Calibration of the Microparameters of Rock Specimens by Using Various Machine Learning Algorithms
Publication: International Journal of Geomechanics
Volume 21, Issue 5
Abstract
High accuracy in the simulation of the discrete-element method (DEM) depends on the proper selection of microparameters. In this study, the range of microparameters was determined through sensitivity analysis. Subsequently, four levels of orthogonal experimental tables were established and 148 sets of data were collected. In addition, five data mining methods, namely, support vector regression (SVR), nearest-neighbor regression (NNR), Bayesian ridge regression (BRR), random forest regression (RFR), and gradient tree boosting regression (GTBR), were used to establish a microparameter prediction model. The results indicate that machine learning methods have significant potential in determining the relationship between macro and microparameters of the DEM model. RFR achieved the best performance among the five models whether the input data were collected from the tests of the Brazilian tensile strength and uniaxial compression or only the uniaxial compression test. In addition, the deviation between the predicted and measured macroparameters was less than 8%. This approach allowed for more accurate modeling of complex structures in a rock under various stress conditions through DEM simulations.
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Acknowledgments
The authors gratefully acknowledge the funds received from the National Key Research and Development Plan (Grant No. 2018YFC1504902) and the National Natural Science Foundation of China (Grant Nos. 52079068 and 41772246).
Notation
The following symbols are used in this paper:
- A(e)
- area of each element;
- contact force of FJCM;
- element force;
- Fm(x)
- sum of learners in GTBR;
- Fm−1(x)
- sum of learners in the last step;
- scalar value of normal force;
- shear force in the direction;
- shear force in the direction;
- hm(x)
- basis functions of boosting;
- I
- identity matrix;
- moment of FJCM;
- element moment;
- bending moment;
- scalar value of twisting moment;
- direction normal vector;
- r(e)
- relative position;
- w
- weight matrix;
- α
- complexity parameter of BRR;
- γm
- length of a step;
- ɛ
- free parameter of SVR;
- ξ
- margin of SVR;
- σ(e)
- normal stress;
- τ(e)
- shear stress; and
- φ
- activation function.
References
Bishop, C. M., and M. E. Tipping. 2003. “Bayesian regression and classification.” In Advances in Learning Theory: Methods, Models and Applications, edited by J. A. K. Suykens, I. Horvath, S. Basu, C. Micchelli, and J. Vandewalle, 267–288. Amsterdam, Netherlands: IOS Press.
Camusso, M., and M. Barla. 2009. “Micro-parameters calibration for loose and cemented soil when using particle methods.” Int. J. Geomech. 9 (5): 217–229. https://doi.org/10.1061/(ASCE)1532-3641(2009)9:5(217).
Chen, R. P., P. Zhang, X. Kang, Z. Q. Zhong, Y. Liu, and H. N. Wu. 2019. “Prediction of maximum surface settlement caused by earth pressure balance (EPB) shield tunneling with ANN methods.” Soils Found. 59 (2): 284–295. https://doi.org/10.1016/j.sandf.2018.11.005.
Cong, Y., Z. Q. Wang, Y. R. Zheng, and X. T. Feng. 2015. “Experimental study on microscopic parameters of brittle materials based on particle flow theory.” [In Chinese.] Chin. J. Geotech. Eng. 37 (6): 1031–1040.
Cundall, P. A. 1971. “A computer model for simulating progressive, large-scale movement in blocky rock system.” In Int. Symp. on Rock Mechanics, 2–8. Salzburg, Austria: International Society for Rock Mechanics.
Deng, S. X., Y. L. Zheng, L. P. Feng, P. Y. Zhu, and Y. Ni. 2019. “Application of design of experiments in microscopic parameter calibration for hard rocks of PFC3D model.” [In Chinese.] Chin. J. Geotech. Eng. 41 (4): 655–664.
De Simone, M., L. M. S. Souza, and D. Roehl. 2019. “Estimating DEM micro-parameters for uniaxial compression simulation with genetic programming.” Int. J. Rock Mech. Min. Sci. 118: 33–41. https://doi.org/10.1016/j.ijrmms.2019.03.024.
Ding, X., and L. Zhang. 2014. “A new contact model to improve the simulated ratio of unconfined compressive strength to tensile strength in bonded particle models.” Int. J. Rock Mech. Min. Sci. 69: 111–119. https://doi.org/10.1016/j.ijrmms.2014.03.008.
Dong, L., and X. Li. 2013. “Comprehensive models for evaluating rockmass stability based on statistical comparisons of multiple classifiers.” Math. Probl. Eng. 2013: 395096. https://doi.org/10.1155/2013/395096.
Dong, L. J., J. Wesseloo, Y. Potvin, and X. B. Li. 2016a. “Discriminant models of blasts and seismic events in mine seismology.” Int. J. Rock Mech. Min. Sci. 86: 282–291. https://doi.org/10.1016/j.ijrmms.2016.04.021.
Dong, L. J., J. Wesseloo, Y. Potvin, and X. B. Li. 2016b. “Discrimination of mine seismic events and blasts using the fisher classifier, naive Bayesian classifier and logistic regression.” Rock Mech. Rock Eng. 49 (1): 183–211. https://doi.org/10.1007/s00603-015-0733-y.
He, G. H., E. Z. Wang, and X. L. Liu. 2016. “Modified governing equation and numerical simulation of seepage flow in a single fracture with three-dimensional roughness.” Arab. J Geosci. 9: 81. https://doi.org/10.1007/s12517-015-2036-8.
He, M. C., H. Xie, S. Peng, and Y. Jiang. 2005. “Study on rock mechanics in deep mining engineering.” Chin. J. Rock Mech. Eng. 24 (16): 2803–2813.
Indraratna, B., N. T. Ngo, C. Rujikiatkamjorn, and J. S. Vinod. 2014. “Behavior of fresh and fouled railway ballast subjected to direct shear testing: Discrete element simulation.” Int. J. Geomech. 14 (1): 34–44. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000264.
Leu, S. S., and T. J. W. Adi. 2011. “Probabilistic prediction of tunnel geology using a Hybrid Neural-HMM.” Eng. Appl. Artif. Intell. 24 (4): 658–665. https://doi.org/10.1016/j.engappai.2011.02.010.
Li, D. 2015. “Inversion procedure of meso-parameters for geotechnical materials based on macroscopic experimental data.” [In Chinese.] Master’s thesis, Dept. of Engineering Mechanics, Dalian Univ. of Technology.
Liu, X., S. Wang, E. Wang, J. Wang, and B. Hu. 2008. “Evolutionary rules of flaws in rock subjected to uniaxial compression and rock strength.” [In Chinese.] Chin J Rock Mech Eng. 27 (6): 1195–1201.
Naderpour, H., A. H. Rafiean, and P. Fakharian. 2018. “Compressive strength prediction of environmentally friendly concrete using artificial neural networks.” J. Build. Eng. 16: 213–219. https://doi.org/10.1016/j.jobe.2018.01.007.
Ni, P., and S. Mangalathu. 2018. “Fragility analysis of gray iron pipelines subjected to tunneling induced ground settlement.” Tunnelling Underground Space Technol. 76: 133–144. https://doi.org/10.1016/j.tust.2018.03.014.
Ni, P., S. Mangalathu, and K. Liu. 2020. “Enhanced fragility analysis of buried pipelines through Lasso regression.” Acta Geotech. 15 (2): 471–487. https://doi.org/10.1007/s11440-018-0719-5.
Ni, P., S. Mangalathu, and Y. Yi. 2018. “Fragility analysis of continuous pipelines subjected to transverse permanent ground deformation.” Soils Found. 58 (6): 1400–1413. https://doi.org/10.1016/j.sandf.2018.08.002.
Pedregosa, F. et al., 2011. “Scikit-learn: Machine learning in Python.” J. Mach. Learn. Res. 12 (10): 2825–2830.
Perras, M. A., and M. S. Diederichs. 2014. “A review of the tensile strength of rock: Concepts and testing.” Geotech. Geol. Eng. 32 (2): 525–546. https://doi.org/10.1007/s10706-014-9732-0.
Potyondy, D. 2012. “A flat-jointed bonded-particle material for hard rock.” In Proc., 46th US Rock Mechanics/Geomechanics Symp. Alexandria, VA: American Rock Mechanics Association.
Potyondy, D., and P. A. Cundall. 2004. “A bonded-particle model for rock.” Int. J. Rock Mech. Min. Sci. 41 (8): 1329–1364. https://doi.org/10.1016/j.ijrmms.2004.09.011.
Sagong, M., D. Park, J. Yoo, and J. S. Lee. 2011. “Experimental and numerical analyses of an opening in a jointed rock mass under biaxial compression.” Int. J. Rock Mech. Min. Sci. 48 (7): 1055–1067. https://doi.org/10.1016/j.ijrmms.2011.09.001.
Smola, A. J., and B. Schölkopf. 2004. “A tutorial on support vector regression.” Stat. Comput. 14 (3): 199–222. https://doi.org/10.1023/B:STCO.0000035301.49549.88.
Sun, H., X. Liu, S. G. Zhang, and K. Nawnit. 2020. “Experimental investigation of acoustic emission and infrared radiation thermography of dynamic fracturing process of hard-rock pillar in extremely steep and thick coal seams.” Eng. Fract. Mech. 226: 106845. https://doi.org/10.1016/j.engfracmech.2019.106845.
Vallejos, J. A., J. M. Salinas, A. Delonca, and D. Mas Ivars. 2017. “Calibration and verification of two bonded-particle models for simulation of intact rock behavior.” Int. J. Geomech. 17 (4): 06016030. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000773.
Wang, Y., and F. Tonon. 2009. “Modeling Lac du Bonnet granite using a discrete element model.” Int. J. Rock Mech. Min. Sci. 46 (7): 1124–1135. https://doi.org/10.1016/j.ijrmms.2009.05.008.
Wang, Y., and F. Tonon. 2010. “Calibration of a discrete element model for intact rock up to its peak strength.” Int. J. Numer. Anal. Methods Geomech. 34 (5): 447–469. https://doi.org/10.1002/nag.811.
Wu, S., and X. Xu. 2016. “A study of three intrinsic problems of the classic discrete element method using flat-joint model.” Rock Mech. Rock Eng. 49 (5): 1813–1830. https://doi.org/10.1007/s00603-015-0890-z.
Xu, C., X. Liu, E. Wang, Y. Zheng, and S. Wang. 2018. “Rockburst prediction and classification based on the ideal-point method of information theory.” Tunnelling Underground Space Technol. 81: 382–390. https://doi.org/10.1016/j.tust.2018.07.014.
Yang, S. Q., Y. H. Huang, H. W. Jing, and X. R. Liu. 2014. “Discrete element modeling on fracture coalescence behavior of red sandstone containing two unparallel fissures under uniaxial compression.” Eng. Geol. 178: 28–48. https://doi.org/10.1016/j.enggeo.2014.06.005.
Yang, X. X., P. H. S. W. Kulatilake, X. Chen, H. W. Jing, and S. Q. Yang. 2016. “Particle flow modeling of rock blocks with nonpersistent open joints under uniaxial compression.” Int. J. Geomech. 16 (6): 04016020. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000649.
Yoon, J. 2007. “Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation.” Int. J. Rock Mech. Min. Sci. 44 (6): 871–889. https://doi.org/10.1016/j.ijrmms.2007.01.004.
Zhang, M., M. Li, Y. Shen, Q. Ren, and J. Zhang. 2019. “Multiple mechanical properties prediction of hydraulic concrete in the form of combined damming by experimental data mining.” Constr. Build. Mater. 207: 661–671. https://doi.org/10.1016/j.conbuildmat.2019.02.169.
Zhu, J. B., Z. Y. Liao, and C. A. Tang. 2016. “Numerical SHPB tests of rocks under combined static and dynamic loading conditions with application to dynamic behavior of rocks under in situ stresses.” Rock Mech. Rock Eng. 49 (10): 3935–3946. https://doi.org/10.1007/s00603-016-0993-1.
Zurovac, J., and R. Brown. 2012. Orthogonal design: A powerful method for comparative effectiveness research with multiple interventions. Portland, OR: Center on Healthcare Effectiveness, Mathematica Policy Research.
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Published In
International Journal of Geomechanics
Volume 21 • Issue 5 • May 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Apr 25, 2020
Accepted: Nov 17, 2020
Published online: Mar 10, 2021
Published in print: May 1, 2021
Discussion open until: Aug 10, 2021
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