Introduction

Bridges are essential components of transportation networks, providing critical connectivity across water bodies and flood-prone areas1. However, scour-induced failure remains one of the leading causes of bridge collapses worldwide, particularly during extreme hydrologic events2,3. Scour occurs as flowing water erodes sediment around bridge foundations, leading to progressive undermining and potential structural instability4. In the United States, it is estimated that nearly 60% of bridge failures are attributable to scour-related mechanisms5, and similarly, in New Zealand, at least one major bridge failure per year is linked to foundation scour4. If left unaddressed, local scour near bridge piers and abutments can cause severe damage or total structural failure.

The hydrodynamic processes around bridge piers and abutments are highly complex due to the presence of turbulent flow structures, including horseshoe vortices, wake vortices, and shear layers6. Numerous studies have been conducted to understand local scour behavior around bridge elements. Hong7 investigated the influence of pier proximity to abutments, concluding that nearby piers significantly affect the development and deepening of scour depths near abutments. Oben-Nyarko and Ettema8, however, found contrasting results, reporting that the presence of a pier near an abutment does not always substantially increase abutment scour depth. Meanwhile, Ataie-Ashtiani and Beheshti9 and Hang7 demonstrated that reduced pier–abutment distance intensifies horseshoe vortices and consequently increases scour depth. Melville6 emphasized the necessity of considering piers and abutments as a coupled system rather than isolated elements when evaluating scour mechanisms.

One of the problems that river and bridge engineers face is the accumulation of logs and woody debris upstream of the bridge piers and abutments in river bridges. These floating materials are transported by the flow, especially during floods, and can significantly increase local scour around the piers and abutments, altering the riverbed morphology and consequently raising the risk of bridge failure. In addition to causing environmental problems and obstructing flow, debris accumulation plays a crucial role in changing the shape of the riverbed and jeopardizing the structural stability of bridges. Parola et al. (2000) reported that debris accumulation around bridge piers can significantly influence hydrodynamic forces and local scour, depending on the various shapes, roughness, and porosity of the accumulated debris. Moreover, debris accumulation on bridge piers is an ongoing problem that can alter flow conditions, reduce the effective waterway capacity, and increase the risk of bridge failure (Kattell and Eriksson, 1998; Diehl, 1997).

.Debris can partially or fully block bridge openings, increasing flow constriction, turbulence intensity, and thus enhancing local scour around piers and abutments10,11. Laursen and Toch12, Melville and dongol13, Diehl14, Parola et al.15, Lagasse et al.16, Rahimi et al.17, Kosic et al.18 and Dadamahalleh et al.19 summarized the qualitative impacts of large woody debris accumulation on bridges, highlighting the associated risks of increased scour and structural vulnerability. Wallerstein and Thorne20 and Wallerstein et al.21, through studies based on Mississippi River conditions, attributed debris presence largely to bank erosion processes. Several experimental studies have specifically examined how debris characteristics—such as shape, thickness, and placement—affect local scour around piers. The accumulation of large woody debris has been found to enlarge both the width and depth of scour depths, with the severity depending on debris size and hydraulic conditions16,20. Schalko et al.22 found that large wood (LW) accumulation at bridge piers is primarily governed by the approach flow velocity and log length. Consistently, Palermo et al.23 demonstrated that large debris surrounding bridge piers increases shear stress, flow turbulence, and consequently the scour depth. According to Al-Jubouri et al.24, debris characteristics significantly influence local scour patterns. Furthermore, Pagliara et al.25 indicated that bed slope plays a critical role in scour morphology, especially in the presence of large debris accumulations. The type and placement of debris also influence scour intensity; Khalili et al.26 reported that buried debris causes greater scour depth and width compared to free debris, while Zhang et al.27 showed that dynamic debris jams can double scour depth and increase scour volume up to eight times, generating additional hydraulic head proportional to jam size and Froude number. Al-Khafaji et al.28 revealed that successive bridges can reduce downstream pier scour by 30–40%, whereas debris accumulation intensifies contraction scour by up to 40.5%. Research by Abousaeidi et al.29 demonstrated that debris thickness and pier-abutment proximity substantially influence scour depths. Their experiments indicated an inverse correlation between pier–abutment distance and scour depth, while debris thickness and length were positively associated with deeper scour depths. Notably, rectangular debris produced the most significant scour depths, followed by cylindrical and triangular shapes, with scour depths consistently higher near abutments compared to piers. While these studies have substantially advanced our understanding of scour mechanisms, a critical gap remains: most existing research has evaluated either structural distance or debris effects in isolation, without a combined analysis. Several experimental studies have investigated measures to reduce pier scour in the presence of debris. For instance, the use of slots, collars, and riprap has been shown to decrease scour depth, although their effectiveness depends on the shape and position of debris. Debris accumulation can also amplify morphological changes, such as increasing bedform heights, which can be partially mitigated by auxiliary structures like sills.30,31,32,33.

Despite significant progress in understanding local scour, the combined effects of debris geometry and pier–abutment interaction remain insufficiently studied. This study addresses this gap by examining how debris shape and thickness, together with the spacing between the pier and abutment, influence flow patterns and scour development. The results show that floating debris can substantially intensify scour around both piers and abutments, highlighting the importance of considering debris effects in the design and management of river structures. The main contribution of this research is the development of an integrated understanding of debris-induced scour mechanisms, which improves the accuracy of scour depth predictions and provides practical guidance to river engineers for the design and maintenance of hydraulic structures exposed to floating debris, ultimately supporting more resilient bridge infrastructure under flood conditions.

Materials and methods

Experimental setup

The experiments were conducted at the Water and Hydraulic Structures Laboratory of Department of Water Science and Engineering, Shahid Bahonar University of Kerman, Kerman, Iran. A straight rectangular flume, 8 m long, 0.8 m wide, and 0.6 m deep, with a flat concrete bed and glass sidewalls, was employed. Water was supplied from an underground reservoir using two centrifugal pumps, and the discharge was controlled by a volumetric flowmeter with an accuracy of ± 1%. Flow depth was regulated using an adjustable tailgate at the downstream end. A flow straightener installed at the inlet minimized turbulence and ensured uniform, steady flow conditions. A constant discharge of 30 L/s was selected, resulting in a flow depth of approximately 16.5 cm. The sediment bed consisted of uniform, noncohesive sand with a median particle size of d₅₀ = 0.83 mm and a geometric standard deviation σg = 1.5. These sediment characteristics were selected based on the criteria proposed by Raudkivi and Ettema34 (d₅₀ > 0.7 mm to avoid ripple formation) and by Chiew and Melville35 (σg < 1.3 to minimize sediment-heterogeneity effects). In addition, following Oliveto and Hager36, the flow depth was maintained above 20 mm to avoid roughness-induced suppression of scour depth, and according to Melville and Hadfield37, the pier-diameter–to–flow-depth ratio was kept below 0.7 to prevent scale effects on scour. The bridge substructure comprised a cylindrical steel pier (diameter = 30 mm) and a steel abutment (6 × 12 × 45 cm). Both elements were mounted on a false floor positioned 0.16 m above the main flume bed to realistically simulate a riverbed condition. The relative distance between pier and abutment different at 0.1 and 0.2 times the pier diameter to investigate interaction effects. Debris was simulated using fixed wooden models positioned upstream of the pier. Three debris shapes—rectangular, triangular, and semicircular (half-cylindrical)—were tested. The relative debris thickness varied from 0.09 to 0.39. These geometries were selected to represent typical forms of natural debris (e.g., floating logs). A schematic of the setup, model positions, and debris configurations is presented in Fig. 1.

Fig. 1
figure 1

Sketch of the flume and experimental set-up (a) top view, (b) Side view and (c) various types of debris.

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All tests were performed under clear-water conditions. Scour equilibrium was defined following Kumar et al.38, as the stage at which bed-level variations were less than 1 mm over a 3-h period. Each experiment was continued for 7 h to ensure that equilibrium scour conditions were fully achieved (Fig. 2). Scour depth and bed topography were measured using a point gauge with a precision of 0.1 mm at predefined grid locations. After equilibrium was reached, these grid points were recorded to obtain detailed scour profiles. The three-dimensional scour hole morphology was subsequently plotted and analyzed using Surfer 16 software. This setup provided a controlled environment to examine the combined influence of debris characteristics and pier–abutment interaction on local scour evolution.

Fig. 2
figure 2

Temporal evolution of scour depth toward equilibrium.

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Dimensional analysis

Twenty key characteristic parameters affecting the local scour around bridge pier and abutment identified in Eq. 1.

$${\text{D}}_{{\text{s}}} = {\text{F}}_{1} \left( {{\text{B}},{\text{B}}_{{\text{d}}} ,{\text{ D}},d_{ap} ,{\text{d}}_{50} ,{\text{g}},{\text{ h}},{ }K_{s} ,{ }K_{p} { },{\text{L}}_{{\text{a}}} ,{\text{L}}_{{\text{d}}} ,{\text{ SF}},{\text{ T}}_{{\text{d}}} ,{ }t_{eq} ,t_{ex} ,{\text{ U}},{\text{ W}}_{{\text{a}}} ,W_{d} ,{{ \uprho }},{\upmu },{\uprho }_{{\text{s}}} ,{\upsigma }_{{\text{g}}} ,} \right)$$
(1)

where ds (scour depth), B (channel width), D (foundation diameter), \({d}_{ap}\)(distance between pier and abutment), d50 (average particle diameter of sediment), g (gravitational acceleration), h (flow depth), \({K}_{s}\) (roughness), \({K}_{p}\) (permeability of woody debris), La (abutment length), Ld (debris length), \(\text{SF}\) (debris shape factor) is determined based on the drag coefficients of various debris shapes. \({\text{T}}_{\text{d}}\) debris diameter), \({t}_{ex}\) (experimental time), \({t}_{eq}\) (equilibrium time), U (flow velocity), Wa (abutment width), Wd (debris width), ρ (fluid density), μ (kinematic viscosity of the fluid), ρs (sediment density) and σg is the geometrical standard deviation of sediment particles,. Using dimensional analysis based on the Buckingham π theorem, the following dimensionless relationship was derived. Using dimensional analysis based on the Buckingham π theorem, the following dimensionless relationship was derived, leading to Eq. (2). Since the debris bodies were smooth (\({K}_{s}=0\)) and non-permeability of woody debris (\({K}_{p}=0\)), their related parameters were not included in Eq. (2).

$$\frac{{{\text{D}}_{{\text{s}}} }}{{\text{h}}} = {\text{F}}_{2} \left( {\frac{{\text{B}}}{{\text{h}}},\frac{{\text{D}}}{{\text{B}}},{ }\frac{{d_{ap} }}{{\text{B}}},{ }\frac{{{\text{d}}_{50} }}{{\text{h}}},{\text{ F}}_{{\text{r}}} ,{\text{G}}_{{\text{s}}} ,{ }\frac{{{\text{L}}_{{\text{a}}} }}{{\text{h}}}, \frac{{{\text{L}}_{{\text{d}}} }}{{\text{B}}},{\text{R}}_{{\text{e}}} ,{ }SF, \frac{{{\text{T}}_{{\text{d}}} }}{{\text{h}}},\frac{{t_{ex} }}{{t_{eq} }},{ }\frac{{{\text{W}}_{{\text{a}}} }}{{\text{B}}},\frac{{{\text{W}}_{{\text{d}}} }}{{\text{B}}},{\upsigma }_{{\text{g}}} } \right)$$
(2)

The dimensionless parameter B/h represents the aspect ratio indicating wide channel conditions, while \({\text{F}}_{\text{r}}\) and \({\text{R}}_{\text{e}}\) denote the Froude and Reynolds numbers, respectively. In river engineering analyses, such as pier and abutment scour studies, due to the non-dimensional of \({\text{F}}_{\text{r}}\) and \({\text{R}}_{\text{e}}\), the high range of Reynolds numbers in the flow, and the dominant influence of the Froude number, scaling errors are negligible and can be justifiably disregarded. According to the experimental conditions of this study, the effect of fluid viscosity parameters was neglected due to the large Reynolds number (\({R}_{e}\ge 2000\)). The sediment particle size, d50 = 0.83 mm, \({\text{G}}_{\text{s}}\) . \(\frac{{\text{d}}_{50}}{\text{h}}=0.005\) and \({\upsigma }_{\text{g}}\) < 1.3. All experiments were conducted for a duration equal to the equilibrium scour time (\({t}_{ex}/{t}_{eq}=1\)). In addition, some geometrical parameters of physical models (B, \({\text{L}}_{\text{a}}\), \({\text{W}}_{\text{a}},\) \({\text{L}}_{\text{d}}\) and \({\text{W}}_{\text{d}}\)) had constant values through all experiments. Since these parameters remained constant, they were excluded from the Eq. (2), resulting in the simplification of Eq. (2) to Eq. (3)

$$\frac{{{\text{d}}_{{\text{s}}} }}{{\text{h}}} = {\text{F}}_{3} \left( {\frac{{d_{ap} }}{{\mathbf{B}}}, \frac{{{\text{T}}_{{\text{d}}} }}{{\text{h}}},{ }SF} \right)$$
(3)

All parameters investigated in this study, including geometric, hydraulic, and sediment characteristics, are schematically illustrated in Fig. 3.

Fig. 3
figure 3

Definition of scour parameters at bridge pier and abutment scour, (a) front view (b) top view.

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Results and discussion

The experiments in this research investigate the effect of debris on local scour around the bridge pier and abutment. Debris with different shapes (such as rectangular, semi-circular and triangular) and four values of the relative debris thickness (\({T}_{d}/h\)) (0.09, 0.19, 0.29 and 0.39) were attached to the bridge pier in a submerged state at a relative distance from the sediment bed surface. The bridge piers were positioned at relative distances of 0.1 and 0.2 from the bridge abutment (\({d}_{ap}/B\)). This section explains the effects of the relative thickness and shape of debris at different distances between the bridge pier and abutment, specifically for rectangular debris on local scour depth.

Influence of shape and relative thickness of debris on bridge pier and abutment scour

In this section, the effect of the relative thickness of debris (\({T}_{d}/h\)) on bridge pier and abutment scour was investigated. The experiments were conducted with three geometric shapes of debris: rectangular, semi-circular and triangular, with four relative thicknesses (\({T}_{d}/h\)) of 0.09, 0.19, 0.29, and 0.39.

Observations showed that as the relative thickness of debris (\({T}_{d}/h\)) increases, the scour depth also increases. With an increasing relative debris thickness (\({T}_{d}/h\)), more intense vortex systems developed around the bridge pier and abutment. These vortices detach sediment particles from the riverbed and transport them downstream with the main flow. This enhanced vortical action significantly influenced the maximum relative scour depth (\({d}_{s\_max}/h\)) at both the pier front and the abutment region.

According to Fig. 4, experiments conducted on the three debris shapes (rectangular, semi-circular, and triangular) at a relative distance of 0.1 from the abutment (\({d}_{ap}/B\)) under identical laboratory conditions demonstrate that the rectangular debris generates a larger scour depth compared to the semi-circular and triangular shapes. This can be attributed to the larger blockage effect of rectangular debris, which intensifies flow acceleration around the pier and enhances sediment entrainment. The sharper edges and flat surfaces of rectangular debris created stronger localized vortices compared to the smoother surfaces of semi-circular and triangular debris, thereby increasing scour depth in the pier and abutment regions.

Fig. 4
figure 4

Laboratory experiments were conducted using three types of debris with \({T}_{d}/h\)=0.27 and \({d}_{ap}/B\)= 0.1. (a) Triangular, (b) semi-circular and (c) rectangular.

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Table 1 and Fig. 5 illustrate the effect of the relative thickness of debris (\({T}_{d}/h\)) for the three geometric shapes: rectangular, semi-circular, and triangular. At a relative distance of 0.1 between the pier and abutment (\({d}_{ap}/B\)), when the relative thickness (\({T}_{d}/h\)) of rectangular debris increased from 0.09 to 0.39, the maximum relative scour depth (\({d}_{s\_max}/h\)) increased by 42% in front of the bridge pier and by 47% at the front nose of the bridge abutment. Furthermore, at the same relative distance of 0.1 between the pier and abutment (\({d}_{ap}/B\)), as the relative thickness of the debris (\({T}_{d}/h\)) increased from 0.09 to 0.39, the maximum relative scour depth (\({d}_{s\_max}/h\)) in the presence of semi-circular and triangular debris increased by 30% and 45% in front of the bridge pier, and by 43% and 31% at the front nose of the bridge abutment, respectively. This result is consistent with the observations of Al-Jubouri et al. (2024), who reported that increasing the thickness of floating debris from T/Y = 0.25 to T/Y = 0.5 leads to an increase of up to 5 cm in scour depth around the bridge pier40.

Table 1 Maximum relative scour depth (\({d}_{s\_max}/h\)) values in front of bridge pier and abutment in the presence of debris type with different thicknesses (\({T}_{d}/h\)) for relative distances of 0.1 between pier and bridge abutment (\({d}_{ap}/B\)).
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Fig. 5
figure 5

Influence of debris thickness ratio on local scour depth for: (a) bridge pier and (b) bridge abutment configurations with various debris shapes (rectangular, semi-circular, and triangular) at \({d}_{ap}/B\)=0.1.

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These results underscore the amplifying role of debris thickness in exacerbating local scour through enhanced flow constriction and vortex formation, particularly in confined pier-abutment geometries. The observed increases align with the principle that debris accumulation intensifies shear stresses and turbulence around bridge elements, leading to deeper scour holes39,40. For rectangular debris, the higher scour amplification (42–47%) compared to semi-circular (30–43%) and triangular (31–45%) shapes can be attributed to its sharper edges, which promote greater flow blockage and horseshoe vortex development, consistent with experimental observations on debris-induced scour mechanisms11,24. Comparing parts (a) and (b) of Fig. 5 reveals that the maximum relative scour depth (\({d}_{s\_max}/h\)) at the front nose of the bridge abutment was consistently greater than the maximum relative scour depth (\({d}_{s\_max}/h\)) in front of the bridge pier. This pattern was most pronounced for rectangular debris, where abutment scour depths exceeded pier scour by up to 12% (47% vs. 42% increase relative to baseline), followed by semi-circular (13% difference: 43% vs. 30%) and triangular debris (14% difference: 31% vs. 45%, though triangular showed a reversed trend at the pier). These observations stem from clear-water scour experiments in a controlled flume, highlighting the amplified erosive forces at the abutment due to flow acceleration and vortex intensification in confined geometries. This disparity underscores the role of pier-abutment interactions in redistributing hydraulic forces, where the abutment nose experiences enhanced downflow and shear stresses from the converging flow field, leading to deeper scour holes compared to the pier front 24,41. The consistent superiority of abutment scour aligns with established scour mechanics, where abutment geometries promote stronger horseshoe vortices and secondary currents that erode sediment more aggressively than isolated pier-induced vortices. For rectangular and semi-circular debris, the abutment’s exposure to debris-induced flow constriction exacerbates this effect, resulting in greater relative depths, whereas triangular debris’s upstream positioning may partially shield the pier while still amplifying abutment scour through turbulence spillover11,39.

The results obtained from the analysis of experiments in this research demonstrate that the maximum relative scour depth (\({d}_{s\_max}/h\)) occurs when the debris is rectangular in shape. Therefore, the focus of this study and the experiments has been directed towards examining and analyzing the maximum scour depth under conditions where rectangular debris is present, and the results have been thoroughly discussed and evaluated. This approach is prudent for engineering practice, as it addresses the worst-case scenario for scour risk assessment and management. Effective debris management and scour protection measures should prioritize the removal of block-like debris and focus monitoring efforts on the vulnerable abutment region.

Interactive effect of bridge pier and abutment on scour in the presence of rectangular debris

In this research, experiments were conducted with rectangular debris of relative thicknesses (\({T}_{d}/h\)) of 0.09, 0.19, 0.29, and 0.39 at two relative distances of (0.1 and 0.2) between the bridge pier and abutment (\({d}_{ap}/B\)). Figure 6 illustrates the experiments conducted to measure scour depth around the bridge pier and abutment with rectangular debris of relative thickness (\({T}_{d}/h\)) = 0.19 at two relative distances (0.1 and 0.2) between the bridge pier and abutment (\({d}_{ap}/B\)).

Fig. 6
figure 6

Laboratory experiments were conducted to measure scour depth using rectangular debris with a \({\text{T}}_{\text{d}}/\text{h}\)= 0.19 at two different pier-to-abutment relative distances: (a) \({d}_{ap}/B\)= 0.1 and (b) \({d}_{ap}/B\)=0.2.

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The variation in the distance between the bridge pier and abutment (\({d}_{ap}/B\)) leads to changes in the flow cross-section, flow velocity, and shear stress exerted by the flow on the sedimentary bed6. In this research, by examining the interactive effect of the bridge pier and abutment on scour, it was determined that a decrease in the distance between the bridge pier and abutment (\({d}_{ap}/B\)) intensifies the flow velocity between them, leading to an increase in scour depth. According to Fig. 7, the maximum relative scour depth (\({d}_{s\_max}/h\)) at the bridge pier and abutment in the presence of rectangular debris with a relative thickness (\({T}_{d}/h\)) of 0.39 increased by 22% and 16%, respectively, at a relative distance (\({d}_{ap}/B\)) of 0.1 compared to a relative distance (\({d}_{ap}/B\)) of 0.2. This behavior is also consistent with Melville’s findings6; he states that reducing the spacing between structures leads to increased contraction scour and intensified vortex interaction, which can increase scour depth by approximately 20–25%. Furthermore, the results align with studies by Laursen and Toch12, as they demonstrated that the geometry of the pier and abutment and their reduced spacing lead to increased hydraulic forces, consequently raising scour depth by 15–30%12; a trend also observed in this research when comparing the two distances of 0.1 and 0.2. Regarding pier and abutment scour interaction, the findings of Oben-Nyarko and Ettema8 also confirm this behavior. They reported that the placement of a pier in close proximity to an abutment (approximately 0.1 to 0.2 times the pier width) causes the overlapping of horseshoe vortices, increasing combined scour depth by 10–20%3; a trend similar to the current results and the observed scour increase at a \({d}_{ap}\)/B = 0.1 distance. Furthermore, a comparison of the maximum relative scour depth (\({d}_{s\_max}/h\)) for three different shapes of debris (rectangular, semi-circular, and triangular) with relative thicknesses (\({T}_{d}/h\)) of 0.09, 0.19, 0.29, and 0.39 indicates that relative thicknesses (\({T}_{d}/h\)) less than 0.2 have a minimal impact on increasing the maximum scour depth, as these configurations result in limited flow blockage and subdued vortex formation, particularly when debris is placed upstream or near the bed, consistent with experimental observations on submersion ratios and debris elevation39,41,42.

Fig. 7
figure 7

Effect of pier-to-abutment relative distance (\({d}_{ap}/B\)) on maximum scour depth for rectangular debris with different relative thicknesses (\({T}_{d}/h\) = 0.09, 0.19, 0.29, and 0.39) at \({d}_{ap}/B\)= 0.1 and 0.2; (a) bridge pier and (b) bridge abutment.

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These findings highlight the synergistic role of structural proximity and debris geometry in exacerbating local scour under clear-water conditions, where reduced \({d}_{ap}/B\) ratios enhance flow acceleration in the gap, promoting deeper erosion at both pier and abutment locations6,18. The 22% pier scour increase at \({d}_{ap}/B=0.1\) for rectangular debris underscores the pier’s greater sensitivity to contraction-induced downflow, while the 16% abutment rise reflects amplified shear stresses at the nose due to converging streamlines6,40. For lower \({T}_{d}/h (>0.017)\), the negligible amplification aligns with scenarios where debris submersion is insufficient to significantly alter the horseshoe vortex dynamics, leading to scour depths comparable to no-debris baselines39,41.

Table 2 and Fig. 8 illustrate the variations in the maximum relative scour depth (\({d}_{s\_max}/h\)) with respect to changes in the thickness of rectangular debris for two relative distances (\({d}_{ap}/B\)) of 0.1 and 0.2. Observations indicate that the maximum relative scour depth for debris with a relative thickness (\({T}_{d}/h\)) of 0.09 at a relative distance (\({d}_{ap}/B\)) of 0.1, compared to a relative distance (\({d}_{ap}/B\)) of 0.2 between the pier and bridge abutment, increased by 8% at the bridge abutment (\({d}_{s\_max(A)}/h\)) and by 4% at the bridge pier (\({d}_{s\_max(P)}/h\)). These modest increases at low \({T}_{d}/h\) highlight the onset of proximity-induced amplification, where closer spacing (\({d}_{ap}/B=0.1\)) subtly elevates baseline scour through minor flow accelerations, aligning with integrated models that predict 5–10% enhancements in confined channels even under minimal debris loading. At \({T}_{d}/h=0.09\), the 8% abutment increase versus 4% at the pier further underscores this asymmetry, with debris constriction in narrow gaps (\({d}_{ap}/B=0.1\)) disproportionately affecting the abutment due to amplified shear stresses40,41.

Table 2 Maximum relative scour depth (\({d}_{s\_max}/h\)) values in front of bridge pier and abutment in the presence of rectangular debris with different thicknesses (\({T}_{d}/h\)) for relative distances of 0.1 and 0.2 between pier and bridge abutment (\({d}_{ap}/B\)).
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Fig. 8
figure 8

The percentage of maximum relative scour depth (\({d}_{s\_max}/h\)) in front of (a) bridge pier and (b) abutment, in the presence of rectangular debris was analyzed by comparing the maximum scour depths at relative distances (\({d}_{ap}/B\)) of 0.1 and 0.2 of bridge pier from abutment.

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In summary, the interaction between a bridge pier and abutment creates a compounded scour hazard, which is severely exacerbated by the presence of rectangular debris. The key controlling factors are the relative distance (\({d}_{ap}/B\)) and the relative debris thickness (\({T}_{d}/h\)). A smaller distance (0.1) and a larger thickness (exceeding ~ 0.25) represent the worst-case scenario, with the abutment consistently showing greater vulnerability.

While studies such as those by Kandasamy and Melville44 primarily focused on flow intensity and its effect on piers and abutments, with less attention paid to the role of debris , the present research addresses this gap by investigating the shape and thickness of debris, demonstrating that debris with thicknesses exceeding 0.3h has a significant impact on increasing scour [current study]. Furthermore, the results regarding debris shape differences are consistent with the findings of Raikar and Dey45, who emphasized that the geometric characteristics of an obstruction can influence vortex patterns and consequently alter scour depth.

Longitudinal and transverse profiles of scour hole around bridge pier and abutment

The investigation of the scour hole along the flow path is crucial for understanding the scouring mechanism. Measuring longitudinal and transverse profiles of the scour hole and determining the scour volume in laboratory studies helps identify the dimensions and shape of the scour hole, which is useful for the calibration and validation of numerical models. Figure 9 illustrates the longitudinal profiles of scour around the bridge abutment, and Fig. 10 presents the profiles around the bridge pier, located along the upstream and downstream bed relative to the sediment depth, both with and without debris, for a discharge (Q) of 30 l/s.

Fig. 9
figure 9

Longitudinal profiles of scour hole at bridge abutment with and without rectangular debris of various relative thicknesses (located at relative distance of (\({d}_{ap}/B\)) 0.2 from abutment).

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Fig. 10
figure 10

Longitudinal profiles of scour hole at bridge pier with and without rectangular debris of various relative thicknesses (located at relative distance (\({d}_{ap}/B\)) of 0.2 from pier).

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As shown in these figures, the accumulation of debris enlarges scour hole dimensions and results in sediment transport to farther downstream locations. In other words, the accumulation of debris around these structures reduces the flow cross-section, generates stronger horseshoe and wake vortices around the bridge pier and abutment, and leads to larger scour depths. This process causes sediment erosion and transport downstream, as well as increased scour depth. Furthermore, when flow passes through the scour hole, due to the increased flow depth, the Froude number decreases before entering the downstream bed of the scour depth, resulting in less erosion compared to the upstream bed, aligning with experimental findings where downstream profiles show 20–30% reduced erosion due to wake-induced flow deceleration and lower shear stresses. As shown in the cross-sectional profile in Fig. 11, debris accumulation leads to an increase in the dimensions of the scour hole.

Fig. 11
figure 11

Cross-sectional profile of bridge pier and abutment scour depth in the presence of rectangular debris with various relative thicknesses and without debris at the relative distance of (\({d}_{ap}/B\)) 0.2 from bridge abutment.

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Therefore, the scour depth around the bridge abutment is consistently greater than that around the pier due to the formation of stronger vortices in its vicinity.

Figures 12 and 13 illustrate the topography and contour lines of the sedimentary bed after conducting the experiment with rectangular debris at four relative thicknesses (\({T}_{d}/h\)=0.09, 0.19, 0.29 and 0.39), at a relative distance of 0.2 between the bridge pier and abutment (\({d}_{ap}/B\)).

Fig. 12
figure 12

Final topography of sedimentary bed: (a) rectangular debris with relative thickness (\({T}_{d}/h\)) of a) 0.09, (b) 0.19, (c) 0.29 and (d) 0.39 at relative distance of 0.2 between bridge pier and abutment (\({d}_{ap}/B\)).

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Fig. 13
figure 13

Contour lines of sedimentary bed: a) rectangular debris with relative thickness (\({T}_{d}/h\)) of (a) 0.09, (b) 0.19, (c) 0.29 and (d) 0.39 at relative distance of 0.2 between bridge pier and abutment (\({d}_{ap}/B\)).

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The results indicate that the thickness of debris significantly affects the local scour depth. Thicker debris generates stronger vortices around the pier and abutment, which enhance sediment entrainment from the bed and lead to deeper and more pronounced scour holes. These vortices increase turbulent energy near the bed and accelerate sediment transport downstream. Consequently, as the debris thickness increases, the local scour depth also increases. According to the experimental results, the scour holes at the pier and abutment were deepest in the presence of debris with a relative thickness of 0.39, which produced the strongest vortices, while debris with a relative thickness of 0.09 generated the weakest vortices and resulted in relatively shallower scour holes. In particular, the scour hole depth around the pier and abutment increased by about 89.19% compared to the control case in the presence of rectangular debris with a relative thickness of 0.39. For instance, the scour depth at the pier and abutment with debris of relative thickness 0.09 was approximately 60.72% lower than that observed with debris of relative thickness 0.39, consistent with wood debris studies showing low-thickness accumulations (\({T}_{d}/h<0.17\)) producing 50–70% shallower holes due to minimal vortex development . As observed, the scour volume increased with the relative thickness of the rectangular debris (\({T}_{d}/h\)), with the maximum volume occurring at \({T}_{d}/h=0.39\) and the minimum at \({T}_{d}/h=0.09\). The detailed topographic and contour maps (Figs. 12 and 13) are invaluable, as they visually and quantitatively capture the full three-dimensional nature of the scour hole, which is often more critical for structural stability than the maximum depth alone. The evolution of the scour hole’s planform shape with increasing debris thickness, from a localized depression to an extensive, merged erosion zone, clearly demonstrates the escalating risk to foundation integrity.

These profiles and volumes reveal the three-dimensional scour morphology, where debris-induced vortices expand the hole’s upstream extent and downstream deposition, with abutment scour holes showing 20–30% larger volumes than pier holes due to persistent main-channel exposure. The 89.19% depth increase at \({T}_{d}/h=0.39\) underscores rectangular debris’s role in vortex amplification, exceeding smoother shapes by 15–25% in comparable contractions.

Predicting maximum scour depth in the presence of debris

In this study, an empirical equation (Eq. 4) was developed to predict the maximum scour depth around the bridge pier and abutment in the presence of debris, and this equation was derived within the range of the experiments conducted in this research. In formulating this equation, the importance of incorporating the geometric properties of the debris as a key parameter was identified according to the Eq. 3 of the dimensional analysis. Previous studies have also emphasized the significant role of pier-abutment geometry in determining the patterns and intensity of scour.

$$\frac{{d_{s} }}{h} = 0.44\left( {SF} \right)^{0.09} \left( {\frac{{T_{d} }}{h}} \right)^{0.247} \left( {\frac{{d_{ap} }}{B}} \right)^{{\left( { - 0.123} \right)}}$$
(4)

According to this equation, the parameter \(\frac{{d}_{s}}{h}\) has a direct relationship with \(SF\) and \(\frac{{T}_{d}}{h}\), and an inverse relationship with \(\frac{{d}_{ap}}{B}\). SF values for rectangular, semicircular, and triangular debris were considered 1.5, 0.95, and 0.55, respectively (Munson et al., 2021, White, 2456). The derived empirical equation demonstrates high accuracy in predicting the maximum scour depth, with a determination coefficient (R2) of 0.997, indicating excellent agreement with the experimental results.

Table 3 presents a comparative summary of the results of previous studies and the findings of the present study regarding the effects of debris shape, relative debris thickness (\({T}_{d}/h\)), and relative pier–abutment distance (\({d}_{ap}/B\)) on local scour.

Table 3 Comparison of the present study results with similar studies.
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Conclusions

The accumulation of wood and other floating debris upstream of bridge piers and abutments is a critical issue in river and bridge engineering, as it can alter riverbed morphology, intensify localized scour, and compromise the stability of structures. To better understand these effects, this study experimentally investigated the influence of debris thickness and shape on local scour around a bridge pier and abutment, as well as the interactive effects between the pier and abutment in the presence of rectangular debris. Debris with rectangular, semi-circular, and triangular geometric shapes was used, with relative thicknesses (\({T}_{d}/h\)) of 0.09, 0.19, 0.29, and 0.39. The experiments were conducted at two relative distances of 0.1 and 0.2 between the bridge pier and abutment (\({d}_{ap}/B\)). The results demonstrated that debris thickness (\({T}_{d}/h\)) has a significant influence on scour around the bridge pier and abutment. As \({T}_{d}/h\) increases, stronger vortices are generated around the bridge pier and abutment, leading to an increase in the maximum scour depth. Observations revealed that the debris shape significantly affects the scouring process. In descending order, rectangular, semi-circular, and triangular debris created greater scour depths. At a relative distance of 0.1 (\({d}_{ap}/B\)), rectangular debris with a relative thickness (\({T}_{d}/h\)) of 0.24 increased the maximum scour depth (\({d}_{s}/h\)) in front of the bridge pier by 10.71% and 14.81% and at the abutment nose by 1.47% and 4.54%, compared to semi-circular and triangular debris with the same relative thickness, respectively. Furthermore, at the same relative distance of 0.2 (\({d}_{ap}/B\)), rectangular debris with \({T}_{d}/h\)=0.39 increased the maximum scour depth (\({d}_{s\_max}/h\)) around the bridge pier and abutment by 41.67% and 47.27%, respectively, compared to rectangular debris with \({T}_{d}/h\)=0.09. The results also indicated that increasing the distance between the bridge pier and abutment significantly impacts the scour depth volume; as this distance increases, the scour depth volume exhibit a corresponding increase. In the case of rectangular debris with \({T}_{d}/h\)=0.39, the maximum relative scour depth (\({d}_{s\_max}/h\)) in front of \({d}_{ap}/B\)=0.2 increased by 21.42% and 15.71%, respectively, compared to \({d}_{ap}/B\)=0.1. According to the results, the scour depth around the bridge abutment consistently exceeded that observed around the pier, which can be attributed to the formation of stronger vortices in the vicinity of the abutment. The findings demonstrated that the presence of debris in front of the bridge pier and abutment intensifies the scour depth, potentially leading to bridge failure and resulting in significant financial losses and casualties. Therefore, further research is necessary to prevent and mitigate scour development around bridge piers and abutments. Future studies could focus on investigating the influence of woody debris around abutments or groups of piers to provide a deeper understanding of their effects on scour characteristics and flow dynamics.