**1. Introduction**

A vast amount of research on scour at bridge piers and abutments (referred here to as bridge foundations) has been conducted in the past, mostly focusing on results obtained from flume experiments with subcritical flow conditions, i.e., with a Froude number smaller than 1 and sand as a bed material. Even though some issues are still unresolved, the current knowledge has enabled the development of a number of guidelines for bridge design in different countries, e.g., HEC-18 in the US [1], in New Zealand [2], DWA-M529 in Germany [3], and the Ministry of Public Works in Chile [4], among others. However, there is an important lack of knowledge in transferring these methodologies and theories to bridge foundation design when they are placed in rivers with supercritical flow conditions.

Large-scale supercritical free-surface flows can occur in di fferent environments. Some examples can be found in cases of flooded urban streets, fish-ways, tsunami inland flows, coastal channels, and mountain rivers. This paper focuses on the flow and scouring patterns at bridge foundations in rivers with supercritical conditions. The occurrence of supercritical flows in rivers is defined by high longitudinal slopes (>1%) and/or rapid flood waves. Commonly, steep rivers present gravel beds or mixtures of fine and coarse sediments, containing all possible sizes, from clay and silt up to boulders tens of centimeters in size. In dentritic networks, streams with a low Strahler's order (i.e., <3) are steep and produce flash floods but normally possess a small cross-sectional width. Therefore, deck bridges without foundations in these riverbeds are usually selected. At piedmont, however, rivers widen and it is common to observe cross sections with widths over 50 m, where bridge foundations may have to be included. Salient examples of such configurations are often encountered in steep watersheds subjected to heavy rains, such as on the Panamericana Route along Per ú and Chile, La Réunion Island (Indian Ocean) in Taiwan or Japan, and also in a few European Alpine piedmont rivers (Figure 1). The examples in Figure 1 clearly highlight that supercritical flows are associated with a significant amount of energy for scouring and dynamic loading of the superstructure. Wood debris can also enhance the risk of pier stability. Such flows thus produce among the worst hydraulic conditions for bridge design. A recent bridge collapse due to scour in a supercritical flow occurred at the Rivière Saint Etienne in the La Réunion island due to cyclone Gamède. This bridge, which connected a road with tra ffic of 65,000 vehicles per day, collapsed and modified the terrestrial transport route for a long time (Figure 1f,g), thereby producing large economic losses. This event motivated, in France, the funding of specific experimental studies on flow and scour patterns around bridge foundations in supercritical flows, thus opening a new line of research. This event also evidenced an important lack of knowledge, with implications for the hydraulic design of bridge foundations in many regions of the world where supercritical conditions occur. Indeed, high flow velocities, along with high sediment transport and turbidity, rapid changes in the local morphology, and air entrainment make it complex and sometimes impossible to perform flow and scour measurements in the field [5] or even in laboratory facilities [6].

In this paper, we identify the knowledge gaps in scour at bridge foundations in rivers with supercritical flows. These problem areas can be summarized as knowledge gaps in flow dynamics, past obstacles in flat and scoured beds, and scour patterns and mechanisms. This paper also reviews the applicability and limitations of the existing methodological approaches typically used in subcritical flows and sand beds, including field and laboratory measuring techniques for flow and scour, as well as physical and numerical modeling techniques. The link between experimental or numerical work at the local process scale and the long-term river dynamics that finally determine bridge failures is also highlighted. In most cases, we are forced to start with a well-studied case of scour in sand caused by a subcritical flow to provide a referential basis. The paper concludes with final remarks on the results of our analysis.

**Figure 1.** Photographs of supercritical flows at bridge piers in the Biobío River, Chile (**a**), La Rivière des Galets, La Réunion island (**b**), The Choshui River, Taiwan ((**c**) [7]), and the Arc-en-Maurienne River, France ((**d**) and (**e**) [8]). Photographs of the bridge at Rivière St-Etienne (La Réunion island) before (**f**) and after (**g**) the 2007 collapse ((**g**) [9]). Red arrows indicate the flow direction.

## **2. Flow Patterns around Bridge Foundations**

Scour at bridge foundations involves complex interactions between the three-dimensional, unsteady, and turbulent flow, and the movable riverbed. The flow patterns around foundations have been described for cylinders mounted on plane beds, as well as for cylinders in scoured holes in both sub and supercritical flows. Important differences in the flow field around bridge foundations can be highlighted between these two flow regimes.

#### *2.1. Surface Mounted Emerging Obstacles on Flat Beds*
