The Variation of Scour Depth near Vertical and Inclined Cylindrical Bridge Piers: An Experimental Study

The morphological and the hydraulic conditions of scouring phenomena around bridge piers may reduce the risk of collapse and failure of bridges. For many years, various studies have been conducted to understand the complicated mechanism of scour around bridge piers and explain the effect of functional parameters on flow patterns, scour hole morphology and scour depth prediction [1-9]. However, for the aim of decreasing the strength of the erosive action of water and to consider the modern design of bridges, inclined piers were clearly seen in many countries. Until now, few laboratory studies focused on the associated scour depth with inclined bridge piers. Based on the experimental results ‎[10]‎, a significant relation was revealed between the slope of tapered piers and scour depth. Their study showed that the scour depth clearly affected by the upward slope of tested piers, thus the scour depth increases with increase the width of tapered piers from the bottom toward the top, while narrowing these piers upwardly decreases the depth of scour. Bozkus and Yildiz ‎[11], ‎performed laboratory study to investigate the effect of inclined cylindrical piers on local scour depth for uniform sand bed with two medians diameter (d₅₀=0.5 mm, and 1 mm) under different flow intensities range (V/V_C from 1.2 to 1.86). The authors conducted 44 experiments according to four angles of inclination (ϴ = 2°, 5°, 10° and 15°). The results of their study concluded that the scour depth decreases substantially as the angle of inclination increase downwardly with flow direction, also new empirical formulas were proposed. Experimental study was presented by Ozlap ‎[12], to show the effect of inclination piers group with stream wise direction on scour depth for uniform bed material of d₅₀=0.88 mm under clear water condition. The experiments have been carried out with three angles (ϴ = 0°, 10°, and 15°), the spacing between piers were fixed at four times of pier diameter (4D) with respect to different arrangement of piers group with 72 tests. Their study confirmed that there is a clearly reduction in scour depth for upstream piers related to the increase of angle of inclination. The scour hole dimensions decrease obviously by increasing the angle of piers inclination according to the laboratory results for series of experiments (32 tests for ϴ = 0°, 7°, 14° and 21°) under clear water conditions for uniform sediment of d₅₀ = 0.6 mm‎ [13]. Karimi et al. ‎[14], examined four inclination piers with downstream side (ϴ = 0°, 5°, 10° and 15°) and their effects on scour hole dimensions for sand bed material of d₅₀ = 1.46 mm with varied flow rates (12 to 18 l/s), they concluded that the maximum scour depth occurs with piers angle (ϴ = 0°), while the minimum depth of scour occurs at ϴ = 15°. Omara et al. ‎[15], ‎conducted extensive experimental study for investigating the inclination effect of different piers geometry (square, rectangular and circular) on dimension less scour depth (ds/D) for two bed materials (d₅₀=0.6 and 0.81 mm). The study included the effect of flow depth (0.048 m to 0.08 m), and flow intensity (V/V_C from 0.6 to 1.06) beside four inclination angles (ϴ = 10°, 15°, 21° and 30°). The authors found significant decrease in (ds/D) with increasing the inclined configuration from ϴ = 10° to 30°, also they noted that the best reduction in (ds/D) can be achieved for inclined rectangular piers at ϴ = 30° and length to width ratio (L/W = 7.5). Furthermore, the least reduction was obtained with square piers at different configuration angles. Their study showed that the maximum reduction percentage for circular piers at ϴ = 30° can be ranged from 24% to 35%. Evidently, and due to the scarcity of experiments data for this problem, the present paper was conducted to reveal the effect of pier inclination angles on the scour depth variation for different range of flow intensity based on new experiments under clear water conditions and to introduce new modified empirical formula of scour depth estimation of inclined bridge piers.

3.1 Evaluation of the influence parameters

Table 1 shows the obtained results for the experiments series of this study. As it is shown, the results are listed according to the effect of flow intensity (V/Vc). It is observed that, the increasing of angle of pier inclination (ϴ) decreases the scour depth near pier corresponding to the value of (V/Vc). Figure 3 illustrates the variation of scour depth (d_sa/D) regarding to (V/Vc and ϴ). For V/V_c = 0.495 and by increasing ϴ from 0° to 22°, the observed scour depth (d_sa/D) decreased from ‎1.194‎, to 0.710, while for V/V_c = 0.714 and by the same increasing of (ϴ), (d_sa/D) decreased from ‎1.452‎ to 1.129. Accordingly, by increase ϴ from 0° to 22°, it is noted from Figure 3 for V/V_c=0.824 that, (d_sa/D) can be reduced from 1.613 to 1.323, while for V/V_c=0.989, (d_sa/D) decreased from 1.968 to 1.677. Figure 4 shows the decrease percentage in scour depth due to the effect of pier inclination (ϴ‎) as compared to the observed scour depth of vertical pier (ϴ=0). It can be clearly noted that, the scour depth has been decreased by ‎13.514%‎, 32.432‎%, and 40.541% at V/V_c=0.495, and by ‎11.111‎%, 15.560%‎, and 22.222% at V/V_c=0.714, while at ‎ V/V_c=0.824, it was ‎8%‎, 12‎%, and 18% for ϴ= 10°, 16° and 22° respectively. It is observed at the threshold condition of initiation of motion of bed material (V/V_c=0.989), the scour depth can decrease by ‎4.920%‎, 9.84%‎, and 14.754‎% coinciding with effect of‎ ϴ = 10°, 16° and 22° respectively. As it is apparent in Figure 4, the maximum percentage decrease was observed at ϴ = 22° for all ranges of V/V_c. Generally, the estimated value of decrease proportional to flow intensity (V/V_c) and inclination effect.

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Figure 3. Variation of relative scour depth versus ϴ for different flow intensity

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Figure 4. Variation of percentage decrease in scour depth versus V/V_C for different ϴ

It can be stated that, the increase of ϴ from 10° to 16°, and 16° to 22° increases the percentage reduction by 19% and 8% respectively at V/V_c = 0.495, while at V/V_c = 0.714, it can be seen that, the reduction in scour depth increases by 4.489% and 6.662% due to the same variation increase of (ϴ). In accordance with effect of increase (ϴ) from 10° to 16°, and 16° to 22°, the percentage reduction increases by 4% and 6% respectively at V/V_c = 0.824, while at V/V_c = 0.989, it can be specified by 4.920% and 4.914%. Table 2 summaries a comparison for the obtained results of this study and other related work for (V/V_c ≈ 1), which reveals the effect of hydraulic condition and pier inclination with downstream direction on the scour depth decrease. Furthermore, the comparison shows the expected amount of decrease in scour depth for several angles. Generally, the decrease in scour depth proportional to strength of downward flow near the pier and the difference in the interaction between approach velocity vector and the angle of pier (ϴ), the increase (ϴ) would lead to reduce the strength of downward flow near the pier face due to separation of the approach velocity into two components as compared with one normal component for vertical pier.

Table 1. Experimental results of this study

Table 2. Comparison of change of decrease scour depth near threshold condition (V/V_c ≈ 1) for present study and other studies

Table 3. Measured scour depth of this study and estimated by pervious formulas for vertical pier (ϴ=0)‎

3.2 Assessment of scour depth results with existing formulas for vertical Pier (ϴ=0)

Table 3 illustrates the obtained results of scour depth for vertical pier as compared with that estimated by the most common formulas from previous studies [5, 18-21]. These formulas have been concluded for wide range of experiments and hydraulic condition. The evaluation was conducted according to the accuracy results of each formula using the statistical analysis by mean absolute percentage error (MAPE). As it is apparent in Table 3, the minimum value of MAPE is 3.839%, and it occurs in accordance with the estimated scour depth by Aksoy and Eski [21], so the present results of experiments support using this formula, which can be written as follows:

$\mathrm{d}_{\mathrm{s}} / \mathrm{D}=1.39 \times\left(\mathrm{F}_{\mathrm{d}}\right)^{0.77} \times(\mathrm{Y} / \mathrm{D})^{0.036} \times\left(\mathrm{D} / \mathrm{d}_{50}\right)^{-0.194}$      (5)

where, F_d is the densimetric Froude number of bed material, and can be estimated according to Eq. (6):

$\mathrm{F}_{\mathrm{d}}=\mathrm{V} / \sqrt{\mathrm{gd}_{50}}$     (6)

3.3 New modified empirical formula

To develop new empirical formula for scour depth estimation with inclined piers, this study adopted the modification of the empirical formula concluded by Aksoy and Eski ‎[21]‎ using the coefficient of inclination of pier (K_ϴi). Figure 5 shows the trending curves of (K_ϴi) for V/V_c = 0.495 to 0.989, and 10° ≤ ϴ ≤ 22°, this figure can give a good estimation for the value of (K_ϴi) required to consider the effect of pier inclination. Accordingly, the new modified formula for scour depth estimation of inclined pier can be written as following:

$\mathrm{d}_{\mathrm{sa}} / \mathrm{D}=1.39 \times\left(\mathrm{F}_{\mathrm{d}}\right)^{0.77} \times(\mathrm{Y} / \mathrm{D})^{0.036} \times\left(\mathrm{D} / \mathrm{d}_{50}\right)^{-0.194} \times \mathrm{K}_{\theta i}$      (7)

The new modified formula for scour depth estimation near inclined piers can be applied for uniform sediment under clear water condition (V/V_c = 0.495 to 0.989, 10° ≤ ϴ ≤ 22°, and 1.930 ≤ F_d ≤ 3.843,), which means wide range of flow intensity and applicable configuration of piers inclination. The scatter plot for the measured scour depth of this study and that estimated by the new modified formula Eq. (7) can be shown in Figure 6. It can be clearly seen that, the Eq. (7) showed good agreement for scour depth estimation near inclined piers, whereas, the estimated results fall with (± 9%) error margins.