Abstract
Scour around bridge piers threatens bridge stability. This study uses the Hydrologic Engineering Center River Analysis System to improve depth estimates for various pier shapes. The Colorado State University and Froehlich equations were tested with a one-dimensional model calibrated for circular, square, rectangular, oblong, oval, and cylindrical piers. Sensitivity analysis identified coefficients K2, K3, flow velocity, and depth as key factors, with K2 being most significant. The Colorado State University equation overestimated scour depths, especially for square piers. The Froehlich method provided more accurate predictions, confirming the system's value in hydraulic modeling for bridge stability analysis.
1 Introduction
A sediment scour occurs when water passes around an obstruction within a body [1]. Thus, this phenomenon has damaged the foundations of structures like spillways, bridges, and weirs, making them more prone to erosion that could lead to structural collapse. Three types of scours typically affect rivers and hydraulic structures. The phrase “long-term aggradation and degradation” could mean either deterioration or slow but perceptible changes in bank height and configuration due to geomorphic processes occurring over a long time. Additionally, contraction scour can occur because of natural or artificial features like river embankments or bridge openings that restrict flow rates. Moreover, inside a river's main channel and valley, some piers and abutments cause local scour around bridge foundations [2, 3]. In addition, according to K. Wardhana and F. C. Hadipriono [4], many bridges have been washed away recently by erosion around their piers. The main goals were to identify the causes of pier scour and to develop new methods to protect bridges from its effects. According to P. F. Lagasse and E. V Richardson [5], 1,000 bridges in the US have collapsed in the last 30 years, with 60% of those collapses caused by hydraulic failure. Namely, foundation scours. River flooding is the primary cause of local scouring around bridge piers and abutments, according to the research of G. J. C. M. Hoffmans and H. J. Verheij [6], leading to bridge collapses. Since the 1950s, there have been many studies on scouring bridge piers. Nevertheless, understanding the complex flow patterns, scouring processes, bridge geometry, and the presence of different erodible bed materials like gravel, sand, and clay remains a challenging problem [7]. Promoting a better understanding of scour's origins and developing modern technologies for identifying scour are crucial steps toward mitigating its detrimental impacts. Overestimating construction costs results in high costs, whereas underestimating the equilibrium of scour depth may cause bridge collapse at any time [8]. Scientists conducted significant testing and computational analysis to determine the extent of erosion in various soil components. More studies have refined the equations [9–16] to determine better scour depth. Academics have long used simulation modeling software to predict the scouring depth around bridge piers [17]. This study examines local scour around bridge piers using dry silver paint, wet paint, and Computer Fluid Dynamic (CFD) techniques, comparing results with past research. The findings provide insights into side-by-side pier arrangements' scour mechanisms and drag forces. These software alternatives are adapted to realize a range of modeling needs. However, limitations in time and data availability make it difficult to choose the best application. Scour depths and possible dangers have been assessed in several studies using the HEC-RAS software [18–22]. HEC-RAS is software developed by the US Army Corps of Engineers for hydraulic modeling. It simulates water flowing through rivers and channels, providing tools for steady and unsteady flow calculations, sediment transport, and water quality modeling [23]. Recent research has demonstrated the effectiveness of HEC-RAS in predicting scour depth for parallel bridges, showing significant variations in scour profiles based on bridge configurations and flow conditions [21]. The Galala Bridge Scour Model [24] research investigates the impact of scouring on the bridge's structural integrity over Ambon's Way Ruhu River. The study uses the HEC-RAS 6.4.1 application to evaluate scouring depth using the Colorado State University CSU and Froehlich methods. Based on various flow conditions and recurrence periods, the simulation results indicate that the scouring depth could reach the base of the bridge, potentially compromising its stability and leading to collapse during significant flood events [24]. The HEC-RAS software [25] was used to compute the local scours near bridge piers during large discharge events with extended return durations. This study shows a combination of factors, like high river discharge and velocity and increased vortex flow around the piers, which cause scouring in the lateral piers of the bridge. According to [26], by using the HEC-RAS model, highly accurate predictions can be made on pier scour depth. In supporting this conclusion, both the results of the Babylon Bridge test and those produced by the HEC-RAS program were in concurrence. These studies have shown how important it is to consider pier dimensions, flow parameters, and sediment quality to estimate scouring depth accurately. Utilizing empirical correlations coupled with the HEC-RAS tool, it is feasible to approximate scouring depths and give the best strategies for making bridges more resistant to scouring. The 1D Model simplifies data entry and results display through its user-friendly interface; hence, it is useful in predicting scour depths around bridge piers. In addition, it accurately forecasts local scour near the pier bases. It would be possible to save a considerable amount of money on the construction of bridge foundations if the depth of scour could be estimated during the design stage. Predicting scour depth with high accuracy enables pre-emptive actions to be implemented cheaply [19, 27]. However, the system can only consider what happens if the pier structure blocks hydraulic flow. Consequently, local differences in the orientation angle considerably influence the measurement of the scour depth [28]. Notable among this program's features is its capacity to model one-dimensional channel flow dynamics. This study focuses on improving the accuracy of scour depth predictions close to bridge piers of varying forms using the widely used hydraulic modeling program HEC-RAS. Experimental data in reference [29] form the basis of the study. A one-dimensional model shows how well the software-integrated CSU and Froehlich equations can determine the scour depth for round, square, rectangular, diamond, oval, or cylinder-shaped piers. Using the Monte Carlo technique, a sensitivity analysis was conducted to determine which factors in the CSU equation impact the pier scour depth findings.
2 Experimental data
Data collection uses the experimental model of [29] as the primary data source, and an accurately sized flume was used for laboratory testing with precise measurements of 12.50 m in length, 0.3 m in breadth, and 0.5 m in depth. Accurate flow measurements were obtained using a volumetric flow meter with 1% precision and an integrated electronic gauge within the flume discharge system. This provided 0.05% accuracy with an average flow velocity of 0.29 m s−1 and flow depth of 0.12 m. The time spent doing each experiment was six hours. Figure 1 shows the channel dimensions and a plan view of the flume. For this investigation, a sand bed that was 15 cm thick was used, and it was smoothed before every observation. According to the sieve analysis, the sediments' median diameter (D50) was 0.93 mm, and the gradation factor (σ) was 1.27. Six pier configurations, namely cylindrical (C), square (S), rectangle (Re), diamond (D), oval (OV), and ogival (OG), were examined. Standardized dimensions of 2.5 cm in width were maintained for all shapes except cylindrical, square, and diamond configurations. The oval, rectangle, and ogival shapes had a consistent length of 10 cm, as it is shown in Fig. 2.
3 HEC-RAS 1-D model
4 Hydraulic modeling process
This study utilized HEC-RAS to predict the water level profile and scour depth around bridge piers. For this purpose, the required hydraulic and hydrological data were used. The experimental configuration had a flume of 12.5 m long, 0.3 m wide, and 0.6 m deep. The pier was positioned eight meters away from the upstream end, as it is shown in Fig. 3. The data necessary for modeling was gathered at precise time intervals and included topographic maps generated in AutoCAD. The maps enabled the creation of precise canal cross-sections before and after pier placement.
Figure 4 shows the procedure of the approach methodology used for the 1D HEC-RAS hydraulic model. The input data in HEC-RAS included cross-sectional profiles, bed slope, Manning's roughness coefficient, and discharge values. Additional inputs included coefficients for flow expansion and contraction and the geometric characteristics of the pier and flume configuration. HEC-RAS operates on the assumption that flow contraction occurs when the downstream velocity exceeds the upstream velocity. For slight river cross-section changes the expansion coefficient was set at 0.3 and the contraction coefficient at 0.1. The values used were 0.3 and 0.5 to represent extreme shifts, particularly near bridges. By determining the hydraulic functioning of the bridge, the model derives appropriate equations. Experimental conditions are accurately presented through this system's Graphical User Interface (GUI) to remove extra hydraulic data input and alteration. The HEC-RAS model included pier scouring and sediment transport equations, validated using empirical measurements. Manning's roughness coefficient and slope geometry were adjusted to calibrate this model correctly. These changes ensured that water levels and scour depths at different sections corresponded precisely. HEC-RAS water level estimations and scour depths were compared with experimental flume data for verification purposes. This comparison confirmed that the model accurately reproduced the flowing sand/flow/pier design complex, thus demonstrating its trustworthiness in terms of accuracy. The model parameters were modified whenever inconsistencies occurred during this validation process to align the findings with the experimentally acquired data. By measuring cross sections at regular intervals, it was possible to estimate the carrying capacity for laboratory flumes along a channel due to its smaller size. The model needed a standard depth, bed slope, flow resistance factors, and precise channel geometry to replicate uniform flow conditions accurately. The bridge's geometric data, including its location on the canal, were inputted into HEC-RAS to depict the experimental model accurately. The HEC-RAS bridge model assigned a certain proportion to each of the six pier types: circular, square, diamond, rectangular, oblong, and ogival. The energy equation has variables like river height, water depth, mean flow velocity, acceleration due to gravity, and energy head loss that were employed to find water surface profiles across consecutive cross-sections. Expansion, friction, and contraction losses have been accounted for, allowing the calculation of head losses between cross-sections. Losses of this kind were calculated using Manning's equation, which is based on the hydraulic radius, flow area, discharge rate, and roughness coefficient. Manning's roughness coefficient is the resistance of a channel bed to water flow, typically ranges from 0.010 to 0.016 for very smooth surfaces like glass to rougher surfaces like alluvial channels with giant dunes. Various academic sources support this range as [32, 33]. Additionally, uniform and steady flow conditions, where velocity is constant and the channel is consistent, might also warrant a lower Manning's n because of reduced turbulence and resistance. A lower coefficient might be appropriate in scenarios with higher velocity flow over smooth surfaces as the water interacts less with surface roughness. Several Manning n values were studied concerning a bridgeless open-channel model, emphasizing average velocities at the mid-channel where the bridge existed. Notably, there was a significant difference between observed average velocities and those estimated.
5 Results and discussion
5.1 The pier scouring depth
Predicting the depth of erosion that occurs at diverse pier designs, for example the cylindrical, square, rectangular, diamond, oval, and ogival shapes, is an essential technique in understanding the hydraulic behavior of bridge construction. It applied Froehlich equations and integrated CSU with HEC-RAS software to better understand scouring depth under uniform flow conditions. As it is shown in Fig. 5, the results demonstrate significant diversity among pier shapes. The CSU method accurately predicted the measurement of square piers (5.94 cm), nearly matching the experimental value (6.00 cm). However, the Froehlich approach underestimated the scour depth, measuring 4.64 cm. The experimental value for cylindrical piers was estimated at 4.60 cm; however, the CSU technique expected it to be 5.40 cm, suggesting an overestimation. The Froehlich approach consistently underestimated the erosion depths for different pier designs, like oval and ogival piers. Though the Froehlich approach yielded lower estimations, experimental and CSU methodologies demonstrate considerable agreement regarding rectangular piers. The diamond-shaped pier indicated a scour depth of 5.50 cm from the observed method, while it showed a more excellent value of 6.70 cm by the CSU scheme. The results show significant variation in computational methods for estimating scour depth among different computational methods and designs of piers. However, this procedure superimposes the outcomes of tests despite its limitations, as the Root Mean Squared Error (RMSE) = 1.1 and Nash-Sutcliffe Efficiency (NSE) = −0.3 for the CSU technique. On average, it overestimates the one, which is indicated by Mean Absolute Percentage Error (MAPE) = 24%. This is especially obvious in design cases, where safety should be prioritized. However, with an RMSE of 0.7, a Nash-Sutcliffe efficiency of 0.49, and a mean absolute percentage error of 12%, the Froehlich equation (which is famous for being conservative) was able to show remarkably accurate results. In summary, the CSU method has lower accuracy on NSE and RMSE than the Froehlich method, implying that it provides accurate estimates and aligns well with data. Conversely, using its higher MAPE, the CSU approach tends to exaggerate scouring depths for safety reasons. These findings indicate that while each approach has its strengths and weaknesses when computing scour depth in this case, the best technique would be Froehlich's method instead, which is consistent with other research findings [19, 20, 28, 34, 35]. Therefore, sensitivity analysis is essential to determine pier design and flow characteristics presently not considered by existing models and accurately predict scouring depths around bridge structures.
5.2 Sensitivity analysis
The Monte Carlo simulation technique can assess the uncertainty and sensitivity of variables constituting a one-dimensional HEC-RAS CSU equation. This method entails producing several random samples for each parameter, accounting for their anticipated distributions, and then computing the respective scour depths. Analyzing the obtained data can provide information about the variables' sensitivity, the model's resilience, and the estimate's margin of error. This study primarily concentrates on various pier forms, with a particular emphasis on cylindrical piers. The study starts by selecting correlated variables, namely.
The histogram (Fig. 8) displays the frequency distribution of the scour depth measurements. The distribution exhibits approximate normality, peaking ate 5.5 cm. This peak represents the prevailing scour depth values recorded in the data. The distribution's spread indicates that although values are clustered around the average, there is also a substantial range of scour depths, emphasizing the presence of variability. The variability is crucial for comprehending the spectrum of potential results and the corresponding hazards in projections of scour depth.
The research identifies the best parameter combination that minimizes error percentages via an iterative process directed by the optimization objective function. To determine the global ideal combination, it is necessary to conduct 1,000,000 simulations, each representing a distinct combination of parameters, with the error threshold set at ±2%. This combination produces the optimum model performance with a minimal error of −0.013 percent. Consequently, the reliability and precision of the computational model for estimating the scour depth around cylindrical piers were enhanced. Subsequently, Fig. 9 (modified from Fig. 3) was generated after employing the optimal values of the variables.
6 Conclusion
This study demonstrates that the HEC-RAS software effectively estimates erosion around bridge piers with specific design features. Based on the CSU equation, a comprehensive sensitivity analysis using the Monte Carlo method identified that the parameters K2, K3, flow depth, and velocity significantly impact scour depth predictions, with K2 showing the highest sensitivity. The results revealed notable differences between the CSU and Froehlich methods, with the CSU method generally overestimating scour depths, while the Froehlich method proved more conservative and realistic. The iterative optimization process, involving 1,000,000 simulations, substantially improved model accuracy, reducing the estimation error to 20%, RMSE to 0.6, NSE to 0.62, and MAPE to 11%. This optimization highlighted the effectiveness of the Froehlich method and the enhanced reliability of the HEC-RAS model. The study emphasizes the critical need to thoroughly analyze pier designs and hydraulic flow parameters to predict scouring depths accurately. The improved HEC-RAS modeling tool provides valuable insights for refining scour prediction techniques and enhancing bridge design and safety. However, the study has limitations. Calibration assumptions may compromise the model's accuracy and perform poorly under extreme flow conditions or highly variable sediment transport, which were not thoroughly investigated. Future research should address these limitations by expanding the model's application to various pier configurations and complex hydraulic conditions. Incorporating real-time data could further enhance the model's predictive accuracy and reliability. Addressing these areas will improve HEC-RAS's utility in bridge design and hydraulic engineering.
Funding
This research was funded by Széchenyi István University.
References
- [1]↑
B. W. Melville and A. J. Raudkivi, “Flow characteristics in local scour at bridge piers,” J. Hydraul. Res., vol. 15, no. 4, pp. 373–380, 1977.
- [2]↑
N. P. Cheremisinoff and S. L. Cheng, “Hydraulic Mechanics 2, Civil Engineering Practice,” Technomic Publ. Company, Lancaster, Pennsylvania, USA, 1987.
- [3]↑
A. J. Raudkivi, “Functional trends of scour at bridge piers,” J. Hydraul. Eng., vol. 112, no. 1, pp. 1–13, 1986.
- [4]↑
K. Wardhana and F. C. Hadipriono, “Analysis of recent bridge failures in the United States,” J. Perform. Constr. Facil., vol. 17, no. 3, pp. 144–150, 2003.
- [5]↑
P. F. Lagasse and E. V Richardson, “ASCE compendium of stream stability and bridge scour papers,” J. Hydraul. Eng., vol. 127, no. 7, pp. 531–533, 2001.
- [7]↑
P. F. Lagasse, Effects of Debris on Bridge Pier Scour, vol. 653, Transportation Research Board, 2010.
- [8]↑
F. C. K. Ting, J. L. Briaud, H. C. Chen, R. Gudavalli, S. Perugu, and G. Wei, “Flume tests for scour in clay at circular piers,” J. Hydraul. Eng., vol. 127, no. 11, pp. 969–978, 2001.
- [10]
B. W. Melville, “Local scour at bridge sites,” PhD Thesis, University of Auckland, School of Engineering, 1975.
- [11]
H. N. C. Breusers, G. Nicollet, and H. W. Shen, “Local scour around cylindrical piers,” J. Hydraul. Res., vol. 15, no. 3, pp. 211–252, 1977.
- [12]
B. W. Melville and A. J. Sutherland, “Design method for local scour at bridge piers,” J. Hydraul. Eng., vol. 114, no. 10, pp. 1210–1226, 1988.
- [13]
H. N. C. Breusers and A. J. Raudkivi, Scouring. Rotterdam: Balkema, 1991.
- [15]
D. M. Sheppard, M. Odeh, and T. Glasser, “Large scale clear-water local pier scour experiments,” J. Hydraul. Eng., vol. 130, no. 10, pp. 957–963, 2004.
- [16]
D. M. Sheppard, B. Melville, and H. Demir, “Evaluation of existing equations for local scour at bridge piers,” J. Hydraul. Eng., vol. 140, no. 1, pp. 14–23, 2014.
- [17]↑
R. Malik and B. Setia, “Mechanism of scour around two piers,” Pollack Period., vol. 19, no. 1, pp. 99–104, 2024.
- [18]↑
A. Ghaderi, R. Daneshfaraz, and M. Dasineh, “Evaluation and prediction of the scour depth of bridge foundations with HEC-RAS numerical model and empirical equations (Case Study: Bridge of Simineh Rood Miandoab, Iran),” Eng. J., vol. 23, no. 6, pp. 279–295, 2019.
- [19]↑
M. Al-Jubouri and R. P. Ray, “A comparative study of local scour depth around bridge piers,” Pollack Period., vol. 18, no. 1, pp. 100–105, 2023.
- [20]↑
C. S. Silvia, M. Ikhsan, and A. Wirayuda, “Analysis of scour depth around bridge piers with round nose shape by HEC-RAS 5.0. 7 Software,” J. Phys. Conf. Ser., vol. 1764, 2021, Art no. 012151.
- [21]↑
D. J. Mehta and S. M. Yadav, “Analysis of scour depth in the case of parallel bridges using HEC-RAS,” Water Supply, vol. 20, no. 8, pp. 3419–3432, 2020.
- [22]
X. Yu and X. B. Yu, “1D and 2D hydraulic simulations for bridge scour prediction: A comparative study,” in The Fourth International Conference on Scour and Erosion, Tokyo, Japan, November 5–7, 2008, pp. 226–232.
- [23]↑
G. W. Brunner, “HEC-RAS, River Analysis System Hydraulic Reference Manual,” 2020. [Online]. Available: https://www.hec.usace.army.mil/software/hec-ras/documentation/HEC-RAS Hydraulic Reference Manual-v6.4.1.pdf. Accessed: Aug. 20, 2024.
- [24]↑
O. D. Nara, M. D. Soumokil, V. R. R. Hutubessy, and D. Yatmadi, “Galala bridge scour model on Ambon’s Way Ruhu River,” Int. J. Adv. Eng. Res. Sci., vol. 11, no. 02, pp. 1–7, 2024.
- [25]↑
A. Azizian,A. A. Takoldani, and M. G. Zadeh, “Evaluation of foundation scour of bridges using HEC-RAS 4.0 numerical model and laboratory results” (in Persian), in Fifth National Congress of Civil Engineering, Mashhad, Iran, May 14, 2009, pp. 1–8.
- [26]↑
S. I. Khassaf and S. S. Shakir, “Evaluation of the local scour around group piers (Babil Bridge as case study),” Int. J. Innov. Res. Sci. Eng. Technol., vol. 2, pp. 7409–7420, 2013.
- [27]↑
B. Dalal and S. Deb, “Analysis of scour depth around a bridge pier using HEC-RAS modeling tool, A case study,” in International Conference on Hydraulics, Water Resources and Coastal Engineering, Surat, India, December 23–25, 2021. Lecture Notes in Civil Engineering, vol. 314, pp. 89–100.
- [28]↑
D. Kumar,H. L. Yadav, and S. K. Himanshu, “Estimation of scour depth around bridge piers by Using HEC-RAS,” in Proceedings of Conference on Recent Advances in Civil Engineering, Varanasi, India, October 17–19, 2011, pp. 421–425.
- [29]↑
M. Al-Jubouri, R. P. Ray, and M. S. Al-Khafaji, “Unraveling Debris-Enhanced local scour patterns around non-cylindrical bridge piers: Experimental insights and innovative modeling,” Sustainability, vol. 15, no. 22, 2023, Art no. 15910.
- [30]↑
G. W. Brunner, “HEC-RAS River Analysis System: Hydraulic Reference Manual, Version 5.0,” US Army Corps Eng. Eng. Cent., vol. 547, 2016.
- [31]↑
D. C. Froehlich, “Analysis of onsite measurements of scour at piers,” in Hydraulic Engineering: Proceedings of the 1988 National Conference on Hydraulic Engineering, New York, USA, August 8–12, 1988, pp. 534–539.
- [32]↑
G. J. Arcement, Jr and V. R. Schneider, “Guide for selecting Manning’s roughness coefficients for natural channels and flood plains,” US Geol. Survay Water-supply, 1989, Art no. 2339.
- [33]↑
M. B. Yarahmadi, A. Parsaie, M. Shafai-Bejestan, M. Heydari, and M. Badzanchin, “Estimation of manning roughness coefficient in alluvial rivers with bed forms using soft computing models,” Water Resour. Manag., vol. 37, no. 9, pp. 3563–3584, 2023.
- [34]↑
P. D. Dahe and S. B. Kharode, “Evaluation of scour depth around bridge piers with various geometrical shapes,” Evaluation, vol. 2, no. 7, pp. 41–48, 2015.
- [35]↑
M. Noor, H. Arshad, M. Khan, M. A. Khan, M. S. Aslam, and A. Ahmad, “Experimental and HEC-RAS modelling of bridge pier scouring,” J. Adv. Res. Fluid Mech. Therm. Sci., vol. 74, no. 1, pp. 119–132, 2020.