4.2.2. Bed Level Measurements

At present, only a few successful field measurements of scour during floods have been reported using the numbered-brick technique [5,74], which requires numbered bricks to be placed beneath the river bed by using excavators prior to the flood event. The location of the numbered-brick column can be accurately identified by using a total-station transit. After the flood has receded, excavators are again deployed to dredge the location of the preinstalled bricks to determine the number of bricks that have been washed away during the flood. To this end, one can then evaluate the maximum scour depth at the measuring location based on the remaining number of bricks [75]. Monitoring techniques for scour were reviewed in [76]. Such techniques include poles or sounding weights (with intrusion into the flow), float-out devices and tethered buried switches that can detect scour, and rods buried into the streambed (coupled with various sensors to measure the scour depth). These instrumentations may be robust, but they are limited to a single location and require expensive installation and/or maintenance. Other techniques use sonars, fathometers (acoustic waves), or radars (electromagnetic waves) that are able to locally monitor the scour depth over time but are often limited to low flow velocities, water depths, and/or Suspended Sediment Matter (SSM) concentrations. Ground Penetrating Radars (GPR) allow a spatial view of the erosion but require manual operation and thus cannot be used during heavy-flood flows. Lastly, accelerometers provide a response for the bridge structure to scour. This structural dynamic response is able to provide a global view of the scour, which is of interest for early warning systems but is sensitive to the shape of scour holes and soil type and thus needs a site-specific calibration before monitoring [77].

As a consequence, a combination system based on structural dynamic response together with float-out or buried-typed devices would be the best actual monitoring approach to provide a quantitative description, over time, of the erosion depth at the foot of a bridge foundation in a supercritical flow.

Recent developments on active tracers [78] may allow their use around structures during a flood. Indeed, such systems could provide interesting results on gravel path and velocity but would be di fficult to deploy during extreme events, such as those responsible for supercritical flows.

#### *4.3. Physical Scale Models of Scour at Bridge Foundations*

The authors in [79,80] analyzed the scale e ffects on scour, concluding that the use of laboratory flumes in developing accurate predictors of scour depth at full-scale piers is limited due to scale e ffects that may produce greater scour depths in the laboratory than at actual piers in rivers. The authors in [81] discussed the e ffects of sediment size scaling on the physical modeling of a bridge pier scour. Moreover, for model sediments smaller than d = 0.05 mm cohesion will reduce the scour [30]. Typical Froude scale models do not necessarily simulate the tractive forces and sediment erosion accurately because Froude scaling does not simulate viscous forces. Recently, researchers [82] showed that clear-water and live-bed scour under steady and unsteady flows in a subcritical regime is similar in the prototype and the model if the dimensionless flow work (as proposed in [83]) and the dimensionless grain diameter D\* are equal in both (the prototype and the model). Still, verifications of these scaling laws for supercritical cases are needed before such a scaling approach can be employed with confidence in physical modeling.

Additionally, important di fficulties in the physical modeling of live-bed scour caused by a supercritical flow are the high water and sediment discharges to be supplied as upstream boundary conditions. While the water discharge may be overcome with large pumps, the sediment supply is a challenge in itself. The researchers in [6] supplied up to 400 l/s of water in order to reach their 2 m/s target velocity and 3 kg/s (10.8 t/h) of sediment during their experiments, which lasted up to 2 hours (Figure 5d–i). Moreover, the sediment needed to be regularly removed from the downstream basin in order not to generate backwater curves from downstream and keep the supercritical flow condition in the flume. Flow velocities were measured with propellers and ADV (Figure 5e), ensuring that the system did not produce important disturbances of the flow conditions. Because very loaded flows are prevented from using sonar or optical measurement systems (Figure 6f), the most adapted scour measurement methods appeared to be classical thin rods systems deployed from above the free surface (Figure 5f).

#### *4.4. Advanced Numerical Tools for Simulation of Scour in Supercritical Flows*

Numerical simulations play a significant role in the understanding of the flow hydrodynamics and scour around hydraulic structures, as they can explore conditions that cannot be reproduced experimentally or are inaccessible for measurement devices, complementing the observations, and providing additional insights into sediment-flow interactions and feedback [84]. In the following, numerical simulation techniques to be applied to supercritical scour processes are discussed, including the coupled hydrodynamics and sediment transport approach and the multi-phase flow approach.

#### 4.4.1. Coupled Hydrodynamics and Sediment Transport Approach

First numerical simulations of scour around a bridge pier under a subcritical flow regime were performed about 25 years ago in [85], using the Reynolds-Averaged Navier–Stokes (RANS) equations for the hydrodynamics, coupled with the Exner equation for the bed's morphological evolution in steady flow conditions. Another important milestone was achieved in [86], which provided 3D morphodynamic simulations using a kω SST model, which was able to reproduce vortex shedding at the lee side of a surface mounted cylinder. Sumer [87], in his review on the mathematical modeling of scour, pointed out the free surface e ffects, the influence of small scale turbulence on sediment transport, and the potential e ffects of pore pressure on scour as the main avenues for future research. The study in [88] simulated scour around cylindrical and square piers, using a URANS (Unsteady Reynolds Averaged Navier Stokes) model coupled with an adapted version of the van Rijn model to estimate the bedload transport flux and the Exner equation. Better agreemen<sup>t</sup> was observed in the case where the shear drives the scour, as the HSV dynamics cannot be resolved with a URANS approach. Similar results were observed by [89], with the URANS and scour simulations past a surface mounted cylinder. This study showed that by considering the transport of suspended sediment, there is an improvement of the deposition patterns downstream of the pier. Recently, researchers in [90] proposed the use of a relaxation parameter to adjust the locally amplified bed shear stress due to the action of a horseshoe vortex to properly match the observed scour depth, solving the URANS–Exner equations system.

The work in [12,17,18] studied the dynamics of the HSV system at high-Reynolds numbers, using a hybrid URANS-LES turbulence model. These studies captured, for the first time, the intense velocity fluctuations and low-frequency bimodal oscillations, including the quasi-periodic vortex shedding and merging, and the formation of hairpin vortices, generated by a centrifugal instability that controls HSV dynamics. All these processes increase the instantaneous shear stress near the obstacle, allowing the development of models to study sediment dynamics from a Lagrangian perspective [23,91], as well as a model of bed evolution and bedform development, coupling the coherent-structure resolving model to the Exner equation [24], as shown in Figure 8a. These recent models have shown the potential of high-resolution 3D numerical simulations to predict di fferent aspects of the scour process in subcritical conditions with good agreement. From these investigations, three key features have been identified: (1) Isotropic RANS turbulence models are inherently limited to predict the complex dynamics of an HSV system, as they yield a large turbulent viscosity, increasing the energy dissipation and suppressing the turbulence at the junction; (2) coherent structure resolving turbulence models can capture HSV dynamics, which can resolve the details of bedform formation and initial development of the scour hole in sand beds by turbulent structures; and (3) the main limiting assumption of these models stems from the prediction of instantaneous sediment fluxes from empirical formulas developed for uniform flows in steady and equilibrium conditions, adding ad-hoc formulations to represent the avalanches when the bed slope locally exceeds the angle of repose.

Using a Volume-Of-Fluid (VOF) approach, researchers [92] recently reported the first free surface resolving scour simulations using RANS–Exner type models. According to the author, accounting for the free surface e ffect improves the position of the HSV and the prediction of the mean velocity field, even at a Froude number as low as 0.2. The VOF technique emerges as a promising tool for the advanced numerical simulation of supercritical flows, including the scour at bridge foundations, following the coupled hydrodynamics and sediment transport approach.

**Figure 8.** Instantaneous bed surface and streamlines around a cylindrical pier: (**a**) a subcritical flow with clear water conditions and the scour computed with the LES–Exner model, as in [24], and (**b**) a subcritical flow with live bed conditions computed with the turbulence averaged two-phase flow model, as in [93]. Streamlines are colored by the velocity magnitude.
