Effectiveness of Collars and Hooked-Collars in Mitigating Scour around Different Abutment Shapes

Abstract

Abutment scour is a major cause of bridge failures worldwide, leading to disruptions, economic losses, and loss of life. The present experimental study examines countermeasures against abutment scour using hooked-collar protections on vertical-wall and wing-wall abutments (at 45° and 60°) under different flow conditions. All 60 experiments were performed under sub-critical flow conditions by investigating scour around an abutment 20 cm long, 20 cm wide, and 25 cm tall. Two distinct values of the Froude number, 0.154 and 0.179, and a sediment particle diameter (d₅₀) of 0.88 mm were used throughout the experimental phase. The resulting equilibrium scour around the abutments was compared to those with collar and hooked-collar protections. It was determined that the maximum abutment scour depth reduction was 83.89% when hooked collars were placed on vertical wall abutments beneath the bed surface level, and for wing-wall abutments at 45° and 60°, it was 74.2% and 73.5%, respectively, at the bed surface level. Regression analysis was conducted to assess the non-dimensional scour depth (D_s/Y_f) and scour reduction (R_Ds/Y_f), with a high enough coefficient of determination (R² values of 0.96 and 0.93, respectively), indicating high confidence in the analysis. The sensitivity analysis findings demonstrate that the width of the collar (W_c) and L_a are the most influencing factors affecting D_s/Y_f and RD_s/Y_f.

1. Introduction

Local scour is a process that may take place around piers and abutments, resulting in disastrous results such as the collapse of bridges they may support [1]. The process of local scour develops in the vicinity of piers and abutments and shares various features [2]. As a result, local scour must be thoroughly assessed, understood, predicted, and eventually mitigated against piers and abutments. Alternatively, local scour may culminate in the collapse of the entire bridge structure, with the possibility of a severe death toll and casualties [3]. When the flow passes through a pier or abutment, it divides and merges downstream, creating vortical flow structures that may scoop bed surface material around the abutment, generating local scour [4]. Horseshoe vortices at the foot of the abutment enable the scour hole to widen and deepen, as demonstrated in [5]. Hydraulic scour development can be influenced by a variety of parameters involving flow velocity, sediment properties, channel geometry, and structural design. Addressing scour processes is essential for developing appropriate countermeasures to reduce scours and assure bridge reliability [6]. Besides local scouring, previous research reported that bridge abutment joint collapse is caused by various factors, including axial load and thermally induced flexural strain [7,8]. Furthermore, the orientation of the bridge piles has a significant influence on the fatigue performance of jointless bridges [9].

Numerous hydraulic engineers have conducted experimental investigations to examine the difficulty of local scouring under varied flow scenarios. Several techniques have been suggested and carried out based on studies to reduce local scours near piers and abutments [10]. There are two types of countermeasure approaches for protecting the abutments to prevent local scour: flow modification and bed surface armoring [11]. Bed surface armoring applications employ hard materials such as gabions, riprap stones, cable-tied blocks, concrete mats, or bags to protect bed surface materials from flow-induced instability and scour. Flow modification approaches either block the scour-inducing mechanism or displace the scour hole farther from the abutment’s vicinity [12]. They are parallel-wall, spur-dike, or collar installations on abutments designed to counteract abutment scour in open-channel flow conditions.

Collars were previously tested to counteract local scours around piers by modifying the flow patterns and reducing the erosive forces near the piers, thereby mitigating the potential for sediment erosion and scour formation. Their studies revealed that the width and inclination of the collar were significant variables for its efficacy [6,13,14,15,16]. Experiments showed that collar installation beneath the bed surface level enhanced performance because less bed surface material was scoured by the flow coming below the collar [17]. The effects of the collar on an abutment have also been previously studied by different researchers [13,14,15,18]. When the collar was placed on the abutment of a vertical wall in clear water to have the best protection from scour, collar width was concluded to be an important perimeter. It has been observed that for the best scour protection, the minimum collar width should be 0.23 L_a, placed just below the bed surface level. Ref. [14] also used a wider collar than the abutment’s length, which delayed the onset of scour and reduced the scour, ranging between 9.0% and 37.0%. Protections of various sizes of collar around abutments at various levels and sediment sizes were evaluated. The study found that increasing collar thickness reduces the efficacy of protection, whereas increasing the external collar dimension improves the protection. However, sediment size exhibited no significant influence [15]. An experimental study was conducted to see whether the increase in collar length and its placement below or at the bed surface level would significantly reduce the scour of the vertical wall abutment [15]. It was observed that changing only the abutment length had no significant influence on the timing of formation of local scour depth [19]. However, the height of the collar employed on abutments in relation to the bed surface level exerted a significant impact on scour depth reduction. It was investigated that the collar for the vertical wall beneath the bed surface level and the wing-wall abutments at the bed surface level lowered the scour depths [13]. The application of collars avoided the direct destabilization of bed surface material due to the downflow. As a result, the abutment’s vicinity experienced a reduction in scour depth, and the erosion agents were diverted away from the abutment [20].

Past literature has not explored the effectiveness of the hooked collar of varying positions around the various types of bridge abutments. Therefore, the current investigation aimed to analyze the effectiveness of the varying position of the hooked collar around the bridge abutment for scour mitigation and compare its results to the collar placed around abutments, focusing on the effectiveness of the varying shapes, sizes, and positions of the hooked collar around two different types (wing-wall and vertical-wall) bridge abutments. The objective of this study was to provide the more appropriate position of the hooked collar and assess the implications of using this specific type of abutment for scour reduction. Moreover, the current investigation attempted to provide a more suitable and economical solution for enhancing bridge safety and scour mitigation engineering solutions, therefore filling a significant gap in the field of hydraulic engineering.

2. Materials and Method

2.1. Experimental Setup: Channel Description and Preparation

Experiments were conducted in the hydraulic laboratory of the Civil Engineering Department at the University of Engineering and Technology (UET) in Taxila. All experiments were conducted in a rectangular channel of 20.0 m length, 1.0 m width, and 0.750 m height with clear glass sidewalls. The abutment model is located 7.40 m from the inlet of the channel (see Figure 1a). The constant channel’s bed surface of 30.0 cm was prepared using uniform sand with a median sediment particle diameter (d₅₀) of 0.88 mm, a geometric standard deviation of the sediment particle size of 1.20, and a specific density of 2.56 for all cases. The bed surface was leveled horizontally [13,17]. To eliminate the test section’s unwavering water level, the sandy bed surface should be properly leveled. In addition, a movable tailgate was installed at the downstream end of the channel to manage the water level, and a flow control valve was installed at the channel’s beginning to control the water flow discharge.

2.2. Abutment Conditions

According to [21], scour depth near the trapezoidal bridge abutment was found to be lower compared to vertical abutment. Previously, researchers used abutment models made of different materials [22]. To replicate a specific abutment geometry, the Pashtoon Garhi Bridge located at Kabul River was selected as a reference in the present study. The shape of the abutment on Pashtoon Garhi bridge is trapezoidal and has a length of 2.60 m, width of 1.30 m, and height of 4.50 m, respectively. In the current controlled laboratory investigation, flume and flow rate limitations led to the choice to represent the physical model with a scaled-down experimental model using a scaling ratio of 1/10. The prototype was replicated as a laboratory model using the concept of geometric similarity, whereby the scale of the model to the prototype is linked by the scaling ratio. Previous research clearly showcases the importance of model scaling considerations in controlled laboratory experiments of abutment scour [22]. Herein, through geometric and dynamic similarity considerations, the results of the scaled-down model can be used to understand the impact of various factors affecting abutment scour, including flow conditions and bed surface material characteristics. Specifically, geometric scaling was achieved for the model abutments 20 cm long, 20 cm wide, and 25 cm high, respectively (Figure 1b–e), which allows a direct comparison of these results to Pakistan’s Pashtoon Garhi bridge abutment. Froude scaling was applied to select the flow conditions showcased herein. The choice for sediment size selection is guided by trying to accurately represent both the dynamic processes of scour around the abutment and empirically matching the resulting equilibrium scour geometries for the selected flows with field observations. This common and desired experimental design practice clearly results in coarser sediment than what would be achieved with geometric scaling. These choices need to also be balanced with practical considerations of the geometry of the test area and its construction (the abutments were constructed of wood, similar to Murtaza et al., [22]. Earlier research also reported that the constriction effect significantly influences bridge scour when an abutment occupies most of the part of a channel [23]. They defined the constriction effect as a ratio of abutment length to the channel width [23]. However, Breusers and Raudkivi [23] determined that if the ratio is less than 40%, it would not affect flow structures. In the current investigation, an abutment model occupied 20% of the channel width, and no flow constriction was observed, as specified by [23]. Therefore, for the chosen water depth, the model scale of 1/10 is sufficient to offer a representative physical model for the flow and sediment transport processes while also considering any constriction effects in the channel. The experimental runs were performed with a fixed flow depth (Y_f) = 15.0 cm (to meet the short abutment criteria L_a/Y_f ≤ 1) and two different discharges of 0.027 and 0.032 m³/s. The flow depth remained consistent to minimize the influence of flow shallowness [20].

2.3. Flow Conditions

Pakistan has a long history of floods since 1947 and damaged bridge abutment most of the time. An example of a bridge failure due to scouring in Pakistan is the Hassan Abad Bridge collapse in the Hunza Valley incident in 2022. During the 2022 floods, the bridge abutments experienced significant scour erosion, which undermined the foundation of the bridge.

Based on 25 years of data, Jinnah and Taunsa Barrages exhibit water depths of 1.29–3.30 m and flow velocities of 1.80–2.10 m/s. For the experimental conditions, the estimated range of Froude numbers, F_r, is 0.10–0.59 (considering F_r = U/(g*Y_f)^1/2, where U denotes the mean approach flow velocity), indicating subcritical flow conditions [22]. To replicate these sub-critical flow regimes in a controlled laboratory setting, we selected a water depth of 0.15 m and flow velocities of 0.18 m/s and 0.21 m/s, resulting in Froude numbers of 0.154 and 0.179, respectively. The flow intensity U/U_c, where U_c is the critical velocity of the sediments, was maintained between 0.50 and 0.59, referring to clear water conditions, i.e., U/U_c < 1 [24]. While it is common practice to perform local scour experiments near the threshold flow condition, we opted for lower flow intensities to explore the behavior and mechanisms of local scour under sub-threshold flow conditions. By studying sub-threshold flow conditions, we aimed to gain insights into the processes leading up to scour initiation and enhance our understanding of scour mechanisms under a wider range of flow conditions. In our study, the flow intensities (U/U_c) were 0.50 and 0.59, ensuring clear-water conditions (U/U_c < 1), meaning the flow velocity is insufficient to generally mobilize bed material. This approach aligns with previous research [24]. By maintaining a constant water depth, we ensured a controlled environment to analyze the impact of discharge on scour depth, aligning with the methodologies observed in the literature [3,17]. This also allows for the isolation of the effects of discharge without the confounding influence of varying depths, helping to understand the specific relationship between discharge and sediment dynamics more clearly. By reducing the complexity of the experimental setup, it is easier to manage, control, and replicate the experiments as well as compared to similar studies in the literature [3,22]. The prototype is located in the Kabul River, which originated from the Sanglākh Range located at a distance of 72 Km at Kabul City west and merged into the Indus River at the location of Islamabad, (northwest) Pakistan. Clear water scour is also observed in the prototype section. Additionally, scour is largely a hydrodynamic process, not just a hydraulic one, meaning that near-bed flow velocities and flow structures are crucial for sufficient flow depth. This approach is also relevant in practice and representative of the cases where the flow depths are controlled with hydraulic structures to achieve a fixed flow depth, regardless of the flow discharge. This can happen in a targeted fashion to mitigate the risk of flooding, or it can happen naturally due to local changes in the hydraulic regime locally, e.g., due to log jamming or increased bed scour during higher flows.

The critical shear velocity (U*_c) for the bed surface utilized in this experiment, shown in

Table 1. Characteristic flow and bed surface conditions used in the experiment.

Discharge, Q [m³/s]	Flow Depth, Yf [m]	Sediment Particle Diameter, d₅₀ [m]	Approach Flow Velocity, U [m/s]	Critical Velocity, Uc [m/s]	Critical Shear Velocity, U*c [m/s]	Flow Intensity, U/Uc	Froude Number, Fr
0.0270	0.150	0.00088	0.180	0.359	0.021	0.50	0.154
0.0320	0.150	0.00088	0.210	0.359	0.021	0.59	0.179

, was calculated using the Shields diagram. Recent research [25] revealed that uniform flows may require up to 100 flow depths for mean velocity fields to become essentially independent of the streamwise coordinate, which renders most flows examined in the literature limited in terms of the useful length of the flow beyond which the flow is considered to be fully developed. This is true even for past literature that has been traditionally studying the effect of the turbulent flow field on hydraulic structures scour that has been investigated in terms of the time-averaged velocities, turbulence intensities, Reynolds shear stress, and the turbulent kinetic energy [26]. Furthermore, recent literature has demonstrated that if velocimetry methods have not properly calibrated, results can be significantly erroneous. However, our research does not focus on directly assessing hydrodynamic quantities but rather their effect on scour. For the purposes of showcasing that the flow conditions assessed herein refer to clear water scour, one can assume that the logarithmic profile developed hydraulically rough bed surface under steady uniform flow conditions is a reasonable approximation [13,17]. In this case, the critical velocity U_c can be assessed using the following equation:

U_c/U*_c = 5.75 log (Y_f/k_e) + 6

(1)

where k_e = 2d₅₀ is the equivalent roughness height.

2.4. Experimental Procedure

The tests were conducted in two main phases, i.e., the reference and the exploratory phase. The first phase comprised 1–24 runs so that the abutments were not altered for runs 1 to 6, while runs 7 to 24 represented the abutments with a simple collar. Then, the second phase comprised varying the size and elevation of a hooked collar (see Figure 1b) concerning the bed surface and investigating the most effective combination in reducing the abutment scour depth and volume. This study comprised 60 experiments, half of which were performed in the first phase and half in the second exploratory phase. The two sidewall hook heights and three different widths of the hooked collar were used at three different elevations compared to the bed surface levels, i.e., above bed surface levels, at bed surface levels (see Figure 1b–d, as an example), and below bed surface levels. The optimal configuration was investigated in terms of performance for the implementation of the hooked collar fitted at short abutments of wing walls abutments and vertical walls at 60 degrees and 45 degrees. All the experimental runs in both phases follow the same procedure. At 7.4 m from the upstream-inlet side (see Figure 1b), the unprotected vertical wall and wing wall abutments were oriented at a right angle to the bed, where the compaction and surface leveling of sediment bed took place. To prevent uncontrolled scouring, thin metallic plates were placed over the working section’s sand zone around the abutments before each experimental run. The channel was then filled progressively with water to release any air trapping in the sediment.

After deciding on the appropriate discharge and depth of flow, the experimental run was started, and the metallic plates next to the abutment were carefully lifted. Using point gauges, scour depth was measured every 12 min along the sides and upstream of abutments during the first hour (having an overall measurement instrument uncertainty of ±1 mm). It is interesting to note that the scour process varies for protected and unprotected abutments. The interval between measurement readings then increased. If any displaced sand particles were present, they were collected at the outlet segment at the test section’s end. After each experimental run, water was carefully evacuated from the flume to restrict it from departing the profile of the scour hole generated by the drawdown flush. The scour pattern profiles and scour holes close to the abutments were then precisely and meticulously calculated using the point gauge. Along the upstream and downstream of the abutments, the measuring section of the scour hole profile was roughly 1.40 m long for vertical-wall abutments and 1.60 m long for wing-wall abutments. The 28-h time constraint of each experimental run allowed for achieving the equilibrium scour depth. In the first 6–7 h following the commencement of the tests, most of the scour (60–93%) takes place [13,17]. The maximum scour depth reduction percentage (R_Ds) around the wing-wall and vertical-wall abutments was calculated for each run as follows:

R_Ds = (D_s − D_s*)/D_s × 100%

(2)

where D_s = maximum depth of scour without collar or hooked-collar protection on the abutment, D_s* = maximum depth of scour with collar or hooked-collar in each run.

2.5. Dimensional Analysis

Scour depth around the bridge abutment is dependent on water depth, initial Froude number, and size of bed material. In the present study, it is considered that scour depth around the bridge abutment was a function of the following parameters: Y_f: initial water depth in flume, U: average flow velocity, ρ_w: density of water, v: viscosity of water, d₅₀: sediment particles’ median size, g: gravitational acceleration, B: channel width, W_a: width of abutment, W_c: width of collar, L_a: length of abutment, D_s: scour depth, R_Ds: reduction of scour depth, U_c: critical flow velocity, Z_c: collar vertical position with respect to the bed level, W_HC: width of the hooked collar. Based on these parameters, the following function was assumed for the dimensional analysis:

$$f\left(x\right)=(Y_f,U,{\rho }_w,v,d_{50},g,B,W_a,W_c{L}_a,D_s,R{D}_s,U_c,Z_c,W_{HC})$$

(3)

$$f\left(x\right)=(\frac{Ds}{Y_f},\frac{RDs}{Y_f},\frac{U}{Uc},\frac{Zc}{Y_f},\frac{Wc}{L_a},\frac{U}{\sqrt{g{Y}_f}})$$

(4)

Buckingham’s π-theorem and dimensional analysis were performed to derive the equation below. The equation shows that scour depth around the bridge abutment depends on initial water depth, initial Froude number, the ratio between collar vertical position with respect to the bed surface level and initial water depth (Z_c/Y_f), and the ratio between width of collar and length of abutment ($\frac{Wc}{L_a}$), while U/U_c were kept constant throughout the experimental work. Therefore, the final equation based on dimensional analysis was:

$$f\left(x\right)=(\frac{Ds}{Y_f},\frac{RDs}{Y_f},\frac{Zc}{Y_f},\frac{Wc}{L_a},Fr)$$

(5)

3. Results

3.1. Scour Development without Collar or Hooked-Collar Protections

Figure 2 depicts the longitudinal profiles of the scour hole for various flow conditions of a short abutment with and without collar and hooked collar protection. In all experiments, the upper corner of each abutment showed the greatest amount of scour depth. When the flow rate was increased from U/U_c = 0.50 to 0.59, the volume of the scour holes rose by 11.3%, 8.3%, and 9.8% for vertical-wall and wing-wall abutments at 45° and 60°, respectively. This increase was because of the direct interaction between the abutment and water flow with greater velocity, resulting in the generation of vortical flow structures. As the flow velocity increases, the abutment disrupts the flow, causing the formation of vortical structures, specifically horseshoe vortices, at the base of the abutment. These vortices are generated due to the flow separation and the resulting pressure gradient around the abutment. The concentrated vortical activity leads to enhanced sediment removal at the upstream side, contributing to the scour development observed in the experiments. The generation of these vortices caused the removal of sediment particles from the upstream side of the abutment, which were deposited somewhere downstream. Consequently, a scour hole was developed around the bridge abutment. The abutment’s upstream side’s slope was constantly greater than its downstream side due to the development of a conical scour hole. The findings demonstrated that the angle of repose of the sediment particles (Ø = 30°) was nearly identical to the typical slope of the scour hole upstream. Observation of the scour hole morphologies (see Figure 3) showcases increased scour activity at the upstream edge of the abutment, with the formation of depositional features further downstream. It was observed that, in all flow circumstances, the scour hole around vertical wall abutments was broader than the one around wing-wall abutments. The difference in scour holes around these two types of abutments was because of their geometrical aspect. In the case of vertical-wall abutment, vortex generation starts from the upstream face of the abutment, whereas in the case of wing-wall abutment, vortex generation starts from the outer end of the upstream face of the abutment. However, the morphologies of the scour holes around all abutment shapes were similar.

Equilibrium scour depth is identified by running scour experiments of sufficiently long duration for the scour hole geometry to remain practically unchanged. Herein, equilibrium scour depth is achieved when it has less than a 1 mm variation after 2 h of the trial run, as has been similarly defined in the previous literature (e.g., see [27]). For all tests, more than 95% of the maximum observed scour depth occurred within 24 h since the start of the formation of the scour hole. Thus 28 h was chosen as the time to reach equilibrium scour. Relevant studies from the literature reveal that most of the scour (60–93%) took place during the first 10% of the equilibrium time. Similarly, in the experiments described herein, the highest scour rates occurred in the first few hours [13,17].

Table 2. Flow conditions and scour characteristics for the unprotected abutments.

Test No	Test Name	U [cm/s]	Ds,max [mm]	Vs [m3]	Ds,max Location
					X [mm]	Y [mm]
Run 1	VW	21	118	0.0097	100	150
Run 2	VW	18	106	0.0086	100	150
Run 3	WW (45°)	21	93	0.0096	250	150
Run 4	WW (45°)	18	86	0.0088	250	150
Run 5	WW (60°)	21	102	0.0102	225	150
Run 6	WW (60°)	18	92	0.0092	225	150

shows the characteristics of scour holes for the cases where no scour protection was used. The maximum scour depth at the abutment tip after each experiment is defined as D_s,_max, while the scour hole volume is given as V_s. The tests shown herein (Table 2) include runs 1–2 for the vertical-wall abutments, runs 3–4 for the wing-wall abutments at 45°, and runs 5–6, for the wing-wall abutments at 60°, depending on the flow conditions.

The contour maps of exposed short vertical-wall and wing-wall abutments are shown in Figure 4. For tests Run 1, Run 3, and Run 5, the greatest scour depth around the abutments was measured at 118.0, 93.0, and 102.0 mm, respectively, by using a point gauge. For these tests, the overall scour hole volumes around the abutments were roughly 0.0096, 0.0097, and 0.0102 m^3, respectively, computed using Equations (6) and (7):

V* = V/(D_s · L_a²)

(6)

V* = 1.142 · T_s^0.281

(7)

where D_s is the scour depth, L_a is the abutment length, and V* and T_s are the dimensionless scour volume and time, respectively.

3.2. Scour Development with Collar Protection

The longitudinal profiles of scour geometries are visually compared for the cases of unprotected and collar-protected vertical-wall and wing-wall abutments, as shown in Figure 4, at various elevations (at the bed surface level, below and above).

Table 3. Characteristics of abutments with collar protections and resulting scour geometries for scour experiments at fixed flow conditions (U = 21 cm/s, Y_f = 15 cm, L_a = 15 cm), and variable W_c and Z_c.

Test No	Test Name	Wc/La	Zc/Yf	AC/AT	Ds,max [mm]	RDs [%]	Vs [m3]	RVs [%]	Ds,max Location [mm]
									X	Y
RUN 7	VW-C	2.25	+0.2	0.802	67	43.22	0.0052	46.39	100	150
RUN 8	VW-C	2	+0.2	0.750	77	34.75	0.0055	43.29	100	150
RUN 9	VW-C	2.25	0	0.802	43	63.56	0.0045	53.6	200	350
RUN 10	VW-C	2	0	0.750	65	44.92	0.0051	47.42	150	150
RUN 11	VW-C	2.25	−0.2	0.802	29	75.40	0.0041	57.73	150	300
RUN 12	VW-C	2	−0.2	0.750	42	64.40	0.0043	55.67	150	150
RUN 13	WW-C (45°)	2.25	+0.2	0.790	50	46.20	0.0051	45.16	250	150
RUN 14	WW-C (45°)	2	+0.2	0.740	61	34.40	0.0054	41.94	250	150
RUN 15	WW-C (45°)	2.25	0	0.790	33	64.52	0.0042	54.83	250	320
RUN 16	WW-C (45°)	2	0	0.740	46	50.50	0.0049	47.31	250	320
RUN 17	WW-C (45°)	2.25	−0.2	0.790	32	65.60	0.0043	53.76	275	150
RUN 18	WW-C (45°)	2	-0.2	0.740	47	49.46	0.005	46.24	300	200
RUN 19	WW-C (60°)	2.25	+0.2	0.795	57	44.10	0.0053	49.50	250	150
RUN 20	WW-C (60°)	2	+0.2	0.745	67	34.31	0.0058	42.57	250	150
RUN 21	WW-C (60°)	2.25	0	0.795	37	63.72	0.0044	56.43	250	320
RUN 22	WW-C (60°)	2	0	0.745	48	52.94	0.0052	48.51	250	320
RUN 23	WW-C (60°)	2.25	−0.2	0.795	38	62.75	0.0045	55.45	275	150
RUN 24	WW-C (60°)	2	−0.2	0.745	50	50.98	0.0053	47.53	275	200

Notes: VW = vertical-wall abutment, WW = wing-wall abutment, C = collar, Z_c = elevation of the collar with reference to the bed surface level, D_s,max = maximum scour depth, R_Ds (%) = Reduction percentage of scour depth. The origin for the location of X(mm) and Y(mm) is at 7400 mm from the start of the channel.

demonstrates that for vertical-wall abutments with collars below the bed surface level and at 45° and 60° wing-wall abutments with collars at the bed surface level, the maximum scour depth was decreased by 78.9%, 66.6%, and 65.6%, respectively. As a result, collars at the bed surface level for wing-wall abutments and below the bed surface level for vertical-wall abutments have been found to reduce scour depth significantly. For flow conditions U/U_c = 0.59, tests were performed on three distinct types of abutments (vertical-wall, wing-wall at 45°, and wing-wall at 60° abutments) with varying diameters and collar elevations. The findings are shown in Table 3. This table shows the tested collar width to abutment length (it was kept at 15 cm, as a short abutment has a length equal to or shorter than the channel’s flow depth [13]) and collar elevation to flow depth ratios, as W_c/L_a and Z_c/Y_f, respectively. The result of scour depth around bridge abutments such as wing-wall and vertical wall abutments with collar protection demonstrates a significant scour reduction due to the presence of the collar, in accordance with findings of past research [13]. It was observed that the presence of the collar around the bridge abutments reduced flow velocity significantly, thus causing a reduction in the movement of sediment particles from the upstream side toward the downstream side of the bridge abutments. The collar acts as a physical barrier that disrupts the flow pattern near the abutment, reducing the intensity of the downward flow that typically contributes to sediment displacement. By modifying the flow structure, the collar diminishes the formation of vortices responsible for scouring and sediment transport from the upstream to the downstream side of the abutment. This disruption in flow significantly reduces the movement of sediment particles, thereby mitigating erosion around the abutment.

Additionally, the percent reduction of the maximum scour volume is defined as RV_s, respectively, while A_c/A_T is the ratio of the collar area to the total of the collar and abutment areas. Results for full-size collars on vertical-wall, wing-wall at 45°, and wing-wall at 60° abutments at various elevations are shown in Table 3 for experiment runs 7–12, 13–18, and 19–24. To determine the effects of different flow intensities on the effectiveness of collars for different abutment shapes, a series of tests were conducted utilizing the ideal collar sizes found under the threshold flow condition. The bed surface level (Z_c = 0) was also used to establish the elevation of the applied collar for all abutment forms to maintain the same representative reference conditions throughout all the experiments. Most cases with the greatest scour depth, as shown in Table 3, are farther away from the abutment tip.

3.3. Scour Development with Hooked Collar Protection

Figure 5 depicts the scour profile around the bridge abutment having hooked collar protection. Experiments were done on vertical-wall and wing-wall abutments at 45° and 60° with and without collar protection as a point of reference. In the exploratory phase, hooked collars with variable sidewall hook heights (H_HC) and widths (W_HC) were used, respectively, to prevent scouring at various elevations (Z_HC) above the bed surface level on the vertical-wall and wing-wall abutments. The hooked-collar sidewall height up to 0.35 L_a tended to demonstrate decreasing scour, but after this height was achieved, the scour depth started to rise. A hooked collar is a flow-altering device that is employed to manage abutment scouring by modifying the flow. When placed on an abutment, it acts as an obstruction and hampers downward flow and the formation of vortices. The sidewalls’ height probably contributes significantly to the rise in scour depth by blocking the water’s path as it approaches, which causes a downward flow and the creation of vortices. Overall, it is found that 0.35 L_a is the most practical and efficient sidewall height for lowering maximum scour depth. Hence, for the best results of scour reduction, the hooked collar should be positioned below the bed surface level for vertical walls and at the bed surface level for wing-wall abutments with a width of 2.25 L_a and a sidewall height of 0.35 L_a. For the hooked-collar height testing (H_HC), various factors were considered, such as the anticipated flow conditions, the hydraulic characteristics of the channel, and the intended purpose of the hooked collar.

The specific values chosen for hooked collar heights were intended to evaluate their effectiveness under different flow scenarios and to assess their ability to mitigate scour depths effectively. Although scour depth sometimes decreased as the hooked-collar width expanded, this decrease was extremely slight and may become uneconomical as the hooked-collar width and sidewall height increased. Interestingly, the hooked collar performed noticeably better when scour depth reduction findings were examined between abutments with and without collar protection. Scour was started slowly for both protected vertical-wall and wing-wall abutments, with a delay due to the presence of hooked-collar sidewalls, which worked similarly well in successfully reducing downward flow and horseshoe vortex generation. Figure 6 depicts the contour map of the bridge abutment with hooked collar protection.

3.4. Application of Hooked Collar at the Bed Surface Level

Table 3 illustrates that using a hooked collar on different-shaped abutments led to a decrease in both the maximum depth and the volume of the scour hole under various flow intensities. In each experiment, a hooked collar was employed to map the longitudinal profile of the scour hole at the point where the greatest depth occurred. Figure 5 presents a comparison of longitudinal scour profiles for shielded vertical-wall and wing-wall short abutments with a hooked collar, as opposed to the same conditions in the absence of a hooked collar. The effect of a hooked collar on maximum scour reduction depth at the abutment corner was evident. Specifically, the hooked collar with two different heights of hooks resulted in a 72.8% and 66.9% reduction in scour depth on the vertical wall abutment. For the 45° and 60° wing-wall abutments with a hooked collar, the percentage reduction in scour depth was 74.2%, 63.4%, 73.5%, and 67.6%, respectively. Figure 6 depicts contour maps illustrating the measured scour depth of the bed surface for different abutment shapes in each experiment, all with hooked-collar protection. The protective impact of the countermeasure was consistent across all types of abutments when a full-size collar with a hooked design was employed. Notably, the maximum scour depth shifted to the edge of the hooked collar, situated away from the abutment edge. Furthermore, the volume of the scour hole was reduced compared to studies conducted without this protective measure.

3.5. Application of Hooked Collar below Bed Surface Level

When the hooked collar was positioned below the bed surface level, the bed surface experienced rapid erosion, resembling the configuration observed at the bed surface level, as depicted in Figure 5 and Figure 6. Optimal results were attained when the hooked collar was situated below the bed surface elevation, particularly effective for abutting vertical walls. However, for wing-wall abutments at 45° and 60°, there was no reasonable difference in the reduction of scour depth between the hooked collar below the bed surface and at the bed surface level. It is important to note that the outcomes presented here are only relevant to the specific ranges of crucial variables manipulated in this research. Conditions for attaching the hooked collar at the bed surface level changed during the experiment as sediments on top of the collar were cleansed. Increasing the collar size at a fixed elevation resulted in a greater reduction in the scour rate at the abutment edge, as the size (width and sidewall height) and elevation of the hooked collar were identified as the primary determinants for the scour rate.

A wider hooked collar was found to reduce the size and maximum depth of the scour hole near the abutment point, yielding consistent results for abutments of varied forms. However,

Table 4. Characteristics of abutments with hooked-collar protections and resulting scour geometries for scour experiments at fixed flow conditions (U = 21 cm/s, Y_f =15 cm, L_a = 15 cm), and variable W_HC, Z_HC, and H_HC.

Test No	Test Name	WHC/La	HHC/La	ZHC/Yf	AHC/AT	Ds,max [mm]	RDs [%]	Vs [m3]	RVs (%)	Ds,max Location [mm]
										X	Y
RUN 25	VW-HC	2.25	0.35	+0.2	0.802	56	52.54	0.0048	50.52	100	150
RUN 26	VW-HC	2	0.35	+0.2	0.75	69	41.50	0.0051	47.42	100	150
RUN 27	VW-HC	2.25	0.25	+0.2	0.802	59	50.0	0.0049	49.48	100	150
RUN 28	VW-HC	2	0.25	+0.2	0.75	71	39.83	0.0054	44.33	100	150
RUN 29	VW-HC	2.25	0.35	0	0.802	32	72.80	0.004	58.76	250	350
RUN 30	VW-HC	2	0.35	0	0.75	53	55.0	0.0047	51.54	100	150
RUN 31	VW-HC	2.25	0.25	0	0.802	39	66.90	0.0043	55.67	250	350
RUN 32	VW-HC	2	0.25	0	0.75	55	53.39	0.0045	53.6	100	150
RUN 33	VW-HC	2.25	0.35	−0.2	0.802	19	83.89	0.0039	59.79	150	300
RUN 34	VW-HC	2	0.35	−0.2	0.75	33	72.0	0.0041	57.73	100	150
RUN 35	VW-HC	2.25	0.25	−0.2	0.802	23	80.50	0.0038	60.82	150	300
RUN 36	VW-HC	2	0.25	−0.2	0.75	38	67.79	0.0045	53.6	100	150
RUN 37	WW-HC (45°)	2.25	0.35	+0.2	0.790	47	49.46	0.0048	48.39	250	150
RUN 38	WW-HC (45°)	2	0.35	+0.2	0.740	56	39.78	0.005	46.24	250	150
RUN 39	WW-HC (45°)	2.25	0.25	+0.2	0.790	49	47.32	0.0047	49.46	250	150
RUN 40	WW-HC (45°)	2	0.25	+0.2	0.740	59	36.56	0.0053	43.01	250	150
RUN 41	WW-HC (45°)	2.25	0.35	0	0.790	24	74.20	0.0037	60.21	250	320
RUN 42	WW-HC (45°)	2	0.35	0	0.740	37	60.22	0.0045	51.61	250	320
RUN 43	WW-HC (45°)	2.25	0.25	0	0.790	34	63.44	0.0041	55.91	250	320
RUN 44	WW-HC (45°)	2	0.25	0	0.740	46	50.54	0.0046	50.53	250	320
RUN 45	WW-HC (45°)	2.25	0.35	−0.2	0.790	25	73.12	0.0039	58.06	275	150
RUN 46	WW-HC (45°)	2	0.35	−0.2	0.740	38	59.14	0.0041	55.91	300	200
RUN 47	WW-HC (45°)	2.25	0.25	−0.2	0.790	28	69.89	0.004	56.98	275	150
RUN 48	WW-HC (45°)	2	0.25	−0.2	0.740	39	58.06	0.0043	53.76	300	200
RUN 49	WW-HC (60°)	2.25	0.35	+0.2	0.795	51	50.0	0.005	50.49	250	150
RUN 50	WW-HC (60°)	2	0.35	+0.2	0.745	61	40.20	0.0054	46.53	250	150
RUN 51	WW-HC (60°)	2.25	0.25	+0.2	0.795	54	47.06	0.0052	48.51	250	150
RUN 52	WW-HC (60°)	2	0.25	+0.2	0.745	65	36.27	0.0054	46.53	250	150
RUN 53	WW-HC (60°)	2.25	0.35	0	0.795	27	73.50	0.0039	61.38	250	320
RUN 54	WW-HC (60°)	2	0.35	0	0.745	39	61.76	0.0045	55.45	250	320
RUN 55	WW-HC (60°)	2.25	0.25	0	0.795	33	67.64	0.0041	59.4	250	320
RUN 56	WW-HC (60°)	2	0.25	0	0.745	47	53.92	0.0046	54.45	250	320
RUN 57	WW-HC (60°)	2.25	0.35	−0.2	0.795	29	71.50	0.0039	61.38	275	150
RUN 58	WW-HC (60°)	2	0.35	−0.2	0.745	37	63.72	0.0044	56.44	275	200
RUN 59	WW-HC (60°)	2.25	0.25	−0.2	0.795	33	67.65	0.0042	58.41	275	150
RUN 60	WW-HC (60°)	2	0.25	−0.2	0.745	43	57.84	0.0049	51.48	275	200

Notes: VW = vertical-wall abutment, WW = wing-wall abutment, HC = hooked-collar, ZH_C = elevation of hooked-collar with reference to the bed surface level, D_s,max = maximum scour depth, R_Ds = scour depth reduction, L_a is the length of the abutment, W_HC and H_HC, are the width and height of the hooked-collar respectively. The origin for the location of X[mm] and Y[mm] is at 7.4 m from the start of the channel. The flow is along the channel in the X direction, and the width of the channel (perpendicular to the flow) in the Y direction.

indicates that, unlike using a hooked collar at the bed surface level, employing a hooked collar below the bed surface level for abutments of various forms did not practically lower the maximum scour depth. For vertical-wall abutments with a hooked collar below the bed surface level and 45° and 60° wing-wall abutments with a hooked collar at the bed surface level, the maximum decrease in scour depth is 83.9%, 74.2%, and 73.5%, respectively (Table 4). Using a hooked collar, in comparison to a collar alone or without protection, leads to a greater percentage reduction in scour depth on a vertical wall abutment below the bed surface level and a wing wall abutment at the bed surface level.

3.6. Application of Hooked Collars above the Bed Surface Level

Figure 7 provides a visual representation of the impact of the ratio (Z_c/Y_f) between the collar’s vertical position relative to the bed level and the initial water depth on the scour depth around the bridge abutment. The assessment considered three different values of Z_c/Y_f, revealing an increase in scour depth with higher Z_c/Y_f values. The non-dimensional scour depth around the bridge abutment is illustrated for three distinct geometries in Figure 7, emphasizing the significant influence of Z_c/Y_f on scour depth.

Observations show that as Z_c/Y_f values increased from −0.2 to 0.2, the maximum scour depth occurred under the bridge abutment with a vertical wing wall (at 90 degrees). Specifically, the non-dimensional scour depth increased from 0.19 (Z_c/Y_f = −0.2) to 0.51 (Z_c/Y_f = 0.2) for a vertical wing wall-shaped bridge abutment. Conversely, the minimum non-dimensional scour depth value (0.33) was noted for a wing wall-shaped abutment at 60 degrees under the range of Z_c/Y_f values (−0.2 to 0.2). Furthermore, Figure 7 also depicts the influence of Z_c/Y_f on scour reduction around the bridge abutment. The assessment considered three values of Z_c/Y_f, visually presenting the scour reduction for three different geometries. Results indicate that Z_c/Y_f significantly affects scour reduction around the bridge abutment. As Z_c/Y_f values increased from −0.2 to 0.2, the maximum scour reduction was examined under the bridge abutment with a vertical wing wall (at 90°). The scour reduction increased from 0.25 (Z_c/Y_f = −0.2) to 0.50 (Z_c/Y_f = 0.2) for a vertical wing wall-shaped bridge abutment. Conversely, the minimum non-dimensional scour depth value (0.41) was noted for a wing wall-shaped abutment at 60 degrees under the range of Z_c/Y_f values (−0.2 to 0.2).

3.7. Regression Analysis

3.7.1. Regression Analysis for Dimensionless Scour Depth (D_s/Y_f) Prediction

A hooked collar of varying geometry equations was developed to measure the predicted values of the dimensionless scour depth (Ds/Yf) around the bridge abutment. A non-linear regression analysis was performed to derive an exponential equation. Two types of variables, including dependent and independent variables, were used. Three independent variables were considered for regression analysis, such as the ratio between the width of the collar and the length of the abutment ($\frac{Wc}{L_a}$), the ratio between collar vertical position with respect to the bed level and initial water depth (Z_c/Y_f), and initial Froude number (F_r), while dimensionless scour depth (D_s/Y_f) was considered as a dependent variable. The equation shows relationships between D_s/Y_f, (W_c/L_a), (Zc/Y_f), and F_r. The experimental and predicted values of scour depth are illustrated in Figure 8a. The results demonstrate a satisfactory validation of the equation with experimental results since R² was determined to be 0.96 for a best-fit trendline for both values.

$$\frac{D_s}{Y_f}=-2.7060\times e^{-0.0106Fr}+1.0094\times e^{0.6390\left(\raisebox{1ex}{$W_c$}\!\left/ \!\raisebox{-1ex}{$L_a$}\right.\right)}+0.3855\times e^{2.2117\left(\raisebox{1ex}{$Z_C$}\!\left/ \!\raisebox{-1ex}{$Y_f$}\right.\right)}$$

(8)

To examine the impact of the initial Froude number, the ratio between the width of the collar and the length of the abutment ($\frac{W_c}{L_a}$), the ratio between collar vertical position with respect to the bed level and initial water depth (Z_c/Y_f), the values of these variables were increased by the percentage of 25% from the initial values selected in the study. It was visualized that D_s/Y_f was greatly influenced by an increase in the ratio between the width of the collar and the length of the abutment ($\frac{W_c}{L_a}$), the ratio between collar vertical position with respect to the bed level, the initial water depth (Z_c/Y_f), and the initial Froude number (F_r). The analysis shows that by increasing the values of the ratio between the width of the collar and the length of the abutment ($\frac{W_c}{L_a}$), the ratio between collar vertical position with respect to the bed level and initial water depth (Z_c/Y_f) results in an increase in D_s/y_n (Figure 8c). The scour efficiency was noticed to be increased by increasing the values of F_r (Figure 8d,e).

3.7.2. Regression Analysis for Scour Depth Reduction (R_Ds/Y_f)

A predictive model for dimensionless scour depth (R_Ds/Y_f) around a bridge abutment was established by employing a varied geometry hooked collar. An exponential equation was derived through non-linear regression analysis, utilizing both dependent and independent variables. The regression analysis incorporated three independent variables: the ratio between collar width and abutment length (W_c/L_a), the ratio of collar vertical position to bed level relative to the initial water depth (Z_c/Y_f), and the initial Froude number (F_r). The dependent variable considered was the dimensionless scour depth (R_Ds/Y_f). The resulting equation illustrates the relationships between R_Ds/Y_f and (W_c/L_a), (Z_c/Y_f), and F_r. The experimental and predicted values of scour depth are visually represented in Figure 9a. Notably, the equation demonstrated satisfactory validation against experimental results, as indicated by an R² value of 0.930 for the best-fit trendline of both sets of values. In the current investigation, a regression analysis was performed to derive a relationship between scour depth and various independent variables such as flow conditions, abutment type, and hooked collar geometrical aspect and predicted values of scour depth using multiple linear regression. The regression analysis provides an R² value of 0.93, indicating that 93% of the scour depth can be predicted from the defined input. In the present paper, the higher value of the R² indicates the model precision and a strong impact of independent variables on scour depth prediction. The p-values of each predictor were assessed to check the significance of each independent variable. The p-values of all independent variables, including flow condition, collar width, and abutment, were below the nominal p-value (p < 0.05). The p-value demonstrates that a scour depth is significantly impacted by the variation of independent variables. The regression analysis provides useful insight into the field of hydraulic engineering to predict the scour depth precisely based on various parameters such as abutment type, collar dimensions, and flow conditions. Scour depth prediction is also useful for design of scour protection measures.

$$\frac{{RD}_s}{Y_f}=-1.83\times e^{-6.83Fr}+0.217\times e^{0.72\left(\raisebox{1ex}{$W_c$}\!\left/ \!\raisebox{-1ex}{$L_a$}\right.\right)}-0.0472\times e^{6.188\left(\raisebox{1ex}{$Z_C$}\!\left/ \!\raisebox{-1ex}{$Y_f$}\right.\right)}$$

(9)

3.7.3. Sensitivity Analysis for Scour Reduction

To illustrate the impact of variations in the values of an independent variable while keeping other independent variables constant, a sensitivity analysis was conducted, following the approach outlined by [28]. In this study, sensitivity analysis was also carried out to assess the effects of independent variables, namely the initial Froude number (F_r), the ratio between collar width and abutment length (W_c/L_a), and the ratio between collar vertical position with respect to bed level and initial water depth (Z_c/Y_f), on the dimensionless scour depth (R_Ds/Y_f), the dependent variable), as depicted in Figure 9b. To investigate the influence of the initial Froude number, W_c/L_a, and Z_c/Y_f, the values of these variables were systematically changed by a percentage of 25% from their initially chosen values in the study. The results revealed a substantial impact on R_Ds/Y_f due to an increase in the values of the initial Froude number (F_r) and the ratio between collar vertical position and initial water depth (Z_c/Y_f), as well as the W_c/L_a. The analysis demonstrated that elevating the values of W_c/L_a led to an increase in R_Ds/Y_f (see Figure 9c–e).

The sensitivity analysis of the model for the parameters governing the evolution of scour depth was assessed based on various independent variables such as flow conditions, collar width, and abutment type. It was observed that a 10% increment in the value of Fr resulted in a 15% increase in scour depth. The finding suggests that it is necessary to maintain optimum flow conditions for the mitigation of scour risk around the bridge abutment. Whereas a variation in collar geometry also has a significant influence on scour depth. The result of sensitivity analysis demonstrates that a 20% increment in collar width resulted in a 10% scour reduction around the bridge abutment. By varying collar geometry, it is found that a wider collar effectively mitigates scour depth around the bridge abutment. Furthermore, abutment type also has a greater influence on scour depth around the bridge abutment. The result of the sensitivity analysis demonstrates that a wing wall abutment has 25% scour depth compared to the vertical wall abutment because of its geometry. This has practical engineering implications in selecting the optimal type of scour countermeasures depending on the abutment type and flow conditions, such as wider-shaped hooked collars for vertical wall abutments. In the current investigation, the selection of the regression model was considered based on the non-linear and complex relationship between the dependent variables, including scour depth and scour reduction, and independent variables including collar dimensions, flow conditions, and abutment geometry. The structural parameters’ interactions with flow dynamics caused the scour phenomenon of non-linear behavior around the bridge abutment. This non-linear relationship was captured through non-linear regression analysis, which was more suitable than the linear regression model.

The selection of the non-linear regression models was because of the logarithmic and exponential relationships noticed in the dataset collected from controlled laboratory experiments. The linear regression could not capture the relationship among various variables such as dimensionless scour depth (Ds/Y_f), and independent variables, including the ratio of the width of the collar to the length of the abutment (Wc/L_a), collar vertical position and water depth ratio (Zc/Y_f), and initial Froude number (Fr). The relationship among these variables was complex and non-linear. Therefore, we opted for a non-linear regression model. The non-linear regression model was more suitable and flexible in fitting the dataset and providing the higher R² value of 0.960 for non-dimensionless scour depth and 0.93 for scour reduction. The non-linear regression model not only provides strong prediction but also increases the sensitivity of scour depth against various independent variables which is important for designing effective scour protections.

3.8. Temporal Evolution of Scour Depth

Figure 10 displays the temporal progression of the maximum scour depth for both unprotected and protected abutments using hooked collars (at, above, and below bed levels), for different abutment shapes (vertical wall, wing wall at 45°, and wing wall at 60°). It is shown in all cases that scour depth without and with protection initially increases over time. Similar to past research, equilibrium scour depth is considered to be reached when scour does not increase beyond a certain percentage of the relevant length scale of the hydraulic infrastructure within the duration of 12 or 24 h [29]. According to this, preliminary experimental observations for identifying the duration of experiments for which for all practical purposes the equilibrium scour depth has been reached showed that equilibrium scour will have been reached within the first 24 h. Once the maximum values of the scour depth were attained around the bridge abutment without and with protection, no discernible increment (e.g., greater than the expected experimental errors due to instrumentation and measurement methods uncertainties, which for the case of point depth gages are ±1 mm) in scour depth can be further observed. Therefore, in the current investigation, 24 h was considered a sufficient time duration for measuring scour depth, which is also reasonable according to similar experiments found in the literature [30]. Also consistent with observations from past literature [31], the rate of scour depth increase is significantly higher at the start of the experiment, reaching a plateau very fast. Notably, a significant portion, approximately 70–80%, of the maximum scour depth is typically achieved within the first 5–6 h for most of the experimental runs. Comparing the performance of hooked-collar-protected abutments with those protected solely by collars, it is evident that hooked collars exhibit more satisfactory results in reducing scour. This improvement can be attributed to the sidewalls of the hooked collar, which impede downward flow, mitigate scour generation, and hinder the development of horseshoe vortices upstream by blocking the downward movement of the flow. It displays the temporal progression of the maximum scour depth for both unprotected abutments (vertical wall, wing wall at 45°, and wing wall at 60°) and abutments protected by hooked collars (at, above, and below bed levels). Figure 10 shows that scour depth without and with protection initially increases with time. Once the maximum values of the scour depth were attained around the bridge abutment without and with protection, no increment in scour depth was observed. As seen in Figure 10, up to 24 h of scour depth around the bridge abutment changes with time; therefore, in the current investigation, 24 h was considered as a time duration for measuring scour depth. Afterward, the scour depth starts to reduce around the bridge abutment and reaches an equilibrium position where no sediment particles erode from the upstream side of the bridge abutment towards downstream. The equilibrium time was achieved when water flowed in a channel for 28 h. Therefore, in the current investigation, 28 h was considered an equilibrium time. However, Notably, a significant portion, approximately 70–80%, of the maximum scour depth is achieved within the first 5–6 h of the experiment. Comparing the performance of hooked-collar-protected abutments with those protected solely by collars, it is evident that hooked collars exhibit much more satisfactory results in reducing scour. This improvement can be attributed to the sidewalls of the hooked collar, which impede downward flow, mitigate scour generation, and hinder the development of horseshoe vortices upstream by blocking the downward movement of the flow.

3.9. Scour Depth Prediction

The scour depth reduction was predicted using an equation, the following non-dimensional parameters A_HC/AT, Z_HC/Y_f, U/U_c, and K_s were studied, and their effects on the scour depth reduction percentage were expressed as:

R_Ds % = K₁ K_ks K_U/Uc K_AHC/AT K_ZHC/Yf K_HC/La

(10)

whereas K₁ is an empirical coefficient, and Kks, K_U/Uc, K_AC/AT, K_ZH/Y_f, and K_HC/La are functions of K_s, U/U_c, A_HC/AT, Z_HC/Y_f, and H_HC/L_a, respectively. When analyzing the scour depth and its characteristics based on experimental parameters, consideration was given to the following functions for each parameter:

K_ks = K_s^a

(11)

K_U/Uc = U/Uc^b

(12)

K_AHC/AT = e^{c AHC/AT}

(13)

K_ZHC/Y = e^{d ZHC/Yf}

(14)

K_HHC/La = e^{e HHC/La}

(15)

In this context, the empirical coefficients a, b, c, and d were determined from experimental data. Additionally, specific values of K_s were assigned, with 1, 0.75, and 0.7 utilized for cases involving abutments on vertical walls, wing walls at 45°, and wing walls at 60°, respectively. The application of the least squares method, aimed at minimizing predictive error, facilitated the estimation of the empirical coefficients as outlined below:

K₁ = 1.37, a = 0.18, b = −0.51, c = 4.75, d = −1.3, e = −0.5

The formulation of Equation (11), as presented below, is designed to predict the reduction in the depth of scour achieved when employing full-size collars, in contrast to the scenario with no scour protection:

R_Ds % = 1.37K_s^0.18U/U_c^−0.51 e^{4.75 AHC/AT} e^{−1.3 ZHC/Yf} e^{−0.5 HHC/La}

(16)

Equation (16) serves to demonstrate the alignment of predicted and measured values of scour depth reduction, indicating the reliability of the results obtained. Hence, the outcomes and equations derived in this study are deemed suitable for the investigated parameter ranges. Figure 11a visually depicts the commendable performance of the predicted scour depth reduction achieved using collars, as defined by Equation (16). The correlation coefficient (R²) stands at 0.86, signifying a highly satisfactory agreement between predicted and measured data points. The regression line exhibits lower bounds for predicted and measured scour depths at 37.04% and 39.80%, with upper bounds for predicted and measured scour depths at 92.60% and 80.50%, respectively (Figure 11a).

3.10. Comparison to Past Literature

Previously scour reduction around abutments has been investigated using different countermeasures (see Figure 11b) [11,13]. The scour reduction round bridge abutment by utilizing the collar as a countermeasure was found to be 77–96% [32]. Also, Ref. [33] investigated maximum scour reduction around abutments using a submerged vane structure as a countermeasure to reduce scour by almost 54%. However, in the current study, the maximum scour reduction was 83.89% for the vertical walls with a hooked collar and 74.2% for the wing wall of 45 degrees with a hooked collar (see Table 4). This is because the hooked collar is a flow-altering device that is employed to manage abutment scouring by modifying the flow. When placed on an abutment, it acts as an obstruction and hampers downward flow and the formation of vortices. The sidewall height probably contributes significantly to minimizing scour depth by blocking the approaching flow.

4. Discussion

This study focused on investigating scour reduction round bridge abutments, with the goal of a secure and cost-effective solution through the utilization of collars and hooked collars. The significance of this exploration lies in evaluating the effectiveness of collars and hooked collars in mitigating scour in comparison to existing remedies documented in prior literature. Over the last few decades, various researchers have delved into scour reduction by employing different protective measures around the bridges, providing viable solutions as referenced in [34,35,36]. Comprehensive laboratory studies have covered topics such as the efficiency of scour defences, interactions between piers and abutments [34], the categorization of scour phenomena in compound flumes [35], and abutment destruction [36], focusing on scour induced by both horizontal and upward flow constraints in compound channels. However, prior experimentations primarily focused on equilibrium scour, neglecting temporal dependencies in scour. Presently, research on the temporal development of scour is limited and lacks comprehensive conclusions.

This study investigated how the installation of a vertically positioned hooked collar on the abutment can help reduce scour depth. The presence of a hooked collar on the abutment hinders direct downflow from eroding the bed surface material, redirecting erosive forces to locations farther from the abutment and thereby minimizing scour depth in proximity. In contrast to unprotected abutments, where scour rapidly occurred upstream and downstream, the initial hours of tests with hooked-collar protection showed no signs of scour. By the conclusion of the experiments, the scour hole of the vertical-wall abutment on the upstream face appeared larger and deeper than that on the wing-wall abutments (at 45° and 60°). The depth of the scour hole of the vertical wall abutment downstream was lower than that of the wing wall abutment, attributed to the presence of more wake vortices upstream of the vertical wall abutment. Regardless of the size or height of the hooked collar at the bed surface level, its effectiveness was evident, as it influenced the scour rate in both cases. Moreover, employing a wider hooked collar resulted in a reduced ratio of scouring upstream to downstream of the abutment, further enhancing its effectiveness.

The choice of flow conditions and sediment grain size was made by considering the empirical dataset of the mentioned regions, including Kabul and Indus River. The current investigation aims to experiment with a controlled laboratory setup that reflects scenarios that are similar to scouring around bridge abutments located in a natural river. Although the flow conditions replicated in the channel represent a subset of the possible scenarios of the natural river, they were limited to subcritical conditions, and sediment grain size was approximately uniform. This may not represent the full-scale conditions experienced in diverse riverine environments, yet it may be considered acceptable, given that even for an active specific river section, sediment sizes may vary over time. Future research may expand the range of experimental scenarios by considering more discharge conditions and diverse, representative ranges of non-uniform sediments and their impact on scour around bridge abutments.

Table 4 presents the outcomes obtained by employing a hooked collar on abutments positioned above the bed surface level (runs 25 and 26, runs 31 and 32, and runs 37 and 38). The findings indicate that utilizing a hooked collar on abutments above the bed surface level had a minimal impact on reducing scour near the abutment compared to when the hooked collar was placed at the bed or below the bed surface level. The hooked collar essentially divides the flow into two regions: above and below the level of its placement. In the region above, the hooked collar mitigates the force of downward flow, while in the region below, it diminishes both the downward flow and the strength of shed vortices. However, the reduction in vortex strength was relatively minor compared to conditions where the hooked collar was employed at the bed surface level, resulting in a smaller scour depth reduction in this scenario compared to other protection strategies. To showcase the effectiveness of the hooked collar in minimizing the maximum scour depth at the abutment tip, Figure 9 illustrates its efficiency for various abutment forms when used with different geometries and relative elevations from the bed surface. This figure underscores that deploying a hooked collar at the bed surface level yielded superior results among the investigated levels, excluding the vertical wall abutment. Furthermore, Figure 7 illustrates that, across all abutment designs, the proportion of the hooked-collar area to the overall area of the collar and abutment increased, indicating its growing influence.

To provide a comprehensive understanding of the three-dimensional flow conditions round a bridge foundation, extensive computational investigations have been carried out to predict flow patterns and scour in the vicinity of embedded hydraulic structures [37,38]. In a non-uniform gravel bed, local scours were examined using a combination of experimental and observational data. They introduced a novel equation for predicting optimal scour depth and suggested updated K-factors for the Melville and Coleman relations [38]. Also, a novel equilibrium scour depth relationship was formulated by calculating the overall sediment movement around a bridge pier that is vulnerable to local scour. Several scholars, including [39], have delved into this approach, primarily seeking to develop relations for the determination of the sizes and location ranges of displaced particles. Furthermore, various strategies such as collars, slots, submerged vanes, and sacrificial piles have been implemented to modify or divert flow from the foundation, thereby reducing erosive forces [39]. These investigations focus on determining the geometric characteristics and effectiveness of these proposed techniques. Some researchers have explored the combination of these approaches. For example, [40] investigated seven riprap thicknesses with two distinct collar sizes for circular piers in identical trials (a combination of riprap and collar). Their results demonstrated that using a collar minimized the size and extent of resilient riprap.

4.1. Discussion of Robustness of the Predictive Equations

Multiple linear regression analysis for non-dimensional scour depth yielded an R² value of 0.96, indicating a highly precise model for scour prediction around bridge abutments. The analysis for scour reduction resulted in an R² value of 0.93, showing a strong relationship between scour depth prediction and various independent variables. Both regression models have p-values lower than the nominal range, demonstrating the statistical significance and the robustness of the predictive relationship between flow conditions, abutment type, and hooked collar width.

The sensitivity analysis conducted herein examined the influence of independent variables (initial Froude number (F_r), ratio between collar width and abutment length (W_c/L_a), and ratio between collar vertical position and initial flow depth (Z_c/Y_f)) on the dimensionless scour depth (D_s/Y_f). The analysis revealed that increasing W_c/L_a and Z_c/Y_f resulted in an increase in D_s/Y_f. Additionally, the analysis showed that flow condition and hooked collar width are the most influential factors affecting scour depth. A 10% increment in F_r resulted in a 15% increase in scour depth, while a 20% increment in hooked collar width led to a 10% reduction in scour depth.

The statistical analysis demonstrates significant relationships between F_r, W_HC/L_a, and Z_c/Y_f. The model achieved an R² value of 0.93, providing a strong prediction of scour depth. W_HC/L_a has an indirect relationship with Z_c/Y_f, with increasing W_HC/L_a values resulting in decreases in Z_c/Y_f. A W_HC/L_a value of 2.5 caused a maximum scour depth reduction of 83.9%, demonstrating the efficiency of wider hooked collars for scour protection. The relationship between these variables suggests that using a wider hooked collar in regions of higher flow velocity would be effective for scour mitigation under sub-critical flow conditions.

4.2. Discussion of Countermeasures Placement

A hooked collar around the vertical wall and wing wall abutment reduces scour depth significantly depending upon the length of the abutment and the width of the hooked collar. A vertical wall abutment with W_HC = 2.25 L_a and H_HC = 0.35 L_a can reduce a scour depth up to 83.9%, whereas 67.8% can be reduced with W_HC = 2 L_a and H_HC = 0.25 L_a.

The position of the hooked collar has a crucial role in the scour around the bridge abutment. It was observed that scour depth reduced up to 83.9% for a vertical wall abutment positioned below the bed level, whereas 73.1% and 71.5% were noticed for wing wall abutments at 45° and 60°. However, when the hooked collar was positioned at the bed surface level, it was observed that 74.2% and 73.5% of scour was reduced around the wing wall abutment to 45° and 60° and 72.8% for the vertical wall abutment. Moreover, when the hooked collar was positioned above the bed surface level, vertical wall abutment scour depth was reduced by up to 52.5%, while 49.5% and 50.0% were observed for wing wall abutment at 45° and 60° respectively.

Our experiment is distinctive from previous studies primarily due to the innovative use of hooked-collar protections in various configurations and their demonstrated impact on scour reduction around different abutment shapes at different elevations. In past research, different scour protection methods, like dykes and collars (amongst others), have been studied, but the effectiveness of hooked collars around abutments at different elevations and widths under sub-critical flow conditions has not been examined so far. The experimental setup presented herein, along with a thorough sensitivity analysis, allows us to provide new insights into optimal configurations for minimizing scour, particularly under varying flow conditions and abutment geometries.

4.3. Implications for the Hydraulic Engineering Practice, Limitations and Future Outlook

The current investigation utilized the efficiency of hooked collars in scour reduction for different types of abutments, such as vertical wall and wing wall abutments under sub-critical flow conditions. The practical implication of the findings of the current is that optimally placed hooked collars can offer an effective solution for reducing scour around vertical wall and wing wall abutments under subcritical flow conditions. This can significantly improve the longevity and safety of bridge structures in river environments. The findings support the use of hooked collars not only in new bridge designs but also as a retrofit solution for existing structures facing scour issues. This provides a cost-effective option for improving the resilience of older infrastructure. Hooked collars should be considered as part of a comprehensive integrated scour protection strategy. Engineers should evaluate combining them with other countermeasures such as riprap, guide banks, and spur dikes, especially in areas prone to severe scouring, as well as implementing novel scour risk monitoring approaches [41,42]. Further research into integrating sensors and adaptive technologies with hooked collars could lead to the development of smart scour countermeasures that could provide real-time monitoring for a range of changing flow conditions [43,44]. Before implementing hooked collars, engineers must conduct a thorough assessment of local flow conditions, sediment characteristics, and abutment geometry to ensure the appropriateness and effectiveness of the countermeasure for the specific site. These recommendations can be implemented in the design of new bridge structures or already existing ones.

The experiment targeted a limited number of key variables, such as different abutment shapes and flow intensities, that are critical factors influencing scour. These parameters were chosen to reflect real-world conditions where they most significantly affect scour around bridge abutments. The results clearly show different trends, and the quantification of the differences in the scour processes is of high value in our view. These experiments may also contribute to gaining a better understanding of scour mitigation techniques and provide a foundational basis for future research, as they can be seen as a first step to assessing the parameters that may have a greater weight in defining the scour processes and effectiveness of various scour countermeasures.

5. Conclusions

To establish the most efficient way to use a hooked collar around short abutments for minimizing scour depth, this experimental investigation compared the erosive power of the turbulent flow acting near the riverbed surface between short abutments that were unprotected and those that were collar-protected. The following are the main results of this research:

• The current investigation demonstrates the significance of hooked collar position and placement for scour reduction around bridge abutments of vertical wall abutments and wing wall abutments. It was observed that scour can be reduced up to 83.9% by hooked collars around vertical wall abutments and up to 73.1% for the case of wing wall abutments. Moreover, the placement of hooked collars below the bed surface level resulted in greater scour reduction compared to placing them above or at the bed surface level.
• Multiple linear regression analyses yielded high R² values (0.96 for scour prediction and 0.93 for scour reduction), indicating precise and robust predictive models. Sensitivity analysis highlighted flow conditions and collar width as critical factors affecting the achieved equilibrium scour.
• The results indicate a significant statistical interdependence between various parameters, such as the Froude number (F_r), collar width to abutment length ratio (W_HC/L_a), and relative collar height (Z_c/Y_f). Increasing W_HC/L_a reduces Z_c/Y_f, demonstrating the efficiency of wider collars in scour protection.
• Future research should explore the integration of sensors and adaptive technologies with hooked collars to develop smart countermeasures for real-time monitoring and response to changing flow conditions. Engineers must assess local flow conditions, sediment characteristics, and abutment geometry to ensure the effectiveness of hooked collars for specific sites. These recommendations can be implemented in the design of both new and existing bridge structures.