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22 Figure 4.7. Velocity hydrographs: a) constant, b) true hydrograph. Both hydrographs would lead to the same scour depth. Figure 4.6. Scour of a two-layer soil (soft layer over i. A multiple regression on vmax, and the initial erosion rate z hard layer). that data gave the following relationship: te ( hrs) = 73(t hydro ( years)) (vmax (m s))1.706 0.126 section. An attempt was made to simplify the method to the point where only hand calculations would be needed. This requires the consideration of an equivalent uniform soil and an (z i ( mm hr )) -0.20 ( 4.7) equivalent time for a constant velocity history. The equivalent uniform soil is characterized by an average z versus curve The regression coefficient for Equation 4.7 was 0.77. This over the anticipated scour depth. The equivalent time te is the time te can then be used in Equation 4.3 to calculate the scour time required for the maximum velocity in the hydrograph to at the end of the hydrograph. A comparison between the scour create the same scour depth as the one created by the complete depth predicted by the extended SRICOS Method using the hydrograph (Figure 4.7). The equivalent time te was obtained complete hydrograph and the simple SRICOS Method using for 55 cases generated from 8 bridge sites. For each bridge site, the equivalent time is shown on Figure 4.8. soil samples were collected in Shelby tubes and tested in the EFA to obtain the erosion function z versus ; then the hydro- 4.7 EXTENDED AND SIMPLE graph was collected from the nearest gage station and the SRI- SRICOS-EFA METHOD COS program was used to calculate the scour depth. That scour depth was entered in Equation 4.3, together with the cor- For final design purposes, the extended SRICOS Method responding z i and z max to get te. The z i value was obtained from (E-SRICOS) is used to predict the scour depth z versus time an average z vs curve within the final scour depth by reading t over the duration of the design hydrograph. The method value that corresponded to max obtained from Equation the z proceeds as follows: 4.1. In Equation 4.1, the pier diameter B and the maximum velocity vmax found to exist in the hydrograph over the period 1. Calculate the maximum depth of scour z max for the considered were used. The z max value was obtained from Equa- design velocity by using Equation 4.2. tion 4.2 while using B and vmax for the pier Reynolds Number. 2. Collect samples at the site within the depth z max. The hydrograph at each bridge was also divided into shorter 3. Test the samples in the EFA to obtain the erosion func- period hydrographs, and for each period an equivalent time te versus ) for the layers involved. tions (z was calculated. This generated 55 cases (Briaud et al., 2002). 4. Prepare the flow hydrograph for the bridge. This step The equivalent time was then correlated to the duration of may consist of downloading the discharge hydrograph the hydrograph thydro, the maximum velocity in the hydrograph from a United States Geological Survey (USGS) gage

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23 Figure 4.8. Comparison of scour depth using Extended SRICOS and Simple SRICOS Methods. Figure 4.10. Velocity hydrograph and scour depth versus time curve for Bent 3 of the Brazos River Bridge at US 90A. station near the bridge (Figure 4.9). These discharge layers involved, the velocity hydrograph v versus t, the hydrographs can be found on the Internet at the USGS pier diameter B, the viscosity of the water , and the website (www.usgs.gov). The discharge hydrograph density of the water w. Note that the water depth y is then needs to be transformed into a velocity hydrograph not an input because at this time the solution is limited (Figures 4.10, 4.11, and 4.12). This transformation is to a "deep water" condition. This condition is realized performed by using a program such as HEC-RAS when y 2B; indeed beyond this water depth the scour (1997), which makes use of the transversed river bottom depth becomes independent of the water depth (Melville profile at the bridge site to link the discharge Q (m3/s) to and Coleman, 1999, p. 197). the velocity v (m/s) at the anticipated location of the 6. The SRICOS program proceeds by a series of time bridge pier. steps; it makes use of the original SRICOS Method and 5. Use the SRICOS program (Kwak et al., 1999) with the of the accumulation algorithms described in Figures following input: the z versus curves for the various 4.2, 4.4, 4.5, and 4.6. The usual time step t is 1 day because that is the usual reading frequency of the USGS gages. The duration of the hydrograph can vary from a few days to over 100 years. 7. The output of the program is the depth of scour versus time over the period covered by the hydrograph (Fig- ures 4.10, 4.11, and 4.12). Figure 4.9. Examples of discharge hydrographs: Figure 4.11. Velocity hydrograph and scour depth versus a) Brazos River at US 90A, b) San Marcos River at SH 80, time curve for Bent 3 of the San Marcos River Bridge at c) Sims Bayou at SH 35. SH 80.