to determine where overtopping would occur. <br /> <br />e <br /> <br />E431 will sometimes indicate flow over the roadway before overtopping <br />occurs because it computes flow over the roadway from a weir equation which <br />uses the total head as a parameter. E431 assumes flow over the roadway if <br />the total head is greater than the embankment elevation. E431 apparently <br />does not check the water surface elevation just upstream of the bridge to <br />determine where overtopping occurs. Nevertheless, the proper overtopping <br />discharge can be estimated by interpolating between water surface elevations <br />as discussed above. <br /> <br />6.2.4 Overtopping Depths and Times <br /> <br />Figure 6.2 illustrates the direct method of determining overtopping depths <br />and times as well as the overtopping discharge. Figure 6.2a is the rating <br />curve just upstream of the bridge while figure 6.2b is the family of stage <br />hydrographs for all the floods considered in the analysis. Once these <br />curves are drawn, a base line can be drawn at the embankment elevation and <br />used to determine the overtopping discharge and depths from the rating <br />curves and the overtopping times from the hydrographs. The problem with <br />the direct method is that rating curves and the entire family of stage <br />hydrographs must be developed for each alternative. To facilitate the <br />design process, short-cut methods are described below for determining over- ~ <br />topping depths and times assuming overtopping discharges are known. ,..., <br /> <br />6.2.4.1 Short-cut Method for Determining Overtopping Depths <br /> <br />Figure 6.3a illustrates the direct method of determining overtopping depths <br />for a number of alternatives. This figure represents several rating curves <br />plotted on one graph. The important characteristic to observe in figure 6.3a <br />is that the rating curves tend to parallel the natural rating curve after <br />overtopping occurs; an overtopped roadway essentially acts 1 ike a weir. <br /> <br />If-this parallel characteristic is assumed, overtopping depths can be <br />approximated directly from the natural rating curve as illustrated on <br />figure 6.3b. The absolute elevations are ignored and baselines are <br />established by drawing lines through the rating curves at the appropriate <br />overtopping discharges (assumed to be known from the stage-discharge <br />interpolations). Then, all of the overtopping depths can be estimated <br />from a single rating curve. <br /> <br />e <br /> <br />30 <br />