Numerical Methods in Civil Engineering

Numerical Methods in Civil Engineering

Machine learning models for predicting the bearing capacity of shallow foundations: A Comparative study and sensitivity analysis

Document Type : Research

Authors
1 Assistant Professor, Faculty of Civil, Water & Environmental Engineering, Shahid Beheshti University, Tehran, Iran
2 Bachelor's degree graduate, Faculty of Civil, Water & Environmental Engineering, Shahid Beheshti University, Tehran, Iran.
Abstract
bearing capacity estimation of shallow foundations is the essential requirement in the design of structures and taking a calculation method into account is necessary. All the parameters and uncertainties cannot be factored in by the classic analytical-based methods. Moreover, performing in-site tests require an extensive period of time and many resources. With the development of new methods such as Machine Learning (ML) algorithms in recent decades, a resolution to these challenges has been identified. In this study, classic machine learning regression methods such as KNN, SVM and Decision Tree based models alongside the utilization of Artificial Neural Networks (ANN) regression are examined and compelling results are demonstrated. The dataset in this study is consisting of 97 tests on model foundations and site loadings on granular soil. The results indicate that ML regression methods will have reliable outcome in determination of bearing capacity. But more importantly, the precision of the trained model is closely correlated to data splitting and the ratio of train and test series in the dataset. The importance of splitting procedure was examined through trial and error with parameters of train test data ratio and the random state of sampling. It is indicated that a ratio of 80% for the training set would be an optimum value. Furthermore, relative importance of the input features was examined through a sensitivity analysis which indicated that the internal friction angle of the soil and the depth of the foundation are the most important inputs while using ML regression methods.
Keywords

Subjects


[1] Das, B. M., & Sivakugan, N. (2018). Principles of foundation engineering. Cengage learning.
[2] Dewaikar, D. M., & Mohapatra, B. G. (2003). Computation of bearing capacity factor Nγ-Prandtl's mechanism. Soils and foundations, 43(3), 1-10.
[3] Dewaikar, D. M., & Mohapatro, B. G. (2003). Computation of bearing capacity factor N γ—Terzaghi’s mechanism. International Journal of Geomechanics, 3(1), 123-128.
[4] Meyerhof, G. G. (1963). Some recent research on the bearing capacity of foundations. Canadian geotechnical journal, 1(1), 16-26.
[5] Hansen, J. B. (1970). A revised and extended Equation for bearing capacity.
[6] Vesić, A. S. (1973). Analysis of ultimate loads of shallow foundations. Journal of the Soil Mechanics and Foundations Division, 99(1), 45-73.
[7] Hahn, B. H., & Valentine, D. T. (2017). Introduction to Numerical Methods. Essent. MATLAB Eng. Sci, 295-323.
[8] Fowler, D., & Robson, E. (1998). Square root approximations in Old Babylonian mathematics: YBC 7289 in context. Historia mathematica, 25(4), 366-378.
[9] Goldstine, H. H. (2012). A History of Numerical Analysis from the 16th through the 19th Century (Vol. 2). Springer Science & Business Media.
[10] Bathe, K. J. (2007). Finite element method. Wiley encyclopedia of computer science and engineering, 1-12.
[11] Rosen, S. (1969). Electronic computers: A historical survey. ACM Computing Surveys (CSUR), 1(1), 7-36.
 
[12] Morgenstern, N. U., & Price, V. E. (1965). The analysis of the stability of general slip surfaces. Geotechnique, 15(1), 79-93.
[13] Nilsson, N. J. (1998). Artificial intelligence: a new synthesis. Morgan Kaufmann.
 
[14] Fradkov, A. L. (2020). Early history of machine learning. IFAC-PapersOnLine, 53(2), 1385-1390.
[15] Yeh, Y. C., Kuo, Y. H., & Hsu, D. S. (1993). Building KBES for diagnosing PC pile with artificial neural network. Journal of Computing in Civil Engineering, 7(1), 71-93.
[16] Chan, W. T., Chow, Y. K., & Liu, L. F. (1995). Neural network: an alternative to pile driving Equations. Computers and geotechnics, 17(2), 135-156.
[17] Lee, I. M., & Lee, J. H. (1996). Prediction of pile bearing capacity using artificial neural networks. Computers and geotechnics, 18(3), 189-200.
[18] Shahin, M. A., Jaksa, M. B., & Maier, H. R. (2000). Predicting the settlement of shallow foundations on cohesionless soils using back-propagation neural networks. Australia: Department of Civil and Environmental Engineering, University of Adelaide.
[19] Rezania, M., & Javadi, A. A. (2007). A new genetic programming model for predicting settlement of shallow foundations. Canadian Geotechnical Journal, 44(12), 1462-1473.
[20] Samui, P. (2008). Support vector machine applied to settlement of shallow foundations on cohesionless soils. Computers and Geotechnics, 35(3), 419-427.
[21] Gajan, S. (2021). Application of machine learning algorithms to performance prediction of rocking shallow foundations during earthquake loading. Soil Dynamics and Earthquake Engineering, 151, 106965.
[22] Altınok, E., & Ülker, M. B. (2023, September). Ultimate bearing capacity of closed-ended piles using nonlinear machine learning methods. In AIP Conference Proceedings (Vol. 2849, No. 1). AIP Publishing.
[23] Jibanchand, N., & Devi, K. R. (2023). Application of ensemble learning in predicting shallow foundation settlement in cohesionless soil. International Journal of Geotechnical Engineering, 1-12.
[24] Padmini, D., Ilamparuthi, K., & Sudheer, K. P. (2008). Ultimate bearing capacity prediction of shallow foundations on cohesionless soils using neurofuzzy models. Computers and Geotechnics, 35(1), 33-46.
[25] Kalinli, A., Acar, M. C., & Gündüz, Z. (2011). New approaches to determine the ultimate bearing capacity of shallow foundations based on artificial neural networks and ant colony optimization. Engineering Geology, 117(1-2), 29-38.
[26] Colliot, O. (Ed.). (2023). Machine Learning for Brain Disorders.
[27] Cunningham, P., Cord, M., & Delany, S. J. (2008). Supervised learning. In Machine learning techniques for multimedia: case studies on organization and retrieval (pp. 21-49). Berlin, Heidelberg: Springer Berlin Heidelberg.
[28] Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. nature, 323(6088), 533-536.
[29] Elsafi, S. H. (2014). Artificial neural networks (ANNs) for flood forecasting at Dongola Station in the River Nile, Sudan. Alexandria Engineering Journal, 53(3), 655-662.
[30] Jakkula, V. (2006). Tutorial on support vector machine (svm). School of EECS, Washington State University, 37(2.5), 3.
[31] Samui, P. (2011). Prediction of pile bearing capacity using support vector machine. International Journal of Geotechnical Engineering, 5(1), 95-102.
[32] Cover, T., & Hart, P. (1967). Nearest neighbor pattern classification. IEEE transactions on information theory, 13(1), 21-27.
 
[33] Guo, G., Wang, H., Bell, D., Bi, Y., & Greer, K. (2003). KNN model-based approach in classification. In On The Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE: OTM Confederated International Conferences, CoopIS, DOA, and ODBASE 2003, Catania, Sicily, Italy, November 3-7, 2003. Proceedings (pp. 986-996). Springer Berlin Heidelberg.
[34] Lee, K. C., & Lee, C. H. (2020) Prediction of Complicated Mathematical Problems by Machine Learning of KNN Regression.
[35] Faouzi, J., & Colliot, O. (2023). Classic machine learning algorithms. Machine Learning for Brain Disorders.
[36] Ying, C., Qi-Guang, M., Jia-Chen, L., & Lin, G. (2013). Advance and prospects of AdaBoost algorithm. Acta Automatica Sinica, 39(6), 745-758.
[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] Prokhorenkova, L., Gusev, G., Vorobev, A., Dorogush, A. V., & Gulin, A. (2018). CatBoost: unbiased boosting with categorical features. Advances in neural information processing systems, 31.
[39] González, S., García, S., Del Ser, J., Rokach, L., & Herrera, F. (2020). A practical tutorial on bagging and boosting based ensembles for machine learning: Algorithms, software tools, performance study, practical perspectives and opportunities. Information Fusion, 64, 205-237.
[40] Ke, G., Meng, Q., Finley, T., Wang, T., Chen, W., Ma, W.,& Liu, T. Y. (2017). Lightgbm: A highly efficient gradient boosting decision tree. Advances in neural information processing systems, 30.
[41] Gandhi, G. N. (2001). Study of Bearing Capacity Factors Developed from Laboratory Experiments on Shallow Footings Founded on Cohesionless Soil.
 
[42] Muhs, H., & Weiß, K. (1971). Untersuchung von grenztragfaehigkeit und setzungsverhalten flachgegruende­ter einzelfundamente in ungleichfoermingen nichtbindigen boeden.
[43] Weiß, K. (1970). Der Einfluß der Fundamentform auf die Grenztragfähigkeit flachgegründeter Fundamente, Untersuchungen ausgef von Klaus Weiß: mit 14 Zahlentaf. Ernst.
[44] Muhs, H., Elmiger, R., & Weiß, K. (1969). Sohlreibung und Grenztragfähigkeit unter lotrecht und schräg belasteten Einzelfundamenten; mit 128 Bildern und 13 Zahlentafeln. Ernst.
[45] Muhs, H., & Weiss, K. (1974). Inclined load tests on shallow strip footings.
[46] Briaud, J. L., & Gibbens, R. (1999). Behavior of five large spread footings in sand. Journal of geotechnical and geoenvironmental engineering, 125(9), 787-796.
[47] Barnston, A. G. (1992). Correspondence among the correlation, RMSE, and Heidke forecast verification measures; refinement of the Heidke score. Weather and Forecasting, 7(4), 699-709.
[48] Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International journal of forecasting, 22(4), 679-688.
 
[49] Renaud, O., & Victoria-Feser, M. P. (2010). A robust coefficient of determination for regression. Journal of Statistical Planning and Inference, 140(7), 1852-1862.
 
[50] Willmott, C. J., & Matsuura, K. (2005). Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Climate research, 30(1), 79-82.
[51] Jahed Armaghani, D., Hajihassani, M., Monjezi, M., Mohamad, E. T., Marto, A., & Moghaddam, M. R. (2015). Application of two intelligent systems in predicting environmental impacts of quarry blasting. Arabian Journal of Geosciences, 8, 9647-9665.
[52] Armaghani, D. J., Hatzigeorgiou, G. D., Karamani, C., Skentou, A., Zoumpoulaki, I., & Asteris, P. G. (2019). Soft computing-based techniques for concrete beams shear strength. Procedia Structural Integrity, 17, 924-933.
[53] Famili, A., Shen, W. M., Weber, R., & Simoudis, E. (1997). Data preprocessing and intelligent data analysis. Intelligent data analysis, 1(1), 3-23.
[54] Jović, A., Brkić, K., & Bogunović, N. (2015, May). A review of feature selection methods with applications. In 2015 38th international convention on information and communication technology, electronics and microelectronics (MIPRO) (pp. 1200-1205). Ieee.
[55] Zhou, H., Deng, Z., Xia, Y., & Fu, M. (2016). A new sampling method in particle filter based on Pearson correlation coefficient. Neurocomputing, 216, 208-215.
[56] Rasamoelina, A. D., Adjailia, F., & Sinčák, P. (2020, January). A review of activation function for artificial neural network. In 2020 IEEE 18th World Symposium on Applied Machine Intelligence and Informatics (SAMI) (pp. 281-286). IEEE.
[57] Schmidt-Hieber, J. (2020). Nonparametric regression using deep neural networks with ReLU activation function.
[58] Jiang, Y., & Han, F. (2017). A hybrid algorithm of adaptive particle swarm optimization based on adaptive moment estimation method. In Intelligent Computing Theories and Application: 13th International Conference, ICIC 2017, Liverpool, UK, August 7-10, 2017, Proceedings, Part I 13 (pp. 658-667). Springer International Publishing.
[59] Chen, M., Liu, Q., Chen, S., Liu, Y., Zhang, C. H., & Liu, R. (2019). XGBoost-based algorithm interpretation and application on post-fault transient stability status prediction of power system. IEEE Access, 7, 13149-13158
Volume 9, Issue 2
Autumn 2024
Pages 40-54

  • Receive Date 03 May 2024
  • Revise Date 13 September 2024
  • Accept Date 07 December 2024