## Abstract

Artificial Intelligence (AI) techniques, such as Artificial Neural Networks (ANN) and Adaptive Neuro-Fuzzy Inference Systems (ANFIS), and dimensional analysis-based empirical equations (DAEEs), can estimate scour depth around bridge piers. AI’s accuracy depends on various architectures, while DAEEs’ performance depends on experimental data. This study evaluated the performance of AI and DAEEs for scour depth estimation using flow velocity, depth, size of bed sediment, critical approach velocity, and pier width. The data from a smooth rectangular (20 m × 1 m) flume and a high-precision particle image velocimetry to study the flow structure around the pier – width: 1.5 – 91.5 cm evaluated DAEEs. Various ANNs (5, 10, and 15 neurons), double layer (DL) and triple layers (TL), and different ANFIS settings were trained, tested, and verified. The Generalized Reduced Gradient optimization identified the parameters of DAEEs, and Nash–Sutcliffe efficiency (NSE) and Mean Square Error (MSE) evaluated the performance of different models. The study revealed that DL ANN-3 with 10 neurons (NSE = 0.986) outperformed ANFIS, other ANN (ANN1, ANN2, ANN4 & ANN5) models, and empirical equations with NSE values between 0.76 and 0.983. The study found pier dimensions to be the most influential parameter for pier scour.

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Abdul Razzaq Ghumman, Husnain Haider, Ibrahim Saleh Al Salamah, Md. Shafiquzzaman, Abdullah Alodah, Mohammad Alresheedi, Rashid Farooq, Afzal Ahmed & Ghufran Ahmed Pasha

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## Acknowledgments

Authors also thank “The US Department of the Interior,” *US Geol. Surv. Reston, VA, USA”* for providing access to scour data. The Researchers would like to thank the Deanship of Graduate Studies and Scientific Research at Qassim University for financial support (QU-APC-2024-9/1).

## Author information

### Authors and Affiliations

- Dept. of Civil Engineering, College of Engineering, Qassim University, Buraydah, 51452, Saudi ArabiaAbdul Razzaq Ghumman, Husnain Haider, Ibrahim Saleh Al Salamah, Md. Shafiquzzaman, Abdullah Alodah & Mohammad Alresheedi
- Dept. of Civil Engineering, International Islamic University, Islamabad, 44000, PakistanRashid Farooq
- Dept. of Civil Engineering, University of Engineering and Technology, Taxila, 47050, PakistanAfzal Ahmed & Ghufran Ahmed Pasha

DOIhttps://doi.org/10.1007/s12205-024-1161-x