2.2.1 Reynolds Averaged Navier-Stokes.

For three-dimensional analysis of an incompressible fluid state within the Flow-3D software, the Reynolds-Averaged Navier-Stokes (RANS) equations in the Cartesian coordinate system were employed as outlined by [17]: (1) (2) where t = time, u_i = mean velocity, V_{F =} fractional volume open to flow, x = the coordinate, A_i = fractional area open to flow, G_i = the body accelerations, ρ = fluid density, f_i = the viscous accelerations, p = pressure, and the subscripts i and j refer to the Cartesian coordinate directions (x, y, z).

2.2.2 Turbulence model.

Within Flow-3D modelling, turbulent flow is addressed through five schemes: Prandtl’s mixing length theory, Large Eddy Simulation (LES), Renormalization-Group (RNG), one-equation turbulent energy (k), and the two-equation (k-ε) models as detailed in [16]. Notably, the RNG model, with equations resembling those in the k-ε model, is distinctive for its precision in characterizing flows with robust shear regions and low-intensity turbulence. While air entrainment is assumed to stem from turbulent disturbances at a free surface, for effective turbulence modelling, preference is given to the k-ε or RNG models. In scenarios involving non-laminar flow, as commonly encountered in scour-type simulations, the RNG model is recommended as the primary choice [16].

In this study, both RNG turbulence models were employed for Computational Fluid Dynamics (CFD) simulations using Flow-3D. Noteworthy developments include the recent reformulation of the RNG model. The turbulence eddy, v_t, based on the Boussinesq approximation, plays a pivotal role in solving the turbulence equation [18]. (3) where k and ε are turbulence kinetic energy and dissipation, respectively and C_μ = an empirical coefficient. In the standard k-ε turbulence model, both k and ε are defined by Eqs (4) and (5) [17]: (4) (5) where C₁ and C₂ with corresponding values of 1.44 and 1.92 act as constants in adjusting turbulence dissipation and generation within the ε equation. The RNG model suggests empirical constants σ_k = 1.0 and σ_ε = 1.3 [19]. Taking into consideration the non-flat topography of riverbeds in real-world applications, particularly in the context of sloping surfaces, the critical Shield parameter is modified related to the angle of repose and is presented in Eq (6) according to [20]. (6) where θ’ signifies the critical Shields’ parameter for the onset of particle motion, β represents the slope bed angle, φ indicates the sediment’s angle of repose, and ψ denotes the angle between the upslope direction and the flow. The calculation of the local bed shear stress (τ) is determined by Eq (7): (7) Where ρ_s = the sand density, ρ = the density of fluid, d = the particle diameter, and θ = the Shields’ parameter. The dimensionless bed load transport rate for sediment, as formulated by Meyer-Peter and Muller, is applicable using Eq (8) as detailed by [21].

(8)

The calculation of the volumetric bed-load transport rate (q_b) is determined using Eq (9). (9) where d is the sediment diameter, and in the case of turbulent association, the Shallow Water Flow is applied. Eq (10) is employed to estimate the drag force coefficient concerning flow depth and surface roughness [17]: (10) where k denotes the Von Karman constant (k = 0.40), B is a constant set at 0.71 according to [17], y₀ represents the fluid depth, and [22] assumed k_s as the surface roughness with k_s = 2d₅₀ as specified in [16].

The Volume of Fluid (VOF) and Fractional Area Obstacle Representation Method (FAVOROTM) exemplify volume fraction methodologies. In these techniques, the region is initially subdivided into control volumes or smaller grid elements. An effective means of characterizing element states involves introducing a parameter F, which quantifies the fraction of the element’s volume filled with liquid as detailed in [16]. This function represents the VOF per unit volume and adheres to the following equations: (11) (12) (13)

In this theoretical framework, F_DIF delineates a diffusion term specifically designed for the intricate process of two-fluid mixing. F_SOR signifies the temporal variation of the volume fraction of fluid, intimately linked to the mass source and representing the fractional volume accessible to the flowing medium. R_SOR is identified as a source of mass, while R_DIF is designated as a term accounting for turbulent diffusion. The fractional area open to flow is symbolized as A_x in the x-direction, while A_y and A_z portray analogous area fractions for fluid flow in the y and z directions. The velocity components (u, v, w) are aligned with the coordinate directions (x, y, z) or represented as (r, R_SOR, z), ensuring consistency in the context of spatial orientation.

2.3.1 Experimental setup.

This study used experimental data to assess scour at the outlet of a culvert conducted at the Hydraulics Laboratory of the University of Sulaimani (UoS) in Kurdistan, Iraq. Among the limitations of the present research are the laboratory conditions. In this research, the geometrical parameters of the culvert, including width, length, and longitudinal slope, was considered constant. Also, the width of the channel was fixed. A Perspex flume, measuring 7.9 m in length, 0.7 m in depth, and 0.6 m in width, was utilized with a consistent bed slope of 0.001 and a water recirculation mechanism. The culvert inlet was positioned 4.6 m from the flume inlet to ensure a fully developed flow in the test area. The experimental setup included a sand basin, 4.4 m in length, 0.15 m in depth, and matching the flume’s width. The sands exhibited a median grain size of d₅₀ = 1.1 mm and a geometric standard deviation of σ_g = 2.9 mm, categorizing them as uniform sediment [23, 24]. The sediment was appropriately graded to match the culvert inlet and outlet elevations, and glass material was used for inlet blockages.

This research adhered to Re > 10⁵ to reduce scale effects on scour depth in agreement with [25] and acknowledged that viscous effects diminish beyond Re > 10⁴. The study accounted for the flume width’s influence on scour by maintaining a culvert-to-flume width ratio of 1:3, reflecting insights from [26]. It consistently used fixed culvert dimensions to lessen contraction impacts on scour, focusing on partially full flows and normalized scour depths to gauge effects accurately.

2.3.2 The numerical cases.

In this study, the Flow-3D software version 11.0.4 was used to accurately model experimental scenarios that are currently under peer review. The present study, aimed to bridge the gap between computational predictions and pending experimental outcomes, providing preliminary insights and validations of the simulated models against expected experimental data. This study employed a circular culvert shape, with a barrel length of 1 m and an opening diameter of 0.2 m as shown in Fig 1. To enhance flow stability, both the culvert’s outlet and inlet featured 30° flare transitions [27]. A symmetric hydrograph was adopted to facilitate the conveyance of unsteady flow through the culvert. Under unsteady flow conditions, two different hydrographs were created, and the maximum flow rates from each hydrograph were used as steady cases for the equivalent duration. The hydrograph was generated for both unsteady and steady clear water flow scenarios, comprising nine distinct flow discharges. The duration of each step in the first hydrograph (Q_m = 22 l/s) was 40 minutes, while the second hydrograph (Q_m = 14 l/s) spanned 25 minutes. In cases of partial blockage, the submerged upstream and downstream areas of the culvert could induce a transition from supercritical to subcritical flow near its terminus. The culvert’s capacity determined the maximum flow in the hydrograph. Table 1 provides comprehensive details on the numerical cases conducted in this research.

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Fig 1. Detailed view of culvert with blockage rates.

https://doi.org/10.1371/journal.pone.0312501.g001

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Table 1. Numerical cases.

https://doi.org/10.1371/journal.pone.0312501.t001

The values of critical shear velocity () and critical flow velocity (V_c) were presented based on the equations proposed by [23]. These equations are as follows: (14) (15) where y_w is the water depth. The critical shear velocity, for all cases, depends on the sediment size (d₅₀) and flow depth. In all the test the critical shear was more than the shear velocity and clear water condition was achieved

2.3.3 Model scale.

In the context of the model scale, experiments with small-scale models, as noted by [28], often fail to precisely calculate maximum scour depth, yielding unreliable results. Conversely, large-scale experiments can incur high laboratory costs and facility requirements and might also lead to contraction scour. To mitigate scale effects on scour depth, this research specifically utilized data with Reynolds number R_e >10⁵, following the approach outlined by [25]. It is noteworthy that beyond R_e >10⁴, viscous effects become insignificant, making the Reynolds number a critical factor for reliable results, as emphasized by [28].

2.3.4 Culvert geometry and grid construction.

In utilization of unstructured meshes in a classical culvert setting, typically characterized by a horizontal rectangular channel, becomes particularly advantageous in regions where large gradients of flow parameters are expected. This allows for selective refinement of specific areas, as noted by [29]. While acknowledging the generally lower precision of unstructured meshes, emphasized by [30, 31], their algorithms contribute to reduced latency in simulations and ensure more regular memory access [32]. In the context of multiphase flows, the use of topologically orthogonal meshes tends to minimize numerical issues. Hence, in this study, a structured rectangular hexahedral mesh was deemed more suitable for the problem. Mesh generation, facilitated by the FAVOR technique with orthogonal meshes defined in Cartesian coordinates in Flow-3D, was employed for the complex model shapes. Through trial and error, the mesh dimension of 0.015 m mesh size was decided upon in the x, y, and z directions to strike a balance between the total number of cells and the desired quality and accuracy in the results. Fig 2 illustrates the model coordination and geometry meshing.

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Fig 2.

Depiction of a) the model coordination and geometry meshing. b) boundary conditions. c) Flow visualization with the vortex’s direction and streambed degradation.

https://doi.org/10.1371/journal.pone.0312501.g002

2.3.5 Boundary conditions.

The governing equations for fluid flow motion fall under the category of initial boundary values. This implies that the solution must be determined at both the initial time and the boundary. In establishing the scour model, Fig 2 illustrates the boundary conditions, where a specified flow rate is set at the inlet, the outflow is set at the outlet, and the top side is designated with a specified pressure. The right and left sides, in addition to the bottom side are defined as wall boundaries [9].

2.3.6 Flow pattern and scour formation.

The prediction of localized scour geometry at the culvert outlet is a crucial element in the culvert design process, guiding decisions on erosion protection. Fig 2 presents both a 3D and side view of the streambed, providing insights into scour formation and flow interaction at the culvert outlet under a flow rate of 10 l/s, utilizing the RNG equation. The observed direction of vortices contributes to an initial understanding of the flow structure within scour holes. Notably, as the scour phenomenon intensifies, an increase in vortices at these locations occurs, influencing the overall flow rotation appearance.

2.3.7 Error measurement.

In this research, the accuracy of the numerical model was rigorously assessed using various statistical indicators. To accomplish this, the simulated values of scour depth were compared with the corresponding experimental data. These comparative analyses enabled to identify how closely our model’s predictions aligned with observed results from experimental tests. The correlation coefficient (R²), root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) represented by Eqs (14)–(17) were used to model the evaluation [33]. (16) (17) (18) (19) where n, P_i, O_i, and are respectively the number of data, the value of scour depth or location in the numerical model, the corresponding observed values, the average numerical model data, and the average observational data. The value of R is always between -1≤ R ≤1 and as R was close to +1, the accuracy of the model was optimal. To measure the confidence of the model’s prediction of the observed data, the MAE was used as a common indicator. The sample standard deviation of the differences between simulated values and experimental data is presented by RMSE. The lower the MAE and RMSE values, the better the model performance. The MAPE calculates the average absolute error to show the accuracy of a forecast system.

3.1.1 The first hydrograph.

A study was conducted to confirm the precision of the numerical model through a comparison between experimental observations of bed scour and the outcomes from numerical simulations. Fig 3 illustrates the formation of scour profiles for both experimental and numerical data downstream of the circular culvert, blocked or unblocked, at various flow rates under conditions of unsteady flow achieved through the application of RNG.

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Fig 3.

Scour profile for the first hydrograph: a) non-blocked, b) 15% blocked, and c) 30% blocked. (r, m, and f represent raising limb, maximum flow rate, and falling limb of the hydrograph, respectively).

https://doi.org/10.1371/journal.pone.0312501.g003

Fig 3(A) displays the case of a completely open culvert, where the flow rate begins at Q_r = 6 l/s, climbs to a peak of Q_m = 22 l/s, and subsequently decreases back to Q_f = 6 l/s. In this illustration, both the observed and numerical data at the initial flow rate of Q_r = 6 l/s demonstrates sufficient flow to displace sediment. The deepest scour observed experimentally was near 0.066 m, compared to the numerical finding of approximately 0.0623 m, suggesting a reduction in the observed data’s culvert change rate by approximately 5.6%. The increase in scour depth, as noted in both the experimental and numerical data, corresponded with each incremental rise in discharge rate. The observed data identified the largest scour depth at a reduced flow rate of Q_f = 14 l/s, reaching approximately 0.111 m, whereas the numerical data observed its maximum at a decreased flow rate of Q_f = 6 l/s, marking a depth close to 0.108 m. This outcome indicates that the maximum scour depth measured experimentally was 2.7% greater than that determined numerically.

Fig 3(B) depicts the change in scouring due to a blockage at the inlet of 15%. A comprehensive examination of the scour profiles indicated that at the outset of the stepwise analysis, there was a notable similarity between the data obtained from experiments and that derived from numerical simulations. As the analysis proceeds through subsequent stages, a divergence was observed; the experimental data began to show a considerable deviation from the initial results, while the numerical data exhibited consistency and alignment with the ongoing changes in scour patterns. This observation highlights the complexities involved in accurately capturing the dynamics of scouring processes and underscores the importance of integrating both experimental and computational approaches for a thorough understanding. Within the observed data, the continuity of maximum scour depth progressively rises until reaching a Q_f = 18 l/s, after which it slightly declines. Conversely, in numerical data, this measure continues to ascend steadily up until the final phase of the hydrograph at Q_f = 6 l/s. For both the observed and the simulated data, the peak scour depth was noted at a flow rate decline, with the values reaching approximately 0.119 mm at Q_f = 18 l/s and approximately 0.118 mm at Q_f = 6 l/s, respectively. The data showed a variation rate of approximately 0.84% when comparing the observed data and the numerical data.

Fig 3(C) illustrates the scour pattern resulting from a 30% blockage at the inlet. In this scenario, both the experimental and numerical data indicate an increased level of scour at the culvert’s outlet when compared to prior instances. The size of the scour hole showed a direct correlation with variations in flow rate. Similarly, to the 15% blockage scenario, the depth of scour for the 30% blockage also exhibited greater similarity in later steps than in the initial step for experimental data, whereas the numerical data-maintained consistency and closely followed the changes in scour patterns as the flow rate increased. The deepest scour recorded, both in the observed and numerical data, was at the end of the hydrograph with a Q_f = 6 l/s, measuring 0.132 m and 0.127 m, respectively.

The overall dataset revealed that scour occurrences were more pronounced in the experimental data than in the numerical data. Concerning maximum scour depth, the simulation data showed that a 30% obstruction led to an increase of approximately 6.8% and 14.2%, relative to conditions of a 15% blockage and an unobstructed flow, respectively. This indicates a notable enhancement in the progression of the scouring activity [9, 10].

3.1.2 The second hydrograph.

Fig 4 presents the variation of the scour profile for observed and numerical data at the circular culvert outlet under unsteady flow conditions. The analysis considered experiments with both nonblocked and blocked cases. The second hydrograph has a symmetrical pattern, commencing at a flow rate of Q_r = 2 l/s, reaching a peak rate of Q_m = 14 l/s, and declining to Q_f = 2 l/s.

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Fig 4.

Scour profile for the second hydrograph: a) non-blocked, b) 15% blocked, and c) with 30% blocked.

https://doi.org/10.1371/journal.pone.0312501.g004

Fig 4(A) illustrates the scour pattern observed in the case of a culvert that is fully open. Upon examining the data across various stages of the hydrograph, a comparison between the observed and numerical datasets reveals that the profiles of scouring are remarkably similar to one another. This similarity suggests a consistent correlation between the experimental observations and the numerical simulations throughout the different phases of the hydrograph analysis.

At the initial stage of the hydrograph analysis, an increase in scour profiles is evident in both observed and simulated data, coinciding with a rise in flow rate. The experiment recorded the maximum scour depth at a flow rate of Q_m = 14 l/s, achieving roughly 0.08 m. Conversely, the simulation indicated the deepest scour at the final flow rate of Q_f = 2 l/s, with a depth of approximately 0.098 m. This comparison reveals a disparity in the rate of change, amounting to about 18.4%, between the experimental and numerical results.

Fig 4(B) displays the scour profile resulting from a 15% blockage at the inlet. Throughout the various stages of the hydrograph, specifically at the initial first three flow rates of Q_r = 2, 5, and 8 l/s, the observed data’s scour profiles and those from the numerical analysis follow one another sequentially. However, as the hydrograph progresses beyond these initial rates, the pattern of change continues for the numerical data, whereas in the experimental observations, the outcomes of subsequent stages diverge significantly from the first three flow rates. The deepest scour occurred at an increasing flow rate of Q_r = 11 l/s, reaching almost 0.108 m, whereas, in the numerical analysis, the greatest scour depth was observed at the final flow rate of Q_f = 2 l/s, measuring approximately 0.114 m. This demonstrates that the maximum scour depth in the numerical data exceeded that observed in the experimental data by 5.26%.

Fig 4(C) presents the scour profile for a 30% inlet obstruction. In this scenario, the scouring pattern is similar to the one observed with a 15% blockage, particularly at the onset of the hydrograph for flow rates Q_r = 2 and l/s, where the numerical and observed data are closely aligned. Beyond these initial rates, the experimental data demonstrates a marked deviation from the first couple of stages, a contrast not evident in the numerical data. Here, the numerical data consistently reflects an increment in scour depth proportional to the flow rate, without significant deviation between stages. In instances of a 30% inlet blockage, the greatest scour depth recorded in the experimental setup occurred at a flow rate of Q_f = 5 l/s, reaching approximately 0.135 m, whereas the numerical simulations showed the maximum scour depth at a flow rate of Q_f = 2 l/s, reaching approximately 0.126 m. This comparison reveals that the experimental data’s maximum scour depth exceeded that of the numerical data by 6.7%.

The comparative analysis of the observed and numerical data showed that in scenarios with no blockage and with a 15% blockage, the numerical measurements of maximum scour depth exceeded those from the experimental data. Conversely, with a 30% blockage, the experimental data revealed a greater maximum scour depth compared to the numerical data.

Further analysis highlighted the significant impact of a 30% blockage, as observed in the second hydrograph, on the development of scour profiles. This effect was more pronounced than in unblocked or 15% blocked conditions. In numerical assessments, the depth of scour for a 30% blockage exceeded those of no blockage and a 15% blockage by 22% and 9.5%, respectively. Moreover, experimental observations recorded the deepest scour holes in the 30% blockage scenario, surpassing those in unblocked and 15% blocked conditions by 41% and 20%, respectively [9, 10].

Table 2 provide a detailed evaluation of the upstream (h_u) and downstream flow depths (h_d), Froude Number (F_r), Densimetric Froude Number (F_rd), critical flow velocity (V_c) and the maximum scour depth (d_sm) and its location (X_sm) for the culvert under the first and second hydrograph’s unsteady flow conditions.

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Table 2. Numerical tests condition for unsteady conditions.

https://doi.org/10.1371/journal.pone.0312501.t002

The data show that downstream measurements of F_r and F_rd are consistently higher than upstream, regardless of whether the culvert is non-blocked, a 15% blockage, or a 30% blockage. This indicates a significant enhancement in hydraulic activity after the water passes through the culvert, a trend that remains constant across all blockage conditions, reflecting stable and increased fluid dynamics downstream.

The analysis of critical flow velocities for different discharge rates reveals important insights. For a maximum discharge Q_m = 22 l/s, the critical velocities ranged from 0.24 m/s to 0.30 m/s upstream and from 0.10 m/s to 0.24 m/s in downstream. In comparison, for a Q_m = 14 l/s, the critical velocities were between 0.20 m/s and 0.29 m/s upstream and between 0.13 m/s and 0.27 m/s downstream. These results indicate that higher discharge rates result in higher critical velocities upstream, suggesting a reduction in flow energy downstream. For lower discharge rates, the critical velocities are more consistent between upstream and downstream locations. This pattern underscores the need to consider both discharge rates and flow depths when evaluating critical flow velocities to understand their impact on scour processes around culverts, ultimately aiding in the design of more stable hydraulic structures.

3.3.1 First hydrograph.

The depth and location of the scour at the outlet of a culvert play a pivotal role in determining culvert design and safety [10].

Fig 6 offers a comparison of the deepest scour depths recorded in both physical and numerical studies within circular culvert formations under unsteady flow conditions for the first and second hydrographs at different rates of blockage. To standardize the maximum scour depth, the d_s/d_sm ratio was utilized, where d_s signify the scour depth and d_sm represents the highest scour depth observed. The peak d_sm is noted at t = 360 minutes, starting with an initial flow rate from Q_r = 6 l/s to Q_m = 22 l/s, before decreasing back to Q_f = 6 l/s for the first hydrograph. For the second hydrograph, the flow begins at Q_r = 2 l/s, peaks at Q_m = 14 l/s, and then decreases to Q_f = 2 l/s.

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Fig 6. Comparison of d_sm between observed and numerical data (Q_m = 22 l/s).

https://doi.org/10.1371/journal.pone.0312501.g006

In Fig 6, regarding the first hydrograph with Q_m = 22 l/s, in the case of an unblocked inlet culvert, the variation rates between physical and numerical data across the entire flow range, from the initial rise at Q_r = 6 l/s to the peak Q_m = 22 l/s, and the decrease to Q_f = 6 l/s were recorded as 5.3, 18, 20, 11, 8.3, 8.2, 6.8, 2.8 and 2.0%, respectively. This pattern indicates that in every scenario, the d_sm values obtained from physical measurements exceeded those recorded in the numerical data.

With a 15% blockage at the inlet, the analysis of the d_sm rate differences between the physical and numerical datasets for a 15% blockage revealed that in the initial three ascending steps at flow rates of 6, 10, and 14 l/s, numerical data exceeded physical data by margins of 3.5%, 1.9%, and 1.7%, respectively; and for the latter two descending steps at 10 and 6 l/s, the numerical data exceeded the physical data by margins of 3.3% and 2.9%. In contrast, physical d_sm values surpassed numerical ones at flow rates of Q_r = 18 l/s, Q_m = 22 l/s, and Q_f = 18 and 14 l/s by 7.2%, 6.9%, 7%, and 1.5%, respectively.

For a 30% inlet obstruction, both observed and calculated data demonstrated a steady escalation in d_sm. The rate of change in d_sm between the physical and numerical data revealed that for all flow rates, the physical data results surpass those from the numerical analyses. During the increase in flow rates at 6, 10, 14, 18 l/s up to the maximum of 22 l/s, the variation percentages were approximately 15.8, 13.7, 5.2, 6.3, and 8.1%, respectively. This trend of differential rates continued into the decreasing flow phases of 18, 14, 10, and 6 l/s, with respective discrepancies of approximately 5.7, 5.5, 1.2%, and 4%.

To summarize, the collective findings from both the physical and numerical data demonstrate that heightened inlet blockage corresponds to increased d_sm values. The condition of a 15% blockage yielded deeper scour depths than those observed in unobstructed scenarios, and a 30% blockage condition further amplified scour depths beyond both the unblocked and 15% blocked scenarios. These outcomes highlight the complex interplay between flow rate and blockage degree in determining scour formation [9, 10].

3.3.2 Second hydrograph.

Fig 7 illustrates the maximum scour depth (d_sm) from both physical and numerical data against varying blockage intensities captured at t = 225 minutes. This encompasses a flow rate beginning at Q_r = 2 l/s, peaking at Q_m = 14 l/s, and subsequently diminishing to Q_f = 2 l/s within the framework of the second hydrograph.

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Fig 7. Comparison of d_sm between observed and numerical data (Q_m = 14 l/s).

https://doi.org/10.1371/journal.pone.0312501.g007

In the scenario of a circular culvert analysed through an identical stepwise hydrograph, escalating inlet blockage rates invariably resulted in increased scour depths. For instance, in scenarios without blockage, the analysis comparing physical to numerical data revealed that across all stages of the hydrograph, the numerical maximum scour depth (d_sm) values exceed those of the physical data. The variance in percentages for the ascending phases from Q_f = 2 l/s to Q_m = 14 l/s is approximately 0.4, 23, 16, 6.7, and 10.9%. This trend of increase persists through the subsequent phases of the hydrograph, concluding at Q_f = 2 l/s with differences noted at 14.1, 19.8, 18.5, and 19.7%.

With a 15% blockage at the inlet of the culvert, in the comparative analysis of physical versus numerical datasets across equivalent progressive stages for flow rates transitioning from Q_r = 6 l/s to Q_m = 14 l/s and then to Q_f = 8 l/s, the physical dataset exhibited a higher incidence of d_sm than the numerical dataset, with differences in percentages noted at 7.4, 8.0, 12.4, 1.7, 0.4, and 1.3%, respectively. Conversely, for the subsequent flow rates, the numerical dataset demonstrated greater d_sm accuracy than the physical data, particularly at Q_f = 5 and 2 l/s, with variances amounting to 5.9% and 8.5%, respectively.

When evaluating the impact of a 30% obstruction at the inlet, the comparison of d_sm percentages between actual observations and modelled data shows that d_sm events were more frequently recorded in the experimental data across all incremental stages of the hydrograph. Evaluating the changes from Q_r to Q_m and then to Q_f, the differences were noted at 18.5%, 21.3%, 9.3%, 8.2%, 7.9%, 7.7%, 8.2%, and 6%, respectively, with the greatest discrepancy observed when the flow rate was at Q_r = 5 l/s.

In conclusion, the aggregated data from both the experimental and computational analyses reveal a direct correlation between increased inlet obstruction and elevated d_sm values. Scenarios with a 15% inlet blockage resulted in greater scour depths compared to conditions without any blockage. Furthermore, a blockage of 30% intensified the scour depths even more, surpassing both the unobstructed and 15% obstruction cases. During the d_sm analysis comparing experimental to computational data, it was found that under no blockage conditions, the computational data was higher. However, with a 15% obstruction, the experimental data surpassed the computational data, except at the final two stages of the hydrograph. Moreover, under a 30% obstruction, the experimental data exceeded the computational findings [9, 10].