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.

  • 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.

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];

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.

Dimensional analysis

The pier scour depth with debris accumulation and bed sill relies on the hydraulic variables of the flow and sedimentary bed, the shape of the pier and debris and their dimensions, and time, which can be written as Equation (1):
formula
(1)
where ls is the maximum scour length (m), ws is the maximum scour width (m), y is the approaching flow depth (m), H is the vertical distance from the sand surface to the top of debris (m), U is the approaching flow velocity (m/s), Uc = critical velocity of sediment movement (m/s), b is the channel width (m), D is the pier diameter (m), Ld = debris length (m), Wd = debris width (m), Td = debris thickness (m), d50 = median sediment size (m), ρ = sediment specific weight (kg/m3), ρ = water specific weight (kg/m3), υ = fluid kinematic viscosity (m2/s), g is the gravitational acceleration (m/s2), t is the scour time (s), te = scour equilibrium time (s), nd = debris porosity is the ratio between the debris void volume and the bulk debris volume, ε = relative debris roughness (the log average diameter to the debris pier diameter), Lb = bed sill downstream gap from the bridge pier (m), and percentage blockage ratio. Buckingham's Π theory was utilized and by combining the obtained dimensionless parameters, the dimensionless variables are achieved as Equation (2):
formula
(2)
Debris roughness and permeability do not have much effect on the maximum scour depth (Pagliara & Carnacina 2010), hence, nd and ε are neglected. b can be neglected because channel walls will not affect the scour depth if b/D > 6.25 (Raudkivi & Ettema 1983). When the scour hole reached the equilibrium condition, the term t/te could be ignored. Reynolds number is in the range of turbulent flow, so this combination can be ignored. Debris dimensions are selected based on previous studies and have constant values, therefore, ΔA is constant. The variables u, d50, Gs, and g become dimensionless in the Fd50 is the densimetric Froude number. Finally, the dimensionless effective parameters are as Equation (3):
formula
(3)

Experimental setup

All tests were performed in a rectangular sediment flume (4*0.6*0.2) m, at the hydraulic laboratory of Noshirvani University of Technology in Babol. Several experimental and numerical studies in the field of pier scour process have been conducted and validated in this flume (Akbari Dadamahalleh et al. 2022; Koohsari & Hamidi 2022; Khalili et al. 2023; Hamidi et al. 2024; Mahdian Khalili et al. 2024). The flume has a tailgate for adjusting the approaching flow depth in the channel (Figure 1). Water and sediment depths were measured by a point gauge with an accuracy of 0.1 mm (Figure 1). The approaching flow must have less disturbance and become developed, thus a flow straightener with wire mesh was installed at the channel inlet and a rigid apron with a length of 0.5 m was added to the model to control the flow rate at the beginning of the channel and provide acceptable flow development. Also, the bridge pier was located 3 m downstream of the flow inlet.
Figure 1

Experimental setup.

Figure 1

Experimental setup.

Close modal

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.

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).

Table 1

Time evolution of the maximum depth of the scour hole

t (min)ds/D
Test A1Test B1Test C1
0.767 1.400 0.700 
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 A1Test B1Test C1
0.767 1.400 0.700 
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.

Table 2

Maximum length and width of scour hole

ModelTesty (m)H (m)y/HU/UcFd50y/DLb/Dls/Dws/D
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 
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 
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 
D1 0.04 0.08 0.500 0.599 2.398 1.333 1.033 0.800 
D2 0.06 0.08 0.750 0.370 1.289 2.000 0.233 0.466 
D3 0.08 0.08 1.000 0.265 0.842 2.667 0.233 0.366 
D4 0.04 0.08 0.500 0.599 2.398 1.333 1.200 1.283 
D5 0.06 0.08 0.750 0.370 1.289 2.000 0.366 0.666 
D6 0.08 0.08 1.000 0.265 0.842 2.667 0.266 0.533 
D7 0.04 0.08 0.500 0.599 2.398 1.333 1.066 0.833 
D8 0.06 0.08 0.750 0.370 1.289 2.000 0.366 0.666 
D9 0.08 0.08 1.000 0.265 0.842 2.667 0.233 0.466 
D10 0.04 0.08 0.500 0.599 2.398 1.333 0.866 0.966 
D11 0.06 0.08 0.750 0.370 1.289 2.000 0.266 0.600 
D12 0.08 0.08 1.000 0.265 0.842 2.667 0.233 0.400 
D13 0.04 0.08 0.500 0.599 2.398 1.333 0.900 0.833 
D14 0.06 0.08 0.750 0.370 1.289 2.000 0.266 0.533 
D15 0.08 0.08 1.000 0.265 0.842 2.667 0.233 0.366 
ModelTesty (m)H (m)y/HU/UcFd50y/DLb/Dls/Dws/D
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 
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 
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 
D1 0.04 0.08 0.500 0.599 2.398 1.333 1.033 0.800 
D2 0.06 0.08 0.750 0.370 1.289 2.000 0.233 0.466 
D3 0.08 0.08 1.000 0.265 0.842 2.667 0.233 0.366 
D4 0.04 0.08 0.500 0.599 2.398 1.333 1.200 1.283 
D5 0.06 0.08 0.750 0.370 1.289 2.000 0.366 0.666 
D6 0.08 0.08 1.000 0.265 0.842 2.667 0.266 0.533 
D7 0.04 0.08 0.500 0.599 2.398 1.333 1.066 0.833 
D8 0.06 0.08 0.750 0.370 1.289 2.000 0.366 0.666 
D9 0.08 0.08 1.000 0.265 0.842 2.667 0.233 0.466 
D10 0.04 0.08 0.500 0.599 2.398 1.333 0.866 0.966 
D11 0.06 0.08 0.750 0.370 1.289 2.000 0.266 0.600 
D12 0.08 0.08 1.000 0.265 0.842 2.667 0.233 0.400 
D13 0.04 0.08 0.500 0.599 2.398 1.333 0.900 0.833 
D14 0.06 0.08 0.750 0.370 1.289 2.000 0.266 0.533 
D15 0.08 0.08 1.000 0.265 0.842 2.667 0.233 0.366 

Figure 2(a) presents streamlines around the pier with free debris (Model C). In cases with debris accumulation flow streamlines changes and debris blockage converts the flow. In Figure 2(b) the experimental model of the debris box indicated upstream of the pier protected by attached bed sill (Lb = 0D). Figure 2(c) shows the scour hole forms upstream of the pier protected with the attached bed sill.
Figure 2

(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).

Figure 2

(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).

Close modal

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.

Submergence is a very important factor in the debris blockage effect on bridge pier scour. The length and width of scour hole variations in conditions with debris conditions with different submergence ratios (y/H) were investigated. Figure 3(a) and 3(b) presents reduction variations of the dimensional length and width of the scour hole at Models B and C compared to cases without debris, respectively.
Figure 3

Effect of debris blockage with different submergence ratios on variations of scour hole (a) length and (b) width.

Figure 3

Effect of debris blockage with different submergence ratios on variations of scour hole (a) length and (b) width.

Close modal
In the case of debris blockage when bed sediment was protected with a sill, the length and width of the scour hole were reduced. The effective parameter in this condition is the longitudinal distance between the sill and the pier. Figure 4(a) and 4(b) shows the changes in length and width of the scour hole with different submergence ratios varied by Lb/D compared to the case without debris accumulation and with it, respectively. It can be observed that the length and width of the scour hole reduced with increasing bed sill distance in most of the submergence ratio debris cases. A similar investigation was conducted with changes in length and width of the scour hole protected with a bed sill compared to the case with debris accumulation in Figure 5(a) and 5(b). It concluded that the length and width of the scour hole reduced with increasing bed sill distance in most of the submergence ratios debris cases.
Figure 4

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).

Figure 4

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).

Close modal
Figure 5

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).

Figure 5

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).

Close modal
For practical use of the data achieved from this study, nonlinear regression was employed to propose a prediction equation, and four separate relations were achieved based on dimensional analysis (Equation (3)) to estimate the scour hole length and width in the condition of debris blockage with bed sill protection and without it. Equation (4) suggested ls/D for models B and C which pier considered with buried or free debris without bed sill as Equation (4):
formula
(4)
where RMSE = 0.136 and R2 = 0.897. It can be observed that the length of the scour hole has a direct relation with the densimetric Froude number and flow intensity and has an adverse relation with the submergence ratio. Figure 6 presents the ls/D (Predicted) from Equation (4) and ls/D (Observed) from experimental tests. The application ranges of parameters in Equation (4) are equal to:
formula
(5)
Figure 6

Prediction of the length of scour hole with debris blockage.

Figure 6

Prediction of the length of scour hole with debris blockage.

Close modal
ws/D can be predicted for models B and C including pier with buried or free debris without bed sill as Equation (6):
formula
(6)
where RMSE = 0.148 and R2 = 0.906. It was figured out that the scour hole width has a direct relation with the densimetric Froude number and flow intensity and has an adverse relation with the submergence ratio. The ls/D (Predicted) from Equation (6) and ls/D (Observed) from experimental tests are indicated in Figure 7. Parameters in Equation (6) can be applied in ranges:
formula
(7)
Figure 7

Prediction of the width of scour hole with debris blockage.

Figure 7

Prediction of the width of scour hole with debris blockage.

Close modal
The length of the scour hole can be estimated for model D consisting of the pier with debris blockage and bed sill protection according to Equation (8).
formula
(8)
where RMSE = 0.077 and R2 = 0.982. It can be concluded that ls/D increases by increasing the densimetric Froude number and flow intensity and reduces by increasing the submergence ratio and downstream distance of the bed sill from the pier. The ls/D (Predicted) from Equation (8) and ls/D (Observed) from experimental tests are indicated in Figure 8. Equation (8) can be used for:
formula
(9)
Figure 8

Prediction of the length of scour hole protected by bed sills with debris blockage.

Figure 8

Prediction of the length of scour hole protected by bed sills with debris blockage.

Close modal
The following equation is suggested to estimate the scour hole width for model D including the pier with debris blockage and bed sill protection as follows:
formula
(10)
where RMSE = 0.084 and R2 = 0.952. Based on Equation (10), the scour hole width increases by increasing the densimetric Froude number and flow intensity and reduces by increasing the submergence ratio and downstream distance of the bed sill from the pier. Figure 9 indicates the ws/D (Predicted) from Equation (7) and ws/D (Observed) from experimental tests. Equation (10) can be applicable for:
formula
(11)
Figure 9

Prediction of the width of scour hole protected by bed sills with debris blockage.

Figure 9

Prediction of the width of scour hole protected by bed sills with debris blockage.

Close modal

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.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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