Skip to main content
SpringerLink
Log in

Data-driven approach to solve vertical drain under time-dependent loading

  • Research Article
  • Published:
Frontiers of Structural and Civil Engineering Aims and scope Submit manuscript

Abstract

Currently, the vertical drain consolidation problem is solved by numerous analytical solutions, such as time-dependent solutions and linear or parabolic radial drainage in the smear zone, and no artificial intelligence (AI) approach has been applied. Thus, in this study, a new hybrid model based on deep neural networks (DNNs), particle swarm optimization (PSO), and genetic algorithms (GAs) is proposed to solve this problem. The DNN can effectively simulate any sophisticated equation, and the PSO and GA can optimize the selected DNN and improve the performance of the prediction model. In the present study, analytical solutions to vertical drains in the literature are incorporated into the DNN—PSO and DNN—GA prediction models with three different radial drainage patterns in the smear zone under time-dependent loading. The verification performed with analytical solutions and measurements from three full-scale embankment tests revealed promising applications of the proposed approach.

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

Similar content being viewed by others

Abbreviations

c h :

coefficient of consolidation in the horizontal direction

c v :

coefficient of consolidation in the vertical direction

F c :

parameter to reflect the effect of the decay pattern

H :

soil thickness

k d :

coefficient of permeability of the drain

k h :

horizontal coefficient of permeability

k s :

horizontal coefficient of permeability of the smeared zone

k v :

vertical coefficient of permeability

m v :

coefficient of volume compressibility

q w :

discharge capacity

r d :

drain radius

r e :

equivalent radius of the influence zone

r s :

smeared zone radius

u :

excess pore water pressure

\(\bar{u}\) :

average excess pore water pressure

τ(t):

the surcharge load

ε v :

vertical strain

γ w :

unit weight of water

References

  1. Guo H, Zhuang X, Rabczuk T. A deep collocation method for the bending analysis of Kirchhoff plate. Computers, Materials & Continua, 2019, 59(2): 433–156

    Article  Google Scholar 

  2. Anitescu C, Atroshchenko E, Alajlan N, Rabczuk T. Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials & Continua, 2019, 59(1): 345–359

    Article  Google Scholar 

  3. Samaniego E, Anitescu C, Goswami S, Nguyen-Thanh V M, Guo H, Hamdia K, Zhuang X, Rabczuk T. An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Computer Methods in Applied Mechanics and Engineering, 2020, 362: 112790

    Article  MathSciNet  Google Scholar 

  4. Guo H, Zhuang X, Meng X, Rabczuk T. Integrated intelligent Jaya Runge-Kutta method for solving Falkner-Skan equations for various wedge angles. 2020, arXiv:2010.05682

  5. Hamdia K M, Zhuang X, Rabczuk T. An efficient optimization approach for designing machine learning models based on genetic algorithm. Neural Computing & Applications, 2021, 33(6): 1923–1933

    Article  Google Scholar 

  6. Zhuang X, Guo H, Alajlan N, Rabczuk T. Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates. European Journal of Mechanics. A, Solids, 2020, 2010: 05698

    MATH  Google Scholar 

  7. Ahmad I, Hesham El Naggar M, Khan A N. Artificial neural network application to estimate kinematic soil pile interaction response parameters. Soil Dynamics and Earthquake Engineering, 2007, 27(9): 892–905

    Article  Google Scholar 

  8. Momeni E, Nazir R, Jahed Armaghani D, Maizir H. Prediction of pile bearing capacity using a hybrid genetic algorithm-based ANN. Measurement, 2014, 57: 122–131

    Article  Google Scholar 

  9. Kurup P U, Dudani N K. Neural networks for profiling stress history of clays from PCPT data. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(7): 569–579

    Article  Google Scholar 

  10. Lee S J, Lee S R, Kim Y S. An approach to estimate unsaturated shear strength using artificial neural network and hyperbolic formulation. Computers and Geotechnics, 2003, 30(6): 489–503

    Article  Google Scholar 

  11. Ham B T, Nguyen M D, Dao D V, Prakash I, Ly H B, Le T T, Ho L S, Nguyen K T, Ngo T Q, Hoang V, Son L H, Ngo H T T, Tran H T, Do N M, Van Le H, Ho H L, Tien Bui D. Development of artificial intelligence models for the prediction of compression coefficient of soil: An application of Monte Carlo sensitivity analysis. Science of the Total Environment, 2019, 679: 172–184

    Article  Google Scholar 

  12. Beucher A, Møller A B, Greve M H. Artificial neural networks and decision tree classification for predicting soil drainage classes in Denmark. Geoderma, 2019, 352: 351–359

    Article  Google Scholar 

  13. Abbaszadeh Shahri A, Spross J, Johansson F, Larsson S. Landslide susceptibility hazard map in southwest Sweden using artificial neural network. Catena, 2019, 183: 104225

    Article  Google Scholar 

  14. Chen W, Pourghasemi H R, Kornejady A, Zhang N. Landslide spatial modeling: Introducing new ensembles of ANN, MaxEnt, and SVM machine learning techniques. Geoderma, 2017, 305: 314–327

    Article  Google Scholar 

  15. Khanlari G R, Heidari M, Momeni A A, Abdilor Y. Prediction of shear strength parameters of soils using artificial neural networks and multivariate regression methods. Engineering Geology, 2012, 131–132: 11–18

    Article  Google Scholar 

  16. Tiryaki B. Predicting intact rock strength for mechanical excavation using multivariate statistics, artificial neural networks, and regression trees. Engineering Geology, 2008, 99(1–2): 51–60

    Article  Google Scholar 

  17. Bergado D T, Balasubramaniam A S, Fannin R J, Holtz R D. Prefabricated vertical drains (PVDs) in soft Bangkok clay: A case study of the new Bangkok International Airport project. Canadian Geotechnical Journal, 2002, 39(2): 304–315

    Article  Google Scholar 

  18. Bergado D T, Chaiyaput S, Artidteang S, Nguyen T N. Microstructures within and outside the smear zones for soft clay improvement using PVD only, Vacuum-PVD, Thermo-PVD and Thermo-Vacuum-PVD. Geotextiles and Geomembranes, 2020, 48(6): 828–843

    Article  Google Scholar 

  19. Nghia N T, Lam L G, Shukla S K. A new approach to solution for partially penetrated prefabricated vertical drains. International Journal of Geosynthetics and Ground Engineering, 2018, 4(2): 11–17

    Article  Google Scholar 

  20. Nghia-Nguyen T, Shukla S K, Nguyen D D C, Lam L G, H-Dang P, Nguyen P C. A new discrete method for solution to consolidation problem of ground with vertical drains subjected to surcharge and vacuum loadings. Engineering Computations, 2019, 37(4): 1213–1236

    Article  Google Scholar 

  21. Nguyen T N, Bergado D T, Kikumoto M, Dang H P, Chaiyaput S, Nguyen P C. A simple solution for prefabricated vertical drain with surcharge preloading combined with vacuum consolidation. Geotextiles and Geomembranes, 2021, 49(1): 304–322

    Article  Google Scholar 

  22. Shome R, Tang W N, Song C, Mitash C, Kourtev H, Yu J, Boularias A, Bekris K E. Towards robust product packing with a minimalistic end-effector. In: 2019 International Conference on Robotics and Automation (ICRA). IEEE, 2019, 9007–9013

  23. Lu M M, Xie K H, Wang S Y. Consolidation of vertical drain with depth-varying stress induced by multi-stage loading. Computers and Geotechnics, 2011, 38(8): 1096–1011

    Article  Google Scholar 

  24. Tang X W, Onitsuka K. Consolidation by vertical drains under time-dependent loading. International Journal for Numerical and Analytical Methods in Geomechanics, 2000, 24(9): 739–751

    Article  Google Scholar 

  25. Rujikiatkamjorn C, Indraratna B. Analytical solution for radial consolidation considering soil structure characteristics. Canadian Geotechnical Journal, 2015, 52(7): 947–960

    Article  Google Scholar 

  26. Xie K H, Lu M M, Liu G B. Equal strain consolidation for stone columns reinforced foundation. International Journal for Numerical and Analytical Methods in Geomechanics, 2009, 33(15): 1721–1735

    Article  Google Scholar 

  27. Dey N, Borra S, Ashour A Sand Shi F. Machine Learning in Bio-Signal Analysis and Diagnostic Imaging. Academic Press, 2018, 159–182

  28. Kennedy J, Eberhart R. Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks. IEEE, 1995, 4: 1942–1948

  29. Golberg D E. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison Wesley, 1989

  30. Van Der Malsburg C. Frank Rosenblatt: Principles of neurodynamics: Perceptrons and the Theory of Brain Mechanisms. In: Palm G, Aertsen A, eds. Brain Theory. Berlin: Springer, 1986, 245–248

    Chapter  Google Scholar 

  31. Moghaddasi M R, Noorian-Bidgoli M. ICA-ANN, ANN and multiple regression models for prediction of surface settlement caused by tunneling. Tunnelling and Underground Space Technology, 2018, 79: 197–209

    Article  Google Scholar 

  32. Hagan M T, Menhaj M B. Training feedforward networks with the Marquardt algorithm. IEEE Transactions on Neural Networks, 1994, 5(6): 989–993

    Article  Google Scholar 

  33. Rafiq M Y, Bugmann G, Easterbrook D J. Neural network design for engineering applications. Computers & Structures, 2001, 79(17): 1541–1552

    Article  Google Scholar 

  34. Prechelt L. Early stopping—But when, neural networks: Tricks of the trade. In: Montavon G, Orr G B, Müller K R, eds. Neural Networks: Tricks of the Trade. Springer, 1998, 55–69

  35. Huang S C, Huang Y F. Bounds on the number of hidden neurons in multilayer perceptrons. IEEE Transactions on Neural Networks, 1991, 2(1): 47–55

    Article  Google Scholar 

  36. Kanellopoulos I, Wilkinson G G. Strategies and best practice for neural network image classification. International Journal of Remote Sensing, 1997, 18(4): 711–725

    Article  Google Scholar 

  37. Lin D G, Chang K T. Three-dimensional numerical modelling of soft ground improved by prefabricated vertical drains. Geosynthetics International, 2009, 16(5): 339–353

    Article  MathSciNet  Google Scholar 

  38. Lam L G, Bergado D T, Hino T. PVD improvement of soft Bangkok clay with and without vacuum preloading using analytical and numerical analyses. Geotextiles and Geomembranes, 2015, 43(6): 547–557

    Article  Google Scholar 

  39. Bergado D T, Manivannan R, Balasubramaniam A S. Proposed criteria for discharge capacity of prefabricated vertical drains. Geotextiles and Geomembranes, 1996, 14(9): 481–505

    Article  Google Scholar 

  40. Deng Y B, Liu G B, Lu M M, Xie K H. Consolidation behavior of soft deposits considering the variation of prefabricated vertical drain discharge capacity. Computers and Geotechnics, 2014, 62: 310–316

    Article  Google Scholar 

Download references

Acknowledgements

Financial support provided by Ho Chi Minh City Open University is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Yokohama National University, Yokohama, 240-8501, Japan

    Trong Nghia-Nguyen & Mamoru Kikumoto

  2. Faculty of Civil Engineering, Ho Chi Minh City Open University, Ho Chi Minh City, 70000, Vietnam

    Trong Nghia-Nguyen & Thanh Cuong-Le

  3. Department of Electrical Energy, Metals, Mechanical Constructions and Systems, Faculty of Engineering and Architecture, Ghent University, Ghent, 9000, Belgium

    Samir Khatir

  4. Department of Civil Engineering, School of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, 10520, Thailand

    Salisa Chaiyaput

  5. CIRTECH Institute, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, 708300, Vietnam

    H. Nguyen-Xuan

Authors
  1. Trong Nghia-Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mamoru Kikumoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Samir Khatir
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Salisa Chaiyaput
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. H. Nguyen-Xuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Thanh Cuong-Le
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thanh Cuong-Le.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nghia-Nguyen, T., Kikumoto, M., Khatir, S. et al. Data-driven approach to solve vertical drain under time-dependent loading. Front. Struct. Civ. Eng. 15, 696–711 (2021). https://doi.org/10.1007/s11709-021-0727-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11709-021-0727-7

Keywords

Search

Navigation