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18 Figure 4.1. Example of the SRICOS Method for constant velocity and uniform soil. order to investigate the influence of the difference between depth versus time curve proceeds from Point B on Figure 4.2c the two velocity histories or hydrographs on the depth of until Point C after a time t2. The z versus t curve for the scour at a bridge pier, the case of a sequence of two different sequence of Floods 1 and 2, follows path OA on the curve for yet constant velocity floods scouring a uniform soil was first Flood 1 then switches to BC on the curve for Flood 2. This is considered (Figure 4.2). Flood 1 has a velocity v1 and lasts a shown as curve OAC on Figure 4.2d. time t1 while the subsequent Flood 2 has a larger velocity v2 A set of two experiments was conducted to investigate and lasts a time t2. The scour depth z versus time t curve for this reasoning. For these experiments, a pipe with a diame- Flood 1 is described by: ter of 25 mm was placed in the middle of a flume. The pipe was pushed through a deposit of clay 150 mm thick that was t made by placing prepared blocks of clay side by side in a tight z = ( 4.4) 1 t arrangement. The properties of the clay are listed in Table 4.1. + i1 z zmax 1 The water depth was 400 mm and the mean flow velocity was v1 = 0.3 m/s in Flood 1 and v2 = 0.4 m/s for Flood 2 (Fig- For Flood 2, the z versus t curve is: ure 4.3a). The first of the two experiments consisted of set- ting the velocity equal to v2 for 100 hours and recording the t z versus t curve (Figure 4.3c). The second of the two experi- z = ( 4.5) ments consisted of setting the velocity equal to v1 for 115 hours 1 t + (Figure 4.3b) and then switching to v2 for 100 hours (Fig- i 2 z zmax 2 ure 4.3d). Also shown on Figure 4.3d is the prediction of the After a time t1, Flood 1 creates a scour depth z 1 given by portion of the z versus t curve under the velocity v2 accord- Equation 4.4 (Point A on Figure 4.2b). This depth z 1 would ing to the procedure described in Figure 4.3. As can be seen, have been created in a shorter time t* by Flood 2 because v2 the prediction is very reasonable. is larger than v1 (Point B on Figure 4.2c). This time t* can be found by setting Equation 4.4 with z =z1 and t = t1 equal to 4.3 BIG FLOOD FOLLOWED BY SMALL FLOOD Equation 4.6 with z =z 1 and t = t*. AND GENERAL CASE t1 Flood 1 has a velocity v1 and lasts t1 (Figure 4.4a). It is fol- t* = ( 4.6) zi 2 + t1 z i 2 1 - 1 lowed by Flood 2, which has a velocity v2 smaller than v1 and i1 z zmax 1 zmax 2 lasts t2. The scour depth z versus time t curve is given by Equation 4.4 for Flood 1 and by Equation 4.5 for Flood 2. When Flood 2 starts, even though the scour depth z 1 was due After a time t1, Flood 1 creates a scour depth z 1. This depth z 1 to Flood 1 over a time t1, the situation is identical to having had is compared with z max 2; if z 1 is larger than z max 2 then when Flood 2 for a time t*. Therefore, when Flood 2 starts, the scour Flood 2 starts, the scour hole is already larger than it can be