Introduction:

Bridge local scour which is responsible for structural failures in river-crossing bridges, occurs as a result of the interaction between the flow field and the bridge pier, leading to the removal of bed material and the formation of a scour hole around the foundation. Most existing research on the geometry of bridge piers focus on circular or rectangular piers aligned with the flow. However, real-world bridge piers often deviate from the flow direction due to hydraulic constraints or structural alignment. The alignment angle (α), defined as the deviation of the pier’s longitudinal axis from the flow direction, alters the symmetry of the horseshoe vortex and significantly affects the magnitude and position of the maximum scour depth. Moreover, the ratio of pier length (in the direction of flow) to its width (L/B) modifies the distribution of flow velocities and shear stresses around the pier. Despite numerous experimental studies, the simultaneous effect of these two parameters on local scour depth around non-circular piers, particularly rounded-nosed rectangular piers, has received limited attention. The present study aims to investigate the combined influence of L/B and α on the local scour depth under clear-water conditions.

Methods:

The experiments were conducted in the hydraulic laboratory of Isfahan University of Technology (IUT), Iran. The flume used for this study is a 12-meter-long, 0.6-meter-wide, and 0.5-meter-deep rectangular open channel with a water circulation system. The bed material consisted of uniform sand with a median particle size of d_50=0.78" " mmand a geometric standard deviation σ_g=1.29. Flow depth and discharge were controlled using a tailgate and calibrated pump system. Two pier models were fabricated from transparent Plexiglas to allow clear observation of flow structures. The reference circular pier had a diameter =3" " cm, while the rounded-nosed rectangular pier had a constant width B=3" " cm(equal to the circular pier’s diameter) and variable lengths L=6,9 and 12" " cm, corresponding to aspect ratios L/B=2,3 and 4. The piers were tested at three different alignment angles relative to the flow direction: α=5°,10° and 20°. Thus, a total of 13 experiments were conducted, including the reference circular pier case. The flow velocity was adjusted to achieve clear-water conditions at U/U_c=0.86, where U_c is the critical velocity for the initiation of sediment motion, determined using the Shields criterion. The steady discharge was set at 50 liters per second, corresponding to a flow depth of 18.8 cm. Before each run, the sand bed was leveled and compacted to ensure uniform initial conditions. Each test continued until the scour hole reached equilibrium. After completion, the final bed profile was measured using a digital point gauge with 0.1 mm precision. Longitudinal and transverse profiles were recorded at multiple sections to obtain the maximum local scour depth d_s. All experiments were repeated twice to ensure reproducibility, and the mean values were reported. Flow fluctuations were maintained within ±2% of the set discharge. The experimental data were analyzed using dimensional analysis and regression techniques.

Results:

The scour process followed the formation of a strong downflow on the upstream face, followed by the development of a horseshoe vortex that transported sediment away from the pier base. The equilibrium scour depth was achieved within 5–6 hours.

Effect of Aspect Ratio: At α ≤ 5°, increasing the aspect ratio from 2 to 4 led to a reduction in maximum scour depth which can be attributed to the redistribution of flow momentum along the elongated pier. At α ≥ 10°, the opposite trend was observed. Quantitatively, increasing L/Bfrom 2 to 4 resulted in a 20% decrease in scour depth at α=5°, but a 35% increase at α=20°.

Effect of Alignment Angle: Increasing α from 5° to 20° caused the scour hole to deepen and shift laterally toward the upstream corner of the pier. This behavior results from the asymmetric horseshoe vortex system generated under oblique flow conditions.

The rounded-nosed rectangular pier produced 15–20% less scour depth at α ≤ 5°, confirming its hydraulic efficiency in near-aligned conditions. However, for α ≥ 10°, the scour depth for rectangular piers exceeded that of the circular pier, indicating the negative impact of larger misalignment angles.

Combined Effect of L/B and α: The combined influence of aspect ratio and alignment angle was found to be nonlinear and interactive. For moderate aspect ratios (L/B = 3), the influence of α dominated the scour behavior, while at extreme aspect ratios, both parameters interacted to amplify scour depth.

Bed Morphology: Topographic surveys revealed that for α ≤ 5°, the scour hole was nearly symmetrical and shallow, while at α ≥ 10°, the hole became elongated and skewed toward the upstream corner. The deposition zone downstream expanded with increasing α, reflecting stronger wake vortices.



Conclusion:

The present experimental investigation demonstrated that both pier aspect ratio and alignment angle play crucial and interdependent roles in determining local scour depth around bridge piers. The major conclusions are summarized as follows:

For alignment angles below 5°, increasing the pier aspect ratio (L/B) decreases local scour depth by distributing flow energy along the pier face.

For α ≥ 10°, larger aspect ratios intensify scour by promoting asymmetric vortex formation and higher local shear stresses.

Rounded-nosed rectangular piers perform better than circular piers under small alignment angles (α ≤ 5°), but their performance deteriorates at higher angles.

A modified empirical relationship was proposed to estimate the alignment coefficient K_α, which accurately predicts scour depth with R^2=0.94.

From a practical perspective, pier alignment angles greater than 10° should be avoided in bridge design to minimize local scour risks.

Future work is recommended to examine the effects of surface roughness, pier spacing (group effects), and unsteady flow conditions such as floods using both experimental and computational fluid dynamics (CFD) modeling approaches.