Estimation of Elastic Modulus of Intact Rock using Artificial Neural Network and Nonlinear Regression


1 Department of Civil Engineering, University of Isfahan

2 Department of geology, University of Isfahan


Elastic modulus of intact rock is an essential requirement of many geo-mechanical analyses, especially rock excavation projects. Core samples with high quality and proper geometry are required to directly determine elastic modulus, but providing appropriate core samples from fractured and weathered rocks is not possible. Therefore, models are developed to estimate elastic modulus based on the index intact rock properties. In this study, the optimum estimation of elastic modulus of intact rock is obtained using multi-layer perceptron neural network with back propagation algorithm and data of rock mechanic experiments. The results are compared with the nonlinear regression method. For this purpose, 121 data sets obtained from rock tests of three tunnel projects (Beheshtabad, Rudbar and Sabzkuh) are analyzed. Various parameters are considered to estimate elastic modulus such as porosity, uniaxial compressive strength, compressive wave velocity, tensile strength and density. Based on the optimization of the neural network components, the network with two layer and four neuron in hidden layer, one neuron in the output layer, one data series in the input layer and tansig activation function was chosen as the optimum structure of the neural network. Finally, the neural network model was built using various parameters combinations. The results of the estimation methods are evaluated using their coefficient of determination and root mean square error as performance criteria. The comparison shows better performance of the neural network model relative to the nonlinear regression method. Uniaxial compressive strength, compressive wave velocity and tensile strength are the effective parameters in performance of the neural network model, respectively.


شرکت مهاب قدس، 1383، گزارش مطالعات مرحله دوم طرح سد انحرافی و سیستم انتقال آب سبزکوه.
شرکت توسعه منابع آب و نیروی ایران، 1385، گزارش آزمایش های آزمایشگاهی مکانیک سنگ طرح سد و نیروگاه رودبار لرستان، مطالعات مرحله دوم، وزارت نیرو.
شرکت آب منطقه­ای اصفهان، 1383، گزارشات مطالعات پروژه بهشت آباد، شرکت مدیریت منابع آب ایران، وزارت نیرو.
پسندی.م.، اجل لوییان.ر.، فروغی ابری.ر.، 1392، تخمین خورند سیمان پرده آب­بند با استفاده از شبکه­ی عصبی مصنوعی، زمین شناسی کاربردی پیشرفته، شماره 7، ص 32-43.
ذلولی.ا.، خامه­چیان.م.، نیکودل.م.ر.، 1393، ارزیابی تغییرات مقاومت فشاری تک محوری نمونه­هایی از تراورتن­ها در مقابل تبلور نمک با استفاده از مدل تابع زوال، زمین شناسی کاربردی پیشرفته، شماره 12، ص 14-24.
سازمان زمین شناسی و اکتشافات معدنی کشور، 1387، نقشه پراکندگی سنگ­های کربناته، مقیاس 1:5000000
Anagnos, J.N., Kennedy.T.W., 1972, Practical method of conducting the indirect tensile test, Center for Highway Research University of Texas at Austin.
Basheer.I.A., Hajmeer.M., 2000, Artificial neural networks: fundamentals, computing, design, and application, Journal of microbiological methods, Vol:43, No:1, p: 3-31.
Braspenning.P.J., Thuijsman.F., Weijters.A.J.M.M., 1995, Artificial neural networks: an introduction to ANN theory and practice, Lecture Notes in Computer Science, Springer.
Broch.E., Franklin.J., 1972, The point-load strength test, International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, Vol:9, No:6, p: 669-676.
Chatterjee.S., Hadi.A.S., 2013, Regression analysis by example, John Wiley and Sons, New Jersey.
Christaras.B., Auger.F., Mosse.E., 1994, Determination of the moduli of elasticity of rocks. Comparison of the ultrasonic velocity and mechanical resonance frequency methods with direct static methods, Materials and Structures, Vol:27, No:4, p: 222-228.
Das.S.K., Basudhar.P.K., 2008, Prediction of residual friction angle of clays using artificial neural network, Engineering Geology, Vol:100, No:3, p: 142-145.
Deere.D.U., Miller.R.P., 1966, Engineering Classification and Index Properties of Intact Rock. Technical Report No. AFWL-TR-65-116, Air Force Weapons Laboratory, Kirkland Air Force Base, New Mexico.
Dehghan.S., Sattari.G.H., Chehreh Chelgani.S., Aliabadi.M.A., 2010, Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks, Mining Science and Technology (China), Vol:20, No:1, p: 41-46.
Demuth.H., Beale.M., 1993, Neural network toolbox for use with MATLAB.
Diamantis.K., Gartzos.E., Migiros.G., 2009, Study on uniaxial compressive strength, point load strength index, dynamic and physical properties of serpentinites from Central Greece: test results and empirical relations, Engineering Geology, Vol:108, No:3-4, p: 199-207.
Fahlman.S.E., 1988, An empirical study of learning speed in back-propagation networks, Carnegie Mellon Report, No CMU-Cs, pp. 88–162.
Fu.L.M., 1994, Neural networks in computer intelligence, McGraw-Hill, New York.
Galushkin.A.I., 2007, Neuralnetworks theory, Springer, New York.
Goodman.R.E., 1980, Introduction to rock mechanics, John Wiley and Sons, New York.
Haghnejad.A., Ahangari.K., Noorzad.A., Minaeian.B., 2013, Prediction relations between physical and mechanical properties of rocks-A case study: Asmari Formation in Iran, International Journal of Geosciences Research (IJGR), Vol:1, No:1, p: 1-8.
Hamid.R., Yusuf.K., Rashid.A.K.A., 2010, Optimization of Feed-Forward Neural Networks Configuration used for Bridge Condition Rating Approximation. Latest Trends on Engineering Mechanics, Structures, EMESEG'10 Proceedings of the 3rd WSEAS international conference on Engineering mechanics, structures, engineering geology, p: 408-412.
Hecht-Nielsen.R., 1987, Kolmogorov’s mapping neural network existence theorem, Proceedings of the international conference on Neural Networks, IEEE Press, New York, Vol:3, No:3, p: 11-14.
Heidari.M., Khanlari.G.R., Momeni.A.A., 2010, Prediction of elastic modulus of intact rocks using artificial neural networks and non-linear regression methods, Australian Journal of Basic and Applied Sciences, Vol:4, No:12, p: 5869-5879.
Hertz.J., Krogh.A., Palmer.R.G., 1991, Introduction to the Theory of Neural Computation, Addison-Wesley Publishing Co., Redwood City, CA.
Hoek.E., Diederich.M.S., 2006, Empirical estimation of rock mass modulus, International Journal of Rock Mechanics and Mining Sciences, Vol:43, No:2, p: 203-215.
Hubick.K.T., 1992, Artificial neural networks in Australia. Department of. Industry, Technology and Commerce, Commonwealth of Australia, Canberra.
Hush, D., 1989, Classification with neural networks: a performance analysis, IEEE International Conference on Systems Engineering, p: 277-280.
Jensen.L.R.D., Friis.H., Fundal.E., Møller.P., Jespersen.M., 2010, Analysis of limestone micromechanical properties by optical microscopy, Engineering Geology, Vol:110, No:3-4, p: 43-50.
Kaastra.I., Boyd.M., 1996, Designing a neural network for forecasting financial and economic time series, Neurocomputing, Vol:10, No:3, p: 215-236.
Kanellopoulos.I., Wilkinson.G.G., 1997, Strategies and best practice for neural network image classification, International Journal of Remote Sensing, Vol:18, No:4, p: 711-725.
Khandelwal.M., Singh.T.N., 2009, Correlating static properties of coal measures rocks with P-wave velocity, International Journal of Coal Geology, Vol:79, No:1-2, p:55-60.
Kuhn.H., 2000, Uniaxial Compression Testing, Materials Park, OH: ASM International, p: 143-151.
Lashkaripour.G.R., Nakhaei.M., 2001, A statistical investigation on mudrocks characteristics. In: Proceedings of the ISRM regional symposium of rock mechanics. Espoo, Finland, p: 131–136
Looney.C.G., 1996, Advances in feedforward neural networks: demystifying knowledge acquiring black boxes, Knowledge and Data Engineering, IEEE Transactions on, Vol:8, No:2, p: 211-226.
Negnevitsky.M., 2005, Artificial Intelligence: A Guide to Intelligent Systems. Addison Wesley, Harlow, England, 2nd edition.
Ocak.I., 2008, Estimating the modulus of elasticity of the rock material from compressive strength and unit weight, Journal- South African Institute of Mining and Metallurgy, Vol:108, No:10, p: 621–626.
Ocak.I., 2009, Empirical estimation of intact rock elastic modulus. In: The 21st international mining congress of Turkey. Antalya, Turkey, p: 165–172.
Ocak.I., Evren Seker.S., 2012, Estimation of Elastic Modulus of Intact Rocks by Artificial Neural Network, Rock Mechanics and Rock Engineering, Vol:45, No:6, p: 1047-1054
Okay Aksoy.C., Genis.M., Uyar Aldas.G., Ozacar.V., Ozer.S.C., Yilmaz.O., 2012, A comparative study of the determination of rock mass deformation modulus by using different empirical approaches, Engineering Geology, Vol:131-132, p: 19-28.
Palchik.V., 1999, Influence of porosity and elastic modulus on uniaxial compressive strength in soft brittle porous sandstones, Rock Mechanics and Rock Engineering, Vol:32, No:4, p: 303-309.
Palmstrom.A., Singh.R., 2001, The deformation modulus of rock masses-comparisons between in situ tests and indirect estimates, Tunnelling and Underground Space Technology, Vol:16, No:2, p: 115-131.
Paola.J.D., 1994, Neural network classification of multispectral imagery, The University of Arizona, USA.
Ripley.B.D., 1993, Statistical aspects of neural networks. In Barndorff-Nielsen.O.E., Jensen.J.L.,Kendall.W.S. (eds) Networks and ChaosStatistical and Probabilistic Aspects. Chapman and Hall, London, p:. 40–123
Rohde.J., Feng.H., 1990, Analysis of the variability of unconfined compression tests of rock, Rock Mechanics and Rock Engineering, Vol:23, No:3, p: 231-236.
Sachpazis.C.I., 1990,Correlating Schmidt hardness with compressive strength and Young’s modulus of carbonate rocks, Bulletin of the International Association of Engineering Geology, Vol:42, No:1, p: 75-83.
Shen.J., Karakus.M., Xu.C., 2012, A comparative study for empirical equations in estimating deformation modulus of rock masses, Tunnelling and Underground Space Technology, Vol:32, p: 245-250.
Sonmez.H., Gokceoglu.C., Nefeslioglu.H.A., Kayabasi.A., 2006, Estimation of rock modulus: For intact rocks with an artificial neural network and for rock masses with a new empirical equation, International Journal of Rock Mechanics and Mining Sciences, Vol:43, No:2, p: 224–235.
Tiryaki.B., 2008, Predicting intact rock strength for mechanical excavation using multivariate statistics, artificial neural networks, and regression trees, Engineering Geology, Vol:99, No:1, p: 51-60.
Tucker.M.E., 2009, Sedimentary petrology: an introduction to the origin of sedimentary rocks: John Wiley and Sons.
Tuğrul.A., Zarif.I.H., 1999, Correlation of mineralogical and textural characteristics with engineering properties o selected granitic rock from Turkey, Engineering Geology, Vol:51, No:4, p: 303-317.
Wang.C., 1994, A theory of generalization in learning machines with neural application, Doctoral Dissertation, The University of Pennsylvania, USA.
Wythoff.B.J., 1993, Backpropagation neural networks: a tutorial, Chemometrics and Inteligent Laboratory Systems, Vol:18, No:2, p: 115-155.
Xie.T., Yu.H., Wilamowski.B., 2011, Comparison between Traditional Neural Networks and Radial Basis Function Networks, IEEE International Symposum on Industerial Electronics, p: 1194-1199.
Yagiz, S., 2009, Predicting uniaxial compressive strength, modulus of elasticity and index properties of rocks using the Schmidt hammer, Bulletin of Engineering Geology and the Environment, Vol:68, No:1, p: 55-63.
Zhang.L., Einstein.H.H., 2004, Using RQD to estimate the deformation modulus of rock masses, International Journal of Rock Mechanics and Mining Sciences, Vol:41, No:2, p: 337-341.
Zhang.L., 2005, Engineering properties of rocks, In: Elseviergeoengineering book series, Vol:4, Elsevier, Berlin, p: 180.