Novel metaheuristic classification approach in developing mathematical model-based solutions predicting failure in shallow footing

  • 45 Accesses

  • 2 Citations


This study evaluated and compared several novel classification approaches to develop the most reliable stability model-based solution in the prediction of shallow footing’s allowable settlement. By applying the biogeography-based algorithm, this study presents an optimized metaheuristic classification approach with mathematical-based multi-layer perceptron neural network and fuzzy inference system to achieve a better assessment of the recognition of a complex failure phenomenon. By the contribution of a large number of finite element simulation, and considering seven key factors, the settlement of a shallow footing placed on a two-layered soil was measured as the target variable. Then, to change into the classification method, two overall situations of stability or failure were considered for the proposed soil layer. The ensemble of BBO–MLP and BBO–FIS are developed, and the results are evaluated by well-known accuracy indices. The results showed that employing BBO helps both MLP and FIS to have a better analysis. Besides, referring to the obtained total ranking scores of 6, 5, 11, and 8, respectively, for the MLP, FIS, BBO–MLP, and BBO–FIS, the BBO–MLP found to be the most accurate model, followed by BBO–FIS, MLP, and FIS.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2


  1. 1.

    Cicek E, Guler E (2015) Bearing capacity of strip footing on reinforced layered granular soils. J Civ Eng Manag 21:605–614

  2. 2.

    Mosallanezhad M, Moayedi H (2017) Comparison analysis of bearing capacity approaches for the strip footing on layered soils. Arab J Sci Eng 42:3711–3722

  3. 3.

    Terzaghi K, Peck R, Mesri G (1943) Soil mechanics in engineering practice. Wiley, NewYork

  4. 4.

    Frydman S, Burd H (1997) Numerical studies of bearing-capacity factor N γ. J Geotech Geoenviron Eng 123:20–29

  5. 5.

    Silvestri V (2003) A limit equilibrium solution for bearing capacity of strip foundations on sand. Can Geotech J 40:351–361

  6. 6.

    Lotfizadeh MR, Kamalian M (2016) Estimating bearing capacity of strip footings over two-layered sandy soils using the characteristic lines method. Int J Civ Eng 14:107–116

  7. 7.

    Florkiewicz A (1989) Upper bound to bearing capacity of layered soils. Can Geotech J 26:730–736

  8. 8.

    Michalowski RL, Shi L (1995) Bearing capacity of footings over two-layer foundation soils. J Geotech Eng 121:421–428

  9. 9.

    Dewaikar D, Mohapatra B (2003) Computation of bearing capacity factor Nγ-Prandtl’s mechanism. Soils Found 43:1–10

  10. 10.

    Ghazavi M, Eghbali AH (2008) A simple limit equilibrium approach for calculation of ultimate bearing capacity of shallow foundations on two-layered granular soils. Geotech Geol Eng 26:535–542

  11. 11.

    Keskin MS, Laman M (2013) Model studies of bearing capacity of strip footing on sand slope. KSCE J Civ Eng 17:699–711

  12. 12.

    Ziaee SA, Sadrossadat E, Alavi AH, Shadmehri DM (2015) Explicit formulation of bearing capacity of shallow foundations on rock masses using artificial neural networks: application and supplementary studies. Environ Earth Sci 73:3417–3431

  13. 13.

    Moayedi H, Moatamediyan A, Nguyen H, Bui X-N, Bui DT, Rashid ASA (2019) Prediction of ultimate bearing capacity through various novel evolutionary and neural network models. Eng Comput 35:1–17

  14. 14.

    Bui X-N, Moayedi H, Safuan ARA (2019) Developing a predictive method based on optimized M5Rules–GA predicting heating load of an energy-efficient building system. Eng Comput 36:1–10

  15. 15.

    Liu L, Moayedi H, Rashid ASA, Rahman SSA, Nguyen H (2019) Optimizing an ANN model with genetic algorithm (GA) predicting load-settlement behaviours of eco-friendly raft-pile foundation (ERP) system. Eng Comput 36:1–13

  16. 16.

    Moayedi H, Hayati S (2018) Modelling and optimization of ultimate bearing capacity of strip footing near a slope by soft computing methods. Appl Soft Comput 66:208–219

  17. 17.

    Moayedi H, Mosallanezhad M, Mehrabi M, Safuan ARA (2018) A systematic review and meta-analysis of artificial neural network application in geotechnical engineering: theory and applications. Neural Comput Appl 31:1–24

  18. 18.

    Gao W, Guirao JLG, Basavanagoud B, Wu J (2018) Partial multi-dividing ontology learning algorithm. Inf Sci 467:35–58

  19. 19.

    Alnaqi AA, Moayedi H, Shahsavar A, Nguyen TK (2018) Prediction of energetic performance of a building integrated photovoltaic/thermal system thorough artificial neural network and hybrid particle swarm optimization models. Energy Convers Manage 183:137–148

  20. 20.

    Moayedi H, Mosallanezhad M, Mehrabi M, Safuan ARA, Biswajeet P (2019) Modification of landslide susceptibility mapping using optimized PSO-ANN technique. Eng Comput 35:967–984

  21. 21.

    Nguyen H, Bui X-N, Moayedi H (2019) A comparison of advanced computational models and experimental techniques in predicting blast-induced ground vibration in open-pit coal mine. Acta Geophys 28:1–13

  22. 22.

    Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12:702–713

  23. 23.

    McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5:115–133

  24. 24.

    Gao W, Guirao JLG, Abdel-Aty M, Xi W (2019) An independent set degree condition for fractional critical deleted graphs. Discrete Continuous Dyn Syst-S 12:877–886

  25. 25.

    Nguyen H, Drebenstedt C, Bui X-N, Bui DT (2019) Prediction of blast-induced ground vibration in an open-pit mine by a novel hybrid model based on clustering and artificial neural network. Nat Resour Res 28:1–19

  26. 26.

    Gao W, Wang W, Dimitrov D, Wang Y (2018) Nano properties analysis via fourth multiplicative ABC indicator calculating. Arab J Chem 11:793–801

  27. 27.

    Nguyen H, Jamali Moghadam M, Moayedi H (2019) Agricultural wastes preparation, management and applications in engineering: a review. J Mater Cycles Waste Manage 21:1–13

  28. 28.

    Nguyen H, Mehrabi M, Kalantar B, Moayedi H, Muazu MA (2019) Potential of hybrid evolutionary approaches for assessment of geo-hazard landslide susceptibility mapping. Geomatics Nat Hazards Risk 10:1667–1693

  29. 29.

    Nguyen H, Moayedi H, Sharifi A, Amizah WJW, Safuan ARA (2019) Proposing a novel predictive technique using M5Rules-PSO model estimating cooling load in energy-efficient building system. Eng Comput 35:1–11

  30. 30.

    Shang Y, Nguyen H, Bui X-N, Tran Q-H, Moayedi H (2019) A novel artificial intelligence approach to predict blast-induced ground vibration in open-pit mines based on the firefly algorithm and artificial neural network. Nat Resour Res 28:1–15

  31. 31.

    Gao W, Wu H, Siddiqui MK, Baig AQ (2018) Study of biological networks using graph theory. Saudi J Biol Sci 25:1212–1219

  32. 32.

    Wang B, Moayedi H, Nguyen H, Foong LK, Rashid ASA (2019) Feasibility of a novel predictive technique based on artificial neural network optimized with particle swarm optimization estimating pullout bearing capacity of helical piles. Eng Comput 36:1–10

  33. 33.

    Yuan C, Moayedi H (2019) The performance of six neural-evolutionary classification techniques combined with multi-layer perception in two-layered cohesive slope stability analysis and failure recognition. Eng Comput 36:1–10

  34. 34.

    Zhang X, Nguyen H, Bui X, Tran Q, Nguyen D, Bui D, Moayedi H (2019) Novel soft computing model for predicting blast-induced ground vibration in open-pit mines based on particle swarm optimization and XGBoost. Nat Resour Res 28:1–11

  35. 35.

    Moayedi H, Hayati S (2018) Applicability of a CPT-based neural network solution in predicting load-settlement responses of bored pile. Int J Geomech 18:06018009

  36. 36.

    Moayedi H, Hayati S (2018) Artificial intelligence design charts for predicting friction capacity of driven pile in clay. Neural Comput Appl 31:1–17

  37. 37.

    Jang J-S (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23:665–685

  38. 38.

    Moayedi H, Raftari M, Sharifi A, Jusoh WAW, Rashid ASA (2019) Optimization of ANFIS with GA and PSO estimating α ratio in driven piles. Eng Comput 35:1–12

Download references

Author information

Correspondence to Hossein Moayedi.

Ethics declarations

Conflict of interest

The authors of this manuscript declaring of no conflict of interest to other published works.

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Moayedi, H., Nguyen, H. & Rashid, A.S.A. Novel metaheuristic classification approach in developing mathematical model-based solutions predicting failure in shallow footing. Engineering with Computers (2019).

Download citation


  • Metaheuristic classification
  • Evolutionary algorithms
  • Hybrid
  • Stability