Skip to main content
Log in

Reliability Analysis of Pile Foundation in Cohesionless Soil Using Machine Learning Techniques

  • Technical Paper
  • Published:
Transportation Infrastructure Geotechnology Aims and scope Submit manuscript

Abstract

Because of the inherent uncertainty and unpredictability in pile design, a great deal of study has been done to measure the reliability of the structures. This paper offers machine learning (ML)–based prediction method for allowable load carrying capacity of pile foundation and examines and compares the applicability and adaptability of k-nearest neighbor (KNN), deep neural network (DNN), and random forest (RF) in the reliability investigation of pile embedded in cohesionless soil. These three ML models are applied to 150 datasets, considering five important inputs, namely, the diameter of the pile (d), the angle of the internal friction of the soil (φ), the unit weight of the soil (γ), the friction angle between the soil and the pile (δ), and the factor of safety (FOS) for predicting allowable load carrying capacity (Q). A range of performance metrics, including coefficient of determination (R2), variance account factor (VAF), Legate and McCabe’s index (LMI), A-10 index, Willmott’s index of agreement (WI), root mean square error (RMSE), median absolute deviation (MAD), mean absolute error (MAE), mean square error (MSE), and expanded uncertainty (U95), are employed to assess the efficacy of the well-established ML models. Using performance metrics, the results show that, of the three proposed ML models, DNN had the best predictive performance due to its highest value of R2 = 0.9678 and the lowest value of RMSE = 0.0306 in the training phase and R2 = 0.9853 and RMSE = 0.0145 in the testing phase. The model’s performance is also examined using rank analysis, reliability analysis, regression plot, REC curve, objective function criterion, Akaike information criterion, and error matrix plot. The model’s reliability index (β) is computed using first-order second moment (FOSM) techniques and compared with the actual value. Additionally, to know the effect of each input parameter on the output, a sensitivity analysis is conducted.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig.3
Fig.4
Fig. 5
Fig.6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Data Availability

Data presented in the paper are available with the authors.

References

Download references

Author information

Authors and Affiliations

Authors

Contributions

Rashid Mustafa: Conceptualization, data curation, formal analysis, investigation, methodology, software, validation, visualization, writing (original draft), writing—review and editing. Md Talib Ahmad: Software.

Corresponding author

Correspondence to Rashid Mustafa.

Ethics declarations

Ethics Approval and Consent to Participate

Not applicable.

Consent for Publication

Not applicable.

Competing Interests

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mustafa, R., Ahmad, M.T. Reliability Analysis of Pile Foundation in Cohesionless Soil Using Machine Learning Techniques. Transp. Infrastruct. Geotech. (2024). https://doi.org/10.1007/s40515-024-00391-w

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40515-024-00391-w

Keywords

Navigation