*1.1. The Cost of Scour*

Scour and erosion have been well established as leading causes of bridge failures. Over half of bridge failures in the United States alone have been attributed to scour [1,2]. Damage to roadway infrastructure due to scour can consist of minor erosion or complete failure of a bridge. Restoration of an overwater bridge of any size can require significant expenditure, cause disruption of local traffic and pose appreciable risk to surrounding ecosystems. In addition to capital for reconstruction, costs include rerouting of traffic and potential erection of temporary service bridges which can exceed the cost of replacement itself by 50 percent [3]. Furthermore, it has been estimated that indirect losses incurred by the general public, local business, and industry are five times greater than reconstruction costs alone [4]. Most crucially, due to the sudden nature of collapses caused by scour, failure of this type can result in loss of life.

In 1987, riprap protection around one pier of the Schoharie Creek Bridge on Interstate 90 over Schoharie Creek in New York failed due to spring flooding. The unprotected pier footing failed in tension, causing collapse of the pier and two spans of the bridge, resulting in the deaths of 10 motorists [5]. In 1995, a road bridge on Interstate 5 over Arroyo Pasajero in California collapsed, similarly under flood conditions. The collapse resulted in the deaths of seven motorists. After investigation by

the Federal Highway Administration (FHWA), the cause of failure was found to be bed degradation due to the presence of flooding [4].

In 2013, a single pier of the Bonnybrook Bridge over the Bow River in Alberta, Canada, was undermined due to scour during an unprecedented rainfall event, causing derailment of six cars of a passing Canadian Pacific Railway freight train. Fortunately, the collapse did not result in any fatalities. The derailed train cars were transporting industrial chemicals (including petroleum products) and flammable liquids which were contained during the incident [6,7]. A subsequent investigation by the Government of Canada [7] stated: "If measures are not taken to inhibit local scour, especially at bridges with spread footing foundations, there is an increased risk that high water events will lead to bridge failures."

## *1.2. The Mechanism of Local Scour*

When a structure such as a circular cylinder is introduced into a fluvial environment, there are several features which are induced in the surrounding flow field. One such feature is the downflow, which is formed when the approach flow decelerates leading up to the upstream face of the cylinder. Due to the nature of the velocity profile of the approach flow in an open channel, the pressure changes along the stagnation line, driving the flow downwards. This feature is known as the downflow, which impinges upon the bed at the base of the cylinder [8,9].

A horseshoe vortex (HSV) is formed when the downflow rolls up to form a vortex tube at the junction between the base of the cylinder and the bed. The legs of the HSV wrap around the cylinder extending in the downstream direction and are occasionally broken up and shed. A necklace or collar vortex is formed when the adverse pressure gradient (APG) associated with the stagnation line causes flow separation in the near-bed region. The boundary layer on the bed surface around the pier separates and the vorticity from the approach flow causes formation of a necklace vortex in the region of maximum shear stress in the vicinity of the cylinder. The necklace vortex is broken up in the wake region by the high bed shear stress and interaction with the wake vortices. The necklace vortex contributes to scour [10], and the HSV is one of the primary mechanisms by which sediment is removed from around the base of the cylinder. The vortical motion of the HSV entrains sediment from the bed into the flow around the cylinder. The size and strength of the HSV are related to the size of the scour hole around the cylinder, and both will continue to increase until equilibrium is reached. This is the point at which the strength of the HSV is no longer su fficiently high to continue to remove sediment from the bottom of the scour hole or when the critical shear stress of sediment at the bottom of the scour hole is no longer exceeded [8,9].

The vortices in the von Kármán vortex street are formed due to the shear layers which are detached from either side of the cylinder. Flow velocity is maximized along the separating streamline, and scour is thus initiated along the sides of the cylinder where the bed shear stress is also highest. The wake vortices shed alternately from the cylinder and carry the entrained sediment from the HSV region past the cylinder into the wake region. Downstream of the cylinder, the size of the wake vortices increases, causing them to weaken and deposit the sediment in dune-like formations [9]. From this discussion, it can be inferred that the strength and structure of the downflow, the horseshoe vortex, and the wake vortices are unsteady and highly influential on local scour around a cylinder. It is important to make note of the significant variation in structure, strength, and scale of each of the aforementioned turbulence structures.

#### *1.3. Scale E*ff*ects in Hydraulic Modelling*

Experimental modelling of local scour around a cylinder has been comprehensively explored for an appreciable range of flow, structure, and bed material characteristics. Typical scour experiments involve installation of a cylinder in a sediment recess filled with bed material of a prescribed size within a recirculating flume, from which point scour is allowed to progress until equilibrium is reached. The geometry of the scour formation is then measured to varying levels of detail, where the maximum

depth of scour *dse* (typically located near the upstream face of the cylinder) is the primary quantity of interest. Under prototype conditions, this would theoretically be taken as the minimum required foundation head, or the depth below which pier foundations should be placed in order to avoid the possibility of structural failure due to a loss of lateral support from the bed material. In practice, foundation head is determined on the basis of empirical equations, which have been developed by curve-fitting large quantities of laboratory data acquired through an experimental methodology similar to what is described above. Dimensional analysis has indicated that the maximum depth of scour normalized with pier diameter *dse*/*D* can be evaluated from a set of dimensionless variables which can be further reduced under certain conditions [9,11]. For fully turbulent subcritical flow aligned with a circular cylinder in well-graded erodible sediment, relative scour depth *dse*/*D* can be evaluated as described in Equation (1):

$$d\_{sd} \text{ID} = f \text{ (} \text{l} \text{l/} \text{l} \text{l}, \text{l/} \text{D}, \text{D/} d\_{50} \text{)}\tag{1}$$

In Equation (1), *U* is the average velocity of approach flow, *Uc* is the critical velocity for incipient motion of sediment, *h* is the flow depth, *D* is the cylinder diameter, and *d*50 is the median sediment diameter. The relationship between each dimensionless parameter and *dse*/*D* has been well established in the literature [3,9]. However, analysis has indicated that commonly used empirical equations in the form of Equation (1) have a tendency to overestimate *dse*/*D* values acquired from laboratory measurements [11]. Scale effects, which arise due to the imbalance in force ratios between a model and prototype, are certainly partially responsible for this discrepancy. This is particularly obvious in scaling of relative coarseness, *D*/*d*50, which cannot be equated between the laboratory and the field. If sediment size were to be scaled similarly to cylinder diameter, the bed material would be in the size range for cohesive sediment, and flow-sediment interactions would not be accurately replicated in the model. Therefore, bed material size in the approximate range of *d*50 in the field is used for modelling, and the experimental value of *D*/*d*50 is significantly reduced [11].

There are other model effects to which the poor performance of scour-predicting equations can be attributed. In a laboratory flume experiment, bed sediment is typically well-graded, and the approach flow is well regulated and usually two-dimensional in the central region of flow at the position of the cylinder. These are controlled conditions under which natural river flow rarely, if ever, occurs. Therefore, the differences between a value of *dse*/*D* estimated using an equation derived from laboratory results and an actual maximum depth of scour in the field can be understood. It has also been shown that prediction of scour in experiments with similar values of each governing parameter described in Equation (1) yields different values of *dse*/*D*, which implies that there are additional significant influences in scour modelling which have not been incorporated into scour estimation [12,13].

#### *1.4. The Influence of Blockage Ratio D*/*b on Local Scour*

One such influence which has been previously explored in physical scour modelling is blockage ratio, *D*/*b*, where *b* is the channel width. While the effect of *D*/*b* on flow around bluff bodies has been widely investigated for a fixed bed condition (e.g., [14,15]), the effect of *D*/*b* on local scour has not been clearly established. This is partially due to the generally significant relative width in naturally occurring rivers which mostly eliminates channel blockage as a concern for scour in the field. Nonetheless, in a comprehensive review of pier scour processes, Ettema et al. [9] stated that estimation of *dse*/*D* at a pier can be "complicated" by close channel bank proximity.

The effect of channel blockage in scour experiments has been erroneously defined as negligible when *D*/*b* is less than ten percent [8]. Laboratory flumes are usually constrained in width by facility size, and pier diameter *D* is generally chosen such that relative coarseness *D*/*d*50 is high enough to induce a measurable scour formation. Blockage ratio in experiments is therefore of greater concern than in the field. The influence of blockage ratio on scour around circular cylinders has been investigated by Hodi [16], D'Alessandro [17], and Tejada [18]. A review of these investigations, in which scour experiments were conducted for varying *D*/*b*, can be found in Williams et al. [19] (see Figure 1). The results of this investigation as well as those of both D'Alessandro [17] and Tejada [18] reported

changes in *dse*/*D* when *D*/*b* was ten percent or less, which does not agree with the assumed threshold stated above. Examination of the literature indicates that there are many experiments for which the effects of blockage have been ignored, despite having *D*/*b* > 0.10. Since code-specified design equations were derived from such experiments, a correction factor for the effect of *D*/*b* in prediction of *dse*/*D* was presented by Williams et al. [19].

**Figure 1.** Equilibrium scour formation for *D*/*b* = 0.05 (**left**) and 0.10 (**right**) [19].

However, the results reported by Hodi [16], D'Alessandro [17], Tejada [18], and Williams et al. [19] indicate that while changes to the scour formation (i.e., the extent of the scour hole and the shape of the dune) can be considerable due to the changes in *D*/*b*, changes to *dse*/*D* are minimal in the context of foundation head design.

## *1.5. Time Scale of Local Scour*

The definition of the aforementioned equilibrium state of local scour varies slightly among investigations. As previously described, the most commonly used definition is the point at which the bed shear stress within the scour hole reaches the critical shear stress of the bed material [19,20]. In the field, a point of true equilibrium according to this description is rarely reached, and so the progression of local scour under peak flood discharge is of particular interest for the design of foundation head in prototypes. For instance, the duration of peak discharge for which a foundation head is established may not reach the time to equilibrium, resulting in an overdesigned pier [20]. As such, the time scale of local scour around a circular cylinder is of particular interest to the hydraulic engineer.

There have been several experimental investigations into the progression of local scour under particular hydraulic conditions [20–24]. It has generally been established that scour depth increases rapidly in the early stages of the scour process, and the relationship between elapsed time and scour depth becomes asymptotic as the point of equilibrium is approached. The main objective of some studies has been to develop empirical relations for estimation of the time scale of local scour [21,23].

Guan et al. [24] acquired particle image velocimetry (PIV) measurements in the flow field surrounding a cylinder during the process of local scour. Bed measurements and PIV measurements were taken at various times up to a point of equilibrium, from which the evolution of the horseshoe vortex system was investigated. At 0.5 h, one clockwise vortex was observed near the leading face of the scour hole; when 48 h had elapsed, the system had evolved to generate two clockwise vortices and one smaller counterclockwise vortex [24].

## *1.6. Description of the Current Investigation*

The above review of the literature has indicated the importance of understanding both blockage effects on local scour and the time scale of scour. Further experimentation and analysis will allow for clarification and quantification of these e ffects for future incorporation into design methods used in practice.

In the present work, the e ffect of channel blockage *D*/*b* on the progression of local scour was further investigated. Local scour tests were carried out for varying *D*/*b* and *D*/*d*50, and experimental results were compared with data from literature in order to isolate the influence of blockage ratio on scour depth. Predictive methods from literature were evaluated for the tests under consideration.
