Effects of excavation geometry in energy evolution in underground mines

Abstract

With mines reaching into greater depth, problems with violent failures become more prevalent, such as rockbursts. To assess the potential for such occurrences, understanding energy dynamics is crucial. This study delves into the impact of excavation shape, aspect ratios, inclined angles and in-situ stress on dissipated plastic energy and released kinetic energy through numerical simulations. Detailed analyses of plastic zone around rectangular and elliptical excavations, varying in aspect ratios, unveiled the distinct patterns of tensile and shear plastic zone. Quantitative assessments of dissipated plastic energy and released kinetic energy highlighted contrasting behaviors between rectangular and elliptical excavations across various aspect ratios. Although the relationships between these energies and excavation parameters are found to be intricate, it becomes evident that: with an increase in the aspect ratio, both shear and tensile plastic zones exhibit a growing trend, and their distribution shows a high degree of consistency with regions of energy concentration. When the aspect ratio is below 1.5, elliptical excavations release slightly less kinetic energy than rectangular ones. Beyond 1.5, this relationship reverses. Moreover, upon exploring inclined angles, critical angles were identified, delineating points where the influence of aspect ratio nearly diminishes. Under the given in-situ stress conditions, approximately 50° and 20° serve as the critical angles for dissipated plastic energy and released kinetic energy, respectively. Changes in the degree of in-situ stress anisotropy have a limited impact on the overall energy trends but significantly alter the critical values of aspect ratio and inclination angle. When the in-situ stress ratio matches the excavation aspect ratio, both forms of energy reach their minimum values. These findings illuminate the complex interplay between excavation geometry and energy dissipation, offering invaluable insights for designing effective excavations and devising strategies to mitigate failures.

Keywords

Excavation geometry / Energy evolution / Underground mines / Rockburst

CRediT authorship contribution statement

Linnea Lundvall: Validation, Writing - original draft, Formal analysis. Niklas Burvall: Writing - original draft, Investigation, Software. Zongze Li: Investigation, Writing - review & editing, Funding acquisition. Wenjun Luo: Validation, Data curation, Methodology. Jinyang Fan: Investigation, Writing - review & editing, Formal analysis. Minghe Ju: Validation, Data curation, Methodology. Yang Zou: Supervision, Writing - original draft, Funding acquisition.

Declaration of competing interest

All authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the Opening Research Fund of State Key Laboratory of Coal Mine Disaster Dynamics and Control in China (No. 2011DA105287-FW202409), State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering in China (No. SDGZ2503). The authors are also grateful for the financial support from the Rut and Sten Brand foundation.

References

[1] M. Askaripour, A. Saeidi, A. Rouleau, P. Mercier-Langevin, Rockburst in underground excavations: a review of mechanism, classification, and prediction methods, Undergr. Space 7 (2022) 577-607.

[2] B.P. Simser, Rockburst management in Canadian hard rock mines, J. Rock Mech. Geotech. Eng. 11 (2019) 1036-1043.

[3] Y. Fanjie, Z. Hui, X. Haibin, M.U. Azhar, Z. Yong, C. Fudong, Numerical simulation method for the process of rockburst, Eng. Geol. 306 (2022) 106760.

[4] P. Małkowski, Z. Niedbalski, A comprehensive geomechanical method for the assessment of rockburst hazards in underground mining, Int. J. Min. Sci. Technol. 30 (2020) 345-355.

[5] M. Zhang, J. Zhang, J. Fan, Z. Li, J. Chen, Y. Zou, D. Jiang, D. Nelias, Model interpretability and intensity prediction of rockbursts using a method innovation based on the QGHSCSO-CatBoost algorithm, Rock Mech. Rock Eng. 30 (2025) 1-30.

[6] A. Mazaira, P. Konicek, Intense rockburst impacts in deep underground construction and their prevention, Can. Geotech. J. 52 (10) (2015) 1426-1439.

[7] M. He, Q. Wang, Rock dynamics in deep mining, Int. J. Min. Sci. Technol. 33 (2023) 1065-1082.

[8] J. Fan, J. Chen, D. Jiang, J. Wu, C. Shu, W. Liu, A stress model reflecting the effect of the friction angle on rockbursts in coal mines, Geomech. Eng. 18 (2019) 21-27.

[9] Y. Pan, A. Wang, Disturbance response instability theory of rock bursts in coal mines and its application, Geohazard Mech 1 (1) (2023) 1-17.

[10] N.L.L. Mambou, J. Ndop, J.-M.B. Ndjaka, Redistribution and magnitude of stresses around horse shoe and circular excavations opened in anisotropic rock, Int. J. Min. Sci. Technol. 25 (4) (2015) 615-621.

[11] F. Yang, Z. Li, M. Fourmeau, J. Fan, Z. Yang, D. Jiang, Daniel Nelias, A unified constitutive model for salt rocks under triaxial creep-fatigue loading conditions, Tunn. Undergr. Space Technol. 154 (2024) 106116.

[12] Y. Hu, Z. Sun, J. Ji, Pseudo-dynamic stability analysis of 3D rock slopes considering tensile strength-modified Hoek-Brown failure criterion: seismic UBLA implementations, Eng. Geol. 343 (2024) 107786.

[13] J.H. Yang, C. Yao, Q.H. Jiang, W.B. Lu, S.H. Jiang, 2D numerical analysis of rock damage induced by dynamic in-situ stress redistribution and blast loading in underground blasting excavation, Tunn. Undergr. Space Technol. 70 (2017) 221-232.

[14] H.A. Elsageer, S.D. Butt, A.O. Mohammad Bamousa, W.R.E. Abdellah, M.A.M. Ali, Distribution of Stress Around Underground Excavations. Essentials Rock Mech, Springer, 2024, pp. 173-213.

[15] M.D.G. Salamon, Energy considerations in rock mechanics: fundamental results, J South African Inst Min Metall 84 (8) (1984) 233-246.

[16] E.T. Brown, J.W. Bray, F.J. Santarelli, Influence of stress-dependent elastic moduli on stresses and strains around axisymmetric boreholes, Rock Mech. Rock Eng. 22 (3) (1989) 189-203.

[17] R. Zhao, M. Tao, H. Zhao, C. Wu, W. Cao, Theoretical study on dynamic stress redistribution around circular tunnel with different unloading paths, Comput. Geotech. 163 (2023) 105737.

[18] Z. Li, J. Fan, M. Fourmeau, J. Chen, D. Jiang, D. Nelias, Long-term deformation of rock salt under creep-fatigue stress loading paths: modeling and prediction, Int. J. Rock Mech. Min. Sci. 181 (2024) 105861.

[19] Z.Y. Ai, Q. Liang, Z.K. Ye, K.X. Hu, Stress distribution around arbitrarily shaped shallow buried tunnels in transversely isotropic rock mass, Int. J. Numer. Anal. Methods GeoMech. 49 (5) (2025) 1378-1395.

[20] K. Duan, C.Y. Kwok, Evolution of stress-induced borehole breakout in inherently anisotropic rock: insights from discrete element modeling, J. Geophys. Res. Solid Earth 121 (4) (2016) 2361-2381.

[21] R. Gu, U. Ozbay, Numerical investigation of unstable rock failure in underground mining condition, Comput. Geotech. 63 (2015) 171-182.

[22] H. Xie, C. Li, Z. He, C. Li, Y. Lu, R. Zhang, et al., Experimental study on rock mechanical behavior retaining the in situ geological conditions at different depths, Int. J. Rock Mech. Min. Sci. 138 (2021) 104548.

[23] Y. Zou, W. Sharief, Z. Li, J. Fan, D. Jiang, D. Nelias, Numerical assessment of the influence of residual rock mass properties on destress blasting in deep mine, Earth Energy Sci. 1 (4) (2025) 324-335.

[24] L. Jing, J.A. Hudson, Numerical methods in rock mechanics, Int. J. Rock Mech. Min. Sci. 39 (4) (2002) 409-427.

[25] Y. Zou, P. Zhang, Assessment of Energy Release and Redistribution on Excavation Instabilities for Underground Mining, ISRM Congr., ISRM, 2023. ISRM-15CONGRESS.

[26] E. Eberhardt, Numerical modelling of three-dimension stress rotation ahead of an advancing tunnel face, Int. J. Rock Mech. Min. Sci. 38 (4) (2001) 499-518.

[27] F. Wang, R. Kaunda, Assessment of rockburst hazard by quantifying the consequence with plastic strain work and released energy in numerical models, Int.J. Min. Sci. Technol. 29 (1) (2019) 93-97.

[28] J. Watson, I. Canbulat, C. Zhang, C. Wei, Energies within rock mass and the associated dynamic rock failures, Rock Mech. Rock Eng. 58 (5) (2025) 4935-4958.

[29] I. Vazaios, M.S. Diederichs, N. Vlachopoulos, Assessment of strain bursting in deep tunnelling by using the finite-discrete element method, J. Rock Mech. Geotech. Eng. 11 (1) (2019) 12-37.

[30] J. Zhou, Y. Zhang, C. Li, H. He, X. Li, Rockburst prediction and prevention in underground space excavation, Undergr. Space 14 (2024) 70-98.

[31] S.-J. Miao, M.-F. Cai, Q.-F. Guo, Z.-J. Huang, Rock burst prediction based on in-situ stress and energy accumulation theory, Int. J. Rock Mech. Min. Sci. 83 (2016) 86-94.

[32] J.A. Hudson, J.P. Harrison, Engineering Rock Mechanics: an Introduction to the Principles, Elsevier, 2000.

[33] Szwedzicki Tad, The effect of mining geometry on stability of rock mass around underground excavations, Miner. Resour. Eng. 9 (2) (2000) 265-278.

[34] G. Ren, Z.H. Zuo, Y.M. Xie, J.V. Smith, Underground excavation shape optimization considering material nonlinearities, Comput. Geotech. 58 (2014) 81-87.

[35] L.-T. Xie, P. Yan, W.-B. Lu, M. Chen, G.-H. Wang, Effects of strain energy adjustment: a case study of rock failure modes during deep tunnel excavation with different methods, KSCE J. Civ. Eng. 22 (10) (2018) 4143-4154.

[36] H. Liu, Z. An, X. Liu, X. Wang, Z. Liu, An experimental investigation on the characteristics of excavation-induced failure of rocks surrounding a shaft, Adv. Civ. Eng. 2024 (1) (2024) 7363711.

[37] J.B. Martino, N.A. Chandler, Excavation-induced damage studies at the underground research laboratory, Int. J. Rock Mech. Min. Sci. 41 (8) (2004) 1413-1426.

[38] X. Dong, A. Karrech, H. Basarir, M. Elchalakani, A. Seibi, Energy dissipation and storage in underground mining operations, Rock Mech. Rock Eng. 52 (1) (2019) 229-245.

[39] V. Hajiabdolmajid, P.K. Kaiser, C.D. Martin, Modelling brittle failure of rock, Int. J. Rock Mech. Min. Sci. 39 (6) (2002) 731-741, https://doi.org/10.1016/S1365-1609(02)00051-5.

[40] R.S. Read, 20 years of excavation response studies at AECL's underground research laboratory, Int. J. Rock Mech. Min. Sci. 41 (8) (2004) 1251-1275.

[41] G. Ren, J.V. Smith, J.W. Tang, Y.-M. Xie, Underground excavation shape optimization using an evolutionary procedure, Comput. Geotech. 32 (2) (2005) 122-132.