⚡ electrical engineering

Prediction of Local Scour Depth Around Cylindrical Bridge Piers in Cohesive Soil Using Advanced Machine Learning Algorithms

This study evaluates five machine learning algorithms for predicting local scour depth around cylindrical bridge piers in cohesive soils using 122 laboratory records, finding that the QNET model achieved the highest accuracy (R² = 0.9958) while highlighting the critical influence of the Froude number and the need for cautious interpretation due to the modest sample size.

Original authors: Nazila Kardan, Mehdi Soltani, Mehdi Majedi Asl, Tohid Omidpour

Published 2026-09-01

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CC BY 4.0

Original authors: Nazila Kardan, Mehdi Soltani, Mehdi Majedi Asl, Tohid Omidpour

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Every bridge relies on its foundations to stand firm, but the water flowing beneath it is constantly trying to undermine that stability. When a river current hits a bridge pier, the water swirls and accelerates around the structure, carving out a hole in the riverbed. This process, known as scour, can strip away the soil supporting the bridge, potentially leading to collapse during a flood. For decades, engineers have been able to predict how deep these holes will form in rivers with sandy or gravelly bottoms, where the soil moves grain by grain. However, many rivers flow over cohesive beds, where the soil is sticky and bound together by clay and water. In these conditions, the soil does not wash away easily; instead, it resists erosion in complex ways that depend on how wet the soil is, how much clay it contains, and how strongly the water pushes against it. Because the interaction between the flowing water and this sticky soil is so intricate, predicting exactly how deep a scour hole will become in these environments has remained a difficult and uncertain challenge for civil engineers.

A team of researchers from universities in Iran set out to solve this specific problem by teaching computers to recognize the patterns hidden within past laboratory experiments. They gathered 122 records from previous studies where scientists had measured how deep water carved around cylindrical bridge piers in cohesive soil. Instead of relying on traditional formulas, the team used advanced machine learning algorithms, which are computer programs capable of learning from data to make predictions. They fed the computer five different types of learning systems, including artificial neural networks, which mimic the way human brains connect information, and other mathematical models designed to find relationships between variables. The computer was given four key pieces of information for each experiment: the speed of the water relative to the size of the pier, the amount of water contained within the soil, the percentage of clay in the soil, and a measure of how much force the soil could withstand before it began to erode.

The researchers tested these computer models to see which one could most accurately predict the depth of the scour hole based on those four factors. They split their data into two groups, using most of it to teach the models and saving a smaller portion to test their accuracy on new, unseen examples. One of the models, called QNET, achieved the highest reported performance, though the researchers interpreted this near-perfect score cautiously, noting it likely reflects the specific way the data was split rather than a guarantee of universal accuracy. Another model, the artificial neural network, also performed very well, though with slightly more error than the top performer. The other models, including one that attempts to create a simple mathematical formula from the data, showed lower accuracy when tested on new situations. The study revealed that while the computer models were excellent at finding patterns, the most important factor for accurate prediction was consistently the speed of the water relative to the pier size. However, the models also confirmed that knowing the water speed alone was not enough; the computer needed to know the soil's water content and clay content to make a reliable prediction.

Despite the high accuracy of the top-performing models, the researchers were careful not to declare the problem completely solved. They noted that the computer was trained on a relatively small number of laboratory experiments, and the near-perfect scores might be specific to that particular set of data rather than a guarantee for every river in the world. The study suggests that while machine learning offers a powerful new tool for understanding how water erodes sticky riverbeds, these models should be viewed as sophisticated prediction aids that work best within the limits of the data they were trained on. The findings emphasize that understanding bridge safety in cohesive soils requires looking at both the power of the water and the specific properties of the ground, a combination that traditional methods have struggled to capture effectively. By demonstrating that computers can learn these complex relationships, the research opens a path toward safer bridge designs, provided that future work continues to test these tools against real-world conditions and larger datasets.

Technical Summary: Prediction of Local Scour Depth Around Cylindrical Bridge Piers in Cohesive Soil Using Advanced Machine Learning Algorithms

Problem Statement
Reliable prediction of local scour around cylindrical bridge piers in cohesive beds remains a significant challenge in hydraulic engineering. Unlike non-cohesive sediments, where erosion is governed primarily by grain size and critical velocity, cohesive soil erodibility involves complex, nonlinear interactions between hydraulic forcing and geotechnical resistance. Factors such as water content, clay content, and critical bed shear strength influence interparticle bonding and erosion thresholds, often causing cohesive material to erode as aggregates or blocks rather than individual grains. Traditional empirical relationships, largely developed for non-cohesive sediments, are difficult to apply directly to cohesive beds. While data-driven techniques have shown promise, there is a need for systematic comparisons of different machine-learning paradigms under a common, physically consistent dimensionless framework to ensure model robustness and interpretability.

Methodology
The study utilized a dataset of 122 laboratory records compiled from previous investigations (specifically the cohesive-bed database by Choi and Choi, 2022). The research focused on predicting the dimensionless maximum scour depth ( $d_{max}/D$ ) using four primary predictors:

Water content ( $W_c$ )
Clay content ( $CP$ )
Pier Froude number ( $Fr = V/\sqrt{gD}$ )
Normalized critical bed shear strength ( $\tau_c / (\rho V^2)$ )

The dataset was partitioned into a training set (~~70%) and a holdout test set (~~30%) to evaluate generalization. To systematically assess predictor influence, the authors employed an exhaustive input-subset design, testing all 15 non-empty combinations of the four variables.

Five distinct machine-learning algorithms were evaluated under this common framework:

Artificial Neural Network (ANN): Implemented as a multilayer perceptron.
Support Vector Machine (SVM): Utilizing a radial basis function kernel.
K-Nearest Neighbors (KNN): Using Euclidean-distance-based regression.
Gene Expression Programming (GEP): An evolutionary symbolic-regression technique yielding explicit formulas.
QNET: An alternative neural-network modeling framework.

Performance was assessed using the coefficient of determination ( $R^2$ ), Root Mean Square Error (RMSE), and Willmott's index of agreement ( $DC$ ). Sensitivity analyses were conducted via one-at-a-time predictor deletion to determine the relative influence of each variable.

Key Results

Model Performance: QNET achieved the highest reported performance on the holdout test set, with an $R^2$ of 0.9958, RMSE of 0.0111, and $DC$ of 0.9836. ANN followed with strong performance ( $R^2 = 0.9206$ , RMSE = 0.0303, $DC = 0.9285$ ). SVM and KNN demonstrated intermediate performance, while the full-input GEP configuration showed weaker generalization ( $R^2 = 0.6791$ ), despite providing an explicit symbolic expression.
Predictor Sensitivity: The sensitivity of predictors varied by model and metric.
- In SVM, removing clay content ( $CP$ ) caused the largest drop in $R^2$ , while removing the Froude number ( $Fr$ ) caused the largest drop in $DC$ .
- In QNET and ANN, removing the Froude number ( $Fr$ ) resulted in the most significant decline in $R^2$ and $DC$ , highlighting the critical role of hydraulic intensity.
- GEP results also indicated a strong influence of $Fr$ , though inconsistencies in its reported sensitivity metrics prevented precise quantitative attribution.
Generalization: While QNET and ANN showed high training accuracy, the study noted a measurable generalization gap for ANN (training $R^2$ 0.9996 vs. holdout 0.9206). The near-unity performance of QNET was interpreted cautiously due to the modest sample size and reliance on a single data partition.

Significance and Claims
The paper claims to demonstrate the potential of machine learning for predicting scour in cohesive beds, emphasizing that predictive frameworks must simultaneously account for hydraulic forcing and bed resistance. The study highlights the importance of using physically consistent predictors (such as the Froude number and normalized shear strength) rather than relying solely on statistical fitting.

The authors explicitly state that their results should be interpreted as reported performance for the specific data partition used, rather than as definitive proof of universal model superiority or field-scale generalization. They caution that the near-perfect performance of QNET requires careful interpretation given the limited dataset (122 records) and the lack of repeated resampling or external validation logs. The study concludes that while machine learning offers powerful tools for this domain, the developed models should be regarded as data-driven prediction tools within the represented laboratory domain, not as unrestricted design equations. Future work is suggested to include rigorous external validation using independent datasets (such as those from Gudavalli and Kothyari et al.) and the application of ensemble methods with explainable AI techniques.

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