**3. Experimental Program**

#### *3.1. Threshold Velocity Calculation of Sediment*

Natural uniform river sand was selected as the riverbed material for the tests. The median particle size of the sand is 0.324 mm, and the density of the river sediment is 2.65 g/cm3. Before the start of each test, the riverbed sediment in the scour section was smoothed and kept still for a period of time. Only one type of sand was used in all the tests carried out in this study. The water depth and flow velocity were kept constant at 0.5 m and 0.35 m/s, respectively.

The critical Shields parameter was calculated by the improved empirical formula by Soulsby and Whitehouse [38,39]

$$\theta\_{cr} = \frac{0.30}{1 + 1.2D\_\*} + 0.055[1 - \exp(-0.020D\_\*)] \tag{1}$$

where the non-dimensional particle size *D\** is defined as *D\** = [*g*(*s* − 1)/ν2]1/3*d*50 with ν (=10−<sup>6</sup> m<sup>2</sup>/s) being the kinematic viscosity of water. The Shields parameter due to total friction was obtained according to the measured velocity profile. The Shields parameter θ*s* due to skin friction is defined as

$$\theta\_s = \frac{\tau\_s}{\rho g (s - 1) d\_{50}} = \frac{\mathcal{U}\_{fs}^2}{g (s - 1) d\_{50}} \tag{2}$$

where τ*s* is the shear stress due to skin friction experienced by the sea bed from the flow, ρ is the water density, *g* is the acceleration due to gravity, *s* is the specific gravity of sand, *d*50 is the median particle size of sand, *Ufs* = (<sup>τ</sup>*s*/ρ)<sup>1</sup>/<sup>2</sup> is friction velocity associated with skin friction. The shear stress due to skin friction is calculated by the empirical formula for flat sand surface [39]

$$
\pi\_{\mathfrak{s}} = \rho \mathbb{C}\_{D} \overline{U}^{2} \tag{3}
$$

where the logarithmic relationship for *CD* is *CD* = {κ/[*ln*(*<sup>z</sup>*0*s*/*h*) + 1]}2, κ (=0.4) is the Karman constant, *U¯* is the depth averaged flow velocity, *z*0*s* (=*d*50/12) is the roughness height due to skin friction and *h* is the water depth.

Table 1 summarizes the parameters used in the tests based on the above calculation and the observed sediment start-up phenomena in the experiment. The threshold velocity of sediment at different water depths calculated by the above equations is shown in Figure 5. The threshold velocity of sediment at the water depth of 0.5 m is about 0.303 m/s. Considering that the ripple development effect may affect the scour tests, the test flow velocity is set to be 0.35 m/s, which is only slightly larger than the actual threshold velocity of sediment. The sediment bed was carefully leveled and flattened before the test to ensure that the initial riverbed surface was the same under every working condition. Under such conditions, we observed no ripples in front of the pier model, only ripples behind the pier. In the test, the authors increased the flow velocity incrementally and observed the start-up of sediments. The observed threshold velocity in the test was very close to the threshold velocity calculated by above formula. It can be concluded that this formula is applicable to the sediments used in this paper. According to the skin friction Shields parameter, the tests are all under live-bed conditions. Live-bed scour was also confirmed by the sand ripples observed in the latter tests.


**Table 1.** Parameters of sediment used in the tests.

**Figure 5.** The threshold velocity of selected sediment at different water depths.

## *3.2. Calculation of Equilibrium Scour Time*

Melville and Chiew [40] considered the temporal development of clear-water local scour depth at cylindrical bridge piers in uniform sand beds and put forward a formula to estimate the time taken for equilibrium scour depth development. Bateni et al. [41] presented a Bayesian neural network technique to predict the equilibrium scour depth around a bridge pier and the time variation of scour depth. Melville et al. [42] has divided the local scour process into three stages: initial stage, main scour stage and equilibrium condition. In order to understand the duration required for the scour test, time scale of scour around a vertical pile of a height the same as the water depth is calculated based on the following empirical formula proposed by Sumer et al. [43]

$$S(t) = S\_0(1 - \exp^{-t/T})\tag{4}$$

where *S* is the scour depth, *S*0 is the equilibrium scour depth, *t* is time and *T* is defined as the time scale of scour. Sumer et al. [43] found that time scale of scour around a vertical slender pile follows

$$T = \frac{D^2}{\left[g(s-1)d\_{50}^3\right]^{1/2}}T^\* \tag{5}$$

$$T^\* = \frac{\delta}{2000D} \theta\_s^{-2.2} \tag{6}$$

where *D* is the representative dimension of the vertical pile (diameter for a circular pile or dimension perpendicular to flow for a rectangular cylinder), δ is the boundary layer thickness and *T\** is the non-dimensional time scale of scour. By using δ = 0.30 m, Equations (5) and (6), the time scale for *D* = 0.1 m is *T* = 720. By substituting *S*(*t*)/*S*0 = 0.95 and the above calculated time scales into Equation (4), the time taken for scour reaching 95% of equilibrium scour depth for *D* = 0.1 m is estimated as *t*= 36 min.

Yang et al. [44] carried out a study on the evolution of hydrodynamic characteristics with scour holes developing around pile groups, which demonstrates a high scouring rate for the early stage and the scouring phenomenon almost reached equilibrium after 240 min. Zhang et al. [45] established a set of three-dimensional numerical models to investigate the mechanisms of local scour around three adjacent piles with different arrangements under steady currents by as short as 500 s scour time. The total scour testing time of each test is thus set to be 120 min, which is much larger than the calculated approximate equilibrium scour time.
