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The prediction of the ultimate bearing capacity of the pile under axial load is one of the important issues for many researches in the field of geotechnical engineering. In recent years, the use of computational intelligence techniques such as different methods of artificial neural network has been developed in terms of physical and numerical modeling aspects. In this study, a database of 100 prefabricated steel and concrete piles is available from existing publications to solve issues related to pile’s bearing capacity analysis. Three different artificial neural network algorithms were developed for comparing and verifying the obtained results at analyzing the bearing capacity of pile in soils. During the modeling process, the geometric properties of different piles, soil materials properties, friction angle and flap numbers (hammer blows) were selected as input parameters to the selected network and the output from the network was considered as the bearing capacity of the pile. Finally, the performance of radial base function type neural networks was compared with model tree method and predictive neural networks based on different learning algorithms such as Levenberg-Marquardt and Bayesian Regulation Back Propagation Algorithms. It was observed that the radial base neural network in some cases achieved better results from accuracy based on common statistical parameters such as correlation coefficient, mean absolute error percentage and root mean square error as compared to other stated methods and it showed the acceptable performance in modeling and predicting the desired output close to the target's results.

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The available studies for estimating the characteristics of hydraulic jump are only for artificial or natural beds, and very limited researches have simultaneously considered artificial and natural beds. The aim of this study is to present comprehensive equations and models for predicting the characteristics of hydraulic jump in artificial and natural rough beds with various dimensions, arrangement and roughness forms. The experimental data of different researches on two artificial and natural rough beds (containing 559 data series) were collected. After randomization, the data were used in combination of 75-25 for training and testing the two intelligent models of K-nearest neighbors (KNN) and M5 model tree with various scenarios and their performance were evaluated in estimation of hydraulic jump characteristics (including sequent depth, energy loss and shear force coefficient). Then, the existing empirical equations examined and calibrated and new optimized equations were derived using Solver command in Excel software. The results of the best intelligent models were analyzed and compared with the best calibrated and new optimized equations. Both the intelligent models had the same performance. In the M5 model tree, the best scenario of all the three parameters of sequent depth (R²=0.90), energy loss (R²=0.94), and shear force coefficient (R²=0.81) obtained by using Froude number as input parameter. The best empirical equations were Abbaspour et al.'s (R²=0.90), Abbaspour and Farsadizadeh's (R²=0.90), and Akib et al.’s (R²=0.83) for the sequent depth, the energy loss and the shear force coefficient, respectively. The calibrated and new optimized equations had a similar precision as the intelligent models, but their errors were less than that of the best empirical equations.