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Strength evaluation of granite block samples with different predictive models

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Abstract

Over the last decade, application of soft computing techniques has rapidly grown up in different scientific fields, especially in rock mechanics. One of these cases relates to indirect assessment of uniaxial compressive strength (UCS) of rock samples with different artificial intelligent-based methods. In fact, the main advantage of such systems is to readily remove some difficulties arising in direct assessment of UCS, such as time-consuming and costly UCS test procedure. This study puts an effort to propose four accurate and practical predictive models of UCS using artificial neural network (ANN), hybrid ANN with imperialism competitive algorithm (ICA–ANN), hybrid ANN with artificial bee colony (ABC–ANN) and genetic programming (GP) approaches. To reach the aim of the current study, an experimental database containing a total of 71 data sets was set up by performing a number of laboratory tests on the rock samples collected from a tunnel site in Malaysia. To construct the desired predictive models of UCS based on training and test patterns, a combination of several rock characteristics with the most influence on UCS has been used as input parameters, i.e. porosity (n), Schmidt hammer rebound number (R), p-wave velocity (Vp) and point load strength index (Is(50)). To evaluate and compare the prediction precision of the developed models, a series of statistical indices, such as root mean squared error (RMSE), determination coefficient (R2) and variance account for (VAF) are utilized. Based on the simulation results and the measured indices, it was observed that the proposed GP model with the training and test RMSE values 0.0726 and 0.0691, respectively, gives better performance as compared to the other proposed models with values of (0.0740 and 0.0885), (0.0785 and 0.0742), and (0.0746 and 0.0771) for ANN, ICA–ANN and ABC–ANN, respectively. Moreover, a parametric analysis is accomplished on the proposed GP model to further verify its generalization capability. Hence, this GP-based model can be considered as a new applicable equation to accurately estimate the uniaxial compressive strength of granite block samples.

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References

  1. 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 85:174–186. https://doi.org/10.1016/j.ijrmms.2016.03.018

    Article  Google Scholar 

  2. Singh R, Kainthola A, Singh TN (2012) Estimation of elastic constant of rocks using an ANFIS approach. Appl Soft Comput 12:40–45

    Google Scholar 

  3. Hatheway HW (2009) The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974–2006. Environ Engin Geosci 15:47–48

    Google Scholar 

  4. Gokceoglu C, Zorlu K (2004) A fuzzy model to predict the uniaxial compressive strength and the modulus of elasticity of a problematic rock. Eng Appl Artif Intell 17:61–72

    Google Scholar 

  5. Baykasoğlu A, Güllü H, Çanakçı H, Özbakır L (2008) Prediction of compressive and tensile strength of limestone via genetic programming. Expert Syst Appl 35:111–123

    Google Scholar 

  6. Armaghani DJ, Mohamad ET, Momeni E et al (2016) Prediction of the strength and elasticity modulus of granite through an expert artificial neural network. Arab J Geosci 9:48

    Google Scholar 

  7. Mohamad ET, Jahed Armaghani D, Momeni E, Abad SVANK (2014) Prediction of the unconfined compressive strength of soft rocks: a PSO-based ANN approach. Bull Eng Geol Environ. https://doi.org/10.1007/s10064-014-0638-0

    Article  Google Scholar 

  8. Yazdani B (2012) Shear strength parameters of shale based on triaxial compression test. Universiti Teknologi Malaysia, Johor Bahru

    Google Scholar 

  9. Yazdani Bejarbaneh B, Jahed Armaghani D, Mohd Amin MF (2015) Strength characterisation of shale using Mohr-Coulomb and Hoek-Brown criteria. Meas J Int Meas Confed. https://doi.org/10.1016/j.measurement.2014.12.029

    Article  Google Scholar 

  10. Mohamad ET, Armaghani DJ, Momeni E et al (2016) Rock strength estimation: a PSO-based BP approach. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2728-3

    Article  Google Scholar 

  11. 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

    Article  Google Scholar 

  12. Kahraman S, Altun H, Tezekici B (2006) Sawability prediction of carbonate rocks from shear strength parameters using artificial neural networks. Int J Rock Mech Min Sci 43:157–164

    Google Scholar 

  13. Nazir R, Momeni E, Armaghani DJ, Amin MFM (2013) Correlation between unconfined compressive strength and indirect tensile strength of limestone rock samples. Electron J Geotech Eng 18:1737–1746

    Google Scholar 

  14. Nazir R, Momeni E, Armaghani DJ, Amin MFM (2013) Prediction of unconfined compressive strength of limestone rock samples using l-type schmidt hammer. Electron J Geotech Eng 18:1767–1775

    Google Scholar 

  15. Armaghani DJ, Mohamad ET, Momeni E, Narayanasamy MS (2015) An adaptive neuro-fuzzy inference system for predicting unconfined compressive strength and Young’s modulus: a study on Main Range granite. Bull Eng Geol Environ 74:1301–1319

    Google Scholar 

  16. 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

    Google Scholar 

  17. Beiki M, Majdi A, Givshad A (2013) Application of genetic programming to predict the uniaxial compressive strength and elastic modulus of carbonate rocks. J rock Mech Min 63:159–169

    Google Scholar 

  18. Yilmaz I, Yuksek G (2009) Prediction of the strength and elasticity modulus of gypsum using multiple regression, ANN, and ANFIS models. Int J Rock Mech Min Sci 46:803–810

    Google Scholar 

  19. Liang M, Mohamad ET, Faradonbeh RS et al (2016) Rock strength assessment based on regression tree technique. Eng Comput 32:343–354. https://doi.org/10.1007/s00366-015-0429-7

    Article  Google Scholar 

  20. Yesiloglu-Gultekin N, Gokceoglu C, Sezer EA (2013) Prediction of uniaxial compressive strength of granitic rocks by various nonlinear tools and comparison of their performances. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2013.05.005

    Article  Google Scholar 

  21. Jahed Armaghani D, Tonnizam Mohamad E, Hajihassani M et al (2016) Application of several non-linear prediction tools for estimating uniaxial compressive strength of granitic rocks and comparison of their performances. Eng Comput. https://doi.org/10.1007/s00366-015-0410-5

    Article  Google Scholar 

  22. Armaghani DJ, Safari V, Fahimifar A et al (2018) Uniaxial compressive strength prediction through a new technique based on gene expression programming. Neural Comput Appl 30(11):3523–3532

    Google Scholar 

  23. Momeni E, Nazir R, Armaghani DJ, Mohamad ET (2015) Prediction of unconfined compressive strength of rocks: a review paper. J Teknol 77(11):43–50

    Google Scholar 

  24. Koopialipoor M, Jahed Armaghani D, 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

    Article  Google Scholar 

  25. Koopialipoor M, Murlidhar BR, Hedayat A et al (2019) The use of new intelligent techniques in designing retaining walls. Eng Comput. https://doi.org/10.1007/s00366-018-00700-1

    Article  Google Scholar 

  26. 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

    Article  Google Scholar 

  27. 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 78:3799–3813

    Google Scholar 

  28. Shi X, Jian Z, Wu B et al (2012) Support vector machines approach to mean particle size of rock fragmentation due to bench blasting prediction. Trans Nonferrous Met Soc China 22:432–441

    Google Scholar 

  29. Zhou J, Li X, Mitri HS (2015) Comparative performance of six supervised learning methods for the development of models of hard rock pillar stability prediction. Nat Hazards 79:291–316

    Google Scholar 

  30. Zhou J, Li E, Yang S et al (2019) Slope stability prediction for circular mode failure using gradient boosting machine approach based on an updated database of case histories. Saf Sci 118:505–518

    Google Scholar 

  31. Zhou J, Li E, Wei H et al (2019) Random forests and cubist algorithms for predicting shear strengths of Rockfill materials. Appl Sci 9:1621

    Google Scholar 

  32. Zhou J, Koopialipoor M, Murlidhar BR et al (2019) Use of intelligent methods to design effective pattern parameters of mine blasting to minimize flyrock distance. Nat Resour Res. https://doi.org/10.1007/s11053-019-09519-z

    Article  Google Scholar 

  33. Wang M, Shi X, Zhou J, Qiu X (2018) Multi-planar detection optimization algorithm for the interval charging structure of large-diameter longhole blasting design based on rock fragmentation aspects. Eng Optim 50:2177–2191

    Google Scholar 

  34. Yang H, Koopialipoor M, Armaghani DJ et al (2019) Intelligent design of retaining wall structures under dynamic conditions. STEEL Compos Struct 31:629–640

    Google Scholar 

  35. Xu H, Zhou J, G Asteris P et al (2019) Supervised machine learning techniques to the prediction of tunnel boring machine penetration rate. Appl Sci 9:3715

    Google Scholar 

  36. Mohamad ET, Armaghani DJ, Momeni E et al (2018) Rock strength estimation: a PSO-based BP approach. Neural Comput Appl 30:1635–1646

    Google Scholar 

  37. Bejarbaneh EY, Bagheri A, Bejarbaneh BY, Buyamin S, Chegini S (2019) A new adjusting technique for PID type fuzzy logic controller using PSOSCALF optimization algorithm. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2019.105822

    Article  Google Scholar 

  38. Shao Z, Armaghani DJ, Bejarbaneh BY et al (2019) Estimating the friction angle of black shale core specimens with hybrid–ANN approaches. Measurement. https://doi.org/10.1016/j.measurement.2019.06.007

    Article  Google Scholar 

  39. Shams S, Monjezi M, Majd VJ, Armaghani DJ (2015) Application of fuzzy inference system for prediction of rock fragmentation induced by blasting. Arab J Geosci 8:10819–10832

    Google Scholar 

  40. Meulenkamp F, Grima M (1999) Application of neural networks for the prediction of the unconfined compressive strength (UCS) from Equotip hardness. Int J rock Mech Min Sci 36:29–39

    Google Scholar 

  41. Singh VK, Singh D, Singh TN (2001) Prediction of strength properties of some schistose rocks from petrographic properties using artificial neural networks. Int J Rock Mech Min Sci 38:269–284

    Google Scholar 

  42. Dehghan S, Sattari GH, Chelgani SC, Aliabadi MA (2010) Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks. Min Sci Technol 20:41–46

    Google Scholar 

  43. Li W-X, Dai L-F, Hou X-B, Lei W (2007) Fuzzy genetic programming method for analysis of ground movements due to underground mining. Int J Rock Mech Min Sci 44:954–961

    Google Scholar 

  44. Majdi A, Beiki M (2010) Evolving neural network using a genetic algorithm for predicting the deformation modulus of rock masses. Int J Rock Mech Min Sci 47:246–253

    Google Scholar 

  45. Asadi M, Eftekhari M, Bagheripour MH (2011) Evaluating the strength of intact rocks through genetic programming. Appl Soft Comput 11:1932–1937

    Google Scholar 

  46. Karakus M (2011) Function identification for the intrinsic strength and elastic properties of granitic rocks via genetic programming (GP). Comput Geosci 37:1318–1323

    Google Scholar 

  47. Ravandi EG, Rahmannejad R, Monfared AEF, Ravandi EG (2013) Application of numerical modeling and genetic programming to estimate rock mass modulus of deformation. Int J Min Sci Technol 23:733–737

    Google Scholar 

  48. Specht DF (1991) A general regression neural network. IEEE Trans Neural Netw 2:568–576

    Google Scholar 

  49. Simpson PK (1990) Artificial neural systems: foundations, paradigms, applications, and implementations. Pergamon, Tarrytown NY, p 207

    Google Scholar 

  50. Jahed Armaghani D, Hajihassani M, Yazdani Bejarbaneh B et al (2014) Indirect measure of shale shear strength parameters by means of rock index tests through an optimized artificial neural network. Meas J Int Meas Confed 55:487–498. https://doi.org/10.1016/j.measurement.2014.06.001

    Article  Google Scholar 

  51. Khandelwal M, Marto A, Fatemi SA et al (2017) Implementing an ANN model optimized by genetic algorithm for estimating cohesion of limestone samples. Eng Comput 34:307–317

    Google Scholar 

  52. Basheer IA, Hajmeer M (2000) Artificial neural networks: fundamentals, computing, design, and application. J Microbiol Methods 43:3–31

    Google Scholar 

  53. Dreyfus G (2005) Neural networks: methodology and applications. Springer, Berlin, Heidelberg

    MATH  Google Scholar 

  54. Bejarbaneh BY, Bejarbaneh EY, Amin MFM  et al (2018) Intelligent modelling of sandstone deformation behaviour using fuzzy logic and neural network systems. Bull Eng Geol Environ 77:345–361

    Google Scholar 

  55. Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: IEEE Congress on Evolutionary Computation, pp 4661–4667

  56. Hajihassani M, Jahed Armaghani D, Marto A, Tonnizam Mohamad E (2014) Ground vibration prediction in quarry blasting through an artificial neural network optimized by imperialist competitive algorithm. Bull Eng Geol Environ 74:873–886. https://doi.org/10.1007/s10064-014-0657-x

    Article  Google Scholar 

  57. Khandelwal M, Mahdiyar A, Armaghani DJ et al (2017) An expert system based on hybrid ICA–ANN technique to estimate macerals contents of Indian coals. Environ Earth Sci 76:399. https://doi.org/10.1007/s12665-017-6726-2

    Article  Google Scholar 

  58. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization, vol 200. Technical report-tr06, Erciyes University, Computer Engineering Department

  59. 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

    Google Scholar 

  60. 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

    Google Scholar 

  61. 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 nuclear Atlantic conference (INAC 2009)

  62. Cramer NL (1985) A representation for the adaptive generation of simple sequential programs. In: Proceedings of the first international conference on genetic algorithms, pp 183–187

  63. Koza JR (1992) Genetic programming II. Automatic discovery of reusable subprograms, vol 13, no 8. MIT Press, Cambridge, MA, USA, p 32

    Google Scholar 

  64. Ferreira C (2001) Algorithm for solving gene expression programming: a new adaptive problems. Complex Syst 13:87–129

    MATH  Google Scholar 

  65. Faradonbeh RS, Jahed Armaghani D, Monjezi M (2016) Development of a new model for predicting flyrock distance in quarry blasting: a genetic programming technique. Bull Eng Geol Environ. https://doi.org/10.1007/s10064-016-0872-8

    Article  Google Scholar 

  66. 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

    Google Scholar 

  67. Ferreira C (2006) Gene expression programming: mathematical modeling by an artificial intelligence. Springer, New York

    MATH  Google Scholar 

  68. Silva S, Almeida J (2003) Dynamic maximum tree depth. Genetic and evolutionary computation conference. Springer, New York, pp 1776–1787

    Google Scholar 

  69. Shirani Faradonbeh R, Monjezi M, Jahed Armaghani D (2016) Genetic programing and non-linear multiple regression techniques to predict backbreak in blasting operation. Eng Comput. https://doi.org/10.1007/s00366-015-0404-3

    Article  Google Scholar 

  70. Faradonbeh RS, Armaghani DJ, Monjezi M, Mohamad ET (2016) Genetic programming and gene expression programming for flyrock assessment due to mine blasting. Int J Rock Mech Min Sci 88:254–264

    Google Scholar 

  71. Ulusay R, Hudson JA, ISRM (2007) The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974–2006. Comm Test methods Int Soc Rock Mech Compil arranged by ISRM Turkish Natl Group, Ankara, p 628

  72. Swingler K (1996) Applying neural networks: a practical guide. Academic Press, New York

    Google Scholar 

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

    MATH  Google Scholar 

  74. Caudill M (1988) Neural networks primer, part III. AI Expert 3:53–59

    Google Scholar 

  75. Nourani V, Baghanam AH, Adamowski J, Gebremichael M (2013) Using self-organizing maps and wavelet transforms for space–time pre-processing of satellite precipitation and runoff data in neural network based rainfall–runoff modeling. J Hydrol 476:228–243

    Google Scholar 

  76. Ahmadi MA, Ebadi M, Shokrollahi A, Majidi SMJ (2013) Evolving artificial neural network and imperialist competitive algorithm for prediction oil flow rate of the reservoir. Appl Soft Comput 13:1085–1098

    Google Scholar 

  77. Marto A, Hajihassani M, Jahed Armaghani D et al (2014) A novel approach for blast-induced flyrock prediction based on imperialist competitive algorithm and artificial neural network. Sci World J. https://doi.org/10.1155/2014/643715

    Article  Google Scholar 

  78. Hrnjica B, Danandeh Mehr A (2018) Optimized genetic programming applications: emerging research and opportunities: emerging research and opportunities. IGI Global. https://doi.org/10.4018/978-1-5225-6005-0(ISBN: 1522560068)

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Authors and Affiliations

  1. Institute of Architecture Engineering, Huanghuai University, Zhumadian, 463000, Henan, China

    Qiancheng Fang

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

    Behnam Yazdani Bejarbaneh

  3. Department of Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    Mohammad Vatandoust

  4. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Danial Jahed Armaghani

  5. Geotropik, Centre of Tropical Geoengineering, School of Civil Engineering, Faculty of Engineering, Universiti Teknologi Malaysia, 81310, Skudai, Johor, Malaysia

    Bhatawdekar Ramesh Murlidhar & Edy Tonnizam Mohamad

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Fang, Q., Yazdani Bejarbaneh, B., Vatandoust, M. et al. Strength evaluation of granite block samples with different predictive models. Engineering with Computers 37, 891–908 (2021). https://doi.org/10.1007/s00366-019-00872-4

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