AN EFFICIENT CALIBRATION PROCESS FOR THE PREDICTION OF ROCK STRENGTH THROUGH MACHINE LEARNING ALGORITHMS

Numerical models based on the discrete element method (DEM) have been widely used to predict the mechanical behaviors of rocks in rock engineering applications. Nevertheless, calibration of the model parameters is done by running numerous simulations and this time-consuming simulation process precludes the numerical platforms to be used as a practical tool in such applications. This study aims to accelerate the calibration process of the micro-parameters of three-dimensional (3D) numerical models built based on DEM and facilitate the generation of an efficient database by using machine learning algorithms in the prediction of rock strength. Namely, these algorithms are linear regression (LR), decision tree (DT) regression, and random forest (RF) regression. The appropriate methodology for predicting the uniaxial compressive strengths (UCS) of certain rock types was investigated using a dataset consisting of micro-parameters of 87 DEM-based rock models, generated through an open-source code, Yade. The performance of such methods was evaluated by using metrics including R-squared score (R2), mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE), and then their statistical discrepancies were analyzed. The most accurate prediction of UCS was obtained in the LR method and the lowest percentage of performance was derived from the RF algorithms. LR method provides the results efficiently during calibration of the micro-parameters of a DEM-based rock model.

Keywords:

Rock strength, Discrete element method, Numerical model calibration Machine learning,

PDF

___

[1] Potyondy, D.O., Cundall, P.A., Lee, C.A. (1996). Modelling rock using bonded assemblies of circular particles. 2nd North American Rock Mechanics Symposium; 1996 Montreal Canada, 1937–1944.
[2] Hazzard, J.F., Young, R.P., Maxwell, S.C. (2000). Micromechanical modeling of cracking and failure in brittle rocks. Journal of Geophysical Research, 105(7), 16683–16697.
[3] Potyondy, D.O., Cundall, P.A. (2004). A bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences, 41 (8):1329–1364.
[4] Al-Busaidi, A., Hazzard, J.F., Young, R.P. (2005). Distinct element modeling of hydraulically fractured Lac du Bonnet granite. Journal of Geophysical Research-Atmospheres, 110 (6), doi: 10.1029/2004JB003297.
[5] Cho, N., Martin, C.D., Sego, D.C. (2007). A clumped particle model for rock. International Journal of Rock Mechanics and Mining Sciences, 44, 997–1010.
[6] Wang, Y., Tonon, F. (2009). Modeling Lac du Bonnet granite using a discrete element model. International Journal of Rock Mechanics and Mining Sciences, 46, 1124–1135.
[7] Plassiard, J.P., Belheine, N., Donzé, F.V. (2009). A spherical discrete element model: calibration procedure and incremental response. Granular Matter, doi: 10.1007/s10035-009-0130-x.
[8] Potyondy, D.O. (2012). A flat-jointed bonded-particle material for hard rock. In: Proceedings of the 46th US rock mechanics/geomechanics symposium, American Rock Mechanics Association, Chicago, USA.
[9] Scholtés, L., Donzé, F.V. (2013). A DEM model for soft and hard rocks: role of grain interlocking on strength. Journal of the Mechanics and Physics of Solids, 61, 352–369.
[10] Ding., X., Zhang, L. (2014). A new contact model to improve the simulated ratio of unconfined compressive strength to tensile strength in bonded particle models. International Journal Rock Mechanics Mining Science, 69, 111–119.
[11] Dinç, Ö., Scholtès, L. (2018). Discrete analysis of damage and shear banding in argillaceous rocks. Rock Mechanics Rock Engineering, 51(5), 1521–1538.
[12] Dinç Göğüş, Ö. (2020). 3D discrete analysis of damage evolution of hard rock under tension. Arabian Journal of Geosciences 13: 661, https://doi.org/10.1007/s12517-020-05684-1.
[13] Dinç Göğüş Ö., Avşar, E. (2022). Stress levels of precursory strain localization subsequent to the crack damage threshold in brittle rock. Plos One, 17(11): e0276214. https://doi.org/10.1371/journal.pone.0276214.
[14] Meulenkamp, F., Alvarez Grima, M. (1999). Application of neural networks for the prediction of the unconfined compressive strength (UCS) from Equotip hardness. International Journal of Rock Mechanics and Mining Sciences, 36:29–39.
[15] Singh, T.N., Dubey, R.K. (2000). A study of transmission velocity of primary wave (P-Wave) in coal measures sandstone. Journal of Scientific & Industrial Research India, 59:482–486.
[16] Kahraman, S., Alber, M. (2006). Estimating the unconfined compressive strength and elastic modulus of a fault breccia mixture of weak rocks and strong matrix. International Journal of Rock Mechanics and Mining Sciences, 43:1277–1287.
[17] Çobanoğlu, I., Çelik, S.B. (2008). Estimation of uniaxial compressive strength from point load strength, Schmidt hardness and P-wave velocity. Bulletin of Engineering Geology and the Environment, 67:491–498.
[18] Zorlu, K, Gökçeoğlu, C., Ocakoğlu, F., Nefeslioğlu, H.A., Açıkalın, S. (2008). Prediction of unconfined compressive strength of sandstones using petrography-based models. Engineering Geology, 96:141–158.
[19] Yilmaz, I., Yüksek, A.G. (2008). An example of artificial neural network (ANN) application for indirect estimation of rock parameters. Rock Mechanics and Rock Engineering, 41(5):781–795.
[20] Sarkar, K., Tiwary, A., Singh, T.N. (2010). Estimation of strength parameters of rock using artificial neural networks. Bulletin of Engineering Geology and the Environment, 69:599–606.
[21] Kahraman, S., Alber, M., Fener, M., Günaydın, O. (2010). The usability of Cerchar abrasivity index for the prediction of UCS and E of Misis Fault Breccia: regression and artificial neural networks. Expert Systems with Applications, 37(12): 8750-8756.
[22] Çevik, A., Sezer, E.A., Cabalar, A.F., Gökçeoğlu, C. (2011). Modeling of the unconfined compressive strength of some clay-bearing rocks using neural network. Applied Soft Computing, 11:2587–2594.
[23] Yağız, S., Sezer, E.A., Gökçeoğlu, C. (2011). Artificial neural networks and nonlinear regression techniques to assess the influence of slake durability cycles on the prediction of uniaxial compressive strength and modulus of elasticity for carbonate rocks. International Journal for Numerical and Analytical Methods in Geomechanics, 36, 1636–1650. doi:10. 1002/nag.1066.
[24] Ceryan, N., Okkan, O., Kesimal, A. (2012). Application of Generalized Regression Neural Networks in Predicting the Unconfined Compressive Strength of Carbonate Rocks. Rock Mechanics and Rock Engineering, 45:1055–1072.
[25] Liu, Z. B., Shao, J. F., Xu, W. Y., Wu, Q. (2015). Indirect estimation of unconfined compressive strength of carbonate rocks using extreme learning machine. Acta Geotechnica, 10, 651–663.
[26] Mahmoodzadeh, A., Mohammadi, M., Salim, S., Farid Hama Ali, H., Hashim Ibrahim, H., Nariman Abdulhamid, S., Nejati, H.R., Rashidi, S. (2022). Machine learning techniques to predict rock strength parameters. Rock Mechanics and Rock Engineering, 55 (3), 1721–1741.
[27] Wang, Y., Zhang, X., and Liu, X. (2021). Machine learning approaches to rock fracture mechanics problems: Mode-I fracture toughness determination. Engineering Fracture Mechanics, 253, doi:10.1016/j.engfracmech.2021.107890.
[28] Waqas, M. (2018). Discrete element and artificial intelligence modeling of rock properties and formation failure in advance of shovel excavation. Ph.D. Thesis, Mining Engineering, Missouri University of Science and Technology, 254.
[29] Fathipour-Azar, H. (2022). Machine learning-assisted distinct element model calibration: ANFIS, SVM, GPR, and MARS approaches. Acta Geotechnica, 17:1207–1217.
[30] Šmilauer, V. et al. (2015). Yade Documentation 2nd edition. doi:10.5281/zenodo.34073. http://yade-dem.org.
[31] Dinç Göğüş, Ö. (2021). Mikro Parametrelerin Makro Mekanik Kaya Davranışı Üzerindeki Etkisi: Ayrık Elemanlar Yöntemiyle Model Kalibrasyonu. Jeoloji Mühendisliği Dergisi, 45: 67-82.
[32] Doğan, İ., Doğan, N. (2020). Model Performans Kriterlerinin Kronolojisine ve Metodolojik Yönlerine Genel Bir Bakış: Bir Gözden Geçirme. An Overview of Chronology and Methodological Aspects of Model Performance Criteria: A Review. Turkiye Klinikleri Journal of Biostatistics, 12(1):114-25.
[33] Willmott, C.J., Matsuura, K. (2005). Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Climate Research, 30(1):79-82.
[34] Cover, T.M., Thomas, J.A. (1991). Elements of information theory. John Wiley & Sons, New York, NY, 774.
[35] Battiti, R. (1994) Using mutual information for selecting features in supervised neural net learning. IEEE Transactions on Neural Networks, 5(4):537-50.