Research on damage characteristics and constitutive model of rock mass under true triaxial cyclic loading based on acoustic emission

Abstract

Aiming at the problem of deep surrounding rock instability induced by roadway excavation or mining disturbance, the true triaxial loading system was used to conduct graded cyclic maximum principal stress σ ₁ and intermediate principal stress σ ₂ tests on sandstone to simulate the effect of mining stress in actual underground engineering. The influences of each principal stress cycle on the mechanical properties, acoustic emission (AE) characteristics, and fracture characteristics of sandstone were analyzed. The damage characteristics of sandstone under true triaxial cyclic loading were studied. Furthermore, the damage constitutive model of rock mass under true triaxial cyclic loading was established based on AE cumulative ringing count. The quantitative investigation was conducted on cumulative-damage changes in circulating sandstone, which elucidated the mechanism of damage deterioration in sandstone subjected to true triaxial cyclic loading. The results show that the influence of the graded cycle σ ₁ on limit maximum principal strain ε _1max and limit minimum principal strain ε _3max was significantly greater than that of the limit intermediate principal strain ε _2max. Graded cycle σ ₂ had a greater impact on ε _2max and a smaller impact on ε _3max. The elasticity modulus of sandstone decreased exponentially with the increased cyclic load amplitude, while the Poisson ratio increased linearly. b of AE showed a trend of increasing, decreasing, slightly fluctuating, and finally decreasing during cycling σ ₁. b showed a trend of slight fluctuation, large fluctuation, and finally increase during cycling σ ₂. Sandstone specimens experienced mainly tensile failure, tensile-shear composite failure, and mainly shear failure with increased initial σ ₂ or σ ₃. This was determined by analyzing the rise angle-average frequency of the AE parameter, corresponding to the rock specimens from splitting failure to shear failure. Besides, the mechanical damage behavior of sandstone under true triaxial cyclic loading could be well described by the established constitutive model. At the same time, it was found that the sandstone damage variable decreased with increased σ ₂ during cycling σ ₁. The damage variable decreased first and then increased with increased σ ₃ during cycling σ ₂.

Keywords

rock mechanics / true triaxial cyclic principal stress / acoustic emission / constitutive model / damage variable

References

[1] BagdeM N, PetrosV. Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading [J]. International Journal of Rock Mechanics and Mining Sciences, 2005, 42(2): 237-250

[2] Aghaei AraeiA, RazeghiH R, GhalandarzadehA, et al.. Effects of loading rate and initial stress state on stress - strain behavior of rock fill materials under monotonic and cyclic loading conditions [J]. Scientia Iranica, 2012, 19(5): 1220-1235

[3] ZhouX P, QianQ H, YangH Q. Rock burst of deep circular tunnels surrounded by weakened rock mass with cracks [J]. Theoretical and Applied Fracture Mechanics, 2011, 56(2): 79-88

[4] HuH-r, XiaB-w, LuoY-f, et al.. Energy characteristics of sandstones with different crack angles under true triaxial cyclic loading and unloading [J]. Energy Science & Engineering, 2022, 10(4): 1418-1430

[5] LiuC, YinG-z, LiM-h, et al.. Deformation and permeability evolution of coals considering the effect of beddings [J]. International Journal of Rock Mechanics and Mining Sciences, 2019, 117: 49-62

[6] EberhardtE, SteadD, StimpsonB. Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression [J]. International Journal of Rock Mechanics and Mining Sciences, 1999, 36(3): 361-380

[7] EberhardtE, SteadD, StimpsonB, et al.. Identifying crack initiation and propagation thresholds in brittle rock [J]. Canadian Geotechnical Journal, 1998, 35(2): 222-233

[8] YouM-q. Strength and deformation of rock under complex loading path [J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 21(1): 23-28 (in Chinese)

[9] NishiK, KokushoT, EsashiY. Dynamic shear modulus and damping ratio of rocks for a wide confining pressure range [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1984, 21(5): A172

[10] LinY-s, GeH-k, WangS-c. Experimental study on dynamic and static mechanical parameters of rock [J]. Chinese Journal of Rock Mechanics and Engineering, 1998, 17(2): 216-222 (in Chinese)

[11] SoomroM H A A, IndraratnaB, KarekalS. Critical shear strain and sliding potential of rock joint under cyclic loading [J]. Transportation Geotechnics, 2022, 32: 100708

[12] DuanM-k, JiangC-b, YuH, et al.. Experimental research on energy dissipation and seepage properties of coal under loading-unloading conditions at different stress levels [J]. Rock and Soil Mechanics, 2018, 39(4): 1346-1354 (in Chinese)

[13] LiuY, DaiF, DongL, et al.. Experimental investigation on the fatigue mechanical properties of intermittently jointed rock models under cyclic uniaxial compression with different loading parameters [J]. Rock Mechanics and Rock Engineering, 2018, 51(1): 47-68

[14] PengK, ZhouJ-q, ZouQ-l, et al.. Effect of loading frequency on the deformation behaviours of sandstones subjected to cyclic loads and its underlying mechanism [J]. International Journal of Fatigue, 2020, 131: 105349

[15] TiwariR P, RaoK S. Post failure behaviour of a rock mass under the influence of triaxial and true triaxial confinement [J]. Engineering Geology, 2006, 84(3): 112-129 4

[16] DongC-l, FanC-t, LuX-y, et al.. Mechanical and energy evolution characteristics of sandstone under true triaxial cyclic loading [J]. Applied Sciences, 2023, 13(12): 7230

[17] LiuC-y, ZhaoG-m, XuW-s, et al.. Experimental study on failure characteristics of single-sided unloading rock under different intermediate principal stress conditions [J]. International Journal of Mining Science and Technology, 2023, 33(3): 275-287

[18] DuanM-k, JiangC-b, GuoX-w, et al.. Experimental study on mechanical and damage characteristics of coal under cyclic true triaxial loading [J]. Chinese Journal of Rock Mechanics and Engineering, 2021, 40(6): 1110-1118 (in Chinese)

[19] XuW-s, ZhaoG-m, MengX-r, et al.. Anisotropy and energy evolution mechanism of rock mass under true triaxial loading-unloading [J]. Journal of China Coal Society, 2023, 48(4): 1502-1515 (in Chinese)

[20] ShaP, WuF-q, ChangJ-y. Unloading strength and failure pattern of marble under true triaxial test [J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(9): 2084-2092 (in Chinese)

[21] ZhaoG-m, LiuZ-x, MengX-r, et al.. Energy evolution of sandstone under true triaxial cyclic principal stress [J]. Rock and Soil Mechanics, 2023, 44(7): 1875-1890 (in Chinese)

[22] MogiK. Effect of the triaxial stress system on fracture and flow of rocks [J]. Physics of the Earth and Planetary Interiors, 1972, 5: 318-324

[23] KwasniewskiM, TakahashiM, LiX. On the dilatant behavior of sandstone under true triaxial compression conditions [J]. Publications of the Institute of Geophysics, Polish Academy of Sciences, Series M: Miscellanea, 2002, 24(340): 321-324

[24] DuanM-k, JiangC-b, YinW-m, et al.. Experimental study on mechanical and damage characteristics of coal under true triaxial cyclic disturbance [J]. Engineering Geology, 2021, 295: 106445

[25] JiangC-b, DuanM-k, YinG-z, et al.. Experimental study on seepage properties, AE characteristics and energy dissipation of coal under tiered cyclic loading [J]. Engineering Geology, 2017, 221: 114-123

[26] DuanM-k, JiangC-b, XingH-l, et al.. Study on damage of coal based on permeability and load-unload response ratio under tiered cyclic loading [J]. Arabian Journal of Geosciences, 2020, 13(6): 250

[27] DuanM-k, JiangC-b, GanQ, et al.. Experimental investigation on the permeability, acoustic emission and energy dissipation of coal under tiered cyclic unloading [J]. Journal of Natural Gas Science and Engineering, 2020, 73: 103054

[28] LiM-h, YinG-z, XuJ, et al.. A novel true triaxial apparatus to study the geomechanical and fluid flow aspects of energy exploitations in geological formations [J]. Rock Mechanics and Rock Engineering, 2016, 49(12): 4647-4659

[29] DongL-j, ZhangL-y. Error analysis of b-value of acoustic emission for rock fracture [J]. Journal of Yangtze River Scientific Research Institute, 2020, 37(8): 75-81 (in Chinese)

[30] LiY-h, LiuJ-p, ZhaoX-d, et al.. Study on b-value and fractal dimension of acoustic emission during rock failure process [J]. Rock and Soil Mechanics, 2009, 30(9): 2559-2563 2574

[31] LiuC-y, ZhaoG-m, XuW-s, et al.. Experimental investigation on failure process and spatiotemporal evolution of rockburst in granite with a prefabricated circular hole [J]. Journal of Central South University, 2020, 27(10): 2930-2944

[32] SongY-q, MaH-f, LiuJ-c, et al.. Experimental study on uniaxial acoustic emission damage characteristics of freeze-thaw limestone [J]. Chinese Journal of Rock Mechanics and Engineering, 2022, 41(S1): 2603-2614 (in Chinese)

[33] YueJ G, KunnathS K, XiaoY. Uniaxial concrete tension damage evolution using acoustic emission monitoring [J]. Construction and Building Materials, 2020, 232: 117281

[34] AiT, WuS-y, ZhangR, et al.. Changes in the structure and mechanical properties of a typical coal induced by water immersion [J]. International Journal of Rock Mechanics and Mining Sciences, 2021, 138: 104597

[35] ZhangZ-z, GaoF. Experimental investigation on the energy evolution of dry and water-saturated red sandstones [J]. International Journal of Mining Science and Technology, 2015, 25(3): 383-388

[36] ZhaoY-c, YangT-h, XuT, et al.. Mechanical and energy release characteristics of different water-bearing sandstones under uniaxial compression [J]. International Journal of Damage Mechanics, 2018, 27(5): 640-656

[37] LiuH, LinJ-h, YangG-s, et al.. Acoustic emission test on tensile damage characteristics of sandstone under freeze-thaw cycle [J]. Journal of Mining & Safety Engineering, 2021, 38(4): 830-839 (in Chinese)

[38] WuX-z, LiuJ-w, LiuX-x, et al.. Study on the coupled relationship between AE accumulative ring-down count and damage constitutive model of rock [J]. Journal of Mining & Safety Engineering, 2015, 32(1): 28-34 41

[39] YangM-h, ZhaoM-h, CaoW-g. Method for determining the parameters of statistical damage softening constitutive model for rock [J]. Shuili Xuebao, 2005, 36(3): 345-349 (in Chinese)

RIGHTS & PERMISSIONS

Central South University