Effect of oblique incident wave perturbation on rock spalling: An insight from DEM modelling

Abstract

In order to study spalling failure characteristics of rock under oblique incidence of stress wave, a split Hopkinson pressure bar (SHPB) spalling test with a special shaped striker was simulated by Particle Flow Code (PFC). The oblique section angles selected in this study were 30°, 45° and 60°, respectively. The spalling failure characteristics of rock with oblique incidence of stress waves at 5.2 m/s, 5.6 m/s and 6.2 m/s impact levels were analyzed and compared with those for 90° section incidence. The results show that when the angle of the oblique section greater than 45°, the stress wave will be directly reflected into a tensile wave when it encounters the oblique section, and then the reflected tensile waves and compressive waves will alternately appear. When the angle of the oblique section is less than 45°, the reflected stress wave is superimposed multiple times with the incident stress wave in the oblique section, and induces the spalling of the oblique section. Based on the longitudinal wave propagation theory, the function of stress in the 30° oblique section has been derived. The possible fracture position of the oblique section is obtained, which is consistent with the simulation results.

Keywords

split Hopkinson pressure bar (SHPB) / oblique section / spalling / wave superpose / numerical simulation

References

[1] DavisonL, StevensA L, KippM E. Theory of spall damage accumulation in ductile metals [J]. Journal of the Mechanics and Physics of Solids, 1977, 25(1): 11-28

[2] WangL-liFoundation of stress waves, 1992, Beijing, National Defense Industry Press[M]

[3] RossmanithH P, UenishiK. The mechanics of spall fracture in rock and concrete [J]. Fragblast, 2006, 10(3–4): 111-162

[4] LingZ, BaiY-long. Study on the relation between fractal features of spalling surface and microstructures of an Al-alloy [J]. Explosion and Shock Waves, 1994, 14(1): 1-8(in Chinese)

[5] BaiY-l, KeF-j, XiaM-fen. Formulation of statistical evolution of microcracks in solids [J]. Acta Mechanica Sinica, 1991, 7(1): 59-66 in Chinese)

[6] AntounT, SeamanL, CurranD R, et al. Spall fracture, 2003, New York, Springer[M]

[7] ZHANG Lei, HU Shi-sheng, CHEN De-xing, et al. Spalling characteristics of concrete materials [J]. Explosion and Shock Waves, 2008(3): 193–199. DOI: 1001-1455(2008)03-0193-07. (in Chinese)

[8] BraraA, KlepaczkoJ. An experimental method for dynamic tensile testing of concrete by spalling [J]. International Journal of Impact Engineering, 2001, 25(4): 387-409

[9] WeerheijmJ, van DoormaalJ C A M. Tensile failure of concrete at high loading rates: New test data on strength and fracture energy from instrumented spalling tests [J]. International Journal of Impact Engineering, 2007, 34(3): 609-626

[10] SchulerH, MayrhoferC, ThomaK. Spall experiments for the measurement of the tensile strength and fracture energy of concrete at high strain rates [J]. International Journal of Impact Engineering, 2006, 32(10): 1635-1650

[11] KhosravaniM R, WagnerP, FröhlichD, et al. . Dynamic fracture investigations of ultra-high performance concrete by spalling tests [J]. Engineering Structures, 2019, 201: 109844

[12] LiX-b, TaoM, GongF-q, et al. . Theoretical and experimental study of hard rock spalling failure under impact dynamic loading [J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(6): 1081-1088(in Chinese)

[13] HuangL-q, WangJ, MomeniA, et al. . Spalling fracture mechanism of granite subjected to dynamic tensile loading [J]. Transactions of Nonferrous Metals Society of China, 2021, 31(7): 2116-2127

[14] ManK, LiuX-l, SongZ-fei. Experimental study on spalling of deep rock under half-sine stress wave disturbance[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(3): 428-434(in Chinese)

[15] ZhaoH-t, TaoM, LiX-b, et al. . Estimation of spalling strength of sandstone under different pre-confining pressure by experiment and numerical simulation [J]. International Journal of Impact Engineering, 2019, 133103359

[16] LiX-b, TaoM, WuC-q, et al. . Spalling strength of rock under different static pre-confining pressures [J]. International Journal of Impact Engineering, 2017, 9969-74

[17] StaceyT R, RojasE. A potential method of containing rockburst damage and enhancing safety using a sacrificial layer [J]. Journal of the South African Institute of Mining and Metallurgy, 2013, 113: 565-573

[18] MUDAU A, STACEY T R, GOVENDER R. Experimental investigations into sacrificial support for containment of rockburst damage [C]//Eighth International Conference on Deep and High Stress Mining. Australian Centre for Geomechanics, Perth, 2017. DOI: https://doi.org/10.36487/acg_rep/1704_31_mudau.

[19] LiX-b, ZouY, ZhouZ-long. Numerical simulation of the rock SHPB test with a special shape striker based on the discrete element method [J]. Rock Mechanics and Rock Engineering, 2014, 47(5): 1693-1709

[20] QiuJ-d, LiD-y, LiX-b, et al. . Effect of preexisting flaws on spalling fracture of granite [J]. Explosion and Shock Waves, 2018, 38(3): 665-670(in Chinese)

[21] LiuH-y, CongY, ZhangL-m, et al. . Macro and micro failure mechanism of surrounding rock of small span tunnel under different stress paths [J]. Journal of Central South University, 2022, 29(5): 1616-1629

[22] ChenS-j, FengF, WangY-j, et al. . Tunnel failure in hard rock with multiple weak planes due to excavation unloading of in situ stress [J]. Journal of Central South University, 2020, 27(10): 2864-2882

[23] TaoM, MaA, PengK, et al. . Fracture evaluation and dynamic stress concentration of granite specimens containing elliptic cavity under dynamic loading [J]. Energies, 2019, 12(18): 3441

[24] ZUO Yu-jun, TANG Chun-an, GONG Feng-qiang. Numerical simulation on spallation process induced by reflection of stress wave under different free faces [J]. Journal of Jishou University (Natural Science Edition), 2006(6): 80–83. DOI: https://doi.org/10.3969/j.issn.1672-7207.2006.06.031. (in Chinese)

[25] ZuoY-j, ZhuW-c, TangC-a, et al. . Numerical simulation on spallation process of in homogeneous medium induced by reflection of stress wave [J]. Journal of Central South University (Natural Science Edition), 2006, 3761177-1182(in Chinese)

[26] WengL, WuQ-h, ZhaoY-l, et al. . Dynamic response and failure of rock in initial gradient stress field under stress wave loading [J]. Journal of Central South University, 2020, 27(3): 963-972

[27] GuiY L, ZhaoZ Y, ZhouH Y, et al. . Numerical simulation of P-wave propagation in rock mass with granular material-filled fractures using hybrid continuum-discrete element method [J]. Rock Mechanics and Rock Engineering, 2016, 49(10): 4049-4060

[28] GUI Y, ZHAO Z. Numerical investigation on the effect of fracture filling material on P-wave propagation [C]//ISRM 2nd International Conference on Rock Dynamics: From Research to Engineering, 2016, 295–300. DOI: https://doi.org/10.1201/b21378-44.

[29] XieH-p, ZhuJ-b, ZhouT, et al. . Conceptualization and preliminary study of engineering disturbed rock dynamics [J]. Geomechanics and Geophysics for Geo-energy and Geo-resources, 2020, 6(2): 1-14

[30] PotyondyD O, CundallP A. A bonded-particle model for rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2004, 41(8): 1329-1364