DOI QR코드

DOI QR Code

Soft computing based mathematical models for improved prediction of rock brittleness index

  • Abiodun I. Lawal (Department of Energy Resources Engineering, Inha University) ;
  • Minju Kim (Department of Energy Resources Engineering, Inha University) ;
  • Sangki Kwon (Department of Energy Resources Engineering, Inha University)
  • Received : 2021.12.15
  • Accepted : 2023.03.07
  • Published : 2023.05.10

Abstract

Brittleness index (BI) is an important property of rocks because it is a good index to predict rockburst. Due to its importance, several empirical and soft computing (SC) models have been proposed in the literature based on the punch penetration test (PPT) results. These models are very important as there is no clear-cut experimental means for measuring BI asides the PPT which is very costly and time consuming to perform. This study used a novel Multivariate Adaptive regression spline (MARS), M5P, and white-box ANN to predict the BI of rocks using the available data in the literature for an improved BI prediction. The rock density, uniaxial compressive strength (σc) and tensile strength (σt) were used as the input parameters into the models while the BI was the targeted output. The models were implemented in the MATLAB software. The results of the proposed models were compared with those from existing multilinear regression, linear and nonlinear particle swarm optimization (PSO) and genetic algorithm (GA) based models using similar datasets. The coefficient of determination (R2), adjusted R2 (Adj R2), root-mean squared error (RMSE) and mean absolute percentage error (MAPE) were the indices used for the comparison. The outcomes of the comparison revealed that the proposed ANN and MARS models performed better than the other models with R2 and Adj R2 values above 0.9 and least error values while the M5P gave similar performance to those of the existing models. Weight partitioning method was also used to examine the percentage contribution of model predictors to the predicted BI and tensile strength was found to have the highest influence on the predicted BI.

Keywords

Acknowledgement

This work was supported by Inha University Research Grant (2023).

References

  1. Adegoke, M., Wong, H.T., Leung, A.C.S. and Sum, J. (2019), "Two noise tolerant incremental learning algorithms for single layer feed-forward neural networks", J. Ambient Intell. Human Comput., https://doi.org/10.1007/s12652-019-01488-8. 
  2. Akinwekomi, A.D. and Lawal, A.I. (2021), "Neural network-based model for predicting particle size of AZ61 powder during high energy mechanical milling", Neural. Comput. Appl., 33, 17611-17619, https://doi.org/10.1007/s00521-021-06345. 
  3. Altindag, R. (2010), "Assessment of some brittleness indices in rock-drilling efficiency", Rock Mech. Rock Eng., 43(3), 361-370. https://doi:10.1007/s00603-009-0057-x. 
  4. Altindag, R. and Guney, A. (2010), "Predicting the relationships between brittleness and mechanical properties (UCS, TS and SH) of rocks", J. Sci. Res. Essay, 5, 35-39. https://doi.org/10.5897/SRE.9000753. 
  5. Andreev, G.E. (1995), Brittle failure of rock materials: Test results and constitutive models, Rotterdam: A. A. Balkema.
  6. Armaghani, D.J., Mamou, A., Maraveas, C., Roussis, P.C., Siorikis, V.G., Skentou, A.D. and Asteris, P.G. (2021), "Predicting the unconfined compressive strength of granite using only two non-destructive test indexes", Geomech. Eng., 25(4), 317-330. https://doi.org/10.12989/gae.2021.25.4.317. 
  7. ASTM (1995), Standard practice for preparing rock core specimens and determining dimension and shape tolerances. American Society for Testing and Materials. D4543. 
  8. ASTM (1995), Standard test method for splitting tensile strength of intact rock core specimens. American Society for Testing and Materials. D3967. 
  9. ASTM (1995), Standard test method for unconfined compressive strength of intact rock core specimens. American Society for Testing and Materials. D2938. 
  10. Bishop, C.M. (1995), Neural network for pattern recognition, 1st Ed. Oxford University Press. 
  11. Breiman, L., Friedman, J.H., Olshen, R.A. and Stone, C.J. (1984), Classification and regression trees. Monterey, CA: Wadsworth & Brooks/Cole Advanced Books & Software. ISBN 978-0-412-04841-8. 
  12. Cheng, W., Jin, Y. and Chen, M. (2015), "Reactivation mechanism of natural fractures by hydraulic fracturing in naturally fractured shale reservoirs". J. Nat. Gas Sci Eng., 23, 431-439. https://doi:10.1016/j.jngse. 2015.01.031. 
  13. Craven, P. and Wahba, G. (1979). "Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation". Numer. Math., 31, 317-403. https://doi.org/10.1007/BF01404567. 
  14. Dehghan, S., Sattari, G., Chelgani, S.C. and Aliabadi, M. (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. https://doi.org/10.1016/S1674-5264(09)60158-7. 
  15. Ebrahimi, E., Monjezi, M., Khalesi, M.R. and Armaghani, D.J. (2015), "Prediction and optimization of back-break and rock fragmentation using an artificial neural network and a bee colony algorithm", Bull. Eng. Geol. Environ., 75, 27-36. https://doi.org/10.1007/s10064-015-0720-2. 
  16. Fattahi, H. and Hasanipanah, M. (2021), "Predicting the shear strength parameters of rock: A comprehensive intelligent approach", Geomech. Eng., 27(5), 511-525. https://doi.org/10.12989/gae.2021.27.5.511. 
  17. Friedman, J.H. (1991), "Multivariate adaptive regression splines", Ann. Stat., 19(1), 1-67. https://doi.org/10.1214/aos/1176347963. 
  18. Garson, G.D. (1991), "Interpreting neural network connection weights", Artif. Intell. Exp., 6, 47-51. https://doi.org/10.5555/129449.129452. 
  19. Gevrey, M., Dimopoulos, I. and Lek, S. (2003), "Review and comparison of methods to study the contribution of variables in artificial neural network models", Ecol. Modell., 160(3), 249-264. https://doi.org/10.1016/S0304-3800(02)00257-0. 
  20. Guo, J.C., Luo, B., Zhu, H.Y., Wang, Y.H., Lu, Q.L. and Zhao, X. (2015), "Evaluation of fracability and screening of perforation interval for tight sandstone gas reservoir in western Sichuan Basin", J. Nat. Gas Sci. Eng., 25, 77-87. https://doi.org/10.1016/j.jngse.2015.04.026. 
  21. Hajiabdolmajid, V. and Kaiser, P. (2003), "Brittleness of rock and stability assessment in hard rock tunnelling", Tunn. Undergr. Sp. Technol., 18(1), 35-48. https://10.1016/S0886-7798(02)00100-1. 
  22. Huang, X.R., Huang, J.P., Li, Z.C., Yang, Q.Y., Sun, Q.X. and Wei, C. (2015), "Brittleness index and seismic rock physics model for anisotropic tight-oil sandstone reservoirs", Appl. Geophys., 12(1), 11-22. https://10.1007/s11770-014-0478-0. 
  23. Hucka, V. and Das, B. (1974), "Brittleness determination of rocks by different methods". International Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 11, 389-392. https://doi.org/10.1016/0148-9062(74)91109-7. 
  24. Hussain, A., Surendar, A., Clementking, A., Kanagarajan, S. and Ilyashenko, L.K. (2018), "Rock brittleness prediction through two optimization algorithms namely particle swarm optimization and imperialism competitive algorithm". Eng. Comput., 35, 1027-1035. https://doi.org/10.1007/s00366-018-0648-9. 
  25. Kaunda, R.B. and Asbury, B. (2016), "Prediction of rock brittleness using nondestructive methods for hard rock tunnelling", J. Rock Mech. Geotech. Eng., 8(4), 533-540, http://dx.doi.org/10.1016/j.jrmge.2016.03.002. 
  26. Koopialipoor, M., Noorbakhsh, A., Ghaleini, E.N., Armaghani, D.J. and Yagiz, S. (2019), "A new approach for estimation of rock brittleness based on non-destructive tests", J. Nondestruct. Eval., 34(4), 354-375. https://doi.org/10.1080/10589759.2019.1623214. 
  27. Lawal, A.I. (2020), "An artificial neural network-based mathematical model for the prediction of blast-induced ground vibration in granite quarries in Ibadan, Oyo State, Nigeria", Sci. African, 8, e00413. https://doi.org/10.1016/j.sciaf.2020.e00413. 
  28. Lawal, A.I. and Idris, M.A. (2019), "An artificial neural network-based mathematical model for the prediction of blast-induced ground vibrations". Int. J. Environ Std., 77(2), 318-334. https://doi.org/10.1080/00207233.2019.1662186. 
  29. Lawal, A.I. and Kwon, S. (2020), "Application of artificial intelligence in rock mechanics: an overview", J. Rock Mech. Geotech. Eng., 13, 248-266. https://doi.org/10.1016/j.jrmge.2020.05.010. 
  30. Lawal, A.I., Kwon, S., Aladejare, A.E. and Oniyide, G.O. (2022), "Prediction of the static and dynamic mechanical properties of sedimentary rock using GPR, ANN, and response surface method", Geomech. Eng., 28(3), 4547-4563. https://doi.org/10.12989/gae.2022.28.3.313. 
  31. Lawal, A.I., Oniyide, G.O., Kwon, S., Onifade, M., Koken, E, and Ogunsola, N.O. (2021a), "Prediction of mechanical properties of coal from non-destructive properties: A comparative application of MARS, ANN, and GA", Nat. Resour. Res., 30(6), 4547-4563.  https://doi.org/10.1007/s11053-021-09955-w
  32. Lawal, A.I., Kwon, S., Hammed, O.S. and Idris, M.A. (2021b), "Blast-induced ground vibration prediction in granite quarries: An application of Gene expression programming, ANFIS, and Sine Cosine algorithm optimized ANN", Int. J. Min. Sci. Tech., 31, 265-277.  https://doi.org/10.1016/j.ijmst.2021.01.007
  33. Lawn, B.R., Jensen, T. and Arora, A. (1976), "Brittleness as an indentation size effect", J. Mat. Sci., 11(3), 573-575. https://doi:10.1007/BF00540940. 
  34. Leathwick, J.R., Rowe, D., Richardson, J., Elith, J. and Hastie, T. (2005), "Using multivariate adaptive regression splines to predict the distributions of New Zealand's freshwater diadromous fish", Fresh W Biol., 50, 2034-2051. https://doi:10.1111/j.1365-2427.2005.01448.x 
  35. Meng, F.Z., Zhou, H., Zhang, C.Q., Xu, R.C. and Lu, J.J. (2015), "Evaluation methodology of brittleness of rock based on post-peak stress-strain curves", Rock Mech. Rock Eng., 48(5), 1787-1805. https://doi:10.1007/s00603-014-0694-6. 
  36. Quinlan, J.R. (1992), "Learning with continuous classes", Adams S (ed) Proceedings of AI'92. World Scientific, Singapore. 
  37. Rickman, R., Mullen, M.J., Petre, J.E., Grieser, W.V. and Kundert, D. (2008), "A practical use of shale petrophysics for stimulation design optimization: All shale plays are not clones of the Barnett Shale", SPE 115258 Proceeding of Annual Technical Conference, Society of Petroleum Engineers, Denver, CO, USA. 
  38. Rybacki, E., Meier, T. and Dresen, G. (2016), "What controls the mechanical properties of shale rocks? - Part II: Brittleness", J. Pet. Sci. Eng., 144, 39-58. https://doi:10.1016/j.petrol.2016.02.022. 
  39. Sihag, P., Karimi, S.M. and Angelaki, A. (2019), "Random forest, M5P and regression analysis to estimate the field unsaturated hydraulic conductivity". App. W. Sci., 9, 129. https://doi.org/10.1007/s13201-019-1007-8. 
  40. Sun, D., Lonbani, M., Askarian, B., Armaghani, D.J., Tarinejad, R., Pham, B.T. and Huynh, V.V. (2020). "Investigating the applications of machine learning techniques to predict the rock brittleness index", Appl. Sci., 10, 1691. doi:10.3390/app10051691 
  41. Sun, H., Du, W.S. and Chi, L. (2021), "Uniaxial compressive strength determination of rocks using X-ray computed tomography and convolutional neural networks", Rock Mech. Rock Eng., 54, 4225-4237. https://doi.org/10.1007/s00603-021-02503-1. 
  42. Tarasov, B. and Potvin, Y. (2013), "Universal criteria for rock brittleness estimation under triaxial compression", Int. J. Rock Mech. Min. Sci., 59, 57-69. https://doi.org/10.1016/j.ijrmms.2012.12.011. 
  43. Wang, H., Cai, R., Zhou, B., Aziz, S., Qin, B., Voropai, N., Gan, L. and Barakhtenko, E. (2020), "Solar irradiance forecasting based on direct explainable neural network", Energ. Convers. Manage, 226, 113487, https://doi.org/10.1016/j.enconman.2020.113487. 
  44. Xia, Y., Zhou, H., Zhang, C., He, S., Gao, Y. and Wang, P. (2019), "The evaluation of rock brittleness and its application: a review study", Eur. J. Environ. Civ., 22(1), 239-279. https://doi.org/10.1080/19648189.2019.1655485. 
  45. Yagiz, S. (2009), "Assessment of brittleness using rock strength and density with punch penetration test", Tunn. Undergr. Sp. Technol., 24(1), 66-74. https://doi:10.1016/j.tust.2008.04.002. 
  46. Yagiz, S. and Gokceoglu, C. (2010), "Application of fuzzy inference system and nonlinear regression models for predicting rock brittleness", Exp. Syst. Appl., 37(3), 2265-2272. https://doi.org/10.1016/j.eswa.2009.07.046. 
  47. Yagiz, S., Ghasemi, E. and Adoko, A.C. (2018), "Prediction of rock brittleness using genetic algorithm and particle swarm optimization techniques", Geotech. Geol. Eng., 36, 3767-3777, https://doi.org/10.1007/s10706-018-0570-3. 
  48. Yuvaraj, P., Murthy, A.R, Iyer, N.R, Samui, P. and Sekar, S.K. (2013), "Multivariate adaptive regression splines model to predict fracture characteristics of high strength and ultra high strength concrete beams", Tech Sci. Press, CMC, 36(1), 73-97.