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29 CHAPTER 3 PIER-SCOUR PROCESSES 3.1 Introduction Pier scour processes are intricate and challenging to formulate (even empirically or approximately), let alone fully comprehend. This statement holds for scour at all types of piers, especially those whose geometry consists of several components (column, pile cap, piles). The processes are made more complicated by the highly three-dimensional and unsteady characteristics of the flow field at piers, and by the nature of boundary material erosion. Furthermore, the complexities can be readily amplified by variations in bridge- waterway geometry, boundary material in which a pier is founded, and other considerations like woody-debris or ice accumulation at a pier. Figure 3-1 illustrates some of the complexities for a representative bridge waterway, e.g., different boundary materials, proximity of abutment. The ensuing sections begin by examining pier scour of boundary material at a cylindrical pier founded in a rectangular channel bed or floodplain; most methods for estimating pier scour were developed for this situation. Considered then are factors adding complexity to scour at actual bridge sites. Such factors include pier-form complexity, pier location relative to bridge waterway morphology, and debris accumulation. These factors primarily affect pier flow field. The scour processes are discussed in terms of variables associated with the component sets of variables influencing pier scour. 1. Pier foundation material; 2. Pier flow field; and, 3. Erosion of foundation material at a pier.
30 Figure 3-1 Sketch showing flow through a bridge site involving complex interactions between the floodplain, the main channel and the piers situated close to the floodplain and main channel, especially during high flow conditions 3.2 Pier Foundation Material Rivers channels and floodplains form in widely varying combinations of rock, sediment, and soils (or clays). The great majority of scour-prone bridge waterways, however, comprise main channel beds formed of alluvial sediments (non-cohesive material), at least through the upper strata of the beds. Therefore the majority of pier-scour studies have focused on scour at piers in alluvial beds. The floodplains of such channels typically are a mix of sediments and soils (cohesive sediment, possibly with organic content, and clay). It is not uncommon for piers to be founded in clay or on rock beds, sometimes underlying upper strata of alluvial sediments. Comparatively few studies focus on scour at piers in clay or rock, though notable pier failures have involved piers on clay or rock. Scour-hole formation at piers in sediment has been observed frequently, especially in laboratory flumes. Accordingly, much of the review in subsequent sections of this report summarizes scour in a single layer of sediment. In this regard, the main variables characterizing single layers of sediment are relatively easily identified and expressed in terms of non-dimensional parameters (Chapter 5). Much less frequently observed, and fraught with potentially numerous additional variables, is scour in layered sediments, and in clay and rock. Chapter 5 outlines the essential aspects of these parameters. They include variables characterizing layer
31 dimensions (for layered sediments and soils), strength for soils and rocks, and structure of joints and fractures (rocks). Somewhat different scour forms evolve in accordance with whether scour occurs in sediment, clay, or rock, as depicted in Figure 3-2. In terms of scour form, it also is useful to include a view of scour by air flow at a cylinder in snow (Figure 3-3), a light cohesive boundary material. An important observation for the scour forms in Figures 3-2 and 3-3 is that the overall scale of scour depth does not seem to vary markedly with the different foundation materials, though scour geometry does vary to some extent. The well-known inverted-frustum form of scour hole develops at piers in single layers of sediment, the upstream side-slope of the scour hole being related closely to the static angle of repose of the sediment (Figure 3-2a). For strong cohesive material (clay), the scour hole is less regular, with deepest scour occurring at the pier flanks. For weaker cohesive material, like snow, the scour hole is more cylindrical, as cohesion enables the material to have a vertical face. Scour in rock is influenced by jointing and fracturing in the rock, and consequently can produce a notably irregular scour form. Scour in sand and gravel produce a deposition mound or bar behind the pier. Scour in other materials does not. (a) (b)
32 (c) Figure 3-2 Differences in scour form at a cylinder; (a) sand bed, (b) clay bed (Briaud et al. 2004), and (c) rock bed (Hopkins and Beckham, 1999). The maximum depth of scour is approximately similar for each material, but the location of deepest scour differs Figure 3-3 Scour in a weak cohesive material (snow) 3.3 Pier Flow Field To understand pier scour, it is necessary understand the flow field at a pier, and how the flow field varies with pier size and form, as well as flow depth and foundation material. A difficulty in this respect, however, is that the flow field is a class of junction flow (i.e., flow at the junction of a structural form and a base plane), a notably three-dimensional, unsteady flow field marked by interacting turbulence structures. The eroding forces exerted on the foundation material supporting the pier are generated by flow contraction around the pier, by a pronounced down-flow at the pierâs leading edge, and by turbulence structures of a wide range of turbulence scales. Variations of pier width and form, and flow depth, alter the flow field, enhancing or weakening these flow features.
33 In terms of prevailing ranges of pier width, a, and flow depth, y, it is convenient to identify and discuss three categories of pier flow field, which produce significantly different pier scour morphologies: 1. Narrow piers (y/a > 1.4), for which scour typically is deepest at the pier face; 2. Transitional piers (0.2 < y/a < 1.4); and, 3. Wide piers (y/a < 0.2), for which scour typically is deepest at the pier flank. Under design flow conditions, i The values of y/a indicated for the flow-field categories are based on data trends delineating differences in the relationship between scour depth and y/a (e.g., Melville and Coleman 2000). Figure 4-1, subsequently in Chapter 4, defines pier width, a, in terms of as-constructed pier form. The foregoing categories are defined better in terms of effective pier width, a* , which takes into account approach flow angle and pier form. The ensuing sub-sections briefly describe the main flow features and illustrate how they differ for these three categories of flow field. For substantially more detailed descriptions of the flow field, refer for example to Kirkil et al. (2006, 2008). The closing sub-section takes a moment to show examples of the detailed insights now obtainable using numerical models of pier flow fields, insights presently not accessible from laboratory or field investigation. The pier flow field may become more complicated if the pier has a complex shape, such as a column supported on a pile cap underpinned by a pile cluster, as in Figures 1-2 or 1- 3. Additionally, the close presence of an abutment and/or a channel bank further complicates the flow field. 3.3.1 Narrow Piers The main features of the flow field at narrow piers can be explained by viewing the flow field commensurate with scour at an isolated circular cylindrical pier in a relatively deep, wide channel. Figure 3-4 illustrates the main features of the flow field for a pier founded in sediment, and conveys a sense of the flow field intricacies to be considered when attempting to understand scour at a simple, single-column pier. For a sediment foundation, scour is deepest at the pier face. An interacting and unsteady set of flow features entrains and transports sediment from the pier foundation. They include: flow impact against the pier face, producing a down- flow and an up-flow with roller; flow converging, contracting, then diverging; the generation, transport and dissipation of large-scale turbulence structures (macro- turbulence) at the base of the pier-foundation junction (commonly termed the horseshoe vortex); detaching shear layer at each pier flank; and, wake vortices convected through the pierâs wake. The features evolve as scour develops.
34 Figure 3-4 The main flow features forming the flow field at a narrow pier of circular cylindrical form. Early research focused on flow immediately upstream of the pier (dashed area) Flow approaching the pier decelerates, impinges against the pierâs centreline, and then strongly deflects both down and up the pierâs face. These two vertical flows act almost as wall-attached jet-like flows along the pierâs centreline, one directed up toward the free surface, and the other down toward the bed. The up-flow attains a height approximating a stagnation head, interacts with the free surface, and forms a surface roller or vortex. The stagnation pressure on the upstream face of the pier attains a maximum near the level where these two jet-like flows form. Also, at the stagnation line the deceleration is greatest. The deceleration decreases as the bed and, respectively, the free surface are approached. The down-flow is driven by the resulting downward gradient (below the still water level) of stagnation pressure along the pierâs leading face. This downward gradient results largely because the velocity distribution of the approach flow is commensurate with a fully turbulent shear flow; i.e., velocity generally decreases toward the bed. As the scour hole develops, the down-flow is augmented by the approach flow diverging into the scour hole. In addition to the vertical component of flow at the pierâs leading face, flow contracts as it passes around the pierâs sides. Local values of flow velocity and bed shear stress thereby increase around the pierâs sides. For many piers, the increases are such that scour begins at the sides of a pier. Once the scour region develops as a hole fully around the pier, the down-flow and the necklace (or horseshoe) vortices strengthen. Scour-hole formation draws flow into the hole. The influences of turbulence structures have become better realized during the past decade, though they are not yet adequately understood and taken into account by scour- depth relationships. Research prior to about 1990 focused essentially on flow approaching a pier, and the horseshoe vortex system at the scour-hole base, with little attention given to the turbulence structures around the entire pier. The turbulence structures, together with local flow convergence/contractions, around the broad fronts and Earl y focu
35 flanks of piers, or between piles of complex pier configurations, are erosive flow mechanisms of primary importance. The turbulence structures are not isolated from each other. They intrinsically connect within the flow field. Also, it is not enough to focus on one category of turbulence structure, notably the well-known (but still inadequately understood) horseshoe vortex system; or on one flow convergence; e.g., the down-flow at the leading edge of a pier. As significant as these individual flow features are, they alone do not account for sediment erosion from a scour hole. The flow field, during all stages of scour development, is marked by the presence of organized, coherent turbulence structures, notably: 1. A horseshoe vortex system formed of several necklace vortices (the standard term for junction flows) commonly termed the horseshoe vortex. It forms around the pierâs leading perimeter. These vortices wrap around the pierâs base such that the legs are oriented approximately parallel to the approaching flow. The legs break up and are shed intermittently; 2. Small but very energetic elongated eddies (vortex tubes whose main axis is approximately vertical relative to the bed) in the detached shear layers; 3. Large-scale rollers or wake vortices, which form behind the two flanks of the pier, and are shed into its wake. As they advect away from the pier, the wake vortices expand in diameter, then dissipate and break up; 4. A horizontal vortex formed by flow passing over the stationary, depositional mound formed at the exit slope from the scour hole. The location and amplitude of the mound depend on the power of the wake vortices shed from the pier (the weaker the vortices, the closer the mound to the pier); and, 5. A surface roller situated close to the junction between the free surface and the upstream face of the pier. The roller is akin to a bow wave of a boat moving through water. In summary, the down-flow impingement on the bed, along with the wide range of turbulence structures present in the flow field, entrain and transport material from the scour hole. The details and interaction of the flow field vary with pier shape, angle of attack, and the stage of scour development between initiation and equilibrium, but the essential consideration is that these flow features are responsible for scour. Therefore, to understand how scour develops, to model scour, and to estimate scour depth it is necessary to understand the general structure of the flow field, and determine how flow entrains and transports foundation material from the scour hole. Also, it is important to recognize that the flow field evolves during different stages of scour. The flow field becomes even more complicated if the pier has a complex shape, such as a column supported on a pile cap underpinned by a pile cluster, as in Figure 1-2. Additionally, the flow field can be complicated by debris or ice accumulation, the proximity of an abutment, and aspects of channel morphology.
36 3.3.2 Transition Piers The main flow-field features described for narrow piers exist in the flow field of piers within the transition range of y/a, but the features now begin to alter in response to reductions of y and or increases in a. The closer proximity of the water surface to the foundation boundary (for constant pier width), or the increased width of a pier (for constant flow depth), partially disrupt the formation of the features, and thereby reduce their capacity to erode foundation material. Though further research is needed to systematically describe and document the flow field changes, ample data show that reductions in y/a result in shallower scour depths for this transition category of flow field (see Section 4.3). Figure 3-5 depicts a sequence of flow field adjustments commensurate with three values of y/a, indicating how the scour capacity of flow field reduces. The down-flow at the pier face becomes less well developed because it has a shortened length over which to develop, whereas the up-flow associated with the (flow stagnation) bow wave remains essentially unchanged. The vorticity (circulation) of the large-scale turbulence structures (horseshoe vortex) aligned more-or-less horizontally in the pier flow field weakens as the down-flow weakens, and the vertically aligned turbulence structures (wake vortices) also weaken due to the increased importance of bed friction in a shallower flow. 3.3.2 Wide Piers For wide piers, the flow approaching the pier decelerates, turns, and flows laterally along the pier face before contracting and passing around the sides of the pier. The down-flow at the pier face is weakly developed, and only slightly erodes the foundation at the pier centerplane. The circulation of the necklace vortices peaks at vertical sections situated around the flanks of the pier. Flow velocities near the pier are greatest where flow contracts around the pierâs sides. Erosive turbulence structures now principally comprise wake vortices and the part of the horseshoe vortex system located in the scour region close to each flank of the pier. Deepest scour occurs at the pier flanks. Figure 3-6 schematically illustrates the flow field around a wide pier. For a given flow depth, greater pier width increases flow blockage and therefore causes more of the approach flow to be swept laterally along the pier face than around the pierâs flanks. Increased blockage modifies the lateral distribution of approach flow over a longer distance upstream of a pier. The flow field around each side of a wide pier is essentially the same as that at an abutment built with a solid foundation extending with depth into the foundation material (also that at a long spur dike or coffer dam).
37 Figure 3-5 Variation of flow field with reducing approach flow depth; narrow to transitional pier of constant pier width. The sketches contain the horseshoe vortex, the bow vortex, and the lee-wake vortices. The downflow is represented by the vertical arrow close to the upstream face of the pier
38 Figure 3-6 Main features of the flow field at a wide pier (y/a < 0.2) Since 1990, and especially in the recent ten years, major progress has been made with numerical modeling of flow at piers. The models available today can resolve all the main flow features and their unsteady interactions. It is useful to include here short examples of the highly detailed information available from such models. 3.2.4 New Insights from Numerical Modeling Initial Flow Field. Before scour when the bed is flat, adverse pressure gradients slowing the approach flow cause flow separation near the bed. The incoming boundary layer on the bottom surface around the pier separates. The resulting necklace vortices (forming the horseshoe vortex system) develop within the separated region around the upstream part of the pierâs base, and are a consequence of the reorganization of the boundary layer vorticity downstream of the flow separation line. The necklace vortices have the same sense of rotation as the vorticity in the upstream boundary layer. For most flow conditions, the location, size and intensity (circulation) of the necklace vortices vary in time. Phenomena such as vortex pairing between a secondary necklace vortex and the primary necklace vortex, or between two secondary necklace vortices and vortex bursting phenomena occur. As the dominant upstream boundary layer vorticity is in the transverse direction, due to the adverse pressure gradients close to the upstream face of the pier, the necklace vortices originating in the separation region stretch around the pier. The sides of the vortex lines become oriented in the streamwise direction, with the vorticity being of opposite sense in the two sides (legs). The main necklace vortices entrain fluid from the
39 down-flow at the upstream face of the pier, drawing it out toward the bed. Another interesting phenomenon is that the capacity of the wake roller vortices to entrain sediment is strongly dependent on the shape of the pier. Compared to circular cylinders and cylinders with smooth edges, cylinders with sharp edges (e.g., piers of rectangular shape) tend to form strong roller vortices that maintain their coherence until the bed surface. As a result, strong bed friction velocity values occur beneath the rollers that are convected in the near wake region (e.g., see Figure. 3-10). This flow field aspect explains the higher rates of scour observed behind piers of rectangular section compared to circular piers during the initial stages of the scour process. The strength, evolution, and fluctuating formation of the vortices upstream of the pier are affected by flow Reynolds number (yV/ν), the characteristics of the bed roughness, the shape and size of the evolving scour hole, the level of free-stream turbulence, and the shape of the pier. Developing Scour Hole. Once a scour hole forms around the pier, the initial system of vortices changes substantially, their size and behaviour dictated by the shape of the scour hole. In other words, the horseshoe vortex system now forming in the scour hole is similar to a recirculation flow region forming due to the drop in the bed elevation at the upstream side of the scour hole. The necklace vortices forming the horseshoe vortex system are visualized in Figure 3-7 for a circular pier with a large scour hole close to equilibrium scour depth. An important flow feature is the shedding of energetic vortices inside the detaching separation layer forming on each pier flank. In most cases, these vortices resemble vortex tubes. Away from the pier, the axis of these vortex tubes is close to vertical. For circular piers that do not contain sharp edges (as for a rectangular pier) the vortices are tilted sideways in the near bed region, because the angle at which flow separates from the pier varies with distance from the bed. For the usual range of pier diameters and approach-flow velocities, the separation angle is about 170o near the bed and decreases to about 850 away from the bed (the 0o location is at the pierâs leading edge) if the wake is subcritical. Such insights are available from Large Eddy Simulation numerical models (Kirkil et al. 2006, 2008), and to some extent from Particle-Image Velocimetry experiments (e.g., Unger and Hager 2007). These energetic vortices can entrain sediment, conveying it through the wake vortex system. The portion of the flow field in the near wake is dominated by the shedding of large- scale roller or wake vortices that can induce large, unsteady forces on the bed as they are convected away from the pier. The forces are sufficient to transport sediment away from the scour hole as it develops. The regularity of shedding of the roller vortices can be significantly affected by the upwelling of flow close to the symmetry plane behind the pier. The suppression of the vortex shedding has been observed both experimentally and numerically for circular and rectangular piers in shallow flows with a large scour hole (Kirkil et al. 2008).
40 Figure 3-8 is a useful illustration of the highly three-dimensional and contorted path of flow and suspended sediment particles through a scour hole. The paths involve extensive rotations and vertical movements. The form of the pier and the stage of scour development affect the entrainment and transport of foundation material from the scour hole. Figure 3-7 Visualization of the main vortices forming the horseshoe vortex system,(HV) system in the mean flow field around a circular pier in a scoured bed. HV1 is the main necklace vortex; HV2 and BAV are secondary necklace vortices; JV is a junction corner vortex (Kirkil et al., 2008)
41 Figure 3-8 Numerical simulation showing example flow paths (and fine-sediment paths) around a pier during scour; (a) top view, (b) side view (Kirkil et al., 2008) 3.4 Erosion of Foundation Material The main flow features work together in entraining and transporting foundation material from around a pier, and thereby determining scour morphology and the potential maximum scour depth. The following description outlines how the flow field erodes sediment to form a scour hole at a narrow pier in sediment, the most commonly studied pier scour situation. The illustrations shown are from numerical modeling, including from flow around a simulated transitional pier. Flume studies over the years (e.g., Melville and Raudkivi 1977, Dargahi 1990, Oliveto and Hager 2002) show that scour initiates in the contracted flow region along the pier flanks, and beneath the detaching shear layer and wake vortices shed behind the pier. The initial scour zones grow and extend back around the pier face. The down-flow at the pier face impinging on the erodible bed quickly erodes a groove immediately adjacent to the front of the pier. As the groove deepens, it triggers the formation of a frustum-shaped scour hole around the pierâs upstream perimeter. Further deepening of the groove undermines the scour-hole slope, causing local avalanches of sediment, which then the flow sweeps from the scour hole, thus maintaining the slope at the local repose angle of the sediment as scour deepens. The down-flow together with the horseshoe vortex system comprise the two main flow features responsible for the
42 removal of sediment particles and the growth of the upstream side of the scour hole formed in sediment. Because sediment erodes from all around the pier base, other flow features facilitate scour. At the pierâs sides, flow contracts and accelerates, which results into a local increase of the bed shear stress. The convection of highly energetic vortex tubes within the detached shear layers usually results in a strong amplification of the bed shear stress at the pier flanks. Additionally, the main necklace vortices in the horseshoe vortex system remove sediment not only from the upstream part of the scour hole, but also from the pier flanks as patches of highly vortical fluid detach from the legs of these necklace vortices. This is one of the main mechanisms that explains the growth of the scour hole both laterally and behind the pier. Figure 3-9, from a numerical simulation (Kirkil et al., 2009), shows the momentary formation of streaks of high bed shear stress behind the pier. These streaks occur when one side of a necklace vortex is stretched toward the back of the pier and a streak (or eddy) of vorticity detaches from the necklace vortex. As this streak moves away from the pier, its vorticity is high enough to significantly amplify the bed shear stress beneath it. The wake vortices play an important role transporting sediment away from the pier. Depending on the flow conditions and the shape of the pier, they also can induce locally high bed-shear-stress values as they are convected away from the pier. This role becomes especially pronounced for transitional and wide piers. For example, the contours of instantaneous bed friction velocity shown in Figure 3-10 illustrate this occurrence for flow past a large-aspect ratio rectangular pier on at flat bed at the start of the scour. The strength of the wake vortices and the local amplification of the bed friction velocity beneath them are much smaller for circular piers of same width. A deposition-dune or mound forms downstream of the pier due to the deceleration of the sediment particles entrained in the regions of high bed shear stress and pressure fluctuations. The deceleration occurs once the particles entrained by the various eddies move downstream of the pier and these eddies weaken and eventually dissipate. Some of the sediment particles are entrained into the recirculation region behind the pier. These particles can move away from the bed as a result of their entrainment by upwelling motions. As the scoured region at the upstream base of the pier grows, the overall size of the horseshoe vortex system increases but the down-flow velocity near the scour-hole base reduces as do the bed shear-stress values. In the case of clear-water scour, when these stresses decay close to the local value (adjusted for gravitational force effects) corresponding to the threshold for sediment entrainment, scour deepening ceases and the flow and bathymetry are at an equilibrium scour condition. In reality, even at equilibrium conditions some local intermittent erosion and deposition of bed particles occurs (e.g., Roulund et al., 2005), but the overall scour form does not alter. The foregoing description indicates the importance of understanding the interactions of the turbulence structures in elucidating pier scour. This consideration is even more
43 critical for piers of complex geometry. Then, the complexity of the flow and of the dynamic interactions among the main coherent structures is even greater; e.g., the effects of the underflow beneath a pile cap, the vortex shedding taking place in the wake of the exposed foundation elements supporting the main pile. The literature lacks a detailed study of these processes. The foregoing description is for erosion of sediment. The description must be modified for erosion of clay or rock. Turbulence structures play an even larger role in eroding these latter two materials. Figure 3-9 Distribution of instantaneous bed shear stress around a narrow circular pier with scour hole. Note the high value beneath the leg of the main necklace vortex on the right side of the pier. This streak of vorticity is detaching from the horseshoe vortex and is convected behind the pier parallel to the deformed bed (Kirkil et al., 2008) Figure 3-10 Numerical simulation showing distribution of instantaneous bed friction velocity in the flow past a high aspect ratio rectangular cylinder at the start of the scour process (flat bed) Ï/ÏV 2 u * /V
