VERIFICATION OF THE TIME SCALE PARAMETER (T=DVa) Uni directional flow was used in order to validate the scour time scale parameter.

Based on the dimensional analysis presented in section 3.2.5, it is to be expected that the time taken to produce a particular scour depth will be directly proportional to the square of the pipeline diameter ( T «= ). Thus if the pipeline diameter is doubled the time needed to produce the same relative depth of scour is quadrupled. For a fixed pipeline diameter, the time to generate a particular depth of scour hole is inversely proportional to the relevant sediment transport rate ( T «: q/^ ). As it is not possible to measure the local sediment transport rate directly under the pipeline ( qp ) with any degree of accuracy, it is therefore necessary to adopt the undisturbed sediment transport rate (q j as a scaling factor. Two sets of experiments were carried out to verify the time scale parameter, namely test (UF/TS/D) and test (UF/TS/qJ.

6.2.1.1 TEST (UF/TS/D)

This test was canied out with a fixed sediment transport rate while using four different model pipeline diameters namely 12.5, 25, 50 and 75 mm. A summary of the test parameters is given in table 6.1. The magnitude of the Shields parameter for the flow chosen, is slightly in excess of the value for initial sediment motion which is about 0.06, for the sand size used. The results of this test, namely the time to generate a particular depth of scour hole for different model pipeline diameters are shown plotted in figure 6.1.

Test parameters

Velocity measurement height, y (mm) 25

Flow velocity, Uy , (m/s) 0.258

Water temperature, ( ° C ) 17.2 Bed shear velocity, U^., ( m/s) 0.0131

Bed shear stress, Tq , ( N/m^ ) 0.171 Shields Parameter, (t* ) 0.073

Sediment Transport Rate, q„ ( kg/s/m) 1.47x10^

Table 6.1: Parameters for test (UF/TS/D) (using eqns. 3.45, 3.25 and 5.1 respectively)

As can be seen in figure 6.1 for different h/D values, the slope of the fitted lines is in reasonable agreement with the theoretical value given the experimental measurement difficulties and the fundamental difficulties previously discussed concerning the choice of % and its varying highly non-linear dependence on local bed shear stress. Figure 6.1 therefore demonstrates that, scaling works very adequately during the middle tunnel erosion process (for example, h/D=0.3 corresponds to T ). These findings are in close agreement with those reported by Paskin (1992). However, it should be noted that at the early stage of the tunnel erosion (i.e. initial breakthrough, h/D=0.1) and also the late tunnel

erosion phase (i.e. h/D=0.5 ) the experimental values of the D exponent deviate up to approximately 15 percent from the theoretical value. This may be attributed to the fact that, at the initial breakthrough the rate of scouring is very high and as a result the scouring time is very small, generating considerable uncertainty in the measurements. Also q, may not be representative of qp at these high initial transport rates as previously discussed in section 3.2.5. Gap ratios h/D=0.4 and 0.5 coincide with the onset of vortex shedding, as also noted by Bearman and Zdravkovich (1978). Vortex shedding in turn enhances the rate of scouring below the pipeline. This behaviour is consistent with the results of the studies conducted by Mao (1986) and Paskin (1992).

6.2.1.2 TEST (UF/TS/g, )

In order to verify the inverse proportionality of the time scale with the sediment transport rate, the test (UF/TS/q, ) was carried out using a fixed model pipeline diameter and different flow velocities, ranging from 0.24 to 0.365 m/s. The 25 mm diameter model pipeline used in the test had a blockage ratio (D/d), ranging from 0.1 to 0.15 for the different flow velocities. This low blockage ratio had a very limited effect on the results as pointed out for example by Littlejohns (1973), who demonstrated that the water depth influence will be small if it is greater than three times the diameter of the pipeline (i.e. blockage ratio = 0.33). However quantifying the blockage ratio is extremely difficult, since during the test it will alter with changing scour depth under the pipeline. A summary of the test parameters are tabulated in table 6.2. The time to produce a particular depth of scour (h/D) for different values of the sediment transport rate is illustrated in figures 6.2, a and b.

Table 6.2 shows the magnitudes of the Shields parameter, %*, used in the test UF/TS/q„ ranging from 0.064 to 0.136. As the Shields critical value for the initial sediment motion for this sand grain size is about 0.05 to 0.06, it is apparent that the conditions for the lower sediment transport rates used in the test are very close to the so called "clear water" condition. As can be seen in figure 6.2 (a), the

coefficients of proportionality are somewhat less than the theoretical value which equals to -1. However closer inspection of the data in figure 6.2 (a) reveals that taking larger values of the sediment transport rates as a sub-set, results in a steeper slope for the best fit lines. Data was therefore split up into two series and the corresponding lines of the best fit have been drawn in figure 6 . 2 (b).

Test Flow No.

param eters _{1 2 3 4 5 6 7 8} Uy (m/s) 0.24 0.26 0.28 0.29 0.305 0.326 0.338 0.365 T ( ° C ) 17.1 16.8 16.8 17 17.2 17 16.9 18 U^ (m/s) 0.0122 0.0131 0.0141 0.0145 0.0152 0.0161 0.0166 0.0178 To ( N/m^ ) 0.1487 0.170 0.199 0.210 0.229 0.258 0.276 0.315 T* 0.064 0.0734 0.0859 0.091 0.099 0.111 0.119 0.136 R e, 1.6 1.72 1.85 1.90 1.99 2.11 2.18 2.39 q, ( kg/s/m ) 8.5E-6 1.5E-5 2.7E-5 3.5E-5 5E-5 7.9E-5 l.OE-4 1.9E-4

Table 6.2: Parameters for test ( UF/TS/q, ) (using eqns. 3.45, 3.25 and 5.1 respectively)

In the first series magnitudes of the Shields parameter have values less than 0.099 and the corresponding values for the second series are 0.099<t*<0.136. As can be seen in figure 6 . 2 (b), the larger magnitudes of gradients of T* and % demonstrate a close inverse proportionality between scour time and sediment transport rate as predicted by theory. The data for small h/D values once again deviates from this pattern for the reasons previously discussed in section 6.2 .1.

As discussed in section 5.4.1, the sediment transport equation employed in the present study was the relationship given by Grass & Ayoub (1982). The argument put forward by Grass et al. (1992) is that, for a series of U intervals, the

relationship between bed load sediment transport rate, q^, and flow velocity close to the bed, can be approximately represented by a corresponding series of simple power relationships, q,=AU", (see section 3.2.5, and also Raudkivi, 1990). In the present study the Shields parameter values used, were at the lower range of the Shields parameter values which have been utilised by Grass and Ayoub (1982), and sediment transport rates for these low bed shear stresses are extremely small and very difficult to measure.Therefore at low bed shear stress values beyond the range covered by Grass and Ayoub, uncertainty exists in the accuracy of the absolute transport magnitudes derived from relevant prediction formulae. Figures 6 . 2 (a) and (b) exhibit the fact that the validity of the time scale parameter in particular for larger h/D values are more satisfactory than for the smaller values.

6.2.2 EFFECT OF BED LEVELLING ON THE M AXIM UM SCOUR