Local scour is responsible for most bridge failures around the world every year. In a streambed, the flow interferes with bridge piers and leads to the creation of multiple vortices, which remove sediment in the vicinity of the piers, and a scour hole is formed [1
]. When the scour hole deepens sufficiently, it causes bridge failure. The failures significantly increase the costs of temporary maintenance and also ecological impacts on downstream ecosystems, such as spawning beds [2
]. Because of the complicated process of scour around bridge piers, the local scour depth at complex pier (LSCP (is a complicated phenomenon and hence its accurate predictions are a critical issue for the design of bridge foundations. In other words, overestimation of LSCP may lead to extra construction costs and even bridge failure around their foundations [3
An accurate prediction of LSCP is a hot topic in river engineering because overestimated and underestimated predictions lead to an increase in the dimensions of the bridges, resulting in an increase of the construction costs and bridge failure, respectively [4
]. Therefore, a reliable prediction of LSCP for a safe, economic and technically sound structure is of paramount importance. In a river, when a high volume of water flows, scouring of particles around the base of the bridges occurs, and then a scour hole appears around bridge piers. If the LSCP is not predicted correctly, the bottom level of the local scour hole will exceed the original level of the pier foundation. As a result, as time passes and the volume of water flowing increases, local scour depth develops and the bridge’s base loses strength, and eventually it will be destroyed [2
]. Almost 53% of all bridge failures are attributed to flood and scour [5
Over the past decades, the mechanisms and prediction of scour hole occurence at the simple pier and a group of piles have been widely investigated. Due to economic and technical issues, the piers with complex geometry have developed to become the most common foundation type of bridge piers in alluvial streambeds [6
]. The term “complex pier” (CPs) is used in contrary to the simple pier. By definition, the complex pier is a term that defines a special kind of non-uniform pier that is comprised of a column, a pile cap, and a pile group [7
]. At piers with complex geometry, due to scouring during a flood, the pile cap position with respect to the initial stream bed level changes. As a result, the influence of pile cap may be changed from a protective to intensifying role at the scour process when it is entirely buried and exposed to the flow, respectively [7
]. Such roles increase the complicity of scour mechanisms and prediction at CPs [8
To estimate local scour depth at complex pier (ys
), a few empirical methods have been proposed including the FHWA design methodology, Hydraulic Engineering Circular No. 18. (HEC-18) [9
], the Florida Department of Transportation (FDOT) bridge mechanisms scour manual [2
]. In addition, a procedure was proposed by Amini and Mohammad [7
] which, based on field data, gives reasonable estimates of the scour depth at CPs [12
]. For calculations of scour depth, the HEC-18 and FDOT methods apply a superposition procedure to combine the effect of each element of CPs. However, the methods presented by Lee and Hong [1
], Amini et al. [6
], and Arneson et al. [9
] provided relations for an equivalent width (be
) for that around a CP to be used in simple pier equations where be
is the diameter of a circular simple pier that produces scour depth equal to the CP, for the same sediment and flow conditions. Apart from HEC-18 and FDOT methods, Mueller and Wagner [13
] used field data to examine the efficacy of 20 bridge pier scour depth estimation methods and found that these methods predict the scour depth inaccurately with a large number of overestimations.
In recent years, ensemble machine learning models have become popular among environmental researchers not only for classification issues to generate susceptibility maps [14
] but also for regression problems to simulate and predict an environmental variable such as wastewater hydraulics [37
], saturated hydraulic conductivity [38
], shear strength of soft soil [39
], soil moisture [40
], and soil temperature [41
]. The advantages of artificial intelligence (AI) have encouraged numerous researchers to use methods and techniques based on AI to estimate the depth of scour [42
]. Based on artificial neural networks (ANNs), some local scour depth estimation methods have been proposed. In case of bridge scouring, Cheng and Cao [46
] for predicting local scour depth at simple bridge piers, proposed an intelligent fuzzy radial basis function neural network inference model (IFRIM). Their model was a hybrid of the fuzzy logic, the artificial bee colony algorithm and radial basis function neural network. Najafzadeh et al. [47
] presented a group method of data handling, using the back propagation algorithm and quadratic polynomial. They found that the AI-based model provides accurate predictions of scour at simple piers. In the case of local scour prediction at pile group, Zounemat-Kermani et al. [48
] and Hosseini et al. [49
] reported the accuracy of the ANNs and the neuro-fuzziness system in comparison with empirical methods.
However, contrary to the simple piers and pile groups, due to the complication of the scour mechanism, and the variation of influential parameters, the ensemble machine learning methods have been rarely developed to estimate the scour around the complex piers. The positive and different point of this study with other studies is that there is no applied an ensemble model to predict the LSCP. In other words, although some models and techniques have been used and suggested for predicting the LSCP, the proposed model, RS-REPTree, has not been yielded for this purpose worldwide. Therefore, the main aim of this study was to use a hybrid intelligence model to predict current-induced local scour at complex piers. The presented model enhances the accuracy of scouring predictions and the understanding of the local scour at the complex pier and its dominant variables.
The flow disturbances around obstacles such as bridge piers, inserted into an alluvial streambed, induce local scouring which is one of the most common being riverbed scour. Since the late 1950s the estimation of scour at bridges has attracted the attention of many researchers [88
Unlike the local scour at simple pier, the scour at CPs is a complex phenomenon. However, the accurate estimation of equilibrium scour depth at CPs is vital for safe designing of the bridges. The experimental data were used to compare the most commonly used method for predicting scour depth at CPs. Based on data set analyses, an ensemble model was constructed to improve the accuracy of local scour depth prediction of REPTree as a base classifier. The statistical measurements indicated that the best values for the number of seeds and iterations were 6 and 10, respectively.
The capabilities and performance of the empirical methods and obtained models in scour prediction were evaluated using statistical tests. Overall, the statistical tests showing the relationship between observed and predicted scour depths indicated that all machine learning models are with higher power prediction than the empirical models. The inaccuracy of empirical methods at CPs scour including HEC-18 and FDOT methods was reported [6
]. In contrast, the superiority of intelligent models to empirical methods for scour predicting was stated by Zounemat-Kermani et al. [48
] and Hosseini et al. [49
]. The same results can be concluded from the correlation between the observed and predicted values of local scour depth for empirical and machine learning models. The lowest values of R were obtained for HEC-18 and the highest belonged to the RS-REPTree as 0.620 and 0.945, respectively. Moreover, the boxplot and Friedman’s test of the models support the above statements.
In the case of detecting the dominant parameters at inducing local scour at CPs, the sensitivity analyses were conducted and the parameters were ordered according to their effectiveness. The results depicted that the pile cap location (Y) in respect to undisturbed streambed is the most important parameter which influence the scouring at CPs. These results are consistent with those reported by [51
]. Furthermore, the pile cap width (bpc), thickness (T) and column width (bc) are with higher influences on LSCP, respectively. These results are in agreement with the findings of Ferraro et al. [90
] and Moreno et al. [89
]. It should be noted that unlike the simple piers and pile group [91
], the role of the parameters at producing LSCP is various versus the pile cap level in respect to undisturbed streambed. Particularly when the pile cap is lower or inside the scour hole, the pile cap prevents scouring. This process continues until flow penetrates below the pile cap and the pile cap becomes undercut. The undercutting of pile caps intensifies the scour depth. As the level of pile cap reached the position for undercutting, apart from column and pile cap, the pile group is exposed to the flow, and contributes towards scouring. As the pile cap level increased, the pile group prevents the scouring and diminishes the LSCP [50
]. In this case, the LSCP depends on the pile cap and pile group characteristics. It is worth noting that the bridge pier models used to obtain the data in this research were selected so that the sediment size and flow depth effects on LSCP became negligible and flow intensity was in a confined range.
The ensemble models could more decrease the noise and over-fitting problems between the training dataset, resulting in enhancing the accuracy of the model [15
]. Basically, the findings depicted that the RS-REPTree ensemble model could well enhance the prediction accuracy of the REPTree as a classifier for the prediction of local scour depth at piers with complex geometry. This finding is in agreement with Cheng and Cao [46
] who reported the capability of the IFRIM as a promising tool for civil engineers to estimate local scour at piers with simple geometry.