Evolutionary computing to determine the skin friction capacity of piles embedded in clay and evaluation of the available analytical methods

Research output: Contribution to journalArticle


Colleges, School and Institutes


Deep foundations are very important elements in the routine design of railways and bridges when the loads applied due to these important structures are higher than the bearing capacity of the soil. However, the methods currently available to calculate the bearing capacity of driven piles embedded in clay have been developed based on empirical factors derived from limited tests. Hence, further assessment of these methods and the development of new methods are urgently required. This paper discusses the development of a new robust model to calculate the skin friction capacity of driven piles using the multi-objective evolutionary polynomial regression (MOGA-EPR) analysis. The paper also evaluates the accuracy of the available analytical methods. Real field results of skin friction capacity of driven piles have been used to achieve the objectives of the study. The results showed that the MOGA-EPR predicts the skin friction of driven piles with an excellent accuracy and better than the available analytical methods, with a mean absolute error (MAE), a root mean square error (RMSE), mean (μ), a standard deviation (σ), a coefficient of determination (R 2), the variance account for (VAF) and a20-index of 3.4, 4.6, 1.03, 0.24, 0.98, 99, and 0.75, respectively, for the training data, and 4.2, 5.3, 1.12, 0.15, 0.91, 97 and 0.77, respectively, for testing data. In addition, a novel model to predict the skin friction capacity of driven piles has been proposed based on the MOGA-EPR analysis and this model can be used by engineers and researcher with confidence. The evaluation of the analytical methods illustrated that the Lambda method accuracy is better than the Alpha and Beta methods as this method scored a less mean error (MAE = 7.8 and RMSE = 12.5), a less standard deviation (σ = 0.21), a higher coefficient of determination (R 2 = 0.91), and higher value for the variance account for (VAF = 89) compared with the other analytical methods. In addition, the Beta method scored lowest compared with the other analytical methods with MAE, RMSE, μ, σ, R 2, VAF and a20-index of 17.2, 28.0, 1.07, 1.00, 0.55, 40 and 0.37, respectively. The findings of this study will help to achieve robust calculations of pile capacity and reduce uncertainty associated with the choice of the analytical method used in the design of driven piles in clay.


Original languageEnglish
Article number100372
JournalTransportation Geotechnics
Early online date19 May 2020
Publication statusE-pub ahead of print - 19 May 2020


  • Analytical methods, Driven piles, Evolutionary polynomial regression analysis, Skin friction