Effect of Spacing and Skewness on Side-by-Side Bridge Piers

Most bridge collapses globally are caused by local scour, which is probably the most common danger to bridge piers and foundations [1].

Recently, several studies have investigated the impact of different factors on the creation of vortex systems around bridge piers. These factors can be classified into three groups: (1) flow parameters, such as approach velocity and flow depth; (2) sediment parameters, including median size, size distribution, and sediment density; and (3) pier characteristics, including shape, type, and dimensions [2-7]. A significant factor that increases the scour danger of bridges is the pier geometry. The pier geometry significantly influences the development and resistance of the vortex system [1, 6, 8-12].

The vertical shape of the pier at the riverbed substantially affected the flow structure. This leads to significant variations in the flow field based on the pier shape, resulting in different scour patterns. The most important variables in the scour process are the vortices generated from the pressure differentials when the water velocity profile encounters an obstruction. The scouring mechanism occurs because of the complex vortex of a system. This system includes a horseshoe vortex, wake vortex, trailing vortex, and bow-wave vortex [12, 13].

According to the study conducted by Namaee and Sui [14], the horseshoe vortex, which is mainly caused by the downflow, is located on the pier's upstream face. The horseshoe vortex and fast flow close to the piers increased the bed shear stress, resulting in localized scour formation around the piers. Then, the horseshoe and wake vortices gradually subsided, the scouring process decreased, and the bed shear stress decreased. Consequently, the bed shear stress exceeds the critical shear stress, causing the scour hole to reach an equilibrium state where the sediment particles are no longer transported or moved into suspension. There are two types of vortices: wake vortices caused by the separation area at the sides and downstream of the pier, and horseshoe vortices at the front side of the pier [15].

Two different situations related to sediment transport may cause scour: (1) clear water, which refers to the absence of sediment transport in the approach channel bed, and (2) live beds, which refers to the transport of bed sand in the approach flow. In the first condition, at the start of the sediment motion, the shear stress at the bed is less or, most likely, equal to the critical shear stress at the bed; in the second condition, the shear stress at the bed exceeds the critical shear stress. Localized and general scours are the two main types of scour. The combination of contraction and local scour results in localized scour rather than general scour owing to the presence of the bridge. Ignoring the local scour phenomena in the pier design may lead to a high mortality rate or significant financial loss. Sediment particle movement is related to the creation of an armor layer in the scour hole surrounding piers. As a result, coarser grains remain behind while finer sediment particles move. The remaining finer grains are concealed by the bigger grains, and the coarser grains to greater flow [16]. Armoring is primarily caused by selective erosion, wherein the critical shear stress for movement (τ*c) exceeds the shear stress at the bed of finer sediment particles (τ). When there is clear water flow, scour at bridge piers can take a long time to stabilize, mainly if the flow velocity is close to the threshold for the first sediment movement. This is because of the removal of the entire volume of sediment particles from the scour hole and the interaction of flowing water with the pier under the influence of vortices, which determine the equilibrium scour depth. When the scour depth is at equilibrium, it ceases to fluctuate over time [17].

Based on the literature review above, pier erosion is a complicated phenomenon that can have serious repercussions, including the whole or partial collapse of bridges. In the coming decades, there will be a significant increase in flood occurrences and unanticipated variations in river flow as a consequence of warming [18], uneven distribution of rainwater [19], caused by water pollution [20], and human activities [21]. Several studies involving deep lab tests have been conducted to examine pier scours. In most of these tests, the scour at the pier was examined under conditions of uniform sediment. Based on a review of the literature, it was discovered that there has yet to be much research done on scour surrounding side-by-side piers, and there have not been enough studies published on when sediment conditions are non-uniform and with varying spacings between side-by-side bridge piers.

3.1 Material of bed

The amount of natural sediment can vary greatly, depending on the geology and stream strength of the area. Sediment size is crucial because it affects sediment settling velocity and specific gravity. Particle characteristics influence the scour depth. Cohesionless sediment (i.e., non-uniform Iraqi soil) was used as the bed material for each experiment to achieve the MSD. As shown in Figure 2, a soil-grading test (sieve analysis) was performed by Arneson et al. [22] to determine the types and characteristics of the sand used in this investigation. The bed material specifications are listed in Table 1.

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Figure 2. Distribution curves of non-uniform sediments

Table 1. The specification of bed material

The starting velocity of coarse particles in non-uniform materials is less than that of uniform materials with identical particle sizes, and the starting velocity of finer particles in non-uniform materials is higher than that of uniform materials with identical particle sizes, as seen in the study of Xu et al. [23]. Because coarse grains are more likely to be exposed to flow while transporting non-uniform soil, they are easier to entrain than uniform sediment particles of the same particle size.

3.2 Experimental setup and measurement

The tests were conducted at a private hydraulic laboratory in Babylon. The flume was made of a steel frame constructed with glass walls. It is horizontally non-tilting, 8.5 m long, 0.98 m wide, and 0.6 m deep. The work section was 2.1 m long and 0.204 m deep. Located 2.5 m upstream from the flume inlet section, the section has been filled with cohesion-less soil d₅₀₌0.873 mm Additionally, water is pumped from the main reservoir tank into an overhead tank located upstream of the flume. A wooden gate suppressor was used in the upstream approach section, and baffles (two screens) were positioned every 50 cm from the flume entrance to smooth the flow (steady continuous flow) into the bed section. A rectangular gate 0.98×0.6 m was supplied at the flume outlet section to make the water depth at the head and end of the flume equal and hence to control the flow velocity. The water utilized from the flume was then discharged into the outlet tank. The pump extracts water from the reservoir at the downstream terminus of the flume and conveys it to the upstream terminus via a 4-inch-diameter pipeline that runs parallel to the flume. Four reservoir tanks exist, one located in the outflow flume with dimensions 1×0.98×0.55 m, separated by a rectangular gate, and three parallel to the flume with a size 1.25×1.25×0.5 m. A centrifugal pump positioned at the end of the downstream of the flume delivered the flow rate via a 3-inch-diameter pipe. An ultrasonic flow meter was employed to quantify the water discharge, and all depths were gauged using a movable point gauge affixed to a brass rail at the upper section of the flume side with an accuracy of - 0.1 mm, as shown in Figure 3.

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Figure 3. The experimental flume

3.3 General experiment procedures

1. The models were installed at the required spacing and skew angles (vertically or skew angles). Changes in pier position and direction may significantly affect the flow pattern.
2. The bed material, consisting of sand with a mean grain size d₅₀=0.873 mm, was positioned in the work section. The sand was leveled using a scraper, and the initial bed elevations were verified at random spots using a point gauge to ensure proper leveling. The sand layer had a thickness of 20.4 cm.
3. The gate is closed downstream. The pump started operating, and its speed was gradually increased until the required flow rate was attained. The tailgate was verified to preserve the correct flow depth of the flume.
4. The timer recorded the time during each test. When the time limit ended, the flow stopped and the flume was gradually emptied to prevent the scour hole from changing.
5. After the sand was left to dry, the positions and sizes of the MSD points were recorded. During the initial hours, data on the MSD were recorded every few minutes. The initial hours of every test are critical because many readings are required to correctly determine the early stage of the maximum scour depth vs. time graph.
6. After changing the skew angle, pier shape, and pier spacing, the sand was leveled again and the processes were repeated.

3.4 Scour conditions

In the series of tests, fourteen experiments were shown in terms of flow skew-angle $\alpha=0^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}$, the corresponding steady discharge was $12.5 \mathrm{lit} / \mathrm{sec}$, approach velocity, $V$, critical velocity, $V_c$, Armor peak velocity are valid only for $\sigma_g>1.3$ (non-uniform sediments), $V_a$, flow density, $\left(\left[V-\left(V_a-V_c\right)\right]\right) / V_c<1$ for non-uniform sediments, clear water scours conditions are present, maximum scour depth, ds, and Froude number, $F r<1$ (subcritical for all cases), with soil (sand $d_{50}=0.873 \mathrm{~mm}, d_{50 a}=1.267 \mathrm{~mm}$), and approach flow depth $Y_o=0.05 \mathrm{~m}$, pier diameter $\left(\mathrm{D}_{\mathrm{p}}\right)$, and pier spacing $(\mathrm{S})$.

$d_{50 a}=\frac{d \max }{1.8}$

$d_{\max }=$maximum particle size

The critical shear velocities in the armored beds were obtained from Eqs. (1) and (2) [13]:

$\begin{gathered}0.1 \mathrm{~mm}<d_{50 a}<1 \mathrm{~mm} \\ V_{* c a}=0.0115+0.0125 d_{50 a}^{1.4}\end{gathered}$          (1)

$\begin{gathered}1 \mathrm{~mm}<d_{50 a}<100 \mathrm{~mm} \\ V_{* c a}=0.0305 d_{50 a}^{0.5}-0.0065 d_{50 a}^{-1}\end{gathered}$         (2)

The mean critical velocity on the armored bed was:

$\frac{V c}{V * c a}=5.75 \log \left[5.53 \frac{Y o}{d_{50 a}}\right]$           (3)

$V_{* c a}$: mean critical velocity in armored bed.

Finally, $V_a=0.8 V_{c a}$.

$\frac{\left[V-\left(V_a-V_c\right]\right.}{V_f}<1$ (for non-uniform sediment)           (4)

Then $Q=V A$.

Fourteen experiments were conducted to investigate the local scour pattern in a horizontal open channel under clear water flow conditions utilizing different shapes, skew angles, and spacing between piers around three side-by-side rectangular and lenticular bridge piers.

1. At the beginning of each run, the rate of scour hole creation was larger; it then decreased with time and asymptotically approached an equilibrium value, with a maximum period of approximately 180-210 minutes. The maximum equilibrium scour depth of a clear-water local scour is a function of the relative size D_p/d₅₀, relative depth Y_o/D_p, and spacing ratio S/D_p, and the MSD occurs at the pier near the abutment upstream in all experiments.
2. The pier shape and skew angle influenced the initial scour rate and equilibrium scour depth. The maximum scour from the upstream side of the pier is approximately two-thirds of its length.
3.  For lenticular pier when α=0° and S/D_p=3, the lowest scour observed with the scour depths are 1.6, 1.4, and 1.55 cm for P₁, P₂, and P₃, respectively because its geometry is assumed to be the most efficient protective measure against horseshoe vortices which cause local scour; the scour starts merely from the upstream face and ends at mid-section, it is the best compared to rectangular piers, and the MSD scour hole is identified at α=30° and S/D_p=1, with scour depths measuring 8.87, 8.3, and 7.2 cm for P₁, P₂, and P₃, respectively.
4. A rectangular pier has a higher scour than other geometries because of the maximum exposed area, in which the deepest MSD scour hole is observed for α=30°, and S/D_p=1 for the rectangular pier scour depths are 10.6, 8.8, and 6.5 cm for P₁, P₂, and P₃, respectively, the rectangular pier is regarded as the weakest pier shape.
5. Smaller scour depths were obtained when the skew angle was 0°. Based on the scour profiles, the skew angle is in control of both horizontal expansion (the length increases in the direction of the transverse axis of the pier cross-section) and vertical deepening of the scour hole around the pier, in addition to the longitudinal deposition of sand downstream, as found in the study [26].
6. For α=0°, the scour depth decreases when the spacing increases. Previous studies confirm this, and α=30° shows the same pattern, but α=45° shows the opposite, where the scour depth is greater when S/Dp=3 than when S/Dp=1, because of the blockage caused by sediments between the piers, which makes it harder to transport the sediments and increases the exposed area that intercepts the flow; additionally, decreasing the spacing between the pier and abutment upstream, thereby increasing the velocity. Accordingly, the strength of the vortex increased, and the shear stress increased, thus increasing the sediment transport and hole depth.
7. According to the results, the maximum scour depth decreases as the grain size of the armor layer increases. The literature revealed Similar findings have been previously reported [27].