Skip to main content
SpringerLink
Log in

Probabilistic analysis of gravity retaining wall against bearing failure

  • Research
  • Published:
Asian Journal of Civil Engineering Aims and scope Submit manuscript

Abstract

Machine learning (ML) models have been extensively used in the stability check of gravity retaining wall. They are renowned as the most capable methods for predicting factor of safety (FOS) of gravity retaining wall against bearing failure. In this work, FOS against bearing is predicted based on extreme gradient boosting (XGBoost), random forest (RF) and deep neural network (DNN). To establish homogeneity and distribution of datasets, Anderson−Darling (AD) and Mann−Whitney U (M−W) tests are carried out, respectively. These three machine learning models are applied to 100 datasets by considering six influential input parameters for predicting FOS against bearing failure. The execution of the established machine learning models is assessed by several performance parameters. The obtained results from computational approach shows that DNN attained the best predictive performance with coefficient of determination (R2) = 0.998 and root mean square error (RMSE) = 0.006 in the training phase and R2 = 0.929 and RMSE = 0.053 in the testing phase. The models result are also analyzed by using rank analysis, regression error characteristics curve, and accuracy matrix. Sensitivity analysis is carried to know the relative importance of input variables.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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
Fig. 14

Similar content being viewed by others

References

  • Alghaffar, M., & Wellington, C. (2005). Reliability analysis of retaining walls designed to British and European standards. Structure and Infrastructure Engineering, 1, 271–284.

    Article  Google Scholar 

  • Ali, Z. H., & Burhan, A. M. (2023). Hybrid machine learning approach for construction cost estimation: An evaluation of extreme gradient boosting model. Asian Journal of Civil Engineering. https://doi.org/10.1007/s42107-023-00651-z

    Article  Google Scholar 

  • Asteris, P.G., & Mokos, V.G. (2020). Concrete compressive strength using artificial neural networks. Neural Comput. Appl., 32, 11807–11826.Babu, G.L.S., Srivastava, A. (2007). Reliability analysis of allowable pressure on shallow foundation using response surface method. Comput. Geotech, 34(3), 187–194.

  • Basha, B. M., & Babu, G. L. S. (2008). Optimum design of cantilever sheet pile walls in sandy soils using inverse reliability approach. Computers and Geotechnics, 35, 134–143.

    Article  Google Scholar 

  • Benuwa, B. B., Zhan, Y., Ghansah, B., Wornyo, D. K., & Kataka, F. B. (2016). A review of deep machine learning. International Journal of Engineering Research in Africa, 24, 124–136.

    Article  Google Scholar 

  • Bowles, J.E. (1997). Foundation Analysis and Design. Fifth Edition, The McGraw Hill Companies, Inc.

  • Breiman, L. (2001). Random Forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324

    Article  MATH  Google Scholar 

  • Chen, T., & Guestrin, C. (2016). XGBoost: A scalable tree boosting system. 22nd ACM SIGKDD Int. Conf. Knowl., 785–794. https://doi.org/10.1145/2939672.2939785

  • Chen, H., Asteris, P., & Armaghani, D. J. (2019). Assessing dynamic conditions of the retaining wall: Developing two hybrid intelligent models. Applied Sciences. https://doi.org/10.3390/app9061042

    Article  Google Scholar 

  • Chouksey, S. K., & Fale, A. (2017). Reliability analysis of counterfort retaining wall. International Journal of Civil Engineering and Technology, 8, 1058–1073.

    Google Scholar 

  • Christian, J. T. (2004). Geotechnical engineering reliability: How well do we know what we are doing? Journal of Geotechnical Geoenvironmental Engineering, 130, 985–1003.

    Article  Google Scholar 

  • Cornell, C. (1969). A Probability-Based Structural Code. Inj. Proc., 66, 974–985.

    Google Scholar 

  • Dao-Bing, Z., Zhi-bin, S., & Chuan-qu, Z. (2013). Reliability analysis of retaining walls with multiple failure modes. Journal of Centeral South University., 20, 2879–2886. https://doi.org/10.1007/s11771-013-1809-z

    Article  Google Scholar 

  • Das, B. M. (1998). Principles of Foundation Engineering (4th ed.). Brooks/Cole Publishing Company.

    Google Scholar 

  • Goh, A. T. C., & Kulhawy, F. H. (2005). Reliability assessment of serviceability performance of braced retaining walls using a neural network approach. International Journal for Numerical and Analytical Methods in Geomechanics, 29, 627–642.

    Article  MATH  Google Scholar 

  • Goh, A. T., Phoon, K. K., & Kulhawy, F. H. (2009). Reliability analysis of partial safety factor design method for cantilever retaining walls in granular soils. J. Geotech. Geoenviron. Eng., 135, 616–622.

    Article  Google Scholar 

  • GuhaRay, A., Mondal, S., & Mohiuddin, H. H. (2018). Reliability analysis of retaining wall subjected to blast loading by finite element approach. J. Inst. Eng. India Ser. A, 99, 95–102. https://doi.org/10.1007/s40030-018-0273-z

    Article  Google Scholar 

  • Hashmi, A. F., Ayaz, M., Bilal, A., et al. (2023). GA-based hybrid ANN optimization approach for the prediction of compressive strength of high-volume fly ash concrete mixes. Asian J Civ Eng, 24, 1115–1128. https://doi.org/10.1007/s42107-022-00557-2

    Article  Google Scholar 

  • Hasofer, A. M., & Lind, N. C. (1974). Exact and invariant second-moment code format. Journal of the Engineering Mechanics Division, 100, 111–121.

    Article  Google Scholar 

  • IS: 6403 (1981). Code of practice for determination of bearing capacity of shallow foundations. Bureau of Indian Standards, New Delhi, India.

  • Jena, R., Pradhan, B., Beydoun, G., Nizamuddin, A., Sofyan, H., & Affan, M. (2019). Integrated model for earthquake risk assessment using neural network and analytic hierarchy process: Aceh province. Indonesia. Geosci. Front., 11(2), 613–634.

    Article  Google Scholar 

  • Jiang, S., Xiao, R., Wang, L., Luo, X., Huang, C., Wang, J. H., Chin, K. S., & Nie, X. (2019). Combining Deep Neural Networks and Classical Time Series Regression Models for Forecasting Patient Flows in Hong Kong. IEEE Access, 7, 118965–118974.

    Article  Google Scholar 

  • Kardani, N., Bardhan, A., Samui, P., Nazem, M., Zhou, A., & Armaghani, D. J. (2021). A novel technique based on the improved firefly algorithm coupled with extreme learning machine (ELM-IFF) for predicting the thermal conductivity of soil. Engineering Computations. https://doi.org/10.1007/s00366-021-01329-3

    Article  Google Scholar 

  • Kaveh, A., Kalateh-Ahni, M., & Fahimi-Farzam, M. (2013). Constructability optimal design of reinforced concrete retaining walls using a multi-objective genetic algorithm. Structural Engineering and Mechanics (Techno Press), 2(47), 227–245. https://doi.org/10.12989/SEM.2013.47.2.227

  • Kaveh, A., Gholipour, Y., & Rahami, H. (2008). Optimal design of transmission towers using genetic algorithm and neural networks. International Journal of Space Structures, 23(1), 1–19.

    Article  Google Scholar 

  • Kaveh, A., & Iranmanesh, A. (1998). Comparative study of backpropagation and improved counterpropagation neural nets in structural analysis and optimization. International Journal of Space Structures, 13, 177–185.

    Article  Google Scholar 

  • Kaveh, A., & Jafarpour Laien, D. (2017). Optimal design of reinforced concrete cantilever retaining walls using CBO, ECBO and VPS algorithms. Asian Journal of Civil Engineering, 18(4), 657–671.

    Google Scholar 

  • Kaveh, A., & Khalegi, A. (1998). Prediction of strength for concrete specimens using artificial neural network. Asian Journal of Civil Engineering, 2(2), 1–13.

    Google Scholar 

  • Kaveh, A., & Khavaninzadeh, N. (2023). Efficient training of two ANNs using four meta-heuristic algorithms for predicting the FRP strength. In Structures, 52, 256–272.

    Article  Google Scholar 

  • Kaveh, A., & Soleimani, N. (2015). CBO and DPSO for optimum design of reinforced concrete cantilever retaining walls. Asian Journal of Civil Engineering, 6(16), 751–774.

    Google Scholar 

  • Kumar, A., & Roy, P. (2017). Reliability analysis of retaining wall using imprecise probability. International Conf. on structural safety and Reliability, 288–297.

  • Kumar, M., Bardhan, A., Samui, P., Hu, J. W., & Kaloop, M. R. (2021). Reliability Analysis of Pile Foundation Using Soft Computing Techniques: A Comparative Study. Processes, 9, 486. https://doi.org/10.3390/pr9030486

    Article  Google Scholar 

  • Liaw, A., & Wiener, M. (2002). Classification and regression by random forest. R News, 2(3), 18–22. http://CRAN.R-project.org/doc/Rnews/

  • Low, B. K., Zhang, J., & Tang, W. H. (2011). Efficient system reliability analysis illustrated for a retaining wall and a soil slope. Computers and Geotechnics, 38, 196–204.

    Article  Google Scholar 

  • Mann, H.B., & Whitney, D.R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The annals of mathematical statistics, 50–60.

  • Menon, D., & Mangalathu, S. (2011). Reliability analysis and design of cantilever RC retaining walls against sliding failure. International Journal of Geotechnical Engineering, 5, 131–141.

    Article  Google Scholar 

  • Mishra, P., Samui, P., & Mahmoudi, E. (2021). Probabilistic Design of Retaining Wall Using Machine Learning Methods. Applied Science, 2–14.

  • Murthy, V. N. S. (2003). Geotechnical Engineering: Principles and Practices of Soil Mechanics and Foundation Engineering. Marcel Dekker Inc.

    Google Scholar 

  • Mustafa, R., Samui, P., Kumari, S. (2023). Seismic Performance of Gravity Retaining Walls Under Quasi-static Approach Using Probabilistic Analysis. Transp. Infrastruct. Geotech. https://doi.org/10.1007/s40515-023-00298-y

  • Pradeep, T., Bardhan, A., Burman, A., & Samui, P. (2021). Rock Strain Prediction Using Deep Neural Network and Hybrid Models of ANFIS and Meta-Heuristic Optimization Algorithms. Infrastructures, 6(9), 129. https://doi.org/10.3390/infrastructures6090129

    Article  Google Scholar 

  • Ray, R., Kumar, D., Samui, P., Goh, A. T. C., & Zhang, W. (2021). Application of soft computing techniques for shallow foundation reliability in geotechnical engineering. Geoscience Frontiers, 12, 375–383.

    Article  Google Scholar 

  • Razali, N. M., & Wah, Y. B. (2011). Power comparison of shapiro-wilk, kolmogorov-smirnov, lilliefors and anderson-darling tests. Journal of Statistical Modeling and Analytics, 2(1), 21–33.

    Google Scholar 

  • Salmi, Z. J., Khodakarami, M. I., & Behnamfar, F. (2023). Development of seismic fragility curves for RC/MR frames using machine learning methods. Asian J Civ Eng, 24, 823–836. https://doi.org/10.1007/s42107-022-00533-w

    Article  Google Scholar 

  • Shahin, M.A., Maier, H.R., Jaksa, M.B. (2003). Neural and neuro-fuzzy techniques applied to modelling settlement of shallow foundations on granular soils. Int. Congress on Modelling and Simulation, 1886–1891.

  • Terzaghi, K., Peck, R.B., & Mesri, G. (1996). Soil Mechanics in Engineering Practice. Third Edition, A Willey-Interscience Publication.

  • Wang, H., Chen, H., Wang, Y., & Han, L. (2020a). Reliability analysis for stability of the gravity retaining wall under mountain torrent. System Science & Control Engineering, 8, 434–440.

    Article  Google Scholar 

  • Wang, L., Wu, C., Tang, L., Zhang, W., Lacasse, S., Liu, H., & Goh, L. (2020b). Efficient reliability analysis of earth dam slope stability using extreme gradient boosting method. Acta Geotechnica, 15, 3135–3150.

    Article  Google Scholar 

  • Wu, C., Hong, L., Wang, L., Zhang, R., Samui, P., & Zhang, W. (2022). Prediction of wall deflection induced by braced excavation in spatially variable soils via convolutional neural network. Gondwana Research. https://doi.org/10.1016/j.gr.2022.06.011

    Article  Google Scholar 

  • Xiang, Y., Goh, A. T. C., Zhang, W., & Runhong, Z. (2018). A multivariate adaptive regression splines model for estimation of maximum wall deflections induced by braced excavation in clays. Geomechanics and Engineering, 14, 315–324.

    Google Scholar 

  • Xiao, Z., Huang, J., Wang, Y., & Xia, H. (2014). Random Reliability Analysis of Gravity Retaining Wall Structural System. International Conference on Mechanics and Civil Engineering, 199–204. https://dx.doi.org/https://doi.org/10.2991/icmce-14.2014.36

  • Yong, W., Zhang, W., Nguyen, H., Bui, X., Choi, Y., Nguyen, T., Zhou, J., & Tran, T. T. (2022). Analysis and prediction of diaphragm wall deflection induced by deep braced excavations using finite element method and artificial neural network optimized by metaheuristic algorithms. Reliability Engineering and System Safety, 221, 108335.

    Article  Google Scholar 

  • Zevgolis, I.E., & Bourdeau, P.L. (2006). System Reliability of Cantilever Retaining Wall with Correlated Failure Modes. In GeoCongress: Geotechnical Engineering in the Information Technology Age, 1–6. https://doi.org/10.1061/40803

  • Zhang, B., Zhang, Z., & Zheng, P. (2022). Reliability analysis of gravity retaining wall. Proceedings of the 8th International Conference on Civil Engineering. https://doi.org/10.1007/978-981-19-1260-3_44

  • Zhang, W. G., & Goh, A. T. C. (2013). Multivariate adaptive regression splines for analysis of geotechnical engineering systems. Computers and Geotechnics, 48, 82–95.

    Article  Google Scholar 

  • Zhang, W., Zhang, R., & Goh, A. T. C. (2017a). Multivariate adaptive regression splines approach to estimate lateral wall deflection profiles caused by braced excavations in clays. Geotechnical and Geological Engineering, 36, 1349–1363.

    Google Scholar 

  • Zhang, W. G., Zhang, Y. M., & Goh, A. T. C. (2017b). Multivariate adaptive regression splines for inverse analysis of soil and wall properties in braced excavation. Tunneling and Underground Space Technology, 64, 24–33.

    Article  Google Scholar 

  • Zhou, G. M., Li, Y., & Zhang, F. (2014). Analysis of Reliability Calculation and System Analysis of Gravity Retaining Walls. Applied Mechanics and Materials, 556–562, 862–866. https://doi.org/10.4028/www.scientific.net/amm.556-562.862

    Article  Google Scholar 

Download references

Acknowledgements

Not applicable.

Funding

No funding was received for conducting this study.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, National Institute of Technology Patna, Patna, Bihar, 800 005, India

    Rashid Mustafa, Pijush Samui & Sunita Kumari

  2. Centre of Tropical Geoengineering (GEOTROPIK), Institute for Smart Infrastructure and Innovative Construction (ISIIC), Department of Civil Engineering, Universiti Teknologi Malaysia, 81310, Johor, Malaysia

    Edy Tonnizam Mohamad & Ramesh Murlidhar Bhatawdekar

Authors
  1. Rashid Mustafa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pijush Samui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sunita Kumari
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Edy Tonnizam Mohamad
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ramesh Murlidhar Bhatawdekar
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

RM: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing-original draft, Writing-review & editing; PS: Data curation, Software, Supervision, Validation; SK: Supervision, Validation; ETM: Validation; RMB: Validation.

Corresponding author

Correspondence to Rashid Mustafa.

Ethics declarations

Conflict of interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Availability of data and material

Data presented in the paper are available with authors.

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., Samui, P., Kumari, S. et al. Probabilistic analysis of gravity retaining wall against bearing failure. Asian J Civ Eng 24, 3099–3119 (2023). https://doi.org/10.1007/s42107-023-00697-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42107-023-00697-z

Keywords

Search

Navigation