2509001239
  • Open Access
  • Article

Assessment of Bearing Capacity of Concrete Piles in Alluvial Soils Using Bio and Swarm-Optimized Artificial Neural Network Models

  • Jitendra Khatti 1, *,   
  • Denise-Penelope N. Kontoni  2, 3

Received: 12 Aug 2025 | Revised: 30 Aug 2025 | Accepted: 04 Sep 2025 | Published: 10 Sep 2025

Abstract

This study presents an optimal performance model for predicting the bearing capacity of concrete piles in alluvial soils by comparing Artificial Neural Network (ANN) models optimized with Particle Swarm Optimization (PSO), Harris Hawks Optimization (HHO), Grey Wolf Optimization (GWO), Genetic Algorithm (GA), and Artificial Bee Colony (ABC). A database of 194 data points was collected from the literature and preprocessed. Multicollinearity and cosine amplitude sensitivity analyses were then performed. Of the dataset, 164 data points were used for training and 30 for testing. Performance evaluation showed that the ABC_ANN model achieved over 95% accuracy in both phases. Further validation through Taylor plots, scores (35 for both training and testing), regression error characteristic curves (areas = 0.1982 for training and 0.1078 for testing), generalizability ranking (first), and uncertainty analyses confirmed the superior predictive capability of the ABC_ANN model. Curve-fitting analysis indicated a slight overfitting (1.97) for the ABC_ANN model, followed by the HHO_ANN model. This overfitting was mainly attributed to multicollinearity in features such as soil layer depth, ground elevation, pile tip elevation, and the standard penetration blow count at the pile shaft (a highly sensitive feature, sensitivity = 0.98). Nevertheless, discrete accuracy metrics consistently verified the robustness of the ABC_ANN model in predicting pile bearing capacity. Therefore, this study identifies the ABC_ANN model as an optimal tool to support geotechnical engineers and designers in estimating the bearing capacity of concrete piles.

References 

  • 1.
    Coyle, H.M.; Sulaiman, I.H. Bearing capacity of foundation piles: State of the art. Highw. Res. Rec. 1970, 333, 87.
  • 2.
    Wrana, B. Pile load capacity–calculation methods. Stud. Geotech. Et Mech. 2015, 37, 83–93.
  • 3.
    Meyerhof, G.G. Some recent research on the bearing capacity of foundations. Can. Geotech. J. 1963, 1, 16–26. https://doi.org/10.1139/t63-003.
  • 4.
    Jeong, S.; Kim, D.; Park, J. Empirical bearing capacity formula for steel pipe prebored and precast piles based on field tests. Int. J. Geomech. 2021, 21, 04021165. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002112.
  • 5.
    Alielahi, H.; Adampira, M. Comparison between empirical and experimental ultimate bearing capacity of bored piles—A case study. Arab. J. Geosci. 2016, 9, 78. https://doi.org/10.1007/s12517-015-2211-y.
  • 6.
    Wassel, A.L.-B. Empirical formulas to predict the axial capacity of driven piles using in-situ dynamic load testing data. Int. J. Mach. Learn. Comput. 2019, 9, 776.
  • 7.
    Ribeiro, D.B.; Pereira, J.L.J.; Lorena, A.C. Optimizing Empirical Methods for Calculating the Bearing Capacity of Concrete Piles. In Encontro Nacional de Inteligência Artificial e Computacional (ENIAC); SBC: Belém, Brazil, 2024; pp. 132–143. https://doi.org/10.5753/eniac.2024.245084.
  • 8.
    Eslami, A.; Aflaki, E.; Hosseini, B. Evaluating CPT and CPTu based pile bearing capacity estimation methods using Urmiyeh Lake Causeway piling records. Sci. Iran. 2011, 18, 1009–1019. https://doi.org/10.1016/j.scient.2011.09.003.
  • 9.
    Mijena, E.H. A comparison of friction piles bearing capacity based on theoretical and empirical mathematical models. Master’s Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 2012.
  • 10.
    Luo, Z.; Dong, F. Statistical investigation of bearing capacity of pile foundation based on Bayesian reliability theory. Adv. Civ. Eng. 2019, 2019, 9858617. https://doi.org/10.1155/2019/9858617.
  • 11.
    Zhao, Z. A Reliable Prediction Method to Forecast Pile Bearing Capacity Using Classic NB Base Hybrid Schemes. J. Inst. Eng. (India) Ser. A 2025, 106, 31–44. https://doi.org/10.1007/s40030-024-00852-y.
  • 12.
    Umar, I.H.; Salga, M.S.; Lin, H.; et al. Performance characterisation of machine learning models for geotechnical axial pile load capacity estimation: An enhanced GPR-based approach. Geomech. Geoengin. 2025, 20, 846–887. https://doi.org/10.1080/17486025.2025.2468645.
  • 13.
    Suzuki, N.; Nagai, K. Updating pile bearing capacity estimation using multiple piling data and spatial correlation. Georisk: Assess. Manag. Risk Eng. Syst. Geohazards 2025, 19, 1–17. https://doi.org/10.1080/17499518.2024.2449377.
  • 14.
    Sun, Z.-J.; Han, Y.-F.; Jiang, F.; et al. Prediction of ultimate bearing capacity of single pile in composite formation based on HGS-XGBoost algorithm. Appl. Geophys. 2025, 1–18. https://doi.org/10.1007/s11770-025-1203-2.
  • 15.
    Sun, Z.; Han, Y.; Jiang, F.; et al. Leveraging data-driven machine learning techniques to enhance bearing capacity estimation in prebored and precast piles. Expert Syst. Appl. 2025, 285, 128070. https://doi.org/10.1016/j.eswa.2025.128070.
  • 16.
    Onyelowe, K.C.; Hanandeh, S.; Kamchoom, V.; et al. Developing advanced datadriven framework to predict the bearing capacity of piles on rock. Sci. Rep. 2025, 15, 11051. https://doi.org/10.1038/s41598-025-96186-1.
  • 17.
    Nhat, L.V.; Anh, T.N.; Van, H.T.V. Ultimate bearing capacity of bored piles in clayey sand determined using artificial neural networks. Transp. Infrastruct. Geotechnol. 2025, 12, 132. https://doi.org/10.1007/s40515-025-00592-x.
  • 18.
    Khan, A.; Khan, M.; Khan, W.A.; et al. Predicting pile bearing capacity using gene expression programming with SHapley Additive exPlanation interpretation. Discov. Civ. Eng. 2025, 2, 58. https://doi.org/10.1007/s44290-025-00215-x.
  • 19.
    Ji, Y. Estimation of pile-bearing capacity of rocks via reliable hybridization techniques. Multiscale and Multidisciplinary Modeling. Exp. Des. 2025, 8, 103. https://doi.org/10.1007/s41939-024-00674-2.
  • 20.
    Hu, J.; Xia, C.; Wu, J.; et al. Estimating the pile-bearing capacity utilizing a reliable machine-learning approach. Multiscale Multidiscip. Model. Exp. Des. 2025, 8, 1–32. https://doi.org/10.1007/s41939-025-00761-y.
  • 21.
    Fattahi, H.; Ghaedi, H. Forecasting Pile Bearing Capacity Using an Innovative RES-Based Approach. Indian Geotech. J. 2025, 55, 1629–1642. https://doi.org/10.1007/s40098-024-01036-y.
  • 22.
    Eslami, A.; Rahimi, A.; Nobahar, M. Ultimate load bearing of helical piles prediction and evaluation using machine learning-based algorithms. Geomech. Geoengin. 2025, 20, 661–686. https://doi.org/10.1080/17486025.2024.2438077.
  • 23.
    Chen, B.; Hai, M.; Di, G.; et al. Enhanced Dung Beetle Optimizer-Optimized KELM for Pile Bearing Capacity Prediction. Build. 2025, 15, 2654. https://doi.org/10.3390/buildings15152654.
  • 24.
    Cai, L.; Zhu, D.; Xu, K. The implementation of a machine-learning-based model utilizing meta-heuristic algorithms for predicting pile bearing capacity. Indian Geotech. J. 2025, 55, 210–225. https://doi.org/10.1007/s40098-024-00933-6.
  • 25.
    Yousheng, D.; Keqin, Z.; Zhongju, F.; et al. Machine learning based prediction model for the pile bearing capacity of saline soils in cold regions. In Structures; Elsevier: Amsterdam, The Netherlands, 2024. https://doi.org/10.1016/j.istruc.2023.105735.
  • 26.
    Yaychi, B.M.; Esmaeili-Falak, M. Estimating axial bearing capacity of driven piles using tuned random forest frameworks. Geotech. Geol. Eng. 2024, 42, 7813–7834. https://doi.org/10.1007/s10706-024-02952-9.
  • 27.
    Yang, X. Prediction of pile-bearing capacity using Least Square Support Vector Regression: Individual and hybrid models development. Multiscale Multidiscip. Model. Exp. Des. 2024, 7, 2701–2715. https://doi.org/10.1007/s41939-023-00357-4.
  • 28.
    Xu, M.; Zhu, Z. Utilizing meta-heuristic algorithms for load-bearing capacity prediction in piles with support vector regression. Multiscale Multidiscip. Model. Exp. Des. 2024, 7, 5445–5459. https://doi.org/10.1007/s41939-024-00527-y.
  • 29.
    Tran, T.H.; Nguyen, B.P.; Tran, T.D. Machine learning applications in Pile load capacity prediction: Advanced analysis of pile driving forces and depths in urban Ho Chi Minh City construction sites. Indian Geotech. J. 2024, 55, 1795–1800. https://doi.org/10.1007/s40098-024-01055-9.
  • 30.
    Shen, Y. Optimized systems of multi-layer perceptron predictive model for estimating pile-bearing capacity. J. Eng. Appl. Sci. 2024, 71, 52. https://doi.org/10.1186/s44147-024-00386-x.
  • 31.
    Arbi, S.J.; Hassan, W.; Khalid, U.; et al. Optimized machine learning-based enhanced modeling of pile bearing capacity in layered soils using random and grid search techniques. Earth Sci. Inform. 2025, 18, 1–21. https://doi.org/10.1007/s12145-025-01784-2.
  • 32.
    Kumar, M.; Kumar, D.R.; Khatti, J.; et al. Prediction of bearing capacity of pile foundation using deep learning approaches. Front. Struct. Civ. Eng. 2024, 18, 870–886. https://doi.org/10.1007/s11709-024-1085-z.
  • 33.
    Khatti, J.; Khanmohammadi, M.; Fissha, Y. Prediction of time-dependent bearing capacity of concrete pile in cohesive soil using optimized relevance vector machine and long short-term memory models. Sci. Rep. 2024, 14, 32047. https://doi.org/10.1038/s41598-024-83784-8.
  • 34.
    Karakaş, S.; Taşkın, G.; Ülker, M.B.C. Re-evaluation of machine learning models for predicting ultimate bearing capacity of piles through SHAP and Joint Shapley methods. Neural Comput. Appl. 2024, 36, 697–715. https://doi.org/10.1007/s00521-023-09053-3.
  • 35.
    Gu, W.; Liao, J.; Cheng, S. Bearing capacity prediction of the concrete pile using tunned ANFIS system. J. Eng. Appl. Sci. 2024, 71, 39. https://doi.org/10.1186/s44147-024-00369-y.
  • 36.
    Gang, L. Improving the estimation of the pile bearing capacity via hybridization technique based on adaptive network based fuzzy inference. J. Ambient. Intell. Humaniz. Comput. 2024, 15, 4043–4060. https://doi.org/10.1007/s12652-024-04878-9.
  • 37.
    Amjad, M.; Ahmad, I.; Ahmad, M.; et al. Prediction of pile bearing capacity using XGBoost algorithm: Modeling and performance evaluation. Appl. Sci. 2022, 12, 2126. https://doi.org/10.3390/app12042126.
  • 38.
    Karaboga, D. An idea based on honey bee swarm for numerical optimization. Dep. Comput. Sci. 2005, 1–10.
  • 39.
    Mirjalili, S.; Mirjalili, S.M.; Lewis, A. Grey wolf optimizer. Adv. Eng. Softw. 2014, 69, 46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007.
  • 40.
    Heidari, A.A.; Mirjalili, S.; Faris, H.; et al. Harris hawks optimization: Algorithm and applications. Future Gener. Comput. Syst. 2019, 97, 849–872. https://doi.org/10.1016/j.future.2019.02.028.
  • 41.
    Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of ICNN’95-International Conference on Neural Networks, Perth, WA, Australia, 27 November–1 December 1995; Volume 4. https://doi.org/10.1109/ICNN.1995.488968.
  • 42.
    Edelmann, D.; Móri, T.F.; Székely, G.J. On relationships between the Pearson and the distance correlation coefficients. Stat. Probab. Lett. 2021, 169, 108960. https://doi.org/10.1016/j.spl.2020.108960.
  • 43.
    Smith, G.N. Probability and statistics in civil engineering. In Collins Professional and Technical Books; Nichols Publishing Company: New York, NY, USA, 1986; p. 244.
  • 44.
    Hair, J.F.; Wolfinbarger, M.; Money, A.H.; et al. Essentials of Marketing Research, 3rd ed.; McGraw-Hill/Irwin: New York, NY, USA, 2013.
  • 45.
    Khatti, J.; Grover, K.S. Prediction of compaction parameters for fine-grained soil: Critical comparison of the deep learning and standalone models. J. Rock Mech. Geotech. Eng. 2023, 15, 3010–3038. https://doi.org/10.1016/j.jrmge.2022.12.034.
  • 46.
    Asteris, P.G.; Skentou, A.D.; Bardhan, A.; et al. Predicting concrete compressive strength using hybrid ensembling of surrogate machine learning models. Cem. Concr. Res. 2021, 145, 106449. https://doi.org/10.1016/j.cemconres.2021.106449.
  • 47.
    Ahmad, M.; Hu, J.L.; Ahmad, F.; et al. Supervised learning methods for modeling concrete compressive strength prediction at high temperature. Mater. 2021, 14, 1983. https://doi.org/10.3390/ma14081983.
  • 48.
    Liang, W.; Luo, S.; Zhao, G.; et al. Predicting hard rock pillar stability using GBDT, XGBoost, and LightGBM algorithms. Math. 2020, 8, 765. https://doi.org/10.3390/math8050765.
  • 49.
    Pham, T.A.; Tran, V.Q.; Vu, H.L.T.; et al. Design deep neural network architecture using a genetic algorithm for estimation of pile bearing capacity. PLoS ONE 2020, 15, e0243030. https://doi.org/10.1371/journal.pone.0243030.
  • 50.
    Golbraikh, A.; Tropsha, A. Beware of q2! J. Mol. Graph. Model. 2002, 20, 269–276. https://doi.org/10.1016/S1093-3263(01)00123-1.
  • 51.
    Huang, J.; Asteris, P.G.; Manafi Khajeh Pasha, S.; et al. A new auto-tuning model for predicting the rock fragmentation: A cat swarm optimization algorithm. Eng. Comput. 2022, 38, 2209–2220. https://doi.org/10.1007/s00366-020-01207-4.
  • 52.
    Mohammed, A.; Kurda, R.; Armaghani, D.J.; et al. Prediction of compressive strength of concrete modified with fly ash: Applications of neuro-swarm and neuro-imperialism models. Adv. Concr. Constr. 2021, 11, 489–512. https://doi.org/10.12989/acc.2021.11.5.489.
  • 53.
    Mawlood, Y.; Salih, A.; Hummadi, R.; et al. Comparison of artificial neural network (ANN) and linear regression modeling with residual errors to predict the unconfined compressive strength and compression index for Erbil City soils, Kurdistan-Iraq. Arab. J. Geosci. 2021, 14, 485. https://doi.org/10.1007/s12517-021-06712-4.
Share this article:
How to Cite
Khatti, J.; Kontoni , D.-P. N. Assessment of Bearing Capacity of Concrete Piles in Alluvial Soils Using Bio and Swarm-Optimized Artificial Neural Network Models. Bulletin of Computational Intelligence 2025, 1 (1), 53–75. https://doi.org/10.53941/bci.2025.100004.
RIS
BibTex
Copyright & License
article copyright Image
Copyright (c) 2025 by the authors.