An Interpretable Machine Learning Approach for Predicting Bearing Capacity of Driven Piles Using SHAP

Miri, Seyed Emad; Shaarbaf, Seyed Amin Mousavi; Mohammadnezhad, Hamid

doi:10.61882/NMCE.2510.1102

An Interpretable Machine Learning Approach for Predicting Bearing Capacity of Driven Piles Using SHAP

Document Type : Research

Authors

Seyed Emad Miri ¹

Seyed Amin Mousavi Shaarbaf ¹

Hamid Mohammadnezhad ²

¹ BSc, Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran

² Assistant Professor, Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran

10.61882/NMCE.2510.1102

Abstract

Determination of the ultimate pile bearing capacity is still one of the major concerns in geotechnical engineering due to the complex interaction between soil and structure. This study employs interpretable machine learning models to provide precise predictions of pile capacities while identifying the role of the key design variables. A detailed data set of 100 steel and concrete piles is evaluated by including eight important design variables: effective pile length, cross-sectional area, Flap number, drained cohesion, drained soil friction angle, effective unit weight of soil, pile–soil friction angle, and pile material. Prediction models for the pile capacities are established using the Random Forest, XGBoost, CatBoost, and Extra Trees algorithms, which are validated through a strict 5-fold cross-validation. The results show that the Extra Trees algorithm is the most stable and has the highest predictive capability, with a coefficient of determination (R2) of 0.95 ± 0.03 and RMSE of 1806 ± 999. Furthermore, SHapley Additive exPlanations (SHAP) analysis is performed to calculate the importance of the design parameters, indicating that effective pile length, cross-sectional area, and Flap number are the major contributing factors. This reveals that the proposed unique combination of Flap number with cutting-edge machine learning analysis is an accurate, clear, and viable process for pile capacities.

Keywords

Driven pile

Bearing capacity

Flap Number

Machine learning

Interpretability

SHAP

Subjects

Geotechnical Engineering

[1] Lee, I. M., & Lee, J. H. (1996). Prediction of pile bearing capacity using artificial neural networks. Computers and geotechnics, 18(3), 189-200.

[2] Meyerhof, G. G. (1976). Bearing capacity and settlement of pile foundations. Journal of the Geotechnical Engineering Division, 102(3), 197-228.

[3] Coyle, H. M., & Castello, R. R. (1981). New design correlations for piles in sand. Journal of the Geotechnical Engineering Division, 107(7), 965-986.

[4] Masouleh, S. F., & Fakharian, K. (2008). Application of a continuum numerical model for pile driving analysis and comparison with a real case. Computers and Geotechnics, 35(3), 406-418.

[5] Momeni, E., Maizir, H., Gofar, N., & Nazir, R. (2013). Comparative study on prediction of axial bearing capacity of driven piles in granular materials. Jurnal Teknologi, 61(3), 15-20.

[6] Momeni, E. (2012). Axial bearing capacity of piles and modelling of distribution of skin resistance with depth (Doctoral dissertation, Universiti Teknologi Malaysia).

[7] Payan, M., Asadi, P., Jamaldar, A., Salimi, M., Ranjbar, P. Z., Armaghani, D. J., ... & Sheng, D. (2025). Artificial intelligence-based predictive models for shear wave velocity of soils: A comprehensive review. Engineering Applications of Artificial Intelligence, 155, 111095.

[8] Ghorbanzadeh, S., Armaghani, D. J., Salimi, M., & Payan, M. (2026). Predictive models for dynamic properties of soils using machine learning approaches: A comprehensive review. Engineering Applications of Artificial Intelligence, 163, 113014.

[9] Khodkari, N., Hamidian, P., Khodkari, H., Payan, M., & Behnood, A. (2024). Predicting the small strain shear modulus of sands and sand-fines binary mixtures using machine learning algorithms. Transportation Geotechnics, 44, 101172.

[10] Ngamkhanong, C., Keawsawasvong, S., Jearsiripongkul, T., Cabangon, L. T., Payan, M., Sangjinda, K., ... & Thongchom, C. (2022). Data-driven prediction of stability of rock tunnel heading: an application of machine learning models. Infrastructures, 7(11), 148.

[11] Dashtgoli, D. S., Sadeghian, R., Ardakani, A. R. M., Mohammadnezhad, H., Giustiniani, M., Busetti, M., & Cherubini, C. (2024). Predictive modeling of shallow tunnel behavior: Leveraging machine learning for maximum convergence displacement estimation. Transportation Geotechnics, 47, 101284.

[12] Sangdeh, M. K., Salimi, M., Khansar, H. H., Dokaneh, M., Ranjbar, P. Z., Payan, M., & Arabani, M. (2024). Predicting the precipitated calcium carbonate and unconfined compressive strength of bio-mediated sands through robust hybrid optimization algorithms. Transportation Geotechnics, 46, 101235.

[13] Mohammadnezhad, H., & Eslami, S. (2024). Machine learning models for predicting the bearing capacity of shallow foundations: A Comparative study and sensitivity analysis. Numerical Methods in Civil Engineering, 9(2), 40-54.

[14] MolaAbasi, H., Khajeh, A., Chenari, R. J., & Payan, M. (2022). A framework to predict the load-settlement behavior of shallow foundations in a range of soils from silty clays to sands using CPT records. Soft Computing, 26(7), 3545-3560.

[15] Moayedi, H., & Armaghani, D. J. (2017). Optimizing an ANN model with ICA for estimating bearing capacity of driven pile in cohesionless soil. Engineering With Computers, 34(2), 347–356. https://doi.org/10.1007/s00366-017-0545-7

[16] Nazir, R., & Momeni, E. (2013). Prediction of axial bearing capacity of spread foundations in cohesionless soils using artificial neural network. Proc. GEOCON, 747-757.

[17] Shaik, S., Krishna, K. S. R., Abbas, M., Ahmed, M., & Mavaluru, D. (2018). Applying several soft computing techniques for prediction of bearing capacity of driven piles. Engineering With Computers, 35(4), 1463–1474. https://doi.org/10.1007/s00366-018-0674-7

[18] Jesus, J. N., Maria do Socorro, C., & de SM Gadéa, A. (2022). PREDICTING LOAD CAPACITY OF PRECAST CONCRETE PILES USING SPT AND ARTIFICIAL NEURAL NETWORK. In XLIII Ibero-Latin American Congress on Computational Methods in Engineering (Vol. 4, No. 04).

[19] Momeni, E., Nazir, R., Armaghani, D. J., & Maizir, H. (2014). Prediction of pile bearing capacity using a hybrid genetic algorithm-based ANN. Measurement, 57, 122-131.

[20] Goh, A. T. (1995). Back-propagation neural networks for modeling complex systems. Artificial intelligence in engineering, 9(3), 143-151.

[21] Goh, A. T. (1996). Pile driving records reanalyzed using neural networks. Journal of Geotechnical Engineering, 122(6), 492-495.

[22] Arbi, S. J., Hassan, W., Khalid, U., Ijaz, N., Maqsood, Z., & Haider, A. (2025). Optimized machine learning-based enhanced modeling of pile bearing capacity in layered soils using random and grid search techniques. Earth Science Informatics, 18(4), 1-21.

[23] Nguyen, D. D., Nguyen, H. P., Vu, D. Q., Prakash, I., & Pham, B. T. (2023). Using GA-ANFIS machine learning model for forecasting the load bearing capacity of driven piles. Journal of Science and Transport Technology, 3(2), 26-33.

[24] Kardani, N., Zhou, A., Nazem, M., & Shen, S. L. (2020). Estimation of bearing capacity of piles in cohesionless soil using optimised machine learning approaches. Geotechnical and Geological Engineering, 38(2), 2271-2291.

[25] Ankah, M. L. Y., Adjei-Yeboah, S., Ziggah, Y. Y., & Asare, E. N. (2025). Advanced hybrid machine learning models with explainable AI for predicting residual friction angle in clay soils. Scientific Reports, 15(1), 25868.

[26] Kannangara, K. P. M., Zhou, W., Ding, Z., & Hong, Z. (2022). Investigation of feature contribution to shield tunneling-induced settlement using Shapley additive explanations method. Journal of Rock Mechanics and Geotechnical Engineering, 14(4), 1052-1063.

[27] Waris, K. A., Rahaman, M. a. U., & Basha, B. M. (2025). Detection and prediction of slope stability in unsaturated finite slopes using interpretable machine learning. Modeling Earth Systems and Environment, 11(4). https://doi.org/10.1007/s40808-025-02454-4

[28] Li, S., Hai, M., Zhang, Q., Zhou, B., Wang, M., & Zhao, Z. (2025). Study on an interpretable prediction model for pile bearing capacity based on SHAP and BP neural networks. Scientific Reports, 15(1), 28134.

[29] Khan, A., Khan, M., Khan, W. A., Afridi, M. A., Naseem, K. A., & Noreen, A. (2025). Predicting pile bearing capacity using gene expression programming with SHapley Additive exPlanation interpretation. Discover Civil Engineering, 2(1), 58.

[30] Milad, F., Kamal, T., Nader, H., & Erman, O. E. (2015). New method for predicting the ultimate bearing capacity of driven piles by using Flap number. KSCE Journal of Civil Engineering, 19, 611-620.

[31] Eslami, A. (1997). Bearing capacity of piles from cone penetration test data. University of Ottawa (Canada).

[32] Hansen, J. B. (1963). Discussion of “Hyperbolic stress-strain response: Cohesive soils”. Journal of the Soil Mechanics and Foundations Division, 89(4), 241-242.

[33] Bowles, J. E., & Guo, Y. (1996). Foundation analysis and design (Vol. 5, p. 127). New York: McGraw-hill.

[34] Tomlinson, M. J., & Woodward, J. (1994). Pile design and construction practice. Chapman and Hall.

[35] Prakash, S., & Sharma, H. D. (1991). Pile foundations in engineering practice. John Wiley & Sons.

[36] Fellenius, B. H. (1989). Predicted and observed axial behavior of piles. In Proceedings of the Symposium on Driven Pile Bearing Capacity Prediction (pp. 75–115). American Society of Civil Engineers

[37] Chen, T., & Guestrin, C. (2016, August). Xgboost: A scalable tree boosting system. In Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining (pp. 785-794).

[38] Breiman, L. (2001). Random forests. Machine learning, 45, 5-32

[39]Prokhorenkova, L., Gusev, G., Vorobev, A., Dorogush, A. V., & Gulin, A. (2018). CatBoost: unbiased boosting with categorical features. Neural Information Processing Systems, 31, 6639–6649. https://papers.nips.cc/paper/7898-catboost-unbiased-boosting-with-categorical-features.pdf

[40] Geurts, P., Ernst, D., & Wehenkel, L. (2006). Extremely randomized trees. Machine learning, 63, 3-42.

[41] Lundberg, S. M., & Lee, S. I. (2017). A unified approach to interpreting model predictions. Advances in neural information processing systems, 30.