**1. Introduction**

Scour is one of the most common damages to bridges in fluvial environments. The approaching flow diverted by a pier leads to a series of large-scale turbulence coherent structures, e.g., horseshoe vortex, surface roller, and wave vortices, which consequently increase the kinetic energy and the eroding capacity of the flow. A scour hole forms around the pier when the surrounding erodible bed materials are significantly entrained and eroded away by flow features. At the same time, the pier itself is further exposed. The existence of a scour hole significantly alters the inherent frequency, stress, or bearing conditions of the pier and leads to either a settling, bending, or aggravated wobbling e ffect. The failure of a bridge foundation damages not only the engineering purposes of the bridge itself but also possibly the downstream ecological environment, e.g., spawning beds (Melville and Coleman [1]).

Bridge piers are usually built with complex geometry due to mechanical, geotechnical, and structural considerations. Thus, complex pier forms are more widely adopted around the world than the single pier form with uniform cross-sections. A typical complex bridge pier often consists of a wall-like column supporting the bridge deck and superstructures, a pile-cap under the column, and a group of piles supporting the pile-cap. Complex bridge piers are usually built in close proximity to each other for large bridges with multiple lanes, parallel companion bridges (especially highway-railway bridges combination), and bridges with continuous spans on flood plains. The remnants of previously

existing bridges that have been demolished or destroyed may also influence adjacent newly built ones. Figure 1 show the typical cases of complex piers in close proximity. The flow field and sediment transport mechanism are significantly altered at a complex pier with another one nearby. Thus, the existing scour predictors may not be applied to such situations directly and need further adjustment with caution.

**Figure 1.** Typical cases of complex bridge piers in close proximity: (**a**) Maria Skłodowska-Curie Bridge in Warsaw, Poland; (**b**) Ryde Bridge in Sydney, Australia; (**c**) Unknown bridge under construction. (Photos from internet).

Previous studies have paid much attention to current-induced scour at multiple piles (Hannah [2]; Elliott and Baker [3]; Zhao and Sheppard [4]; Sumer et al. [5,6]; Ataie-Ashtiani and Beheshti [7]; Amini et al. [8]; Liang et al. [9]; Lança et al. [10]; Das and Maxumdar [11]; Wang et al. [12]; Khaple et al. [13]; and Kim et al. [14]) and scour at complex piers (Jones and Sheppard [15]; Coleman [16]; Sheppard and Glasser [17]; Ataie-Ashtiani et al. [18]; Grimaldi and Cardoso [19]; Beheshti & Ataie-Ashtiani [20,21]; Moreno et al. [22–24]; Ferraro et al. [25]; Amini et al. [26]; Baghbadorani et al. [27]; and Yang et al. [28]), respectively. However, there is still no solution for dealing with scenarios with multiple complex piers, indicating an obvious gap of the existing knowledge. This gap is the impetus of the present study. As a result of the insufficient knowledge, people usually tend to design with large safety redundancy when dealing with real engineering practices, leading to excessive cost and push the original budget much higher. In addition, it is also worth mentioning that the interaction between bridge piers and other bridge foundation components, e.g., the abutments, has also been studied by Oben-Nyarko and Ettema [29] and Sturm et al. [30,31]. They found that the extent and depth of the abutment's scour hole is much greater than that of a nearby pier and thus the scour aggravation caused by pier proximity is usually negligible.

This paper is aimed at providing an insight into the scour pattern at complex bridge piers in close proximity and determining the quantitative and qualitative scour features under both clear-water and live-bed flow regime. The morphological response of the erodible bed at the adjacent piers may vary significantly with or without general sediment transport and bed-form migration, which are common fluvial factors that should not be neglected.
