*3.2. Equilibrium Bed Level*

The equilibrium scour depths are calculated using the temporal evolution curves shown in Figure 5 and the extrapolation method validated by Yang et al. [28]. Figure 6 shows the equilibrium bed level for each pier arrangemen<sup>t</sup> in the present study with a viewing direction perpendicular to the approaching flow. This figure acts as a supplement to the temporal evolution data to clearly illustrate the maximum range of scouring excavation that can possible happen under clear-water flow regime. The scour at inner and outer pile columns are generally symmetric for aligned complex piers, while an oblique alignment leads to more complex scour patterns at and between the two piers. The scour between piers under clear-water flow regime is found to be caused by the expansion and merging of the scour holes rather than contraction scour due to the symmetric scour pattern observed in Figure 6a, and thus the spatial distribution of in-between scour generally follows the natural profile of the scour holes. For the staggered and tandem pier arrangemen<sup>t</sup> tested, the greatest scour occurred at the leading side (pile A1 and B1) of the upstream pier. The protection effect of the upstream pier is similar to the performance of sacrificial piles as stated by Melville and Hadfield [33]. This protection is due to the increased sediment supply for the downstream pier and, as also mentioned above and observed during the experiments, the lee-wake turbulence and the vortex shedding path caused by the upstream pier overlapped with the downstream pier.

**Figure 6.** Equilibrium bed-levels: (**a**) side-by-side arrangemen<sup>t</sup> without skew angle; (**b**) side-by-side arrangemen<sup>t</sup> with 30◦ skew angle; (**c**) staggered arrangement; and (**d**) tandem arrangement. The measuring locations can also be referred in Figure 3 for more detailed information.
