Scour depth prediction is an important aspect of designing a bridge pier structure in a river. Proper modeling of scour depth ensures the sustainability of the structure. An attempt is made to develop a scour depth model for the bridge pier using an adaptive network-based fuzzy inference system (ANFIS) and gene expression programming (GEP). The scour depth is found to be influenced by various independent parameters such as pier diameter, flow depth, approach mean velocity, critical velocity, Froude number, bed sediment, and geometric standard deviation of bed particle size. Gamma tests are performed to identify the best input parameter combinations to predict scour depth. In the present study, two separate models have been developed for clear-water scouring (CWS) and live-bed scouring (LBS). For different ranges of input parameters, the scour depth ratio is computed and error analysis is performed. Results indicate that the ANFIS model (R2CWS = 0.95, MAPECWS = 9.39% and R2LBS = 0.95, MAPELBS = 5.29%) is the most accurate predictive model in both scour conditions as compared to the GEP model and existing models of previous researchers. However, for the low value of pier diameter (b) to flow depth (y) ratio (<0.25), the present ANFIS model apportioned unsatisfactory results for LBS only.

Experiments were performed in the symmetric compound channel with diverging and converging floodplains for different relative flow depths to investigate the resistance characteristics of overbank flow in nonprismatic sections. The effectiveness of Manning’s $n$ , Darcy-Weisbach’s $f$ and Chezy’s $C$ are analyzed. Manning’s roughness coefficient relies upon the nondimensional parameters like width ratio, aspect ratio, relative flow depth, angles (diverging and converging angles), relative distance, bed slope, Reynolds number, and Froude number. A multivariable regression model has been developed by taking care of the aforementioned geometric and hydraulic parameters to estimate the Manning’s roughness coefficient for nonprismatic compound channels. The nonlinear regression models are developed using pertinent experimental data obtained from laboratory experiments and the data from other researchers on the compound channel with nonprismatic floodplains. The present model gives satisfactory results as compared to other approaches for different experimental channels and field data by providing less error.

Discharge estimation in rivers is the most important parameter in flood management. Predicting discharge in the converging and diverging compound open channel by analytical approach leads to solving a system of complex nonlinear equations. In this study, the gene expression programming (GEP) is used for modeling and predicting of flow discharge in the non-prismatic compound open channel. Existing approaches on discharge estimation are surveyed in order to carry out a comparison among them and the proposed GEP model. Comparison of results showed that the divided channel method with vertical division lines with the coefficient of determination (0.74) and root-mean-square error (0.0093) is accurate among the analytical approaches. The non-dimensional parameters like friction factor ratio, area ratio, hydraulic radius ratio, bed slope, width ratio, relative flow depth, angle of converging or diverging, relative longitudinal distance, and flow aspect ratio have been taken as input parameters for predicting discharge. Gamma test has been performed and provided the best combination of input parameters as friction factor ratio, hydraulic radius ratio, relative flow depth, and bed slope which influence the discharge significantly. Results demonstrate that the conveyance capacity computed by the GEP model gives far better outcomes than the customary models. The GEP model with a coefficient of determination greater than 0.80 and mean absolute percentage error less than 15% for the testing stage has a suitable performance for predicting the discharge in the non-prismatic compound open channel.

The study of scouring around bridge piers is very significant and plays a very important role in the safe and economical design of bridge piers. The term scouring is a process by which bed particles around the periphery of the pier get eroded and removed over a certain depth resulting in the formation of a scour hole around the bridge piers. This paper presents a detailed investigation of local scouring around six different shapes namely rectangular, circular, chamfered, joukowsky, oblong, and sharp-nosed of bridge pier models for selecting the best and most economical bridge pier shapes based on local scouring. For the experimental studies, local scour depth is measured around all six different shapes of bridge piers with varying discharges and velocities of 0.0169 m³ s⁻¹ to 0.0355 m³ s⁻¹ and 0.17 m s⁻¹ to 0.30 m s⁻¹ respectively. It is found that scour depth around the rectangular shape of bridge pier is larger due to development of strong intensity of horseshoe vortex caused by flat exposed frontal area and scour depth around the sharp nose shape of the pier is smaller because of flow is bifurcated due to smooth curvature caused less intensity of development of horseshoe vortex. In the comparison of obtained results, it is reported that scour depth around a pier is exactly proportional to velocity of approach flow and exposed frontal area of the bridge pier. The result of this study can be likely used to help in selecting the best shape of the bridge piers as sharp nose shape of bridge piers is better among the other six bridge pier shapes for design purposes.

In recent history, local scour around the bridge piers has been a major cause of bridge failure; therefore, it is important to precisely predict the equilibrium scour depth. When the flow of water interacts with the bridge pier in the mobile bed, it usually results in local scour. In this paper, a total of 442 clear-water scouring (CWS) data and 300 live-bed scouring (LBS) data are collected from literature to model scour depth using a support vector machine. A sensitivity study was also carried out to assess the reliability of the model, and the strength of the proposed model is tested via an error analysis. The coefficient of determination ( R²) value was found to be greater than 0.90 for both CWS and LBS. The present model is compared with more than 10 popular existing models and it has been discovered to be more reliable and efficient in estimating scour depth around bridge piers.