ABSTRACT
Studying the influences of the debris settled by the flood upstream of the bridge pier on the scour is important. In the present study, experimental tests were performed as four models including the bridge pier, the bridge pier with buried debris, the bridge pier with the free debris, and the bridge pier with free debris and the bed sill with the downstream gap equal to 0, 1, 2, 3, and 4 times of pier diameter. The results showed that buried debris increased the maximum length of the scour hole (ls), and the maximum width of the scour hole (ws) by about 50, and 180% respectively in comparison with the alone pier. It resulted that buried debris has a more increased effect than free debris. Free debris at low submergence ratios reduces ls by up to 27%, and in high submergence ratios increases it by up to 37%. Also, free debris increases ws in all submergence ratios, which is by up to 127% for the critical case compared to the case without debris. At all distances, the bed sill reduces ls and ws, and the best performance for reducing ls and ws is when it is attached to the bridge pier.
HIGHLIGHTS
Predicting length and width of the scour hole.
Effect of debris blockage on pier scour was evaluated.
Utilizing bed sill for protecting pier with debris blockage.
Experimental approach was suggested for scour hole of bridge pier.
NOTATIONS
- b
channel width [L]
- d16
16% finer particle diameter [L];
- d50
50% finer particle diameter [L];
- d84
84% finer particle diameter [L];
- ds
maximum scour depth [L];
- D
pier diameter [L];
- Fd50
densimetric Froude number [M0L0T0];
- g
gravitational acceleration [LT−2];
- H
vertical distance from the sand surface to the top of debris [L];
- ls
maximum scour length [L];
- Lb
bed sill downstream gap from the bridge pier [L];
- Ld
debris length [L];
- nd
debris porosity (ratio between the debris void volume and the bulk debris volume) [M0L0T0];
- t
scour time [T];
- te
scour equilibrium time [T];
- Td
debris thickness [L];
- U
approaching flow velocity [LT−1];
- Uc
critical velocity of sediment movement [LT−1];
- ws
maximum scour width [L];
- Wd
debris width [L];
- y
approaching flow depth [L];
- ΔA
percentage blockage ratio [M0L0T0];
- ε
relative debris roughness (the log average diameter to the debris pier diameter) [M0L0T0];
- ρ
water specific weight [ML−3];
- ρs
sediment specific weight [ML−3];
- σg
(d84/d16)0.5 [M0 L0T0];
- υ
fluid kinematic viscosity [L2T−1];
INTRODUCTION
Natural factors such as wind, storms, landslides, avalanches, floods, and outflows from dams cause broken trees, and large pieces of wood and small foliage originating from bushes to be floated in the river flow. These bodies are combined with different sizes and shapes and transported by the water flow upstream of the bridge pier. These floating materials often accumulate in the form of rectangular cubes, regardless of the bridge pier geometry and the debris shape. In flood cases, debris aggregation upstream of the pier increases and blocks the river cross-section. This reduction in river width reduces the flow discharge, increases water depth, and changes the flow pattern. The blockage occurrence around the hydraulic structures changes their hydraulic operation (Hasanian Shirvan et al. 2023), around the bridge pier this phenomenon increases the velocity and shear stress and creates a horseshoe vortex upstream and a wake vortex downstream, which increases the scour depth and changes the river bed morphology (Lagasse et al. 2010a). Some studies were conducted on the evaluation of the debris aggregation effect on scour around the bridge pier (Melville & Dongol 1992; Lagasse et al. 2010a, 2010b; Pagliara & Carnacina 2010, 2011a, 2011b; Pagliara et al. 2010; Park et al. 2016; Abousaeidi et al. 2018; Ebrahimi et al. 2018; Rahimi et al. 2018; Pagliara & Palermo 2020; Palermo et al. 2021; Akbari Dadamahalleh et al. 2022; Hamidifar et al. 2022a, 2022b; Zanganeh-Inaloo et al. 2023). The most important results of these investigations will be reviewed in the present study.
The bridge pier's scour is a serious phenomenon in riverbeds and predicting scour holes around the piers is substantial in the bridge pier design (Nou et al. 2022; Hamidi et al. 2024). Foundation scour is one of the main factors of bridge collapse worldwide, which creates different losses (Pizarro et al. 2020). Thus, scour holes around bridge pier and downstream of hydraulic structures were investigated in previous studies, and some methods were utilized to reduce their depth (Chiew 1992; Kothyari et al. 1992; Melville 1997; Melville & Chiew 1999; Grimaldi et al. 2009a, 2009b; Zarrati et al. 2010; Tafarojnoruz et al. 2012; Khaple et al. 2017; Parsaie et al. 2019; Pandey et al. 2020; Raeisi & Ghomeshi 2021; Saad et al. 2021; Chaudhuri et al. 2022; Valela et al. 2022; Yang et al. 2022; Dah-Mardeh et al. 2023; Huda et al. 2023; Mahdian Khalili & Hamidi 2023). The rectangular and cylindrical pier created the most critical scour depth and, in these cases, the bridge pier is more aligned to the streamlines which reduces the flow separation, reducing the intensity of the horseshoe vortex decreases the scour value (Chang et al. 2004).
Melville & Dongol (1992) investigated the influence of various debris shapes on scouring around the bridge pier. They considered the pier diameter to be larger than the actual pier diameter and proposed a formula to predict an effective diameter of the bridge pier, which was modified by Lagasse et al. (2010a, 2010b).
Pagliara & Carnacina (2011a, 2011b) evaluated the effect of the accumulation of woody debris with different shapes including rectangular, triangular, and circular on the bridge pier in a laboratory model. They suggested a new formula to estimate scour depth in debris accumulation as a result of flow contraction.
Rahimi et al. (2018) investigated the length, thickness, shape, and position of debris effects on the scour hole. They used a circular bridge pier with a diameter of 0.03 m and a sedimentary bed with an average sediment size of 0.91 mm and debris in rectangular, triangular, and cylindrical shapes. They concluded that the maximum scour depth increases by increasing the thickness of debris and rectangular debris creates the largest scour depth. Also, the scour depth first increases when the debris is located far from the surface, and as the relative depth of the debris reaches 0.46, the debris behaves like a collar, and the scour depth reduces.
Ebrahimi et al. (2018) evaluated the sharp-nose pier scour with debris accumulation in shapes of circular, plate, and semi-pyramidal shapes in a laboratory study. They observed that when the debris approaches the bed sediment, the scour depth becomes lower and the maximum scour depth occurs in the case the debris is below the flow level. Also, when debris is positioned on the bed sediment, it partially protects the bed and reduces the scour depth.
Pagliara & Palermo (2020) studied the positions of the bridge pier in the channel width with debris blockage. They observed the maximum value for scour depth increases when the bridge pier is close to the channel wall. They indicated that the scour hole length increases with debris accumulation. Palermo et al. (2021) evaluated the effect of bridge pier position on debris aggregation conditions in a laboratory. They found out that the location of the bridge pier only affects the scour evolution and the bed topography in a shallow depth flow, while, in a deep flow, it has less effect. Also, the location of the bridge pier affects the equilibrium maximum depth of the scour hole in case of debris.
Akbari Dadamahalleh et al. (2022) investigated the influence of the level of woody debris from sedimentary beds on the bridge pier scour in an experimental study. They observed from their results that free debris (upper than the sediment surface) in all approaching flow depths increases the scour depth and buried debris (on the sediment surface) in low flow depths, causing a slight increase in maximum scour depth up to 10% and by increasing flow depth, debris acts as a bed protection and reduces scour depth.
Pagliara & Carnacina (2010) evaluated the influence of utilizing the bed sill in sedimentary beds as a countermeasure in the scour and bed protection, in the attendance of debris on the cylindrical bridge pier. They used two sills with different roughness 61 cm wide and 15 cm high in the sedimentary beds beside the bridge pier. They comprehended from their observations that the buried bed sill in the bed can reduce the amount of scouring reduce the rate of scouring delay the scouring process around the bridge pier and reduce the scour values by debris accumulation.
Hamidifar et al. (2022a) utilized slots on the bridge pier as a scour countermeasure with different types of debris accumulation. They observed that slots reduced bridge pier scour in debris cases, but the mitigation efficacy increased or decreased for a slotted pier with debris in comparison with the pier according to the debris shape. Hamidifar et al. (2022b) evaluated the effect of using a collar as a scour reduction of a cylindrical bridge pier debris accumulation. Their experiments presented that installing a collar decreases the maximum depth of the scour hole by up to 39% compared to the case without the collar and debris, and the collar's efficiency was increased by up to 25% in cases with debris. Zanganeh-Inaloo et al. (2023) investigated the influence of riprap on the scour mitigation of a rectangular bridge pier with varied debris shapes and positions. They figured out that the attendance of debris has no significant influence on the operation of standard-size riprap. But riprap stone median size was important, and by decreasing it by 25% the efficiency of riprap protecting scour was reduced by 10% in the debris cases. Although ds did not vary significantly by changing debris position, the scour hole volume increased in cases with debris close to the bed than when it was located near the water surface.
Previous studies indicated that debris accumulation affects scour morphology and increases scour hole depth. Also, with rectangular debris and cylindrical pier, the critical scour depth forms. The previously suggested equations predicted scour hole depth and scour hole development especially its width and length had not been investigated comprehensively. Based on the increasing influence of debris on the values of bridge pier scour, one countermeasure for reducing it is required. Thus, the present study evaluates the effect of woody debris in a rectangular cubic box in two different level conditions as buried debris (on the sediment surface) and free debris (upper than the sediment surface) on scour hole characteristics especially, its width and length. Also, some tests with free debris and bed sill with the downstream gap equal to 0, 1, 2, 3, and 4 times of pier diameter were performed downstream of the bridge pier. All cases were tested under different approaching flow depths, and densimetric Froude numbers in clear water conditions. Maximum scour length and width and its reduction for different approaching flow intensities (U/Uc) were presented and compared to determine the optimum position of the sill for reducing scour. Reduction and increase in the percentage of maximum scour length and width for each test were computed and compared. Also, suggested equations were provided to predict the scour hole length and width in cases of rectangular debris blockage with and without bed sill protection.
MATERIALS AND METHODS
Dimensional analysis

Experimental setup
Raudkivi & Ettema (1983) suggested the limited value of 0.7 mm for the median sediment size (d50) prevents the formation of ripples. The experimental tests were applied on sand sediment with d50 = 0.82 mm filled the sediment recession in the channel and around the bridge pier at a fixed height of 10 cm. σg = (d84/d16)0.5 is 1.26, thus sediment is uniform. In this study, the cylindrical bridge pier was utilized based on the critical scour rate and its high application in the bridge piers. This pier is made of iron pipe with a diameter of 3 cm and a height of 20 cm. To ensure the development of the inlet flow on the hole development, the pier was installed at a gap of 3 m from the channel inlet. According to Raudkivi & Ettema (1983), if b/D > 6.25, channel walls do not affect the geometry of the scour hole. This ratio for the present study is 20, which satisfies this criterion. Raudkivi & Ettema (1983) suggested the limitation D/d50 > 20–25 to prevent the impact of the sedimentary size on the scour depth. In this study, the pier diameter satisfies this criterion. Wooden debris in nature is concentrated upstream of the bridge pier, mostly in the form of rectangular shape, and based on the study of Rahimi et al. (2018) and Abousaeidi et al. (2018) the accumulation of rectangular wooden debris creates the highest value of scouring around bridge pier. Accordingly, the debris used in this study was designed as a rectangular box. To simulate debris, wood pieces were used with diameters of 0.1 to 0.5 cm in length of 12 cm fixed inside a metal holding box mounted to the bridge pier by screw. The debris box is 5 cm high, 10 cm long, and 12 cm wide and its faces are covered by a mesh. To reduce the scouring hole from the PVC plate was used as a bed sill with a height of 0.1 m, a thickness of 0.3 mm, and a length of 0.6 m in five different conditions with downstream gaps of 0D, 1D, 2D, 3D, and 4D, from the bridge pier.
RESULTS AND DISCUSSIONS
Equilibrium scour time was measured around the bridge pier, during the experimental tests conducted in the present study for three tests of each set of tests (A, B, and C) at U/Uc = 0.599. It was observed that after 5 h the scour hole depth (ds) became constant (Table 1).
Time evolution of the maximum depth of the scour hole
t (min) . | ds/D . | ||
---|---|---|---|
Test A1 . | Test B1 . | Test C1 . | |
1 | 0.767 | 1.400 | 0.700 |
5 | 1.133 | 1.600 | 1.100 |
15 | 1.267 | 1.733 | 1.200 |
30 | 1.400 | 1.933 | 1.300 |
45 | 1.533 | 2.067 | 1.333 |
60 | 1.600 | 2.200 | 1.400 |
120 | 1.767 | 2.400 | 1.533 |
180 | 1.867 | 2.467 | 1.567 |
240 | 1.933 | 2.500 | 1.600 |
300 | 1.967 | 2.533 | 1.633 |
360 | 1.967 | 2.567 | 1.633 |
420 | 1.967 | 2.567 | 1.633 |
480 | 1.967 | 2.567 | 1.633 |
t (min) . | ds/D . | ||
---|---|---|---|
Test A1 . | Test B1 . | Test C1 . | |
1 | 0.767 | 1.400 | 0.700 |
5 | 1.133 | 1.600 | 1.100 |
15 | 1.267 | 1.733 | 1.200 |
30 | 1.400 | 1.933 | 1.300 |
45 | 1.533 | 2.067 | 1.333 |
60 | 1.600 | 2.200 | 1.400 |
120 | 1.767 | 2.400 | 1.533 |
180 | 1.867 | 2.467 | 1.567 |
240 | 1.933 | 2.500 | 1.600 |
300 | 1.967 | 2.533 | 1.633 |
360 | 1.967 | 2.567 | 1.633 |
420 | 1.967 | 2.567 | 1.633 |
480 | 1.967 | 2.567 | 1.633 |
At the end of each test when the equilibrium scour hole was reached, the scour hole characteristics around the bridge pier were measured. The maximum length and width of the scour hole were obtained according to Table 2. Model A included only a pier (control condition), Model B consisted pier with debris located exactly on the surface of the sand (buried debris), Model C included a pier with debris installed on a pier with a vertical distance of D (free debris), and Model D the bed sill was added to the Model D with longitudinal distances 0D, 1D, 2D, 3D, and 4D.
Maximum length and width of scour hole
Model . | Test . | y (m) . | H (m) . | y/H . | U/Uc . | Fd50 . | y/D . | Lb/D . | ls/D . | ws/D . |
---|---|---|---|---|---|---|---|---|---|---|
A | A1 | 0.03 | – | – | 0.838 | 3.688 | 1.000 | – | 0.766 | 0.733 |
A2 | 0.04 | – | – | 0.599 | 2.398 | 1.333 | – | 0.733 | 0.700 | |
A3 | 0.05 | – | – | 0.462 | 1.719 | 1.667 | – | 0.633 | 0.666 | |
A4 | 0.06 | – | – | 0.370 | 1.289 | 2.000 | – | 0.366 | 0.366 | |
A5 | 0.07 | – | – | 0.311 | 1.032 | 2.333 | – | 0.366 | 0.333 | |
A6 | 0.08 | – | – | 0.265 | 0.842 | 2.667 | – | 0.366 | 0.333 | |
A7 | 0.09 | – | – | 0.230 | 0.705 | 3.000 | – | 0.133 | 0.333 | |
B | B1 | 0.03 | 0.05 | 0.600 | 0.838 | 3.688 | 1.000 | – | 0.866 | 1.666 |
B2 | 0.04 | 0.05 | 0.800 | 0.599 | 2.398 | 1.333 | – | 0.833 | 1.166 | |
B3 | 0.05 | 0.05 | 1.000 | 0.462 | 1.719 | 1.667 | – | 0.766 | 1.033 | |
B4 | 0.06 | 0.05 | 1.200 | 0.370 | 1.289 | 2.000 | – | 0.466 | 1.033 | |
B5 | 0.07 | 0.05 | 1.400 | 0.311 | 1.032 | 2.333 | – | 0.433 | 0.633 | |
B6 | 0.08 | 0.05 | 1.600 | 0.265 | 0.842 | 2.667 | – | 0.400 | 0.666 | |
B7 | 0.09 | 0.05 | 1.800 | 0.230 | 0.705 | 3.000 | – | 0.200 | 0.600 | |
C | C1 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | – | 1.000 | 0.966 |
C2 | 0.05 | 0.08 | 0.625 | 0.462 | 1.719 | 1.667 | – | 0.766 | 0.933 | |
C3 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | – | 0.466 | 0.833 | |
C4 | 0.07 | 0.08 | 0.875 | 0.311 | 1.032 | 2.333 | – | 0.300 | 0.600 | |
C5 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | – | 0.266 | 0.366 | |
C6 | 0.09 | 0.08 | 1.125 | 0.230 | 0.705 | 3.000 | – | 0.100 | 0.366 | |
D | D1 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | 0 | 1.033 | 0.800 |
D2 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | 0 | 0.233 | 0.466 | |
D3 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | 0 | 0.233 | 0.366 | |
D4 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | 1 | 1.200 | 1.283 | |
D5 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | 1 | 0.366 | 0.666 | |
D6 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | 1 | 0.266 | 0.533 | |
D7 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | 2 | 1.066 | 0.833 | |
D8 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | 2 | 0.366 | 0.666 | |
D9 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | 2 | 0.233 | 0.466 | |
D10 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | 3 | 0.866 | 0.966 | |
D11 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | 3 | 0.266 | 0.600 | |
D12 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | 3 | 0.233 | 0.400 | |
D13 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | 4 | 0.900 | 0.833 | |
D14 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | 4 | 0.266 | 0.533 | |
D15 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | 4 | 0.233 | 0.366 |
Model . | Test . | y (m) . | H (m) . | y/H . | U/Uc . | Fd50 . | y/D . | Lb/D . | ls/D . | ws/D . |
---|---|---|---|---|---|---|---|---|---|---|
A | A1 | 0.03 | – | – | 0.838 | 3.688 | 1.000 | – | 0.766 | 0.733 |
A2 | 0.04 | – | – | 0.599 | 2.398 | 1.333 | – | 0.733 | 0.700 | |
A3 | 0.05 | – | – | 0.462 | 1.719 | 1.667 | – | 0.633 | 0.666 | |
A4 | 0.06 | – | – | 0.370 | 1.289 | 2.000 | – | 0.366 | 0.366 | |
A5 | 0.07 | – | – | 0.311 | 1.032 | 2.333 | – | 0.366 | 0.333 | |
A6 | 0.08 | – | – | 0.265 | 0.842 | 2.667 | – | 0.366 | 0.333 | |
A7 | 0.09 | – | – | 0.230 | 0.705 | 3.000 | – | 0.133 | 0.333 | |
B | B1 | 0.03 | 0.05 | 0.600 | 0.838 | 3.688 | 1.000 | – | 0.866 | 1.666 |
B2 | 0.04 | 0.05 | 0.800 | 0.599 | 2.398 | 1.333 | – | 0.833 | 1.166 | |
B3 | 0.05 | 0.05 | 1.000 | 0.462 | 1.719 | 1.667 | – | 0.766 | 1.033 | |
B4 | 0.06 | 0.05 | 1.200 | 0.370 | 1.289 | 2.000 | – | 0.466 | 1.033 | |
B5 | 0.07 | 0.05 | 1.400 | 0.311 | 1.032 | 2.333 | – | 0.433 | 0.633 | |
B6 | 0.08 | 0.05 | 1.600 | 0.265 | 0.842 | 2.667 | – | 0.400 | 0.666 | |
B7 | 0.09 | 0.05 | 1.800 | 0.230 | 0.705 | 3.000 | – | 0.200 | 0.600 | |
C | C1 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | – | 1.000 | 0.966 |
C2 | 0.05 | 0.08 | 0.625 | 0.462 | 1.719 | 1.667 | – | 0.766 | 0.933 | |
C3 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | – | 0.466 | 0.833 | |
C4 | 0.07 | 0.08 | 0.875 | 0.311 | 1.032 | 2.333 | – | 0.300 | 0.600 | |
C5 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | – | 0.266 | 0.366 | |
C6 | 0.09 | 0.08 | 1.125 | 0.230 | 0.705 | 3.000 | – | 0.100 | 0.366 | |
D | D1 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | 0 | 1.033 | 0.800 |
D2 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | 0 | 0.233 | 0.466 | |
D3 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | 0 | 0.233 | 0.366 | |
D4 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | 1 | 1.200 | 1.283 | |
D5 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | 1 | 0.366 | 0.666 | |
D6 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | 1 | 0.266 | 0.533 | |
D7 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | 2 | 1.066 | 0.833 | |
D8 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | 2 | 0.366 | 0.666 | |
D9 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | 2 | 0.233 | 0.466 | |
D10 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | 3 | 0.866 | 0.966 | |
D11 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | 3 | 0.266 | 0.600 | |
D12 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | 3 | 0.233 | 0.400 | |
D13 | 0.04 | 0.08 | 0.500 | 0.599 | 2.398 | 1.333 | 4 | 0.900 | 0.833 | |
D14 | 0.06 | 0.08 | 0.750 | 0.370 | 1.289 | 2.000 | 4 | 0.266 | 0.533 | |
D15 | 0.08 | 0.08 | 1.000 | 0.265 | 0.842 | 2.667 | 4 | 0.233 | 0.366 |
(a) Flow around the pier with debris (Model C). (b) Debris accumulation upstream of pier protected with attached bed sill (Model D). (c) Scour hole around pier protected with attached bed sill (Model D).
(a) Flow around the pier with debris (Model C). (b) Debris accumulation upstream of pier protected with attached bed sill (Model D). (c) Scour hole around pier protected with attached bed sill (Model D).
When the debris was accumulated upstream of the bridge pier, the maximum length of the scour hole increased compared to the control condition. Also, the maximum length of the scour hole maintains its reducing trend by increasing the approaching flow depth, so that the maximum increase in the maximum length of the scour hole occurred at y/D = 3 which is 50%. It can be observed that the width of the scour hole was significantly greater in comparison to the initial condition, so that at y/D = 2 the maximum width of the scour hole increases by about 180%. In Model B, the maximum length of the scour hole at y/D = 1.33, 1.66, and 2 increases up to 36%, and with increasing the approaching flow depth was reduced compared to the control condition, with a maximum value of 27%. The maximum width of the scour hole increases compared to the control condition, and at y/D = 2, it increases by about 127%. Also, the maximum width of the scour hole had a decreasing trend with increasing the approaching flow depth and eventually stabilized.
Effect of debris blockage with different submergence ratios on variations of scour hole (a) length and (b) width.
Effect of debris blockage with different submergence ratios on variations of scour hole (a) length and (b) width.
Effect of bed sill distance on length variations of scour hole with debris blockage at different submergence ratios: (a) compared to the case without debris (model A) and (b) compared to the case with debris (model C).
Effect of bed sill distance on length variations of scour hole with debris blockage at different submergence ratios: (a) compared to the case without debris (model A) and (b) compared to the case with debris (model C).
Effect of bed sill distance on width variations of scour hole with debris blockage at different submergence ratios: (a) compared to the case without debris (model A) and (b) compared to the case with debris (model C).
Effect of bed sill distance on width variations of scour hole with debris blockage at different submergence ratios: (a) compared to the case without debris (model A) and (b) compared to the case with debris (model C).
Prediction of the length of scour hole protected by bed sills with debris blockage.
Prediction of the length of scour hole protected by bed sills with debris blockage.
Prediction of the width of scour hole protected by bed sills with debris blockage.
Prediction of the width of scour hole protected by bed sills with debris blockage.
CONCLUSIONS
The present study investigated the geometry of a scour hole around a cylindrical pier with upstream debris accumulation with bed sill protection and without under the experimental method. For this purpose, four experimental models were considered and performed including model A (bridge pier), model B (bridge pier with buried debris accumulation), model C (bridge pier with free debris accumulation), and model D (bridge pier with free debris accumulation and bed sill with different locations).
Results indicated that buried debris increased the maximum length of the scour hole (ls) under varied submergence ratios. The maximum width of the scour hole (ws) increased by about 180% compared to the pier without debris.
Free debris at low submergence ratios reduced ls, and at high submergence ratios increased it. Also, free debris increased ws in all submergence ratios compared to the case without debris, which was up to 127% for the critical condition.
At all distances, the bed sill reduced ls and ws, and the best performance for reducing ls and ws was when it was attached to the bridge pier.
Finally, four separate equations were proposed based on dimensional analysis to predict the length and width of the scour hole in the condition of debris blockage with bed sill protection and without it. Suggested equations had good compatibility with observed data with RMSE = 0.136, 0.148, 0.077, 0.084 and R2 = 0.897, 0.906, 0.982, 0.952 for the length of scour hole with debris without a sill, width of scour hole with debris without a sill, length of scour hole with debris with a sill, width of scour hole with debris with a sill, respectively.
It was concluded length and width of the scour hole increased by increasing the densimetric Froude number (Fd50) and approaching flow intensity (U/Uc), and they reduced by increasing the submergence ratio in case of debris blockage with bed sill and without it. Also, the length and the scour hole width were decreased by increasing the downstream distance of the bed sill from the pier at conditions with debris blockage and bed sill protection.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.