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Estimating and optimizing safety factors of retaining wall through neural network and bee colony techniques

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Abstract

An important task of geotechnical engineering is a suitable design of safety factor (SF) of retaining wall under both static and dynamic conditions. This paper presents the advantages of both prediction and optimization of retaining wall SF through artificial neural network (ANN) and artificial bee colony (ABC), respectively. These techniques were selected because of their capability in predicting and optimizing science and engineering problems. To gain purpose of this research, a comprehensive database consisted of 2880 datasets of wall height, wall width, wall mass, soil mass and internal angle of friction as input parameters and SF of retaining wall as output was prepared. In fact, SF is considered as a function of the mentioned parameters. At the first step of modeling, several ANN models were constructed and the best one among them was selected. The coefficient of determination (R2) value of 0.998 for both training and testing datasets was obtained for the best ANN model which indicates an excellent accuracy level in predicting SF values. In the next step of modeling, the results of selected ANN model were used as an input for the optimization technique of ABC. In general, 11 models of ABC optimization with different strategies were built. As a result, by decreasing wall height value from 10 m to 8 m and 5.628 m and using almost constant values for the other input parameters, SF values were obtained as 2.142 and 5.628, respectively. Results of (8.003, 0.794, 0.667, 1800 and 2800) and (5.628, 0.763, 0.660, 1735 and 2679) were obtained for wall height, wall width, internal friction angle, soil mass and wall mass of the best models with 2.142 and 5.628 SF values, respectively.

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References

  1. Coulomb CA (1776) “Essai sur une Application des Règles de Maximis et Minimis à Quelques Problèmes de Statique Relatifs à L’Architecture,” Mèmoires de la Mathèmatique et de Phisique, présentés à l’Académie Royale des Sciences, par divers savans, et lûs dans sés Assemblées. Annee 1793:343–382

    Google Scholar 

  2. Rankine WJM (1857) On the mathematical theory of the stability of earthwork and masonry. J Franklin Inst 63:84–85

    Article  Google Scholar 

  3. Terzaghi K (1943) Theoretical soil mechanics. Wiley, New York

    Book  Google Scholar 

  4. Leshchinsky D, Vulova C (2001) Numerical investigation of the effects of geosynthetic spacing on failure mechanisms in MSE block walls. Geosynth Int 8:343–365

    Article  Google Scholar 

  5. Yu G-Y, Bai Y-S, Sheng P, Guo R-P (2009) Mechanical performance of a double-face reinforced retaining wall in an area disturbed by mining. Min Sci Technol 19:36–39

    Google Scholar 

  6. Chan YC (1996) Study of old masonry retaining walls in Hong Kong. Geo Report No. 31, Geotechnical Engineering Office, Civil Engineering Department, The Government of Hong Kong, Special Administrative Region, 1996, reprinted 2000

    Google Scholar 

  7. Rankine WJM (1857) On the stability of loose earth. Philos Trans R Soc Lond 147:9–27

    Article  Google Scholar 

  8. Tsagareli ZV (1965) Experimental investigation of the pressure of a loose medium on retaining walls with a vertical back face and horizontal backfill surface. Soil Mech Found Eng 2:197–200

    Article  Google Scholar 

  9. Chang M-F (1997) Lateral earth pressures behind rotating walls. Can Geotech J 34:498–509

    Article  Google Scholar 

  10. O’Neal TS, Hagerty DJ (2011) Earth pressures in confined cohesionless backfill against tall rigid walls—a case history. Can Geotech J 48:1188–1197

    Article  Google Scholar 

  11. Iskander M, Chen Z, Omidvar M et al (2013) Active static and seismic earth pressure for c–φ soils. Soils Found 53:639–652

    Article  Google Scholar 

  12. Armaghani DJ, Hasanipanah M, Mohamad ET (2016) A combination of the ICA-ANN model to predict air-overpressure resulting from blasting. Eng Comput 32:155–171. https://doi.org/10.1007/s00366-015-0408-z

    Article  Google Scholar 

  13. Armaghani DJ, Mohamad ET, Narayanasamy MS et al (2017) Development of hybrid intelligent models for predicting TBM penetration rate in hard rock condition. Tunn Undergr Sp Technol 63:29–43. https://doi.org/10.1016/j.tust.2016.12.009

    Article  Google Scholar 

  14. Hasanipanah M, Noorian-Bidgoli M, Jahed Armaghani D, Khamesi H (2016) Feasibility of PSO-ANN model for predicting surface settlement caused by tunneling. Eng Comput. https://doi.org/10.1007/s00366-016-0447-0

    Google Scholar 

  15. Koopialipoor M, Armaghani DJ, Haghighi M, Ghaleini EN (2017) A neuro-genetic predictive model to approximate overbreak induced by drilling and blasting operation in tunnels. Bull Eng Geol Environ. https://doi.org/10.1007/s10064-017-1116-2

    Google Scholar 

  16. Saghatforoush A, Monjezi M, Faradonbeh RS, Armaghani DJ (2016) Combination of neural network and ant colony optimization algorithms for prediction and optimization of flyrock and back-break induced by blasting. Eng Comput 32:255–266

    Article  Google Scholar 

  17. Hasanipanah M, Jahed Armaghani D, Khamesi H et al (2016) Several non-linear models in estimating air-overpressure resulting from mine blasting. Eng Comput. https://doi.org/10.1007/s00366-015-0425-y

    Google Scholar 

  18. Mohamad ET, Faradonbeh RS, Armaghani DJ et al (2016) An optimized ANN model based on genetic algorithm for predicting ripping production. Neural Comput Appl 28:1–14

    Article  Google Scholar 

  19. Hasanipanah M, Armaghani DJ, Amnieh HB et al (2018) A risk-based technique to analyze flyrock results through rock engineering system. Geotech Geol Eng. https://doi.org/10.1007/s10706-018-0459-1

    Google Scholar 

  20. Koopialipoor M, Armaghani DJ, Hedayat A et al (2018) Applying various hybrid intelligent systems to evaluate and predict slope stability under static and dynamic conditions. Soft Comput. https://doi.org/10.1007/s00500-018-3253-3

    Google Scholar 

  21. Koopialipoor M, Fallah A, Armaghani DJ et al (2018) Three hybrid intelligent models in estimating flyrock distance resulting from blasting. Eng Comput. https://doi.org/10.1007/s00366-018-0596-4

    Google Scholar 

  22. Koopialipoor M, Nikouei SS, Marto A et al (2018) Predicting tunnel boring machine performance through a new model based on the group method of data handling. Bull Eng Geol Environ. https://doi.org/10.1007/s10064-018-1349-8

    Google Scholar 

  23. Jahed Armaghani D, Hasanipanah M, Mahdiyar A et al (2016) Airblast prediction through a hybrid genetic algorithm-ANN model. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2598-8

    Google Scholar 

  24. Hasanipanah M, Jahed Armaghani D, Bakhshandeh Amnieh H et al (2016) Application of PSO to develop a powerful equation for prediction of flyrock due to blasting. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2434-1

    Google Scholar 

  25. Jahed Armaghani D, Mohd Amin MF, Yagiz S et al (2016) Prediction of the uniaxial compressive strength of sandstone using various modeling techniques. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2016.03.018

    Google Scholar 

  26. Hasanipanah M, Shahnazar A, Amnieh H (2017) Prediction of air-overpressure caused by mine blasting using a new hybrid PSO–SVR model. Eng Comput. https://doi.org/10.1007/s00366-016-0453-2

    Google Scholar 

  27. Hamian M, Darvishan A, Hosseinzadeh M et al (2018) A framework to expedite joint energy-reserve payment cost minimization using a custom-designed method based on mixed integer genetic algorithm. Eng Appl Artif Intell 72:203–212

    Article  Google Scholar 

  28. Khodaei H, Hajiali M, Darvishan A et al (2018) Fuzzy-based heat and power hub models for cost-emission operation of an industrial consumer using compromise programming. Appl Therm Eng 137:395–405

    Article  Google Scholar 

  29. Nouri A, Khodaei H, Darvishan A et al (2018) Optimal performance of fuel cell-CHP-battery based micro-grid under real-time energy management: an epsilon constraint method and fuzzy satisfying approach. Energy 159:121–133

    Article  Google Scholar 

  30. Darvishan A, Mollashahi H, Ghaffari V, Janghorban Lariche M (2018) Unit commitment-based load uncertainties based on improved particle swarm optimisation. Int J Ambient Energy. https://doi.org/10.1080/01430750.2017.1423384

    Google Scholar 

  31. Darvishan A, Bakhshi H, Madadkhani M et al (2018) Application of MLP-ANN as a novel predictive method for prediction of the higher heating value of biomass in terms of ultimate analysis. Energy Sour Part A Recover Util Environ Eff. https://doi.org/10.1080/15567036.2018.1514437

    Google Scholar 

  32. Reza Parsaei M, Mollashahi H, Darvishan A et al (2018) A new prediction model of solar radiation based on the neuro-fuzzy model. Int J Ambient Energy. https://doi.org/10.1080/01430750.2018.1456964

    Google Scholar 

  33. Gandomi AH, Kashani AR, Roke DA, Mousavi M (2017) Optimization of retaining wall design using evolutionary algorithms. Struct Multidiscip Optim 55:809–825

    Article  Google Scholar 

  34. Ghaleini EN, Koopialipoor M, Momenzadeh M et al (2018) A combination of artificial bee colony and neural network for approximating the safety factor of retaining walls. Eng Comput. https://doi.org/10.1007/s00366-018-0625-3

    Google Scholar 

  35. Peck RB, Hanson WE, Thornburn TH (1974) Foundation engineering. Wiley New York

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  37. Garrett JH (1994) Where and why artificial neural networks are applicable in civil engineering. J Comput Civil Eng 8:129–130

    Article  Google Scholar 

  38. Fausett L, Fausett L (1994) Fundamentals of neural networks: architectures, algorithms, and applications. Prentice-Hall, Upper Saddle River

    MATH  Google Scholar 

  39. Momeni E, Jahed Armaghani D, Hajihassani M, Mohd Amin MF (2015) Prediction of uniaxial compressive strength of rock samples using hybrid particle swarm optimization-based artificial neural networks. Meas J Int Meas Confed. https://doi.org/10.1016/j.measurement.2014.09.075

    Google Scholar 

  40. Engelbrecht AP (2007) Computational intelligence: an introduction. Wiley New York

    Book  Google Scholar 

  41. Haykin S, Network N (2004) A comprehensive foundation. Neural Netw 2:41

    Google Scholar 

  42. Jahed Armaghani D, Hajihassani M, Monjezi M et al (2015) Application of two intelligent systems in predicting environmental impacts of quarry blasting. Arab J Geosci 8:9647–9665. https://doi.org/10.1007/s12517-015-1908-2

    Article  Google Scholar 

  43. Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2:359–366

    Article  MATH  Google Scholar 

  44. Hecht-Nielsen R (1989) Kolmogorov’s mapping neural network existence theorem. In: Proceedings of international heat transfer on Conference neural networks. pp 11–14

  45. Ripley BD (1993) Statistical aspects of neural networks. Networks chaos—statistical probabilistic Asp 50:40–123

    Article  MATH  Google Scholar 

  46. Paola JD (1994) Neural network classification of multispectral imagery. Master Tezi, University Arizona

    Google Scholar 

  47. Wang C (1994) A theory of generalization in learning machines with neural network applications. Ph.D. thesis, The University of Pennsylvania, USA

  48. Masters T (1993) Practical neural network recipes in C++. Morgan Kaufmann, Burlington

    MATH  Google Scholar 

  49. Kanellopoulos I, Wilkinson GG (1997) Strategies and best practice for neural network image classification. Int J Remote Sens 18:711–725

    Article  Google Scholar 

  50. Kaastra I, Boyd M (1996) Designing a neural network for forecasting financial and economic time series. Neurocomputing 10:215–236

    Article  Google Scholar 

  51. Zorlu K, Gokceoglu C, Ocakoglu F et al (2008) Prediction of uniaxial compressive strength of sandstones using petrography-based models. Eng Geol 96:141–158

    Article  Google Scholar 

  52. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report-tr06, Erciyes university, engineering faculty, computer engineering department

  53. Nozohour-leilabady B, Fazelabdolabadi B (2016) On the application of artificial bee colony (ABC) algorithm for optimization of well placements in fractured reservoirs; efficiency comparison with the particle swarm optimization (PSO) methodology. Petroleum 2:79–89

    Article  Google Scholar 

  54. Ahmad A, Razali SFM, Mohamed ZS, El-shafie A (2016) The application of artificial bee colony and gravitational search algorithm in reservoir optimization. Water Resour Manag 30:2497–2516

    Article  Google Scholar 

  55. Zhang C, Ouyang D, Ning J (2010) An artificial bee colony approach for clustering. Expert Syst Appl 37:4761–4767

    Article  Google Scholar 

  56. Rodriguez FJ, García-Martínez C, Blum C, Lozano M (2012) An artificial bee colony algorithm for the unrelated parallel machines scheduling problem. In: International conference on parallel problem solving from Nature. Springer, pp 143–152

  57. de Oliveira IMS, Schirru R, de Medeiros J (2009) On the performance of an artificial bee colony optimization algorithm applied to the accident diagnosis in a pwr nuclear power plant. In: 2009 International conference on Nuclear Atlanta (INAC 2009)

  58. Irani R, Nasimi R (2011) Application of artificial bee colony-based neural network in bottom hole pressure prediction in underbalanced drilling. J Pet Sci Eng 78:6–12

    Article  Google Scholar 

  59. Ebrahimi E, Monjezi M, Khalesi MR, Armaghani DJ (2016) Prediction and optimization of back-break and rock fragmentation using an artificial neural network and a bee colony algorithm. Bull Eng Geol Environ 75:27–36

    Article  Google Scholar 

  60. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to express their sincere appreciation to the anonymous reviewers for their valuable and constructive suggestions.

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Authors and Affiliations

  1. Department of Geotechnics and Transportation, Faculty of Civil Engineering, Universiti Teknologi Malaysia, UTM, 81310, Skudai, Johor, Malaysia

    Behrouz Gordan

  2. Faculty of Civil and Environmental Engineering, Amirkabir University of Technology, 15914, Tehran, Iran

    Mohammadreza Koopialipoor & Hossein Tootoonchi

  3. PG and Research Department of Computer Science, Don Bosco College, Yelagiri Hills, India

    A. Clementking

  4. Centre of Tropical Geoengineering (GEOTROPIK), Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310, Johor, Malaysia

    Edy Tonnizam Mohamad

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  1. Behrouz Gordan
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Correspondence to Mohammadreza Koopialipoor.

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Gordan, B., Koopialipoor, M., Clementking, A. et al. Estimating and optimizing safety factors of retaining wall through neural network and bee colony techniques. Engineering with Computers 35, 945–954 (2019). https://doi.org/10.1007/s00366-018-0642-2

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