Numerical simulation of dynamic fracture properties of rocks under different static stress conditions

Abstract

When underground cavities are subjected to explosive stress waves, a uniquely damaged zone may appear due to the combined effect of dynamic loading and static pre-load stress. In this study, a rate-dependent two-dimensional rock dynamic constitutive model was established to investigate the dynamic fractures of rocks under different static stress conditions. The effects of the loading rate and peak amplitude of the blasting wave under different confining pressures and the vertical compressive coefficient (K₀) were considered. The numerical simulated results reproduced the initiation and further propagation of primary radial crack fractures, which were in agreement with the experimental results. The dynamic loading rate, peak amplitude, static vertical compressive coefficient (K₀) and confining pressure affected the evolution of fractures around the borehole. The heterogeneity parameter (m) plays an important role in the evolution of fractures around the borehole. The crack propagation path became more discontinuous and rougher in a smaller-heterogeneity parameter case.

Keywords

rock mechanics / coupled static and dynamic loading / numerical simulation / rate-dependent damage constitutive model

References

[1] HuW R, LiuK, PotyondyD O, et al.. 3D continuum-discrete coupled modelling of triaxial Hopkinson bar tests on rock under multiaxial static-dynamic loads [J]. International Journal of Rock Mechanics and Mining Sciences, 2020, 134: 104448

[2] GongF-Q, SiX-F, LiX-B, et al.. Dynamic triaxial compression tests on sandstone at high strain rates and low confining pressures with split Hopkinson pressure bar [J]. International Journal of Rock Mechanics and Mining Sciences, 2019, 113211-219

[3] ZhaoF-J, XieS-Y, PanJ-Z, et al.. Numerical simulation and experimental investigation on rock fragmentation under combined dynamic and static loading [J]. Chinese Journal of Geotechnical Engineering, 2011, 33(8): 1290-1295(in Chinese)

[4] GongF-Q, LiX-B, LiuX-L. Experimental study of dynamic characteristics of sandstone under one-dimensional coupled static and dynamic loads [J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(10): 2076-2085(in Chinese)

[5] LiuS-H, QinZ-H, LouJ-F. Experimental study of dynamic failure characteristics of coal-rock compound under one-dimensional static and dynamic loads [J]. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(10): 2064-2075(in Chinese)

[6] LiX-B, GongF-Q, TaoM, et al.. Failure mechanism and coupled static-dynamic loading theory in deep hard rock mining: A review [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2017, 9(4): 767-782

[7] YangZ-Q, DouL-M, LiuC, et al.. Application of high-pressure water jet technology and the theory of rock burst control in roadway [J]. International Journal of Mining Science and Technology, 2016, 26(5): 929-935

[8] WangS Y, SloanS W, LiuH Y, et al.. Numerical simulation of the rock fragmentation process induced by two drill bits subjected to static and dynamic (impact) loading [J]. Rock Mechanics and Rock Engineering, 2011, 44(3): 317-332

[9] ChenR, LiK, XiaK-W, et al.. Dynamic fracture properties of rocks subjected to static pre-load using notched semi-circular bend method [J]. Rock Mechanics and Rock Engineering, 2016, 49(10): 3865-3872

[10] QianQ-H. The characteristic scientific phenomena of engineering response to deep rock mass and the implication of deepness [J]. Journal of East China University of Technology (Natural Science), 2004, 27(1): 1-5(in Chinese)

[11] TaoJ, YangX-G, LiH-T, et al.. Effects of in situ stresses on dynamic rock responses under blast loading [J]. Mechanics of Materials, 2020, 145: 103374

[12] WangS Y, SunL, YangC, et al.. Numerical study on static and dynamic fracture evolution around rock cavities [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2013, 5(4): 262-276

[13] XuY, DaiF, DuH-B. Experimental and numerical studies on compression-shear behaviors of brittle rocks subjected to combined static-dynamic loading [J]. International Journal of Mechanical Sciences, 2020, 175105520

[14] XiaK-W, YaoW. Dynamic rock tests using split Hopkinson (Kolsky) bar system — A review [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2015, 7(1): 27-59

[15] LiuY, JingF-X, FengY. Study of occurence mechanism and risk analysis of induced rockbrust in roadway [J]. Rock and Soil Mechanics, 2015, 36(S2): 201-207220

[16] FanL F, SunH Y. Seismic wave propagation through an in situ stressed rock mass [J]. Journal of Applied Geophysics, 2015, 12113-20

[17] LiX-B, GongF-Q, WangS-F, et al.. Coupled static-dynamic loading mechanical mechanism and dynamic criterion of rockburst in deep hard rock mines [J]. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(4): 708-723(in Chinese)

[18] LiX-B, ZhouZ-L, LokT S, et al.. Innovative testing technique of rock subjected to coupled static and dynamic loads [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(5): 739-748

[19] ZhouZ-H, ZhangY-Q, YangA-G, et al.. Experimental study on mechanical characteristics of dolomite under three-dimensional coupled static-dynamic loading [J]. Journal of China Coal Society, 2015, 40(5): 1030-1036(in Chinese)

[20] LiX-P, DongQ, LiuT-T, et al.. Research on propagation law of cylindrical stress wave in jointed rock mass under in situ stress [J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(S1): 3121-3131(in Chinese)

[21] WengL, LiX-B, TaheriA, et al.. Fracture evolution around a cavity in brittle rock under uniaxial compression and coupled static-dynamic loads [J]. Rock Mechanics and Rock Engineering, 2018, 51(2): 531-545

[22] ZhangF-R, WuC-Q, WangH-W, et al.. Numerical simulation of concrete filled steel tube columns against BLAST loads [J]. Thin-Walled Structures, 2015, 92: 82-92

[23] LiX-B, WengL. Numerical investigation on fracturing behaviors of deep-buried opening under dynamic disturbance [J]. Tunnelling and Underground Space Technology, 2016, 54: 61-72

[24] LiD-Y, XiaoP, HanZ-Y, et al.. Mechanical and failure properties of rocks with a cavity under coupled static and dynamic loads [J]. Engineering Fracture Mechanics, 2020, 225: 106195

[25] LiuJ-B, LiB. A unified viscous-spring artificial boundary for 3-D static and dynamic applications [J]. Science in China Series E: Engineering & Materials Science, 2005, 48(5): 570-584

[26] LiX-B, FengF, LiD-Y. Numerical simulation of rock failure under static and dynamic loading by splitting test of circular ring [J]. Engineering Fracture Mechanics, 2018, 188184-201

[27] QianX-K, LiangZ-Z, LiaoZ-Y, et al.. Numerical investigation of dynamic fracture in rock specimens containing a pre-existing surface flaw with different dip angles [J]. Engineering Fracture Mechanics, 2020, 223: 106675

[28] HanH-Y, FukudaD, LiuH-Y, et al.. FDEM simulation of rock damage evolution induced by contour blasting in the bench of tunnel at deep depth [J]. Tunnelling and Underground Space Technology, 2020, 103103495

[29] ZhuW C, LiZ H, ZhuL, et al.. Numerical simulation on rockburst of underground opening triggered by dynamic disturbance [J]. Tunnelling and Underground Space Technology, 2010, 25(5): 587-599

[30] JiaP, ZhuW-C. Dynamic-static coupling analysis on rockburst mechanism in jointed rock mass [J]. Journal of Central South University, 2012, 19(11): 3285-3290

[31] WU Ming-xin, ZHANG Chu-han, CHEN Zhen-fu. Study on the direct tensile, splitting and flexure strengths of concrete [J]. Journal of Hydraulic Engineering, 2015. DOI: https://doi.org/10.13243/j.cnki.slxb.2. (in Chinese)

[32] FakhimiA, CarvalhoF, IshidaT, et al.. Simulation of failure around a circular opening in rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2002, 39(4): 507-515

[33] BaiY, ZhuW-C, WeiC-H, et al.. Numerical simulation on two-hole blasting under different in situ stress conditions [J]. Rock and Soil Mechanics, 2013, 34(S1): 466-471(in Chinese)

[34] ZHANG Feng-peng, PENG Jian-yu, ZHANG Xin, et al. Numerical simulation of the effect of in situ stress on rock blasting [J]. Metal Mine, 2015(12): 15–18. (in Chinese)

[35] ZhangF-P, PengJ-Y, FanG-H, et al.. Mechanisms of blasting-induced rock fractures under different static stress and joint properties conditions [J]. Rock and Soil Mechanics, 2016, 37(7): 1839-18461913

[36] TangC A, LinP, WongR H C, et al.. Analysis of crack coalescence in rock-like materials containing three flaws—Part II: Numerical approach [J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(7): 925-939

[37] TangC-A, YangY-F. Crack branching mechanism of rock-like quasi-brittle materials under dynamic stress [J]. Journal of Central South University, 2012, 19(11): 3273-3284

[38] ZhaoJ, LiH B. Experimental determination of dynamic tensile properties of a granite [J]. International Journal of Rock Mechanics and Mining Sciences, 2000, 37(5): 861-866

[39] ZhangQ B, ZhaoJ. A review of dynamic experimental techniques and mechanical behaviour of rock materials [J]. Rock Mechanics and Rock Engineering, 2014, 47(4): 1411-1478

[40] SiX-F, GongF-Q, LiX-B, et al.. Dynamic Mohr-Coulomb and Hoek-Brown strength criteria of sandstone at high strain rates [J]. International Journal of Rock Mechanics and Mining Sciences, 2019, 11548-59

[41] QiC-Z, QianQ-H. Physical mechanism of dependence of material strength on strain rate for rock-like material [J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 24(1): 97-110

[42] ZhaoJ. Applicability of Mohr-Coulomb and Hoek-Brown strength criteria to the dynamic strength of brittle rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2000, 37(7): 1115-1121

[43] ZhengC, ZhangJ-H. SSOR-PCG method used in simulation of geotechnical engineering with finite element method [J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(s1): 2820-2826

[44] YangX, PuC-J, TangX, et al.. Experimental study of effects of manual crack on blasting cracks propagation [J]. Blasting, 2014, 31(2): 26-31

[45] YueZ-W, HuQ-W, ChenB. An experimental study of the interaction between the blast-induced crack and the bedding defect [J]. Journal of Vibration and Shock, 2017, 36(12): 99-104(in Chinese)

[46] LajtaiE Z, LajtaiV N. The collapse of cavities [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1975, 12(4): 81-86

[47] WangY-B. Study of the dynamic fracture effect using slotted cartridge decoupling charge blasting [J]. International Journal of Rock Mechanics and Mining Sciences, 2017, 96: 34-46

[48] WeiC-H, ZhuW-C, BaiY, et al.. Numerical simulation on two-hole blasting of rock under different joint angles and in-situ stress conditions [J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(4): 926-935