New temporal scour depth formula for spur dike using statistical analysis of literature data and formulas

Abstract

Temporal scour depth (ds) estimation at spur dikes is a significant issue for application engineers and researchers because accurate prediction is required for real-time monitoring. Although several formulas were employed, a definitive study is still needed to determine which formula predicts most accurately. Therefore, this study aims to address this need by conducting a comparative analysis of dst prediction formulas at spur dikes under clear water conditions using laboratory datasets spanning the last 20 years. The analysis encompasses 14 parameters, each playing a significant role in scour depth prediction. These parameters include sediment coarseness, flow shallowness, porosity, densimetric Froude number, Reynolds number, spur dike length, height, thickness, orientation, width of flume, relative density, sediment uniformity, flow intensity and time. By considering these parameters, the study aims to identify the best option that will provide a more promising temporal scour depth formula based on a statistical analysis of data and formulas in literatures. Therefore, useful statistical influence factors are used to evaluate eight existing literature formulas alongside a newly derived formula concerning their effectiveness in predicting temporal scour depth. The model has been evaluated using different statistical performance indicators including Coefficient of Determination (R2), Root Mean Squared Error (RMSE), Nash Sutcliffe Efficiency (NSE), and Mean Bias Error (MBE). The weightage of each influencing factor on the accuracy of predictions is calculated using CRITIC, Entropy, and AHP methods. Ranking of each formula based on their performance is determined using PROMETHEE and TOPSIS. The findings of the study reveal that the newly proposed formula most accurately predicts the d, in terms of Pin as well as comparing statistical influence indicators such as R2=0.84, RMSE = 0.13, NSE = 0.86, and MBE-0.003. The ranking of the formulas indicates that the newly developed formula consistently achieves the top position for each combination of weightage, for both the corresponding rankings. The formula of Coleman et al. (2003) is found useful for predicting dau, particularly when equilibrium scour depth (dse) and equilibrium time (te) are known. Additionally, the formulas proposed by Nasrollahi et al. (2008) and Karimi et al. (2012a, b) are found with similar accuracy compared to Coleman et al. (2003). Overall, this study not only identifies the most reliable formula for predicting dar but also emphasizes the importance of considering practical constraints and real-world applicability in engineering solutions. By prioritizing practicality over idealistic approaches, engineers can make informed decisions that strike a balance between accuracy and feasibility.