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A new model based on gene expression programming to estimate air flow in a single rock joint

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Abstract

This paper is aimed to introduce and validate a gene expression programming (GEP) model to estimate the rate of air flow in triaxial conditions at various confining pressures incorporating cell pressure, air inlet pressure and air outlet pressure. To achieve the aim of this study, a series of laboratory experiments were designed and carried out and then a database comprising 47 datasets was prepared to develop new predictive models. A gene expression programming (GEP) model for prediction of air flow was proposed using the prepared datasets. In this regard, a series of sensitivity analyses were performed to choose the best GEP model. For comparison purposes, multiple regression (MR) analysis was also employed for air flow estimation. Several performance indices, i.e., coefficient of determination (CoD), mean absolute error (MAE), root mean square error (RMSE) and variance account for (VAF) were considered and calculated to evaluate the performance prediction of the developed models. Considering both training and testing datasets, the developed GEP model can provide higher performance prediction of rate of air flow in comparison to the MR model.

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References

  • Ahangari K, Moeinossadat SR, Behnia D (2015) Estimation of tunnelling-induced settlement by modern intelligent methods. Soils Found 55(4):737–748

    Article  Google Scholar 

  • Alkroosh I, Nikraz H (2011) Correlation of pile axial capacity and CPT data using gene expression programming. Geotech Geol Eng 29(5):725–748

    Article  Google Scholar 

  • Alkroosh I, Nikraz H (2012) Predicting axial capacity of driven piles in cohesive soils using intelligent computing. Eng Appl Artif Intel 25(3):618–627

    Article  Google Scholar 

  • Al-Yaarubi A (2003) Numerical and Experimental Study of Fluid Flow in a Rough-Walled Rock Fracture, Ph.D. dissertation, Imperial College, London

  • Bahrami A, Monjezi M, Goshtasbi K, Ghazvinian A (2011) Prediction of rock fragmentation due to blasting using artificial neural network. Eng Comput 27(2):177–181

    Article  Google Scholar 

  • Baykasoglu A, Güllü H, Canakci H, Ozbakır L (2008) Prediction of compressive and tensile strength of limestone via genetic programming. Expert Syst Appl 35:111–123

    Article  Google Scholar 

  • Bear J (1972) Dynamics of fluids in porous media. Elsevier, New York

    Google Scholar 

  • Brown SR (1987) Fluid flow through rock joints: the effect of surface roughness. J Geophys Res 92:1337–1347

    Article  Google Scholar 

  • Darcy H (1856) Les Fontaines Publiques de la Ville de Dijon. Victor Dalmond, Paris

    Google Scholar 

  • Durham WB (1997) Laboratory observations of the hydraulic behavior of a permeable fracture from 3800 m depth in the KTB pilot hole. J Geophys Res 102:18405–18416

    Article  Google Scholar 

  • Durham WB, Bonner BP (1994) Self-propping and fluid flow in slightly offset joints at high effective pressures. J Geophys Res 99:9391–9399

    Article  Google Scholar 

  • Ferreira C (2001) Gene expression programming: a new adaptive algorithm for solving problems. Complex Systems 13(2):87–129

    Google Scholar 

  • Ferreira C (2002) Gene expression programming in problem solving. In: Roy R, Köppen M, Ovaska S, Furuhashi T, Hoffmann F (eds) Soft computing and industry: recent applications. Springer, pp 635–654

  • Ferreira C (2006) Gene expression programming: mathematical modeling by an artificial intelligence, 2nd edn. Springer-Verlag, Germany (478 pp)

    Google Scholar 

  • Forchheimer P (1901) Wasserbewegung durch Boden. Z Ver Deutsch Ing 45:1782–1788

    Google Scholar 

  • 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(1):189–201

    Article  Google Scholar 

  • GEPSOFT (2006) GeneXproTools. Version 4.0. Available online: http://www.gepsoft.com/

  • Gordan B, Jahed Armaghani D, Hajihassani M, Monjezi M (2016) Prediction of seismic slope stability through combination of particle swarm optimization and neural network. Eng Comput 32:85–97

    Article  Google Scholar 

  • Güllü H (2012) Prediction of peak ground acceleration by genetic expression programming and regression: a comparison using likelihood-based measure. Eng Geol 141–142:92–113

    Article  Google Scholar 

  • Hajihassani M, Jahed Armaghani D, Marto A, Tonnizam Mohamad E (2015a) Ground vibration prediction in quarry blasting through an artificial neural network optimized by imperialist competitive algorithm. Bull Eng Geol Environ 74:873–886

    Article  Google Scholar 

  • Hajihassani M, Jahed Armaghani D, Monjezi M, Mohamad ET, Marto A (2015b) Blast-induced air and ground vibration prediction: a particle swarm optimization-based artificial neural network approach. Environ Earth Sci 74:2799–2817

    Article  Google Scholar 

  • Hannoura A, Barends FBJ (1981) Non-Darcy flow: a state of art. In: Verruijt A, Barends FBJ (eds) Proceedings of the euromech 143. Balkema PC, Rotterdam, pp 37–51

    Google Scholar 

  • Iwai K (1976) Fundamental studies of fluid flow through a single fracture, Ph.D. dissertation, University of California, Berkeley, California

  • Jaeger JC, Cook NGW (1976) Fundamentals of rock mechanics, 169-171. Chapman and Hall, London

    Google Scholar 

  • Jahed Armaghani D, Hajihassani M, Yazdani Bejarbaneh B, Marto A, Tonnizam Mohamad E (2014) Indirect measure of shale shear strength parameters by means of rock index tests through an optimized artificial neural network. Measurement 55:487–498

    Article  Google Scholar 

  • Jahed Armaghani D, Momeni E, Alavi Nezhad K, Abad SV, Khandelwal M (2015) Feasibility of ANFIS model for prediction of ground vibrations resulting from quarry blasting. Environ Earth Sci 74:2845–2860

    Article  Google Scholar 

  • Koppen M, Ovaska S, Furuhashi T, Hoffmann F (eds), Soft computing and industry—recent applications. Springer-Verlag, pp 635–654

  • Kayadelen C (2011) Soil liquefaction modeling by Genetic Expression Programming and Neuro-Fuzzy. Expert Syst Appl 38:4080–4087

    Article  Google Scholar 

  • Khandelwal M, Jahed Armaghani D (2016) Prediction of Drillability of Rocks with Strength Properties Using a Hybrid GA-ANN Technique. Geotech Geol Eng 34:605–620

    Article  Google Scholar 

  • Khandelwal M, Monjezi M (2013) Prediction of flyrock in open pit blasting operation using machine learning method. Int J Min Sci Tech 23(3):313–316

    Article  Google Scholar 

  • Khandelwal M, Singh TN (2010) Prediction of macerals contents of Indian coals from proximate and ultimate analyses using artificial neural networks. Fuel 89(5):1101–1109

    Article  Google Scholar 

  • Lanaro F (2000) A random field model for surface roughness and aperture of rock fractures. Int J Rock Mech Min Sci 37:1195–1210

    Article  Google Scholar 

  • Lee CH, Farmer I (1993) Fluid flow in discontinuous rocks. Chapman and Hall, London

    Google Scholar 

  • Looney CG (1996) Advances in feed-forward neural networks: demystifying knowledge acquiring black boxes. IEEE Trans Knowl Data Eng 8(2):211–226

    Article  Google Scholar 

  • Mollahasani A, Alavi AH, Gandomi AH (2011) Empirical modeling of plate load test moduli of soil via gene expression programming. Comput Geotech 38(2):281–286

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Monjezi M, Ahmadi Z, Varjani AY, Khandelwal M (2013) Backbreak prediction in the Chadormalu iron mine using artificial neural network. Neural Comput Appl 23(3–4):1101–1107

    Article  Google Scholar 

  • Nelson M, Illingworth WT (1990) A practical guide to neural nets. Addison—Wesley, Reading

    Google Scholar 

  • Oron AP, Berkowitz B (1998) Flow in rock fractures: The local cubic law assumption reexamined. Water Resour Res 34:2811–2825

    Article  Google Scholar 

  • Ozbek A, Unsal M, Dikec A (2013) Estimating uniaxial compressive strength of rocks using genetic expression programming. J Rock Mech Geotech Eng 5(4):325–329

    Article  Google Scholar 

  • Pratt HR, Swolfs HS, Brace WF, Black AD, Handin JW (1977) Elastic and transport properties of an in situ jointed granite. Int J Rock Mech Min Sci Geomech Abstr 14:34–45

    Article  Google Scholar 

  • Pyrak-Nolte LJ, Myer LR, Cook NGW, Witherspoon PA (1987) Hydraulic and mechanical properties of natural fractures in low permeability rock. 6th international congress rock mechanics. ISRM, Montreal, pp 225–231

    Google Scholar 

  • Ranjith PG, Darlington W (2007) Nonlinear single-phase flow in real rock joints. Water Resour Res 43:W09502. doi:10.1029/2006WR005457

  • Ranjith PG, Khandelwal M (2012) Artificial neural network for prediction of air flow in a single rock joint. Neural Comput Appl 21(6):1413–1422

    Article  Google Scholar 

  • Raven KG, Gale JE (1985) Water flow in a natural rock fracture as a function of stress and sample size. Int J Rock Mech Min Sci Geomech Abstr 16:225–234

    Google Scholar 

  • Scheidegger AE (1974) The physics of flow through porous media, 3rd edn. University of Toronto Press, Toronto

    Google Scholar 

  • Skjetne E, Hansen A, Gudmundsson JS (1999) High-velocity flow in a rough fracture. J Fluid Mech 383:1–28

    Article  Google Scholar 

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

    Google Scholar 

  • SPSS Inc (2007) SPSS for Windows (Version 16.0). Chicago: SPSS Inc

  • Teodorescu L, Sherwood D (2008) High energy physics event selection with gene expression programming. Comput Phys Commun 178:409–419

    Article  Google Scholar 

  • Tonnizam Mohamad E, Hajihassani M, Jahed Armaghani D, Marto A (2012) Simulation of blasting-induced air overpressure by means of artificial neural networks. Int Rev Modell Simulations 5:2501–2506

    Google Scholar 

  • Tonnizam Mohamad E, Jahed Armaghani D, Hasanipanah M, Murlidhar BR, Asmawisham Alel MN (2016) Estimation of air-overpressure produced by blasting operation through a neuro-genetic technique. Environ Earth Sci 75:174

    Article  Google Scholar 

  • Tsang YW (1984) The effect of tortuosity on fluid flow through a single fracture. Water Resour Res 20:1205–1215

    Article  Google Scholar 

  • Wittke W (1990) Rock mechanics: theory and applications with case histories. Springer-Verlag, Berlin

    Book  Google Scholar 

  • Xue DJ, Zhou HW, Wang CS, Li DP (2013) Coupling mechanism between mining induced deformation and permeability of coal. Int J Min Sci Technol 23(6):783–787

    Article  Google Scholar 

  • Yagiz S, Gokceoglu C (2010) Application of fuzzy inference system and nonlinear regression models for predicting rock brittleness. Expert Syst Appl 37(3):2265–2272

    Article  Google Scholar 

  • Yang Y, Zang O (1997) A hierarchical analysis for rock engineering using artificial neural networks. Rock Mech Rock Eng 30:207–222

    Article  Google Scholar 

  • Yang Y, Li X, Gao L, Shao X (2013) A new approach for predicting and collaborative evaluating the cutting force in face milling based on gene expression programming. J Network Comput Appl 36:1540–1550

    Article  Google Scholar 

  • Zimmerman RW, Bodvarsson GS (1996) Hydraulic conductivity of rock fractures. Transp Porous Media 23:1–30

    Article  Google Scholar 

  • Zimmerman RW, Yeo IW (2000) Fluid flow in rock fractures: from the Navier-Stokes equations to the cubic law, in Dynamics of Fluids in Fractured Rock, Geophysical Monograph 122, American Geophysical Union, pp 213–224

  • Zimmerman RW, Chen DW, Cook NGW (1992) The effect of contact area on the permeability of fractures. J Hydrol 139:79–96

    Article  Google Scholar 

  • Zimmerman RW, Al-Yaarubi A, Pain CC, Grattoni CA (2004) Non-linear regimes of fluid flow in rock fractures. Int J Rock Mech Min Sci 41(Supplement A):163–169

  • Zorlu K, Gokceoglu C, Ocakoglu F, Nefeslioglu HA, Acikalin S (2008) Prediction of uniaxial compressive strength of sandstones using petrography-based models. Eng Geol 96(3):141–158

    Article  Google Scholar 

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Correspondence to Manoj Khandelwal.

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Khandelwal, M., Armaghani, D.J., Faradonbeh, R.S. et al. A new model based on gene expression programming to estimate air flow in a single rock joint. Environ Earth Sci 75, 739 (2016). https://doi.org/10.1007/s12665-016-5524-6

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