A predictive model based on an optimized ANN combined with ICA for predicting the stability of slopes

  • Wei GaoEmail author
  • Mehdi Raftari
  • Ahmad Safuan A. Rashid
  • Mohammed Abdullahi Mu’azu
  • Wan Amizah Wan Jusoh
Original Article


In this study, we optimized artificial neural network (ANN) with imperialist competition algorithm (ICA) for the problem of slope stability design charts. To prepare training and testing datasets for the ANN and ICA–ANN predictive models, an extensive number of limit equilibrium analysis modelings (e.g., for the lower bound, LB, limit analysis and upper bound, UB, limit analysis) was conducted. The analyses were conducted using OptumG2 computer software and implemented on two-layered cohesive soil layer sets. For each of the LB and UB limit analysis, the database consisted of 320 training datasets and 80 testing datasets. Variables of the ICA algorithm such as the number of countries, the number of initial imperialists and the number of decades were optimized using a series of trial-and-error process. The input parameters that used thorough the OptumG2 finite element modeling (FEM) analysis include depth factor (i.e., the ratio of first soil layer thickness to the slope height), slope angle, undrained shear strength ratio where the output was taken dimensionless stability number. The estimated results for both of datasets (e.g., training and testing) from ANN and ICA–ANN models were assessed based on three known statistical indices namely value account for (VAF), root means squared error (RMSE), and coefficient of determination (R2). To evaluate the performance of proposed models, color intensity rating (CER) and total ranking method (TRM), i.e., based on the result of statistical indices, was used. After 72 trial-and-error processes (e.g., sensitivity analysis on some neurons) the optimal architecture of 3 × 6 × 1 were found for both of the ANN–UB and ANN–LB models. As a result, both models presented excellent performance, however according to the introduced ranking system the ICA–ANN model could slightly perform a better performance compared to ANN. Based on R2, RMSE and VAF values of (0.9999, 0.0107 and 99.9924) and (0.9991, 0.0102 and 99.9913), respectively, were found for training and testing of the optimized ICA–ANN–LB predictive model. Similarly, for the ICA–ANN–UB predictive model, values of (0.9984, 0.0129 and 99.9659) and (0.9984, 0.01047 and 99.9915) were obtained for the R2, RMSE and VAF of training and testing datasets, respectively. However, in the ANN model, the R2 and RMSE for both of the training and testing datasets were (0.9982 and 0.01815) and (0.9972 and 0.01748), respectively. This proves a better performance of the ICA–ANN model in predicting the behaviors of slope stability of cohesive soils and consequently more reliable design solution charts provided herein.


ANN ICA–ANN Optimization Slope stability Design charts 


Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.


  1. 1.
    Koopialipoor M, Armaghani DJ, Hedayat A, Marto A, Gordan B (2018) Applying various hybrid intelligent systems to evaluate and predict slope stability under static and dynamic conditions. Soft Comput 23:1–17Google Scholar
  2. 2.
    Marrapu BM, Jakka RS (2017) Assessment of slope stability using multiple regression analysis. Geomech Eng 13:237–254Google Scholar
  3. 3.
    Nazir R, Ghareh S, Mosallanezhad M, Moayedi H (2016) The influence of rainfall intensity on soil loss mass from cellular confined slopes. Measurement 81:13–25CrossRefGoogle Scholar
  4. 4.
    Li AJ, Khoo SY, Wang Y, Lyamin AV (2014) Application of neural network to rock slope stability assessments. CRC Press-Taylor & Francis Group, Boca RatonCrossRefGoogle Scholar
  5. 5.
    Moayedi H, Huat BB, Mohammad Ali TA, Asadi A, Moayedi F, Mokhberi M (2011) Preventing landslides in times of rainfall: case study and FEM analyses. Disaster Prev Manag Int J 20:115–124CrossRefGoogle Scholar
  6. 6.
    Niroumand H, Kassim KA, Nazir R, Faizi K, Adhami B, Moayedi H, Loon W (2012) Slope stability and sheet pile and contiguous bored pile walls. Electron J Geotech Eng 17:19–27Google Scholar
  7. 7.
    Raftari M, Kassim KA, Rashid ASA, Moayedi H (2013) Settlement of shallow foundations near reinforced slopes. Electron J Geotech Eng 18:797–808Google Scholar
  8. 8.
    Latifi N, Horpibulsuk S, Meehan CL, Abd Majid MZ, Tahir MM, Mohamad ET (2016) Improvement of problematic soils with biopolymer—an environmentally friendly soil stabilizer. J Mater Civ Eng. Google Scholar
  9. 9.
    Moayedi H, Huat BB, Asadi A (2010) Strain absorption optimization of reinforcement in geosynthetic reinforced slope-experimental and FEM modeling. Electron J Geotech Eng 15:1563–1569Google Scholar
  10. 10.
    Nazir R, Moayedi H (2014) Soil mass loss reduction during rainfalls by reinforcing the slopes with the surficial confinement. Int J Geol Environ Eng 8(6):381–384Google Scholar
  11. 11.
    Moayedi H, Huat B, Kazemian S, Asadi A (2010) Optimization of shear behavior of reinforcement through the reinforced slope. Electron J Geotech Eng 15:93–104Google Scholar
  12. 12.
    Georgiadis K (2010) Undrained bearing capacity of strip footings on slopes. J Geotech Geoenviron Eng 136:677–685CrossRefGoogle Scholar
  13. 13.
    Moayedi H, Huat BBK, Kazemian S, Asadi A (2010) Optimization of tension absorption of geosynthetics through reinforced slope. Electron J Geotech Eng 15:93–104Google Scholar
  14. 14.
    Taylor DW (1937) Stability of earth slopes. J Boston Soc Civ Eng 24:197–246Google Scholar
  15. 15.
    Basarir H, Kumral M, Karpuz C, Tutluoglu L (2010) Geostatistical modeling of spatial variability of SPT data for a borax stockpile site. Eng Geol 114:154–163CrossRefGoogle Scholar
  16. 16.
    Alnaqi AA, Moayedi H, Shahsavar A, Nguyen TK (2019) Prediction of energetic performance of a building integrated photovoltaic/thermal system thorough artificial neural network and hybrid particle swarm optimization models. Energy Convers Manag 183:137–148CrossRefGoogle Scholar
  17. 17.
    Shahsavar A, Khanmohammadi S, Khaki M, Salmanzadeh M (2018) Performance assessment of an innovative exhaust air energy recovery system based on the PV/T-assisted thermal wheel. Energy 162:682–696CrossRefGoogle Scholar
  18. 18.
    Shahsavar A, Salmanzadeh M, Ameri M, Talebizadeh P (2011) Energy saving in buildings by using the exhaust and ventilation air for cooling of photovoltaic panels. Energy Build 43:2219–2226CrossRefGoogle Scholar
  19. 19.
    Mohamad ET, Armaghani DJ, Momeni E, Yazdavar AH, Ebrahimi M (2016) Rock strength estimation: a PSO-based BP approach. Neural Comput Appl 1–12Google Scholar
  20. 20.
    Asadi A, Moayedi H, Huat BB, Boroujeni FZ, Parsaie A, Sojoudi S (2011) Prediction of zeta potential for tropical peat in the presence of different cations using artificial neural networks. Int J Electrochem Sci 6:1146–1158Google Scholar
  21. 21.
    Asadi A, Moayedi H, Huat BBK, Parsaie A, Taha MR (2011) Artificial neural networks approach for electrochemical resistivity of highly organic soil. Int J Electrochem Sci 6:1135–1145Google Scholar
  22. 22.
    Mohamad ET, Faradonbeh RS, Armaghani DJ, Monjezi M, Majid MZA (2017) An optimized ANN model based on genetic algorithm for predicting ripping production. Neural Comput Appl 28:393–406CrossRefGoogle Scholar
  23. 23.
    Armaghani DJ, Hasanipanah M, Mahdiyar A, Majid MZA, Amnieh HB, Tahir M (2018) Airblast prediction through a hybrid genetic algorithm-ANN model. Neural Comput Appl 29:619–629CrossRefGoogle Scholar
  24. 24.
    Hasanipanah M, Noorian-Bidgoli M, Armaghani DJ, Khamesi H (2016) Feasibility of PSO-ANN model for predicting surface settlement caused by tunneling. Eng Comput 32:705–715CrossRefGoogle Scholar
  25. 25.
    Li J, Wang J (2010) Research of steel plate temperature prediction based on the improved PSO-ANN algorithm for Roller Hearth Normalizing Furnace. In: 2010 8th World congress on intelligent control and automation (WCICA), pp 2464–2469Google Scholar
  26. 26.
    Marzband M, Parhizi N, Adabi J (2016) Optimal energy management for stand-alone microgrids based on multi-period imperialist competition algorithm considering uncertainties: experimental validation. Int Trans Electr Energy Syst 26:1358–1372CrossRefGoogle Scholar
  27. 27.
    Choobbasti AJ, Farrokhzad F, Barari A (2009) Prediction of slope stability using artificial neural network (case study: Noabad, Mazandaran, Iran). Arab J Geosci 2:311–319CrossRefGoogle Scholar
  28. 28.
    Su GS, Zhang Y, Chen GQ, Yan LB (2013) Fast estimation of slope stability based on gaussian process machine learning. Disaster Adv 6:81–91Google Scholar
  29. 29.
    Chakraborty A, Goswami D (2017) Prediction of slope stability using multiple linear regression (MLR) and artificial neural network (ANN). Arab J Geosci 10:11CrossRefGoogle Scholar
  30. 30.
    Cheng YM, Lansivaara T, Baker R, Li N (2013) Use of internal and external variables and extremum principle in limit equilibrium formulations with application to bearing capacity and slope stability problems. Soils Found 53:130–143CrossRefGoogle Scholar
  31. 31.
    Zhang ZF, Liu ZB, Zheng LF, Zhang Y (2014) Development of an adaptive relevance vector machine approach for slope stability inference. Neural Comput Appl 25:2025–2035CrossRefGoogle Scholar
  32. 32.
    Donald IB, Chen Z (1997) Slope stability analysis by the upper bound approach: fundamentals and methods. Can Geotech J 34:853–862CrossRefGoogle Scholar
  33. 33.
    Niroumand H, Faizi K, Nazir R, Kassin K, Moayedi H (2012) Slope stability of the design concept of the sheet pile and contiguous bored pile walls. Arch Des Sci 65:2–17Google Scholar
  34. 34.
    Kostic S, Vasovic N, Todorovic K, Samcovic A (2016) Application of artificial neural networks for slope stability analysis in geotechnical practice. In: 2016 13th Symposium on neural networks and applications (Neural), pp 89–94Google Scholar
  35. 35.
    McCulloch W, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5:115–133MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Mosallanezhad M, Moayedi H (2017) Developing hybrid artificial neural network model for predicting uplift resistance of screw piles. Arab J Geosci 10:10CrossRefGoogle Scholar
  37. 37.
    Gandomi AH, Alavi AH (2012) A new multi-gene genetic programming approach to non-linear system modeling. Part II: geotechnical and earthquake engineering problems. Neural Comput Appl 21:189–201CrossRefGoogle Scholar
  38. 38.
    Moayedi H, Hayati S (2018) Artificial intelligence design charts for predicting friction capacity of driven pile in clay. Neural Comput Appl. Google Scholar
  39. 39.
    Al Dossary MA, Nasrabadi H (2016) Well placement optimization using imperialist competitive algorithm. J Pet Sci Eng 147:237–248CrossRefGoogle Scholar
  40. 40.
    Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. IEEEGoogle Scholar
  41. 41.
    Soleimani S, Jiao PC, Rajaei S, Forsati R (2018) A new approach for prediction of collapse settlement of sandy gravel soils. Eng Comput 34:15–24CrossRefGoogle Scholar
  42. 42.
    Moayedi H, Armaghani DJ (2018) Optimizing an ANN model with ICA for estimating bearing capacity of driven pile in cohesionless soil. Eng Comput 34:347–356. CrossRefGoogle Scholar
  43. 43.
    Sloan SW (1988) Lower bound limit analysis using finite elements and linear programming. Int J Numer Anal Meth Geomech 12:61–77CrossRefzbMATHGoogle Scholar
  44. 44.
    Zhou J, Chen Q, Wang J (2017) Rigid block based lower bound limit analysis method for stability analysis of fractured rock mass considering rock bridge effects. Comput Geotech 86:173–180CrossRefGoogle Scholar
  45. 45.
    Lim K, Li A, Lyamin A (2015) Three-dimensional slope stability assessment of two-layered undrained clay. Comput Geotech 70:1–17CrossRefGoogle Scholar
  46. 46.
    Chen Z, Wang X, Haberfield C, Yin J-H, Wang Y (2001) A three-dimensional slope stability analysis method using the upper bound theorem: part I: theory and methods. Int J Rock Mech Min Sci 38:369–378CrossRefGoogle Scholar
  47. 47.
    Chen J, Yin J-H, Lee CF (2003) Upper bound limit analysis of slope stability using rigid finite elements and nonlinear programming. Can Geotech J 40:742–752CrossRefGoogle Scholar
  48. 48.
    Zhao L-h, Li L, Yang F, Luo Q, Liu X (2010) Upper bound analysis of slope stability with nonlinear failure criterion based on strength reduction technique. J Cent South Univ Technol 17:836–844CrossRefGoogle Scholar
  49. 49.
    Krabbenhoft K, Lyamin A, Krabbenhoft J (2015) Optum computational engineering (OptumG2). Computer software. (Software accessed since 2013​)
  50. 50.
    Caër T, Souloumiac P, Maillot B, Leturmy P, Nussbaum C (2018) Propagation of a fold-and-thrust belt over a basement graben. J Struct Geol 115:121–131CrossRefGoogle Scholar
  51. 51.
    Zhou H, Liu H, Yin F, Chu J (2018) Upper and lower bound solutions for pressure-controlled cylindrical and spherical cavity expansion in semi-infinite soil. Comput Geotech 103:93–102CrossRefGoogle Scholar
  52. 52.
    Karkanaki AR, Ganjian N, Askari F (2017) Stability analysis and design of cantilever retaining walls with regard to possible failure mechanisms: an upper bound limit analysis approach. Geotech Geol Eng 35:1079–1092CrossRefGoogle Scholar
  53. 53.
    Mahdiyar A, Hasanipanah M, Armaghani DJ, Gordan B, Abdullah A, Arab H, Abd Majid MZ (2017) A Monte Carlo technique in safety assessment of slope under seismic condition. Eng Comput 33:807–817CrossRefGoogle Scholar
  54. 54.
    Yusof MF, Azamathulla HM, Abdullah R (2014) Prediction of soil erodibility factor for Peninsular Malaysia soil series using ANN. Neural Comput Appl 24:383–389CrossRefGoogle Scholar
  55. 55.
    Siddiqui FI, Pathan DM, Osman S, Pinjaro MA, Memon S (2015) Comparison between regression and ANN models for relationship of soil properties and electrical resistivity. Arab J Geosci 8:6145–6155CrossRefGoogle Scholar
  56. 56.
    Verma AK, Kishore K, Chatterjee S (2016) Prediction model of longwall powered support capacity using field monitored data of a longwall panel and uncertainty-based neural network. Geotech Geol Eng 34:2033–2052CrossRefGoogle Scholar
  57. 57.
    Rana MJ, Shahriar MS, Shafiullah M (2017) Levenberg–Marquardt neural network to estimate UPFC-coordinated PSS parameters to enhance power system stability. Neural Comput Appl 1–12Google Scholar
  58. 58.
    Wang C (1994) A theory of generalization in learning machines with neural application. The University of Pennsylvania, PhiladelphiaGoogle Scholar
  59. 59.
    Sharma LK, Vishal V, Singh TN (2017) Developing novel models using neural networks and fuzzy systems for the prediction of strength of rocks from key geomechanical properties. Measurement 102:158–169CrossRefGoogle Scholar
  60. 60.
    Gupta R, Goyal K, Yadav N (2016) Prediction of safe bearing capacity of noncohesive soil in arid zone using artificial neural networks. Int J Geomech 16:7Google Scholar
  61. 61.
    Moayedi H, Rezaei A (2017) an artificial neural network approach for under reamed piles subjected to uplift forces in dry sand. Neural Comput Appl 28:1–10Google Scholar
  62. 62.
    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 66:208–219CrossRefGoogle Scholar
  63. 63.
    Moayedi H, Hayati S (2018) Applicability of a CPT-based neural network solution in predicting load-settlement responses of bored pile. Int J Geomech 18:06018009CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Wei Gao
    • 1
    Email author
  • Mehdi Raftari
    • 2
  • Ahmad Safuan A. Rashid
    • 3
  • Mohammed Abdullahi Mu’azu
    • 4
  • Wan Amizah Wan Jusoh
    • 5
  1. 1.School of Information Science and TechnologyYunnan Normal UniversityKunmingChina
  2. 2.Department of Civil Engineering, Khorramabad BranchIslamic Azad UniversityKhorramabadIran
  3. 3.Centre of Tropical Geoengineering (Geotropik), School of Civil Engineering, Faculty of EngineeringUniversiti Teknologi MalaysiaJohor BahruMalaysia
  4. 4.Department of Civil EngineeringJubail University College, Royal Commission of Jubail and YanbuJubailKingdom of Saudi Arabia
  5. 5.Faculty of civil engineering and environmentUniversiti Tun Hussein Onn MalaysiaBatu PahatMalaysia

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