Coupled numerical modelling of high-voltage electric pulse (HVEP) rock fracturing using COMSOL and 4D-LSM

Abstract

High-voltage electric pulse (HVEP) rock fragmentation has demonstrated substantial potential for sustainable fracturing of hard rocks owing to its energy efficiency. The transient nature and highly disruptive characteristics of its physical fracturing process render experimental investigation of the underlying rock-breaking mechanisms challenging. However, existing numerical studies lack comprehensive models that precisely link electrical breakdown phenomena with mechanical disintegration processes. This study combines COMSOL electrical breakdown simulations with four-dimension lattice spring model (4D-LSM) mechanical analysis to establish a coupled HVEP rock fragmentation model. The core concept of the model construction is to import the temperature field of the plasma channel obtained from the electrical breakdown into the mechanical solver to realize the precise connection between the two stages. The validated numerical model elucidates the full process of HVEP-induced fragmentation under varying electrical parameters. Furthermore, the effects of confining pressure and mineral grain size on fragmentation behavior have been investigated. Finally, parametric simulations across 25 electrical parameter combinations demonstrate the critical role of electrode spacing optimization in achieving energy-efficient rock fragmentation. These findings provide a predictive tool for designing efficient HVEP systems in deep resource extraction and mineral processing engineering.

Keywords

Rock fracturing / High-voltage electric pulse / Thermal-mechanical coupling / Lattice spring model

CRediT authorship contribution statement

Chenghui Liu: Writing – review & editing, Writing – original draft, Investigation, Data curation, Conceptualization. Qin Li: Supervision, Resources, Funding acquisition. Fuxin Rui: Writing – review & editing, Software, Methodology. Tubing Yin: Supervision. Yang Zou: Supervision. Gaofeng Zhao: Writing – review & editing, Validation, Supervision, Software, Resources, Project administration, Funding acquisition, Conceptualization.

Declaration of competing interest

The 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

We particularly acknowledge the financial support from the National Natural Science Foundation of China (Nos. 52209144 and 12472405).

References

[1] Lu GM, Feng XT, Li YH, Zhang XW . The microwave—induced fracturing of hard rock. Rock Mech Rock Eng 2019; 52(9):3017-32.

[2] Rui FX, Zhao GF, Zheng YL, Gong QM, Zhao XB . Electromagnetic—thermo—mechanical coupled modelling of microwave—assisted TBM disc cutting. Tunn Undergr Space Technol 2023; 138:105171.

[3] Guo CG, Sun Y, Yue HT, Li Q, He SZ, Zhang JZ, Zhang Y . Experimental research on laser thermal rock breaking and optimization of the process parameters. Int J Rock Mech Min Sci 2022; 160:105251.

[4] Yu DX, Wang YJ, Li SC, Jiang ZH, Wang JZ . Experimental investigation on failure mode and fracture characteristic of rock samples induced by laser irradiation. Int J Min Sci Technol 2025; 35(10):1827—43.

[5] Li H, Huang ZW, Li JB, Li XJ, Jiang TW, Chen JX . Rock breaking characteristics by swirling impeller abrasive water jet (SAWJ) on granite. Int J Rock Mech Min Sci 2022; 159:105230.

[6] Shangguan JM, Ge ZL, Deng QL, Cui YH, Yao Z . Fluid evolution and fragmentation characteristics under high pressure water jet impact on thermal rock. Int J Min Sci Technol 2025; 35(3):483-97.

[7] Han YC, Zheng C, Liu YH, Xu YF, Liu P, Zhu YJ, Wu XL . Study on the rock—breaking characteristics of high—energy pulsed plasma jet for granite. Geoenergy Sci Eng 2024; 232:212466.

[8] Sun Q, Liu YH, Shen ZP, Han YC, Wang QX, Liu P . A combined thermal spallation and melting technology by plasma jet for deep and hard rock reservoirs. SPE J 2023; 28(1):49-63.

[9] Yan GH, Fu HW, Zhao YM, Sun ZS, Zhang B . A review on optimizing potentials of high voltage pulse breakage technology based on electrical breakdown in water. Powder Technol 2022; 404:117293.

[10] Anders E, Lehmann F, Voigt M . Electric impulse technology: Long run drilling in hard rocks. In: Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering. Newfoundland: American Society of Mechanical Engineers;2015.p.V010T11A008.

[11] Zhang QY, Wang GL, Pan XD, Li YF, He JQ, Qi Y, Yang JS . High voltage electric pulse drilling: A study of variables through simulation and experimental tests. Energies 2023; 16(3):1174.

[12] Schiegg HO, Rødland A, Zhu GZ, Yuen DA . Electro—pulse—boring (EPB): Novel super—deep drilling technology for low cost electricity. J Earth Sci 2015; 26(1):37-46.

[13] Wang E, Shi FN, Manlapig E . Experimental and numerical studies of selective fragmentation of mineral ores in electrical comminution. Int J Miner Process 2012; 112—113:30-6.

[14] Bluhm H, Frey W, Giese H, Hoppe P, Schultheiss C, Strassner R . Application of pulsed HV discharges to material fragmentation and recycling. IEEE Trans Dielect Electr Insul 2000; 7(5):625—36.

[15] Zhu XH, He L, Liu WJ, Luo YX, Zhang YJ, Tang WJ . Numerical and experimental investigation on hydraulic—electric rock fragmentation of heterogeneous granite. Int J Min Sci Technol 2024; 34(1):15-29.

[16] Vorob’ev GA . Electrical breakdown in solid dielectrics. Phys Solid State 2005; 47(6):1083.

[17] Boev S, Vajov V, Levchenko B, Jgun D, Muratov V, Peltsman S, Adam A, Uemura K . In: Electropulse technology of material destruction and boring. Digest of Technical Papers. Baltimore: IEEE; 2002.p.220-5.

[18] Andres U. Development and prospects of mineral liberation by electrical pulses. Int J Miner Process 2010; 97(1—4):31-8.

[19] Zhu XH, Luo YX, Liu WJ, Hu H, Chen MQ . Numerical electric breakdown model of heterogeneous granite for electro—pulse—boring. Int J Rock Mech Min Sci 2022; 154:105128.

[20] Li CP, Duan LC, Wu LJ, Tan SC, Zheng J, Chikhotkin V . Experimental and numerical analyses of electro—pulse rock—breaking drilling. J Nat Gas Sci Eng 2020; 77:103263.

[21] Zhao Y, Liu Y, Xu YL, Wang TY, Liu SW, Lin FC . The plasma path development model (PPDM) in rocks during rock breaking by high—voltage pulse discharge. Curr Appl Phys 2024; 59:136-52.

[22] Niemeyer L, Pietronero L, Wiesmann HJ . Fractal dimension of dielectric breakdown. Phys Rev Lett 1984; 52(12):1033-6.

[23] Wiesmann HJ, Zeller HR . A fractal model of dielectric breakdown and prebreakdown in solid dielectrics. J Appl Phys 1986; 60(5):1770—3.

[24] Noskov MD, Kukhta VR, Lopatin VV . Simulation of the electrical discharge development in inhomogeneous insulators. J Phys D Appl Phys 1995; 28(6):1187.

[25] Li YJ, Lin BQ, Zhang XL, Lin MH . Study on the law of fracture development in plasma—induced broken coal. Rock Mech Rock Eng 2023; 56(7):4995-5007.

[26] Bao XK, Guo JY, Liu Y, Zhao G, Cao JX, Wu JW, Zhao JC . Damage characteristics and laws of micro—crack of underwater electric pulse fracturing coal—rock mass. Theor Appl Fract Mech 2021; 111:102853.

[27] Kang JF, Li CP, Duan LC, Xiao YB, Li A . An experimental and numerical study on the mechanism of high—voltage electro pulse rock—breaking. Rock Mech Rock Eng 2023; 56(3):2185-95.

[28] Zhu XH, Luo YX, Liu WJ . On the rock—breaking mechanism of plasma channel drilling technology. J Petrol Sci Eng 2020; 194:107356.

[29] Rao PP, Feng WK, Ouyang PH, Cui JF, Nimbalkar S, Chen QS . Formation of plasma channel under high—voltage electric pulse and simulation of rock—breaking process. Phys Scr 2024; 99(1):015604.

[30] Andres U. Electrical disintegration of rock. Miner Process Extr Metall Rev 1995; 14(2):87-110.

[31] Laumonier M, Gaillard F, Sifre D . The effect of pressure and water concentration on the electrical conductivity of dacitic melts: Implication for magnetotelluric imaging in subduction areas. Chem Geol 2015; 418:66-76.

[32] Guo X, Zhang L, Behrens H, Ni HW . Probing the status of felsic magma reservoirs: Constraints from the P—T—H₂O dependences of electrical conductivity of rhyolitic melt. Earth Planet Sci Lett 2016; 433:54-62.

[33] Kuznetsova N, Zhgun D, Golovanevskiy V . Plasma blasting of rocks and rocks—like materials: An analytical model. Int J Rock Mech Min Sci 2022; 150:104986.

[34] Yin TB, Liu CH, Chen YJ, Zhuang DD, Wu Y, Dai H, Su JZ . Experimental and numerical study on the facture behavior of heated—granite subjected to high—voltage electric pulse. Eng Fract Mech 2024; 299:109935.

[35] Liu WJ, Hu H, Zhu XH, Luo YX, Chen MQ . The fragmentation mechanism of granite in electrical breakdown process of plasma channel drilling. Geomech Geophys Geo Energy Geo Resour 2023; 9(1):22.

[36] Zhao GF . Developing a four—dimensional lattice spring model for mechanical responses of solids. Comput Meth Appl Mech Eng 2017; 315:881-95.

[37] Rui FX, Zhao GF . Development of the four—dimensional lattice spring model for thermo—mechanical fracturing and large deformation of solids. Eng Anal Bound Elem 2022; 138:390-406.

[38] Timoshkin IV, Mackersie JW, MacGregor SJ . Plasma channel miniature hole drilling technology. IEEE Trans Plasma Sci 2004; 32(5):2055-61.

[39] Zhu XH, He L, Liu WJ, Luo YX . Rock breaking mechanism of electrode bit in heterogeneous granite formation and its optimization. Geothermics 2023; 109:102660.

[40] Yin TB, Liu CH, Zhuang DD, Li XB . Effect of high—voltage electric pulse stimulation on heated—granite: An experimental investigation. J Cent South Univ 2024; 31(5):1526—41.

[41] Burkin VV, Kuznetsova NS, Lopatin VV . Formation of a spall cavity in a dielectric during electrical explosion. J Appl Mech Tech Phys 2010; 51(1):137-44.

[42] Wang F, Konietzky H . Thermal cracking in granite during a heating—cooling cycle up to 1000 ℃: Laboratory testing and real—time simulation. Rock Mech Rock Eng 2022; 55(3):1411—28.

[43] Liu WJ, Zhang YJ, Zhu XH, Luo YX . The influence of pore characteristics on rock fragmentation mechanism by high—voltage electric pulse. Plasma Sci Technol 2023; 25(5):055502.

[44] Ushakov VY, Vajov VF, Zinoviev NT . Electro—Discharge Technology for Drilling Wells and Concrete Destruction. Cham: Springer International Publishing; 2019.

[45] Semkin BV, Usov AF, Kurets VI . The principles of electric impulse destruction of materials. Russian Acad Sci Izv Math 1995:p.8.