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.

Scouring refers to the process by which bed sediment in a river is eroded around the periphery of a bridge abutment or pier. Many empirical models are available to estimate the scour depth for different flow, geometry, and bed roughness condition. However, none of them provide a better estimation of scour depth for a wide range of input parameters. Thus, in this paper, the scour depth around bridge piers has been modelled using M5 tree and hybrid artificial neural network (ANN)-particle swarm optimisation (PSO) techniques by considering the wide range of datasets. The clear-water scouring (CWS) datasets are collected from the literature and five different non-dimensional influencing parameters are selected as input parameters to model the scour depth. A Gamma test (GT) was performed to choose the best input parameter combinations. Based on the lowest gamma value and V-ratio, 4 out of 26 distinct input combinations for CWS depth modelling were chosen in the GT. According to statistical measures, the proposed M5 tree model predicts scour depth better than empirical approaches. Additionally, the developed ANN-PSO model is suitable for determining scour depth in both rectangular and circular shapes of piers. The results of both developed models are compared with other existing models and found to be satisfactory.

The failure of bridges, attributed to bridge pier scouring, poses a significant challenge in ensuring safe and cost-effective design. Numerous laboratory and field experiments have been conducted to comprehend the mechanisms and predict the maximum equilibrium scour depth around bridge piers. Over the last eight decades, various empirical methods have been developed, with different authors incorporating diverse influencing parameters that significantly impact the estimation of equilibrium scour depth around bridge piers. This paper aims to consolidate: (1) available experimental and field data sets on different types of bridge pier scouring, (2) the influence of flow and roughness parameters on both clear water scouring (CWS) and live bed scouring (LBS), and (3) existing empirical equations suitable for computing equilibrium scour depth around a bridge pier under CWS and LBS conditions. The presented research encompasses over 80 experimental/field data sets and more than 60 scour-predicting equations developed for CWS and LBS conditions in the past eight decades. Based on the performance of different empirical models in predicting scour depth ratio, suitable models are recommended for CWS and LBS conditions.

Scouring around a bridge pier involves removing sediment from the riverbed and banks due to water flow. This paper employs eXtreme Gradient Boosting (XGBoost) and support vector machine with particle swarm optimization (SVM-PSO) machine learning (ML) approaches to model the temporal local scour depth around bridge piers under clear water scouring (CWS) conditions. CWS datasets, incorporating bridge pier geometry, flow characteristics, and sediment properties, are collected from existing literature. Five non-dimensional influencing parameters, such as ratio of pier width to flow depth (b/y), ratio of approach mean velocity to critical velocity (V/Vc), ratio of mean sediment size to pier width (d50/b), Froude number (Fr), and standard deviation of sediment (σg), are chosen as input parameters. XGBoost and SVM-PSO ML models demonstrate superior predictive capabilities, achieving coefficient of determination (R2) values exceeding 0.90 and mean absolute percentage error (MAPE) and root mean square error (RMSE) values less than 17.07% and 0.0341, respectively. Comparison with the previous four empirical models based on statistical indices reveals that the proposed XGBoost model outperforms SVM-PSO and empirical models in predicting scour depth, so it is recommended for estimating clear water scour depth under varying temporal conditions within the specified dataset range.

Scouring is a threat to the foundations of bridges, and it frequently results in bridge collapse. Recently, machine-learning approaches have become quite popular in solving hydraulic and hydrologic problems. The present study adopted adaptive neuro-fuzzy inference systems (ANFIS) and gene expression programming (GEP) to model bridge pier scour depth. A temporal scour depth relationship has been proposed based on ANFIS and GEP approaches. In this paper, 500 data sets have been used to model the temporal scour depth using ANFIS and GEP models, in which 80% (400) data sets for training and 20% (100) datasets for testing purposes are used to develop the model. The performance of the GEP model is validated by comparing the results of the developed ANFIS model and other existing empirical equations. It is found that the GEP-based scour depth prediction model is effective in training and validation. The present GEP model accurately predicts the scour depth with a mean absolute percentage error (MAPE) value of less than 12% and an R² value greater than 0.85. Thus, the GEP model can be utilized to predict scour depth around the bridge pier for unsteady flow conditions.