Research Article
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Year 2023, Volume: 7 Issue: 4, 296 - 305, 05.10.2023
https://doi.org/10.31127/tuje.1120669

Abstract

References

  • Dai, F., Wei, M. D., Xu, N. W., Zhao, T., Xu, Y. (2015). Numerical investigation of the progressive fracture mechanisms of four ISRM-suggested specimens for determining the mode I fracture toughness of rocks. Computers and Geotechnics, 69, 424-441.
  • Anderson, T. L. (2017). Fracture mechanics: fundamentals and applications. Fourth edition, CRC Press, 680 pp, ISBN: 978-1-4987-2813-3.
  • Al-Shayea, N. A., Khan, K., & Abduljauwad, S. N. (2000). Effects of confining pressure and temperature on mixed-mode (I–II) fracture toughness of a limestone rock. International Journal of Rock Mechanics and Mining Sciences, 37(4), 629-643.
  • Dwivedi, R. D., Soni, A. K., Goel, R. K., & Dube, A. K. (2000). Fracture toughness of rocks under sub-zero temperature conditions. International Journal of Rock Mechanics and Mining Sciences, 37(8), 1267-1275.
  • Chang, S. H., Lee, C. I., & Jeon, S. (2002). Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimens. Engineering Geology, 66(1-2), 79-97.
  • Alber, M., & Brardt, A. (2003). Factors influencing fracture toughness KIC from simple screening tests. International Journal of Rock Mechanics and Mining Sciences, 5(40), 779-784.
  • Al-Shayea, N. A. (2005). Crack propagation trajectories for rocks under mixed mode I–II fracture. Engineering Geology, 81(1), 84-97.
  • Nasseri, M. H. B., Mohanty, B., & Robin, P. Y. (2005). Characterization of microstructures and fracture toughness in five granitic rocks. International journal of rock mechanics and mining sciences, 3(42), 450-460.
  • Mahanta, B., Singh, T. N., & Ranjith, P. G. (2016). Influence of thermal treatment on mode I fracture toughness of certain Indian rocks. Engineering Geology, 210, 103-114.
  • Brevik, N. Ø. (2016). Experimental study of fracture toughness in sedimentary rocks, Master's thesis, Norwegian University of Science and Technology, Department of Petroleum Engineering and Applied Geophysics, 144.
  • Pakdaman, A. M., Moosavi, M., & Mohammadi, S. (2019). Experimental and numerical investigation into the methods of determination of mode I static fracture toughness of rocks. Theoretical and Applied Fracture Mechanics, 100, 154-170.
  • Ge, Z., Sun, Q., Xue, L., & Yang, T. (2021). The influence of microwave treatment on the mode I fracture toughness of granite. Engineering Fracture Mechanics, 249, 107768.
  • Kuruppu, M. D. (1997). Fracture toughness measurement using chevron notched semi-circular bend specimen. International journal of fracture, 86(4), L33-L38.
  • Wang, J. J., Zhu, J. G., Chiu, C. F., & Zhang, H. (2007). Experimental study on fracture toughness and tensile strength of a clay. Engineering Geology, 94(1-2), 65-75.
  • Zhou, Y. X., Xia, K., Li, X. B., Li, H. B., Ma, G. W., Zhao, J., ... & Dai, F. (2012). Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials. International Journal of Rock Mechanics and Mining Sciences, 49, 105-112.
  • Erarslan, N., & Williams, D. J. (2012). The damage mechanism of rock fatigue and its relationship to the fracture toughness of rocks. International Journal of Rock Mechanics and Mining Sciences, 56, 15-26.
  • Kuruppu, M. D., Obara, Y., Ayatollahi, M. R., Chong, K. P., & Funatsu, T. (2014). ISRM-suggested method for determining the mode I static fracture toughness using semi-circular bend specimen. Rock Mechanics and Rock Engineering, 47(1), 267-274.
  • Sabri, M., Ghazvinian, A., & Nejati, H. R. (2016). Effect of particle size heterogeneity on fracture toughness and failure mechanism of rocks. International Journal of Rock Mechanics and Mining Sciences, 81, 79-85.
  • Wei, M. D., Dai, F., Liu, Y., Xu, N. W., & Zhao, T. (2018). An experimental and theoretical comparison of CCNBD and CCNSCB specimens for determining mode I fracture toughness of rocks. Fatigue & Fracture of Engineering Materials & Structures, 41(5), 1002-1018.
  • Wong, L. N. Y., & Guo, T. Y. (2019). Microcracking behavior of two semi-circular bend specimens in mode I fracture toughness test of granite. Engineering Fracture Mechanics, 221, 106565.
  • Wu, S., Sun, W., & Xu, X. (2022). Study on Mode I Fracture Toughness of Rocks Using Flat-Joint Model and Moment Tensor. Theoretical and Applied Fracture Mechanics, 103403.
  • Pappalardo, G. (2015). Correlation between P-wave velocity and physical–mechanical properties of intensely jointed dolostones, Peloritani mounts, NE Sicily. Rock mechanics and rock engineering, 48(4), 1711-1721.
  • Guha Roy, D., Singh, T. N., & Kodikara, J. (2018). Predicting mode-I fracture toughness of rocks using soft computing and multiple regression. Measurement, 126, 231-241.
  • Afrasiabian, B., & Eftekhari, M. (2022). Prediction of mode I fracture toughness of rock using linear multiple regression and gene expression programming. Journal of Rock Mechanics and Geotechnical Engineering, https://doi.org/10.1016/j.jrmge.2022.03.008
  • Zhixi, C., Mian, C., Yan, J., & Rongzun, H. (1997). Determination of rock fracture toughness and its relationship with acoustic velocity. International Journal of Rock Mechanics and Mining Sciences, 34(3-4), 49-e1.
  • Şengün, N., Altındağ, R. (2010). Kayaçların kırılma tokluğu (Mod-I) ile fiziko-mekanik özellikleri arasındaki ilişkilerinin değerlendirilmesi. Yerbilimleri, 31(2), 127-139.
  • Guha Roy, D., Singh, T. N., Kodikara, J., & Talukdar, M. (2017). Correlating the mechanical and physical properties with mode-I fracture toughness of rocks. Rock Mechanics and Rock Engineering, 50(7), 1941-1946.
  • Jian-An, H., & Sijing, W. (1985). An experimental investigation concerning the comprehensive fracture toughness of some brittle rocks. In International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts (Vol. 22, No. 2, pp. 99-104). Pergamon.
  • Singh, R. N., & Sun, G. X. (1989). The relationship between fracture toughness hardness indices and mechanical properties of rocks. Nottingham University Mining Department Magazine;(UK), 41.
  • Backers, T. (2004). Fracture toughness determination and micromechanics of rock under mode I and mode II loading. Ph.D. Thesis. University of Potsdam, Germany
  • Iqbal, M. J., & Mohanty, B. (2007). Experimental calibration of ISRM suggested fracture toughness measurement techniques in selected brittle rocks. Rock Mechanics and Rock Engineering, 40(5), 453-475.
  • Andersson, J. C. (2007). Rock mass response to coupled mechanical thermal loading: Äspö Pillar Stability Experiment, Sweden (Doctoral dissertation, Byggvetenskap).
  • Stephansson, O., Shen, B., Rinne, M., Amemiya, K., Yamashi, R., & Toguri, S. (2008, October). FRACOD modeling of rock fracturing and permeability change in excavation damaged zones. In The 12th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG). Goa, India.
  • Rinne, M. (2008). Fracture mechanics and subcritical crack growth approach to model time-dependent failure in brittle rock, Doctoral Dissertation, Helsinki University of Technology, Sweden.
  • Lin, Q., Fakhimi, A., Haggerty, M., & Labuz, J. F. (2009). Initiation of tensile and mixed-mode fracture in sandstone. International Journal of Rock Mechanics and Mining Sciences, 46(3), 489-497.
  • Alkılıçgil, Ç. (2010). Development of specimen geometries for mode I fracture toughness testing with disc type rock specimens, Thesis. Middle East Technical University, Turkey.
  • Amrollahi, H., Baghbanan, A., & Hashemolhosseini, H. (2011). Measuring fracture toughness of crystalline marbles under modes I and II and mixed mode I–II loading conditions using CCNBD and HCCD specimens. International Journal of Rock Mechanics and Mining Sciences, 48(7), 1123-1134.
  • Siren, T. (2011). Fracture mechanics prediction for Posiva's Olkiluoto spalling experiment (POSE) (No. POSIVA-WR--11-23). Posiva Oy.
  • Momber, A. W. (2015). Fracture toughness effects in geomaterial solid particle erosion. Rock Mechanics and Rock Engineering, 48(4), 1573-1588.
  • Ebrahimi, R., & Hosseini, M. (2022). Experimental study of effect of number of heating–cooling cycles on mode I and mode II fracture toughness of travertine. Theoretical and Applied Fracture Mechanics, 117, 103185.
  • Roy, D. G., & Singh, T. N. (2020). Predicting deformational properties of Indian coal: Soft computing and regression analysis approach. Measurement, 149, 106975.
  • Yesiloglu-Gultekin, N., Gokceoglu, C., & Sezer, E. A. (2013). Prediction of uniaxial compressive strength of granitic rocks by various nonlinear tools and comparison of their performances. International Journal of Rock Mechanics and Mining Sciences, 62, 113-122.
  • Sharma, L. K., Vishal, V., & Singh, T. N. (2017). Developing novel models using neural networks and fuzzy systems for the prediction of strength of rocks from key geomechanical properties. Measurement, 102, 158-169.
  • Jang, J. S. R. (1992) Neuro-fuzzy modeling: architecture, analyses and applications, dissertation, department of electrical engineering and computer science, University of California, Berkeley, CA 94720.
  • Singh, V. K., Singh, D., & Singh, T. N. (2001). Prediction of strength properties of some schistose rocks from petrographic properties using artificial neural networks. International Journal of Rock Mechanics and Mining Sciences, 38(2), 269-284.
  • Rabbani, E., Sharif, F., Salooki, M. K., & Moradzadeh, A. (2012). Application of neural network technique for prediction of uniaxial compressive strength using reservoir formation properties. International journal of rock mechanics and mining sciences, (56), 100-111.
  • Das, S. K. (2013). Artificial neural networks in geotechnical engineering: modeling and application issues, Metaheuristics in water, geotechnical and transport engineering, 231–270.
  • Ferreira, C. (2001) Gene expression programming: a new adaptive algorithm for solving problems Complex Systems, 13(2), 87-129
  • Friedman, J. H. (1991) Multivariate adaptive regression splines. The Annals of Statistics, 19(1), 1-67

A comparative study to estimate the mode I fracture toughness of rocks using several soft computing techniques

Year 2023, Volume: 7 Issue: 4, 296 - 305, 05.10.2023
https://doi.org/10.31127/tuje.1120669

Abstract

Fracture toughness is an important phenomenon to reveal the actual strength of fractured rock materials. It is, therefore, crucial to use the fracture toughness models principally for simulating the performance of fractured rock medium. In this study, the mode-I fracture toughness (KIC) was investigated using several soft computing techniques. For this purpose, an extensive literature survey was carried out to obtain a comprehensive database that includes simple and widely used mechanical rock parameters such as uniaxial compressive strength (UCS) and Brazilian tensile strength (BTS). Several soft computing techniques such as artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), gene expression programming (GEP), and multivariate adaptive regression spline (MARS) were attempted to reveal the availability of these methods to estimate the KIC. Among these techniques, it was determined that ANN presents the best prediction capability. The correlation of determination value (R2) for the proposed ANN model is 0.90, showing its relative success. In this manner, the present study can be declared a case study, indicating the applicability of several soft computing techniques for the evaluation of KIC. However, the number of samples for different rock types should be increased to improve the established predictive models in future studies.

References

  • Dai, F., Wei, M. D., Xu, N. W., Zhao, T., Xu, Y. (2015). Numerical investigation of the progressive fracture mechanisms of four ISRM-suggested specimens for determining the mode I fracture toughness of rocks. Computers and Geotechnics, 69, 424-441.
  • Anderson, T. L. (2017). Fracture mechanics: fundamentals and applications. Fourth edition, CRC Press, 680 pp, ISBN: 978-1-4987-2813-3.
  • Al-Shayea, N. A., Khan, K., & Abduljauwad, S. N. (2000). Effects of confining pressure and temperature on mixed-mode (I–II) fracture toughness of a limestone rock. International Journal of Rock Mechanics and Mining Sciences, 37(4), 629-643.
  • Dwivedi, R. D., Soni, A. K., Goel, R. K., & Dube, A. K. (2000). Fracture toughness of rocks under sub-zero temperature conditions. International Journal of Rock Mechanics and Mining Sciences, 37(8), 1267-1275.
  • Chang, S. H., Lee, C. I., & Jeon, S. (2002). Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimens. Engineering Geology, 66(1-2), 79-97.
  • Alber, M., & Brardt, A. (2003). Factors influencing fracture toughness KIC from simple screening tests. International Journal of Rock Mechanics and Mining Sciences, 5(40), 779-784.
  • Al-Shayea, N. A. (2005). Crack propagation trajectories for rocks under mixed mode I–II fracture. Engineering Geology, 81(1), 84-97.
  • Nasseri, M. H. B., Mohanty, B., & Robin, P. Y. (2005). Characterization of microstructures and fracture toughness in five granitic rocks. International journal of rock mechanics and mining sciences, 3(42), 450-460.
  • Mahanta, B., Singh, T. N., & Ranjith, P. G. (2016). Influence of thermal treatment on mode I fracture toughness of certain Indian rocks. Engineering Geology, 210, 103-114.
  • Brevik, N. Ø. (2016). Experimental study of fracture toughness in sedimentary rocks, Master's thesis, Norwegian University of Science and Technology, Department of Petroleum Engineering and Applied Geophysics, 144.
  • Pakdaman, A. M., Moosavi, M., & Mohammadi, S. (2019). Experimental and numerical investigation into the methods of determination of mode I static fracture toughness of rocks. Theoretical and Applied Fracture Mechanics, 100, 154-170.
  • Ge, Z., Sun, Q., Xue, L., & Yang, T. (2021). The influence of microwave treatment on the mode I fracture toughness of granite. Engineering Fracture Mechanics, 249, 107768.
  • Kuruppu, M. D. (1997). Fracture toughness measurement using chevron notched semi-circular bend specimen. International journal of fracture, 86(4), L33-L38.
  • Wang, J. J., Zhu, J. G., Chiu, C. F., & Zhang, H. (2007). Experimental study on fracture toughness and tensile strength of a clay. Engineering Geology, 94(1-2), 65-75.
  • Zhou, Y. X., Xia, K., Li, X. B., Li, H. B., Ma, G. W., Zhao, J., ... & Dai, F. (2012). Suggested methods for determining the dynamic strength parameters and mode-I fracture toughness of rock materials. International Journal of Rock Mechanics and Mining Sciences, 49, 105-112.
  • Erarslan, N., & Williams, D. J. (2012). The damage mechanism of rock fatigue and its relationship to the fracture toughness of rocks. International Journal of Rock Mechanics and Mining Sciences, 56, 15-26.
  • Kuruppu, M. D., Obara, Y., Ayatollahi, M. R., Chong, K. P., & Funatsu, T. (2014). ISRM-suggested method for determining the mode I static fracture toughness using semi-circular bend specimen. Rock Mechanics and Rock Engineering, 47(1), 267-274.
  • Sabri, M., Ghazvinian, A., & Nejati, H. R. (2016). Effect of particle size heterogeneity on fracture toughness and failure mechanism of rocks. International Journal of Rock Mechanics and Mining Sciences, 81, 79-85.
  • Wei, M. D., Dai, F., Liu, Y., Xu, N. W., & Zhao, T. (2018). An experimental and theoretical comparison of CCNBD and CCNSCB specimens for determining mode I fracture toughness of rocks. Fatigue & Fracture of Engineering Materials & Structures, 41(5), 1002-1018.
  • Wong, L. N. Y., & Guo, T. Y. (2019). Microcracking behavior of two semi-circular bend specimens in mode I fracture toughness test of granite. Engineering Fracture Mechanics, 221, 106565.
  • Wu, S., Sun, W., & Xu, X. (2022). Study on Mode I Fracture Toughness of Rocks Using Flat-Joint Model and Moment Tensor. Theoretical and Applied Fracture Mechanics, 103403.
  • Pappalardo, G. (2015). Correlation between P-wave velocity and physical–mechanical properties of intensely jointed dolostones, Peloritani mounts, NE Sicily. Rock mechanics and rock engineering, 48(4), 1711-1721.
  • Guha Roy, D., Singh, T. N., & Kodikara, J. (2018). Predicting mode-I fracture toughness of rocks using soft computing and multiple regression. Measurement, 126, 231-241.
  • Afrasiabian, B., & Eftekhari, M. (2022). Prediction of mode I fracture toughness of rock using linear multiple regression and gene expression programming. Journal of Rock Mechanics and Geotechnical Engineering, https://doi.org/10.1016/j.jrmge.2022.03.008
  • Zhixi, C., Mian, C., Yan, J., & Rongzun, H. (1997). Determination of rock fracture toughness and its relationship with acoustic velocity. International Journal of Rock Mechanics and Mining Sciences, 34(3-4), 49-e1.
  • Şengün, N., Altındağ, R. (2010). Kayaçların kırılma tokluğu (Mod-I) ile fiziko-mekanik özellikleri arasındaki ilişkilerinin değerlendirilmesi. Yerbilimleri, 31(2), 127-139.
  • Guha Roy, D., Singh, T. N., Kodikara, J., & Talukdar, M. (2017). Correlating the mechanical and physical properties with mode-I fracture toughness of rocks. Rock Mechanics and Rock Engineering, 50(7), 1941-1946.
  • Jian-An, H., & Sijing, W. (1985). An experimental investigation concerning the comprehensive fracture toughness of some brittle rocks. In International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts (Vol. 22, No. 2, pp. 99-104). Pergamon.
  • Singh, R. N., & Sun, G. X. (1989). The relationship between fracture toughness hardness indices and mechanical properties of rocks. Nottingham University Mining Department Magazine;(UK), 41.
  • Backers, T. (2004). Fracture toughness determination and micromechanics of rock under mode I and mode II loading. Ph.D. Thesis. University of Potsdam, Germany
  • Iqbal, M. J., & Mohanty, B. (2007). Experimental calibration of ISRM suggested fracture toughness measurement techniques in selected brittle rocks. Rock Mechanics and Rock Engineering, 40(5), 453-475.
  • Andersson, J. C. (2007). Rock mass response to coupled mechanical thermal loading: Äspö Pillar Stability Experiment, Sweden (Doctoral dissertation, Byggvetenskap).
  • Stephansson, O., Shen, B., Rinne, M., Amemiya, K., Yamashi, R., & Toguri, S. (2008, October). FRACOD modeling of rock fracturing and permeability change in excavation damaged zones. In The 12th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG). Goa, India.
  • Rinne, M. (2008). Fracture mechanics and subcritical crack growth approach to model time-dependent failure in brittle rock, Doctoral Dissertation, Helsinki University of Technology, Sweden.
  • Lin, Q., Fakhimi, A., Haggerty, M., & Labuz, J. F. (2009). Initiation of tensile and mixed-mode fracture in sandstone. International Journal of Rock Mechanics and Mining Sciences, 46(3), 489-497.
  • Alkılıçgil, Ç. (2010). Development of specimen geometries for mode I fracture toughness testing with disc type rock specimens, Thesis. Middle East Technical University, Turkey.
  • Amrollahi, H., Baghbanan, A., & Hashemolhosseini, H. (2011). Measuring fracture toughness of crystalline marbles under modes I and II and mixed mode I–II loading conditions using CCNBD and HCCD specimens. International Journal of Rock Mechanics and Mining Sciences, 48(7), 1123-1134.
  • Siren, T. (2011). Fracture mechanics prediction for Posiva's Olkiluoto spalling experiment (POSE) (No. POSIVA-WR--11-23). Posiva Oy.
  • Momber, A. W. (2015). Fracture toughness effects in geomaterial solid particle erosion. Rock Mechanics and Rock Engineering, 48(4), 1573-1588.
  • Ebrahimi, R., & Hosseini, M. (2022). Experimental study of effect of number of heating–cooling cycles on mode I and mode II fracture toughness of travertine. Theoretical and Applied Fracture Mechanics, 117, 103185.
  • Roy, D. G., & Singh, T. N. (2020). Predicting deformational properties of Indian coal: Soft computing and regression analysis approach. Measurement, 149, 106975.
  • Yesiloglu-Gultekin, N., Gokceoglu, C., & Sezer, E. A. (2013). Prediction of uniaxial compressive strength of granitic rocks by various nonlinear tools and comparison of their performances. International Journal of Rock Mechanics and Mining Sciences, 62, 113-122.
  • Sharma, L. K., Vishal, V., & Singh, T. N. (2017). Developing novel models using neural networks and fuzzy systems for the prediction of strength of rocks from key geomechanical properties. Measurement, 102, 158-169.
  • Jang, J. S. R. (1992) Neuro-fuzzy modeling: architecture, analyses and applications, dissertation, department of electrical engineering and computer science, University of California, Berkeley, CA 94720.
  • Singh, V. K., Singh, D., & Singh, T. N. (2001). Prediction of strength properties of some schistose rocks from petrographic properties using artificial neural networks. International Journal of Rock Mechanics and Mining Sciences, 38(2), 269-284.
  • Rabbani, E., Sharif, F., Salooki, M. K., & Moradzadeh, A. (2012). Application of neural network technique for prediction of uniaxial compressive strength using reservoir formation properties. International journal of rock mechanics and mining sciences, (56), 100-111.
  • Das, S. K. (2013). Artificial neural networks in geotechnical engineering: modeling and application issues, Metaheuristics in water, geotechnical and transport engineering, 231–270.
  • Ferreira, C. (2001) Gene expression programming: a new adaptive algorithm for solving problems Complex Systems, 13(2), 87-129
  • Friedman, J. H. (1991) Multivariate adaptive regression splines. The Annals of Statistics, 19(1), 1-67
There are 49 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ekin Köken 0000-0003-0178-329X

Tümay Kadakci Koca 0000-0002-6705-9117

Early Pub Date June 22, 2023
Publication Date October 5, 2023
Published in Issue Year 2023 Volume: 7 Issue: 4

Cite

APA Köken, E., & Kadakci Koca, T. (2023). A comparative study to estimate the mode I fracture toughness of rocks using several soft computing techniques. Turkish Journal of Engineering, 7(4), 296-305. https://doi.org/10.31127/tuje.1120669
AMA Köken E, Kadakci Koca T. A comparative study to estimate the mode I fracture toughness of rocks using several soft computing techniques. TUJE. October 2023;7(4):296-305. doi:10.31127/tuje.1120669
Chicago Köken, Ekin, and Tümay Kadakci Koca. “A Comparative Study to Estimate the Mode I Fracture Toughness of Rocks Using Several Soft Computing Techniques”. Turkish Journal of Engineering 7, no. 4 (October 2023): 296-305. https://doi.org/10.31127/tuje.1120669.
EndNote Köken E, Kadakci Koca T (October 1, 2023) A comparative study to estimate the mode I fracture toughness of rocks using several soft computing techniques. Turkish Journal of Engineering 7 4 296–305.
IEEE E. Köken and T. Kadakci Koca, “A comparative study to estimate the mode I fracture toughness of rocks using several soft computing techniques”, TUJE, vol. 7, no. 4, pp. 296–305, 2023, doi: 10.31127/tuje.1120669.
ISNAD Köken, Ekin - Kadakci Koca, Tümay. “A Comparative Study to Estimate the Mode I Fracture Toughness of Rocks Using Several Soft Computing Techniques”. Turkish Journal of Engineering 7/4 (October 2023), 296-305. https://doi.org/10.31127/tuje.1120669.
JAMA Köken E, Kadakci Koca T. A comparative study to estimate the mode I fracture toughness of rocks using several soft computing techniques. TUJE. 2023;7:296–305.
MLA Köken, Ekin and Tümay Kadakci Koca. “A Comparative Study to Estimate the Mode I Fracture Toughness of Rocks Using Several Soft Computing Techniques”. Turkish Journal of Engineering, vol. 7, no. 4, 2023, pp. 296-05, doi:10.31127/tuje.1120669.
Vancouver Köken E, Kadakci Koca T. A comparative study to estimate the mode I fracture toughness of rocks using several soft computing techniques. TUJE. 2023;7(4):296-305.
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