**2. Experimental Setup**

The experiments in the present study were performed in a 2.4-m wide, 0.6-m deep, and 25-m long sediment-recirculating flume in the Fluid Mechanics Laboratory at the University of Auckland. The flume slope is adjustable up to a 1% slope. The flume is equipped with two water pumps, allowing a maximum of 1100 liters per second discharge and one sand pump. A 4.0-m long, 0.6-m deep sediment recess box, i.e., the test section for scour experiments, is located 11-m downstream from the water outlet section. The sediment used in the present study was uniform quartz sand with median particle

diameter *d*50 = 0.84-mm and geometrical standard deviation <sup>σ</sup>*g* = 1.30. This sediment grain size is coarse enough to be considered as non-cohesive and non-ripple-forming.

The complex pier model used in the present study was made from solid materials and represents a form typical of the bridge piers that have failed in the past several decades in New Zealand, as described by Melville and Coleman [1]. These failures include the Bulls Road Bridge on SH1, the Blackmount Road Bridge, the Oreti River Road Bridge, and the Whakatane River Road Bridge. The model consists of a rectangular wall-like column (310-mm long and 30-mm wide), a rectangular pile-cap (362-mm long, 120-mm wide, and 60-mm thick) and a 2 × 4 pile group (25-mm in diameter for each vertical pile). The model has a geometric scale of 3:50 and is similar to the primary model used by Yang et al. [28]. Figure 2 shows the schematic drawings of the configuration of the complex pier model.

**Figure 2.** Model shape and dimensions (unit: mm): (**a**) plan view; (**b**) front view; and (**c**) 3-D view.

Depth-averaged velocities were measured by a Nortek Vectrino+ ADV made in Norway. A relationship was found between the measured flow velocity, the reading of the electromagnetic flow meter, and the working frequency of the pump controller. The scour depth was measured using a SeaTek multiple transducer array (MTA) made in USA; detailed specification can be referred in [32]. Each transducer has a cylindrical shape and is 12.7-mm in diameter and 25.4-mm in length. The transducers were fixed onto a transversal frame across the flume and in holes drilled in the pile cap, to measure instantaneous scour depth around the pier and at each pile throughout the duration of the tests. The transducers emit ultrasound pulses with a frequency up to 20-Hz and thereby measure the distance by analyzing the reflected signal.

Four different pier arrangements were used to represent typical scenarios of complex pier proximity in the field, including: (a) two adjacent side-by-side complex piers that are both aligned to the approaching flow; (b) two adjacent side-by-side complex piers are that are both skewed to the approaching flow with α = 30◦; (c) two aligned complex piers that are staggered with 30◦ angle between the flow direction and the line connecting the pier centres; and (d) two aligned complex piers with tandem arrangement. Besides the side-by-side arrangements, two adjacent complex piers can also support different bridge decks, which are common for companion bridges with multiple lanes. If so, the position relationship between two adjacent piers can be either staggered or tandem. The distance between two adjacent piers is based on typical real cases, while a closer distance is rarely adopted in engineering practices. Figure 3 shows the schematic drawings and photos of the experimental setups before filling the flume. The red circles mark the locations where the MTA transducers were placed to monitor real-time bed level data. Further transducers were also set upstream of the pier to monitor undisturbed bed-forms but are not located in the figure. Figure 4 provides more detailed setup information of the MTA transducers at one of the piers, as well as the numbering scheme for the transducers. Previous studies, including Zhao and Sheppard [4], Lança et al. [10], and Yang et al. [28]

have shown that, for scour at a group of piles or a stand-alone skewed complex pier, the maximum scour depth usually occurs at the downstream end of the upstream pile column, i.e., A3 or A4.

**Figure 3.** Setup of four different pier arrangement: (**a**) side-by-side arrangemen<sup>t</sup> with aligned flow; (**b**) side-by-side arrangemen<sup>t</sup> with 30◦ skew angle; (**c**) staggered arrangement; (**d**) tandem arrangement. The small red circles represent the locations where the multiple transducer array (MTA) transducers were set and real-time bed level data are available.

**Figure 4.** Definition and numbering scheme of the MTA transducers.

The experimental design in the present study in shown in Table 1. The flow depth *y*0 was fixed at 0.15 m. The pile-cap elevation was fixed at *Hc* = 0.06 m and the base of the pile-cap was at the original bed level. This position is typical and leads to enlarged scour hole, as previous studies (Ataie-Ashtiani et al. [18], Moreno et al. [22], and Yang et al. [28]) have shown that the scour depth is maximized when the pile-cap is near the original bed level. For each pier arrangement, a wide range of flow intensity ratios (*U*/*Uc*) were tested, from 0.9 to 4.0–5.2, to investigate scour features under both clear-water (*U*/*Uc* ≤ 1) and live-bed (*U*/*Uc* > 1) flow regimes. When *U*/*Uc* > 1, the sediment particles over the entire channel bed start to move downstream and lead to consecutive migrating dunes with wavy patterns.


**Table 1.** Experimental design ( *Dpc* = pile-cap width, *Lpc* = pile-cap length).
