Prediction of crack coalescence stress in rock-like specimens with non-persistent joints under direct shear test based upon machine learning algorithms

Document Type : Research Article

Authors

1 Dept. of Mining, Faculty of Engineering, Hamedan University of Technology, Hamedan, Iran

2 Dept. of Mining Engineering, Technical Faculties Campus, University of Tehran, Tehran, Iran

3 Dept. of Mining, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran

Abstract

Concretes frequently contain joints and microcrack fractures, and the failure mechanism of these fractures is highly dependent on the pattern of crack coalescence between pre-existing flaws. Determining the non-persistent joints' failure behavior is an engineering challenge that incorporates several factors, including the ratio of the joint surface to the total shear surface, normal stress, and the mechanical characteristics of the concrete. This paper aims to utilize grey wolf optimizer (GWO) and gene expression programming (GEP) algorithms for the prediction of the crack coalescence stress (CCS). For this purpose, 8 input parameters affecting the CCS including jointing coefficient (JC), normal stress (σn), uniaxial compressive strength (σc), tensile strength (σt), Poisson's ratio (υ), modulus of elasticity (E), cohesion strength (C) and internal friction angle (φ) were selected based on the results of 450 direct shear tests conducted on specimens including 2 sets of non-persistent joints made of gypsum, cement, and water. The GWO and GEP techniques were then implemented. Three performance indicators of determination coefficient (R2), root mean square error (RMSE), and mean absolute error (MAE), were employed for the training and testing phases to evaluate the efficiency of the suggested models. The R2 values for GWO and GEP for the training phase were 0.962 and 0.938, respectively, while for the testing phase were 0.996 and 0.981, indicating that the GWO algorithm is more efficient than GEP. Moreover, the findings reveal that the GWO algorithm exhibits lower RMSE and MAE values in both the training and testing phases compared to the GEP method. However, it can be professed that the two methods used have high reliability and accuracy. Also, based on the GEP method, a formula was derived and presented for prediction of CCS. At last, according to the sensitivity analysis, it was found that the normal stress (σn) and jointing coefficient (Cu) have the greatest and least influence on CCS, respectively...

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Main Subjects

References

[1]               Haeri, H., Sarfarazi, V., & Zhu, Z. (2016). Analysis of crack coalescence in concrete using neural networks. Strength of Materials, 48, 850-861.
[2]                 Mirzaei, H., Kakaie, R., Jalali, S. M. E., Shariati, M., & Hassani, B. (2010, June). Experimental investigation of crack propagation and coalescence in rock-like materials under uniaxial compression. In ISRM EUROCK (pp. ISRM-EUROCK). ISRM.
[3]                 Wong, R. H. C., Chau, K. T., Tang, C. A., & Lin, P. (2001). Analysis of crack coalescence in rock-like materials containing three flaws—part I: experimental approach. International Journal of Rock Mechanics and Mining Sciences, 38(7), 909-924.
[4]                 Tang, C. A., Lin, P., Wong, R. H. C., & Chau, K. T. (2001). Analysis of crack coalescence in rock-like materials containing three flaws—part II: numerical approach. International Journal of Rock Mechanics and Mining Sciences, 38(7), 925-939.
[5]                 Einstein, H. H., Veneziano, D., Baecher, G. B., & O'reilly, K. J. (1983, October). The effect of discontinuity persistence on rock slope stability. In International journal of rock mechanics and mining sciences & geomechanics abstracts (Vol. 20, No. 5, pp. 227-236). Pergamon.
[6]                 Reyes, O., & Einstein, H. H. (1991, September). Failure mechanisms of fractured rock-a fracture coalescence model. In 7th ISRM Congress. OnePetro.
[7]                 Bobet, A., & Einstein, H. H. (1998). Fracture coalescence in rock-type materials under uniaxial and biaxial compression. International Journal of Rock Mechanics and Mining Sciences, 35(7), 863-888.
[8]                 Sagong, M., & Bobet, A. (2002). Coalescence of multiple flaws in a rock-model material in uniaxial compression. International Journal of Rock Mechanics and Mining Sciences, 39(2), 229-241.
[9]                 Mughieda, O., & Karasneh, I. (2006). Coalescence of offset rock joints under biaxial loading. Geotechnical & Geological Engineering, 24, 985-999.
[10]             Lee, H., & Jeon, S. (2011). An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. International Journal of Solids and Structures, 48(6), 979-999.
[11]             Haeri, H., Shahriar, K., Marji, M. F., & Moarefvand, P. (2014). Experimental and numerical study of crack propagation and coalescence in pre-cracked rock-like disks. International Journal of Rock Mechanics and Mining Sciences, 67, 20-28.
[12]             Haeri, H., Shahriar, K., Marji, M. F., & Moarefvand, P. (2014). Cracks coalescence mechanism and cracks propagation paths in rock-like specimens containing pre-existing random cracks under compression. Journal of Central South University, 21, 2404-2414.
[13]             Haeri, H., Shahriar, K., Marji, M. F., & Moarefvand, P. (2014). Investigation of fracturing process of rock-like Brazilian disks containing three parallel cracks under compressive line loading. Strength of Materials, 46, 404-416.
[14]             Haeri, H. (2015). Propagation mechanism of neighboring cracks in rock-like cylindrical specimens under uniaxial compression. Journal of Mining Science, 51(3), 487-496.
[15]             Lee, J., Ha, Y. D., & Hong, J. W. (2017). Crack coalescence morphology in rock-like material under compression. International Journal of Fracture, 203, 211-236.
[16]             Asadizadeh, M., Hossaini, M. F., Moosavi, M., Masoumi, H., & Ranjith, P. G. (2019). Mechanical characterization of jointed rock-like material with non-persistent rough joints subjected to uniaxial compression. Engineering Geology, 260, 105224.
[17]             Asadizadeh, M., & Rezaei, M. (2019). Surveying the mechanical response of non-persistent jointed slabs subjected to compressive axial loading utilizing GEP approach. International Journal of Geotechnical Engineering.
[18]             Chen, M., Yang, S., Pathegama Gamage, R., Yang, W., Yin, P., Zhang, Y., & Zhang, Q. (2019). Fracture processes of rock-like specimens containing nonpersistent fissures under uniaxial compression. Energies, 12(1), 79.
[19]             Li, X., Bai, Y., Chen, X., Zhao, X., & Lv, M. (2021). Experimental and numerical study on crack propagation and coalescence in rock-like materials under compression. The Journal of Strain Analysis for Engineering Design, 56(8), 548-562.
[20]             Lin, Q., Cao, P., Wen, G., Meng, J., Cao, R., & Zhao, Z. (2021). Crack coalescence in rock-like specimens with two dissimilar layers and pre-existing double parallel joints under uniaxial compression. International Journal of Rock Mechanics and Mining Sciences, 139, 104621.
[21]             Zhong, Z., Huang, D., Song, Y., & Cen, D. (2022). Three-dimensional cracking and coalescence of two spatial-deflection joints in rock-like specimens under uniaxial compression. International Journal of Rock Mechanics and Mining Sciences, 159, 105196.
[22]             Chang, X., Wang, S., Li, Z., & Chang, F. (2022). Cracking behavior of concrete/rock bi-material specimens containing a parallel flaw pair under compression. Construction and Building Materials, 360, 129440.
[23]             Niu, Y., Wang, J. G., Wang, X. K., Hu, Y. J., Zhang, J. Z., Zhang, R. R., & Hu, Z. J. (2023). Numerical study on cracking behavior and fracture failure mechanism of flawed rock materials under uniaxial compression. Fatigue & Fracture of Engineering Materials & Structures, 46(6), 2096-2111.
[24]             Lajtai, E. Z. (1969). Strength of discontinuous rocks in direct shear. Geotechnique, 19(2), 218-233.
[25]             Gehle, C., & Kutter, H. K. (2003). Breakage and shear behaviour of intermittent rock joints. International Journal of Rock Mechanics and Mining Sciences, 40(5), 687-700.
[26]             Zhang, H. Q., Zhao, Z. Y., Tang, C. A., & Song, L. (2006). Numerical study of shear behavior of intermittent rock joints with different geometrical parameters. International Journal of Rock Mechanics and Mining Sciences, 43(5), 802-816.
[27]             Ghazvinian, A., Sarfarazi, V., Schubert, W., & Blumel, M. (2012). A study of the failure mechanism of planar non-persistent open joints using PFC2D. Rock mechanics and rock engineering, 45, 677-693.
[28]             Cao, P., Fan, W. C., & Zhang, K. (2013). Experimental Research on Failure Modes of Specimen Containing Non-Coplanar Joints. Advanced Materials Research, 779, 332-336.
[29]             Sarfarazi, V., Ghazvinian, A., & Schubert, W. (2016). Numerical simulation of shear behaviour of non-persistent joints under low and high normal loads. Periodica Polytechnica Civil Engineering, 60(4), 517-529.
[30]             Sarfarazi, V., Haeri, H., Shemirani, A. B., & Zhu, Z. (2017). Shear behavior of non-persistent joint under high normal load. Strength of Materials, 49, 320-334.
[31]             Asadizadeh, M., Moosavi, M., Hossaini, M. F., & Masoumi, H. (2018). Shear strength and cracking process of non-persistent jointed rocks: an extensive experimental investigation. Rock Mechanics and Rock Engineering, 51, 415-428.
[32]             Lin, H., Ding, X., Yong, R., Xu, W., & Du, S. (2019). Effect of non-persistent joints distribution on shear behavior. Comptes Rendus Mécanique, 347(6), 477-489.
[33]             Zhang, Y., Jiang, Y., Asahina, D., & Wang, C. (2020). Experimental and numerical investigation on shear failure behavior of rock-like samples containing multiple non-persistent joints. Rock Mechanics and Rock Engineering, 53, 4717-4744.
[34]             Meng, F., Song, J., Wang, X., Yue, Z., Zhou, X., & Wang, Z. (2022). Mechanical behavior of non-persistent joints with different geometric configurations and roughness in solid rock and concrete material. Construction and Building Materials, 337, 127564.
[35]             Guo, Y., Huang, D., & Cen, D. (2024). Crack Propagation and Coalescence Mechanism of a Rock Bridge between a Parallel Fissure Pair in a Direct Shear Test with Unloading Normal Stress. International Journal of Geomechanics, 24(1), 04023258.
[36]             Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in engineering software, 69, 46-61.
[37]             Chawla, V., Chanda, A., & Angra, S. (2019). The scheduling of automatic guided vehicles for the workload balancing and travel time minimization in the flexible manufacturing system by the nature-inspired algorithm. Journal of Project Management, 4(1), 19-30.
[38]             Ferreira, C. (2006). Gene expression programming: mathematical modeling by an artificial intelligence (Vol. 21). Springer.
[39]             Sabzevari, Y., Nasrollahi, A., Sharifipour, M., & Shahinejad, B. (2022). Application of Multivariate Regression and Gene Expression Programming in Modeling Reference Evapotranspiration (Case Study: Khorramabad Station). Irrigation Sciences and Engineering, 45(1), 35-48. (In Persian)
[40]             Armaghani, D. J., Faradonbeh, R. S., Rezaei, H., Rashid, A. S. A., & Amnieh, H. B. (2018). Settlement prediction of the rock-socketed piles through a new technique based on gene expression programming. Neural Computing and Applications, 29, 1115-1125.

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History

  • Receive Date: 06 January 2024
  • Revise Date: 21 February 2024
  • Accept Date: 02 March 2024

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