Skip to main content

Advertisement

Log in

Estimating unconfined compressive strength using a hybrid model of machine learning and metaheuristic algorithms

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

Unconfined Compressive Strength (UCS) is one of the most important mechanical properties in geomechanics and is crucial for reliable geo-mechanical modeling of geological formations. Traditional methods for determining UCS involve a great deal of laboratory testing on core samples, which can be very expensive, or collecting a large amount of data from well logs, which could be equally burdensome. Recently, with increasing demands on real-time, efficient UCS predictions in industries dealing with construction, mining, civil engineering, and even petroleum exploration, the need to realize innovative ways has grown. This paper, therefore, embarks on the introduction of a state-of-the-art machine learning framework that embeds the Multi-Layer Perceptron architecture with advanced meta-heuristic optimization techniques, namely Beluga Whale Optimization and Black Widow Optimization, to predict unconfined compressive strength with high accuracy. That is, unlike ANNs, which on occasions easily get bogged down in difficulties of parameter optimizations and slow convergence, it can enable fast and sure predictions, hence its eminently suitable use in real-time decision-making. Employing an extensive dataset compiled from previous scholarly studies, outstanding predictive performance was realized for this model. Therefore, the best-optimized model of MLBO2 was the superior predictor that gave a maximum \({R}^{2}\) of \(0.998\) and minimum RMSE of \(1.309\) in the test phase. These results confirm that the model is efficient in providing highly accurate UCS predictions with immense added advantages over the existing techniques and can contribute much to the geomechanical domains.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Availability of data and materials

No datasets were generated or analysed during the current study.

References

  1. Ulusay, R. (ed.): The ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 2007-2014. Springer International Publishing, Cham (2015). https://doi.org/10.1007/978-3-319-07713-0

    Book  Google Scholar 

  2. Sahu, A., Sinha, S., Banka, H.: Fuzzy inference system using genetic algorithm and pattern search for predicting roof fall rate in underground coal mines. Int. J. Coal Sci. Technol. 11(1), 1 (2024)

    Article  MATH  Google Scholar 

  3. Yagiz, S., Sezer, E.A., Gokceoglu, C.: 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. Int. J. Numer. Anal. Methods Geomech. 36(14), 1636–1650 (2012)

    Article  Google Scholar 

  4. Song, Z., Wu, Y., Zhang, Y., Yang, Y., Yang, Z.: Mechanical responses and acoustic emission behaviors of coal under compressive differential cyclic loading (DCL): a numerical study via 3D heterogeneous particle model. Int. J. Coal Sci. Technol. 10(1), 31 (2023)

    Article  MATH  Google Scholar 

  5. Zhang, C., Bai, Q., Han, P., Wang, L., Wang, X., Wang, F.: Strength weakening and its micromechanism in water–rock interaction, a short review in laboratory tests. Int. J. Coal Sci. Technol. 10(1), 10 (2023)

    Article  MATH  Google Scholar 

  6. Niu, Q., Jiang, L., Li, C., Zhao, Y., Wang, Q., Yuan, A.: Application and prospects of 3D printing in physical experiments of rock mass mechanics and engineering: materials, methodologies and models. Int. J. Coal Sci. Technol. 10(1), 5 (2023)

    Article  Google Scholar 

  7. Lu, Z., Ju, W., Gao, F., Du, T.: Numerical analysis on the factors affecting post-peak characteristics of coal under uniaxial compression. Int. J. Coal Sci. Technol. 11(1), 2 (2024)

    Article  MATH  Google Scholar 

  8. Kahraman, S.: Evaluation of simple methods for assessing the uniaxial compressive strength of rock. Int. J. Rock Mech. Min. Sci. 38(7), 981–994 (2001)

    Article  MATH  Google Scholar 

  9. Hack R, Huisman M.: Estimating the intact rock strength of a rock mass by simple means, 9th Congr. Int. Ass. Engin. Geol. Env, (2002)

  10. Chang, C., Zoback, M.D., Khaksar, A.: Empirical relations between rock strength and physical properties in sedimentary rocks. J. Pet. Sci. Eng. 51(3–4), 223–237 (2006)

    Article  Google Scholar 

  11. Ceryan, S., Tudes, S., Ceryan, N.: A new quantitative weathering classification for igneous rocks. Environ. Geol. 55, 1319–1336 (2008)

    Article  Google Scholar 

  12. Çobanoğlu, İ, Çelik, S.B.: Estimation of uniaxial compressive strength from point load strength, Schmidt hardness and P-wave velocity. Bull. Eng. Geol. Environ. 67, 491–498 (2008)

    Article  MATH  Google Scholar 

  13. Kahraman, S., Gunaydin, O., Alber, M., Fener, M.: Evaluating the strength and deformability properties of Misis fault breccia using artificial neural networks. Expert Syst. Appl. 36(3), 6874–6878 (2009)

    Article  MATH  Google Scholar 

  14. Oyler, D.C., Mark, C., Molinda, G.M.: In situ estimation of roof rock strength using sonic logging. Int. J. Coal Geol. 83(4), 484–490 (2010)

    Article  Google Scholar 

  15. Ulusay, R., Türeli, K., Ider, M.H.: Prediction of engineering properties of a selected litharenite sandstone from its petrographic characteristics using correlation and multivariate statistical techniques. Eng. Geol. 38(1–2), 135–157 (1994)

    Article  MATH  Google Scholar 

  16. Altindag, R., Alyildiz, I.S., Onargan, T.: Mechanical property degradation of ignimbrite subjected to recurrent freeze–thaw cycles. Int. J. rock Mech. Min. Sci. 41(6), 1023–1028 (2004)

    Article  MATH  Google Scholar 

  17. Kayabali, K., Selcuk, L.: Nail penetration test for determining the uniaxial compressive strength of rock. Int. J. Rock Mech. Min. Sci. 47(2), 265–271 (2010)

    Article  Google Scholar 

  18. Yilmaz, I.: Use of the core strangle test for tensile strength estimation and rock mass classification. Int. J. Rock Mech. Min. Sci. 47(5), 845–850 (2010)

    Article  MATH  Google Scholar 

  19. Gokceoglu, C.: A fuzzy triangular chart to predict the uniaxial compressive strength of the Ankara agglomerates from their petrographic composition. Eng. Geol. 66(1–2), 39–51 (2002)

    Article  MATH  Google Scholar 

  20. Gokceoglu, C., Zorlu, K.: A fuzzy model to predict the uniaxial compressive strength and the modulus of elasticity of a problematic rock. Eng. Appl. Artif. Intell. 17(1), 61–72 (2004)

    Article  MATH  Google Scholar 

  21. Sonmez, H., Tuncay, E., Gokceoglu, C.: Models to predict the uniaxial compressive strength and the modulus of elasticity for Ankara Agglomerate. Int. J. Rock Mech. Min. Sci. 41(5), 717–729 (2004)

    Article  MATH  Google Scholar 

  22. Baykasoğlu, A., Güllü, H., Çanakçı, H., Özbakır, L.: Prediction of compressive and tensile strength of limestone via genetic programming. Expert Syst. Appl. 35(1–2), 111–123 (2008)

    Article  MATH  Google Scholar 

  23. Akbarzadeh, M.R., Ghafourian, H., Anvari, A., Pourhanasa, R., Nehdi, M.L.: Estimating compressive strength of concrete using neural electromagnetic field optimization. Materials (Basel) 16(11), 4200 (2023)

    Article  Google Scholar 

  24. Tejani, G.G., Sadaghat, B., Kumar, S.: Predict the maximum dry density of soil based on individual and hybrid methods of machine learning. Adv. Eng. Intell. Syst. 2(03), 98–109 (2023)

    Google Scholar 

  25. Kahraman, S., Alber, M.: Estimating unconfined compressive strength and elastic modulus of a fault breccia mixture of weak blocks and strong matrix. Int. J. rock Mech. Min. Sci. 43(8), 1277–1287 (2006)

    Article  MATH  Google Scholar 

  26. Yilmaz, I., Yuksek, G.: Prediction of the strength and elasticity modulus of gypsum using multiple regression, ANN, and ANFIS models. Int. J. rock Mech. Min. Sci. 46(4), 803–810 (2009)

    Article  MATH  Google Scholar 

  27. Sarkar, K., Tiwary, A., Singh, T.N.: Estimation of strength parameters of rock using artificial neural networks. Bull. Eng. Geol. Environ. 69, 599–606 (2010)

    Article  MATH  Google Scholar 

  28. Çanakci, H., Pala, M.: Tensile strength of basalt from a neural network. Eng. Geol. 94(1–2), 10–18 (2007)

    Article  MATH  Google Scholar 

  29. Gokceoglu, C., Zorlu, K., Ceryan, S., Nefeslioglu, H.A.: A comparative study on indirect determination of degree of weathering of granites from some physical and strength parameters by two soft computing techniques. Mater Charact 60(11), 1317–1327 (2009)

    Article  MATH  Google Scholar 

  30. Yilmaz, I., Marschalko, M., Bednarik, M., Kaynar, O., Fojtova, L.: Neural computing models for prediction of permeability coefficient of coarse-grained soils. Neural Comput. Appl. 21, 957–968 (2012)

    Article  Google Scholar 

  31. Zhang, Y., et al.: Research on coal-rock identification method and data augmentation algorithm of comprehensive working face based on FL-Segformer. Int. J. Coal Sci. Technol. 11(1), 48 (2024)

    Article  MATH  Google Scholar 

  32. Meulenkamp, F., Grima, M.A.: Application of neural networks for the prediction of the unconfined compressive strength (UCS) from Equotip hardness. Int. J. rock Mech. Min. Sci. 36(1), 29–39 (1999)

    Article  Google Scholar 

  33. Dehghan, S., Sattari, G., Aliabadi, M.A.: Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks. Min. Sci. Technol. 20, 41–46 (2010). https://doi.org/10.1016/S1674-5264(09)60158-7

    Article  Google Scholar 

  34. Mishra, D.A., Basu, A.: Estimation of uniaxial compressive strength of rock materials by index tests using regression analysis and fuzzy inference system. Eng. Geol. 160, 54–68 (2013)

    Article  MATH  Google Scholar 

  35. Moayedi, H., Hayati, S.: Applicability of a CPT-based neural network solution in predicting load-settlement responses of bored pile. Int. J. Geomech. 18(6), 6018009 (2018)

    Article  MATH  Google Scholar 

  36. Zhong, C., Li, G., Meng, Z.: Beluga whale optimization: A novel nature-inspired metaheuristic algorithm. Knowledge-Based Syst. 251, 109215 (2022). https://doi.org/10.1016/j.knosys.2022.109215

    Article  MATH  Google Scholar 

  37. Hill, H., Dietrich, S., Yeater, D., McKinnon, M., Miller, M., Aibel, S., Dove, Al.: Developing a catalog of socio-sexual behaviors of beluga whales (Delphinapterus leucas) in the care of humans. Animal Behav. Cognit. 2(2), 105–123 (2015). https://doi.org/10.12966/abc.05.01.2015

    Article  Google Scholar 

  38. Hayyolalam, V., Kazem, A.A.P.: Black widow optimization algorithm: a novel meta-heuristic approach for solving engineering optimization problems. Eng. Appl. Artif. Intell. 87, 103249 (2020)

    Article  MATH  Google Scholar 

  39. Holland, J.: Adaptation in natural and artificial systems, univ. of mich. press. Ann Arbor 7, 390–401 (1975)

    MATH  Google Scholar 

  40. Narendra, B.S., Sivapullaiah, P.V., Suresh, S., Omkar, S.N.: Prediction of unconfined compressive strength of soft grounds using computational intelligence techniques: a comparative study. Comput. Geotech. 33(3), 196–208 (2006)

    Article  Google Scholar 

  41. Ceryan, N., Okkan, U., Kesimal, A.: Prediction of unconfined compressive strength of carbonate rocks using artificial neural networks. Environ. Earth Sci. 68, 807–819 (2013)

    Article  Google Scholar 

  42. Majdi, A., Rezaei, M.: Prediction of unconfined compressive strength of rock surrounding a roadway using artificial neural network. Neural Comput. Appl. 23, 381–389 (2013)

    Article  MATH  Google Scholar 

  43. Rezaei, M., Majdi, A., Monjezi, M.: An intelligent approach to predict unconfined compressive strength of rock surrounding access tunnels in longwall coal mining. Neural Comput. Appl. 24, 233–241 (2014)

    Article  Google Scholar 

  44. Mohamad, E.T., Armaghani, D.J., Momeni, E., Abad, S.V.A.N.K.: Prediction of the unconfined compressive strength of soft rocks: a PSO-based ANN approach. Bull. Eng. Geol. Environ. 74(3), 745–757 (2015). https://doi.org/10.1007/s10064-014-0638-0

    Article  Google Scholar 

Download references

Acknowledgements

I would like to take this opportunity to acknowledge that there are no individuals or organizations that require acknowledgment for their contributions to this work.

Funding

This work was supported by Chongqing Education Commission (Grant No. KJQN202104014 and No. KJQN202104011).

Author information

Authors and Affiliations

Authors

Contributions

TL: Writing-Original draft preparation. Conceptualization. Supervision. Project administration.

Corresponding author

Correspondence to Ting Li.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, T. Estimating unconfined compressive strength using a hybrid model of machine learning and metaheuristic algorithms. SIViP 19, 164 (2025). https://doi.org/10.1007/s11760-024-03667-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11760-024-03667-3

Keywords

Navigation