Abstract
Rock heterogeneity significantly influences a rock mass's dynamic mechanical behavior and fracture evolution. This study focused on creating heterogeneous sandstone models using the discrete element method and conducting split-Hopkinson pressure bar tests. The results show that heterogeneity has a significant impact on the dynamic mechanical properties of rock. The dynamic compressive strength, elastic modulus, and heterogeneity coefficient exhibit a negative correlation. The weakening effect of heterogeneity on rock strength is greater than its effect on stiffness. Increasing heterogeneity leads to a decrease in strain and kinetic energy at the peak stress point, while friction energy initially decreases and then increases. Rock heterogeneity reduces impact resistance and the occurrence of rock bursts. Moreover, heterogeneity rocks exhibit significant strain rate effects. Acoustic emission (AE) moment tensor analysis reveals that under impact load, tensile or shear fractures are the main sources of failure in heterogeneous rock samples. With increased heterogeneity, tensile fractures gradually transform into compression fractures, while shear fractures slowly increase. Shear fractures have relatively high strength compared to other AE types. The characteristics of acoustic emissions in rock samples follow a roughly normal distribution, and the b value of AE gradually increases with higher heterogeneity. These findings provide valuable insights into the dynamic mechanical response and fracture mechanism of rocks and have practical applications in engineering design and rock disaster prediction.
Similar content being viewed by others
Data availability
Data will be made available on request.
References
Dai S, Gao W, Wang C, Xiao T (2019) Damage evolution of heterogeneous rocks under uniaxial compression based on distinct element method. Rock Mech Rock Eng 52:2631–2647. https://doi.org/10.1007/s00603-018-1689-5
Cheng HM, Yang XB, Pei YY, Song YM (2022) Quantitative investigation on the heterogeneity of deformation fields in sandstone pre-existing cracks during damage evolution. Sci Rep. https://doi.org/10.1038/s41598-022-09600-3
Xu T, Tang CA, Zhao J, Li LC, Heap MJ (2012) Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks. Geophys J Int 189:1781–1796. https://doi.org/10.1111/j.1365-246X.2012.05460.x
Yang BC, Xue L, Wang MM (2018) Evolution of the shape parameter in the Weibull distribution for brittle rocks under uniaxial compression. Arab J Geosci. https://doi.org/10.1007/s12517-018-3689-x
Yang BB, Cao XS, Han TL, Li PF, Shi JP (2022) Effect of heterogeneity on the extension of ubiquitiformal cracks in rock materials. Fract Fract. https://doi.org/10.3390/fractalfract6060317
Zhang T, Yu LY, Li J, Ma LJ, Su HJ, Zhang MW, Xu XL, Peng YX (2022) Numerical investigation of the effects of the micro-parameters of the transgranular contact on the mechanical response of granite. Theor Appl Fract Mech. https://doi.org/10.1016/j.tafmec.2022.103259
Yin TB, Wang P, Li XB, Wu BB, Tao M, Shu RH (2016) Determination of dynamic flexural tensile strength of thermally treated laurentian granite using semi-circular specimens. Rock Mech Rock Eng 49:3887–3898. https://doi.org/10.1007/s00603-016-0920-5
Silva RA, Ceia M, Missagia R, Neto IAL (2019) Analysis of elastic velocities behavior and porosity in carbonates submitted to external pressure variation. J Appl Geophys 166:10–21. https://doi.org/10.1016/j.jappgeo.2019.04.013
Yang XJ, Wang JM, Zhu C, He MC, Gao Y (2019) Effect of wetting and drying cycles on microstructure of rock based on SEM. Environ Earth Sci. https://doi.org/10.1007/s12665-019-8191-6
Cai YY, Yu J, Fu GF, Li H (2016) Experimental investigation on the relevance of mechanical properties and porosity of sandstone after hydrochemical erosion. J Mt Sci 13:2053–2068. https://doi.org/10.1007/s11629-016-4007-2
Li H, Yang CH, Ding XL, William NT, Yin HW, Zhang SN (2019) Weibull linear parallel bond model (WLPBM) for simulating micro-mechanical characteristics of heterogeneous rocks. Eng Anal Bound Elem 108:82–94. https://doi.org/10.1016/j.enganabound.2019.07.018
Li A, Shao GJ, Su JB, Sun Y, Yu TT, Shi HG (2018) Influence of heterogeneity on mechanical and AE behaviours of stratified rock specimens. Eur J Environ Civ Eng 22:s381–s414. https://doi.org/10.1080/19648189.2017.1373709
Li H, Yang J, Han Y, Yang CH, Daemen JJK, Li P (2019) Weibull grain-based model (W-GBM) for simulating heterogeneous mechanical characteristics of salt rock. Eng Anal Bound Elem 108:227–243. https://doi.org/10.1016/j.enganabound.2019.09.001
Wang JT, Zuo JP (2020) Numerical simulation on effect of heterogeneity on mode I fracture characteristics of rock. J Cent South Univ 27:3063–3077. https://doi.org/10.1007/s11771-020-4529-1
Li XF, Li HB, Zhao Y (2017) 3D polycrystalline discrete element method (3PDEM) for simulation of crack initiation and propagation in granular rock. Comput Geotech 90:96–112. https://doi.org/10.1016/j.compgeo.2017.05.023
Pakzad R, Wang SY, Sloan SW (2020) Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis. Int J Numer Anal Methods Geomech 44:1472–1494. https://doi.org/10.1002/nag.3071
Li SC, Li GY (2010) Effect of heterogeneity on mechanical and AE characteristics of rock specimen. J Cent South Univ Technol 17:1119–1124. https://doi.org/10.1007/s11771-010-0605-2
Fathipour-Azar H, Wang JF, Jalali SME, Torabi SR (2020) Numerical modeling of geomaterial fracture using a cohesive crack model in grain-based DEM. Comput Part Mech 7:645–654. https://doi.org/10.1007/s40571-019-00295-4
Hu XJ, Xie N, Zhu QZ, Chen L, Li PC (2020) Modeling damage evolution in heterogeneous granite using digital image-based grain-based model. Rock Mech Rock Eng 53:4925–4945. https://doi.org/10.1007/s00603-020-02191-3
Manouchehrian A, Cai M (2016) Influence of material heterogeneity on failure intensity in unstable rock failure. Comput Geotech 71:237–246. https://doi.org/10.1016/j.compgeo.2015.10.004
Xu Y, Yao W, Xia KW (2020) Numerical study on tensile failures of heterogeneous rocks. J Rock Mech Geotech Eng 12:50–58. https://doi.org/10.1016/j.jrmge.2019.10.002
Feng P, Xu Y, Dai F (2021) Effects of dynamic strain rate on the energy dissipation and fragment characteristics of cross-fissured rocks. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2020.104600
Liu Y, Dai F, Pei PD (2021) A wing-crack extension model for tensile response of saturated rocks under coupled static-dynamic loading. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2021.104893
Wu YZ, Sun ZY, Fu YK (2022) Mechanical properties and energy dissipation law of coal samples with different length-diameter ratios under three-dimensional dynamic and static loading. Chin J Rock Mech Eng 41:877–888. https://doi.org/10.13722/j.cnki.jrme.2021.0920
Wang CL, Zhou BK, Li CF, Cao C, Sui QR, Zhao GM, Yu WJ, Chen Z, Wang Y, Liu B, Lu H (2022) Experimental investigation on the spatio-temporal-energy evolution pattern of limestone fracture using AE monitoring. J Appl Geophys. https://doi.org/10.1016/j.jappgeo.2022.104787
Liu PX, Chen SY, Guo YS, Li PC (2014) Moment tensor inversion of AE. Chin J Geophys Chin Ed 57:858–866. https://doi.org/10.6038/cjg20140315
Zafar S, Hedayat A, Moradian O (2022) Evolution of tensile and shear cracking in crystalline rocks under compression. Theor Appl Fract Mech. https://doi.org/10.1016/j.tafmec.2022.103254
Luo Y, Wang G, Li XP, Liu TT, Mandal AK, Xu MN, Xu K (2020) Analysis of energy dissipation and crack evolution law of sandstone under impact load. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2020.104359
Zhou ZL, Zhou J, Zhao Y, Chen LJ, Li CJ (2021) Microscopic failure mechanism analysis of rock under dynamic brazilian test based on ae and moment tensor simulation. Front Phys. https://doi.org/10.3389/fphy.2020.592483
Wang HC, Zhao J, Li J, Wang HJ, Braithwaite CH, Zhang QB (2022) Fracturing and AE characteristics of matrix-inclusion rock types under dynamic Brazilian testing. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2022.105164
Hazzard JF, Young RP (2002) Moment tensors and micromechanical models. Tectonophysics 356:181–197. https://doi.org/10.1016/s0040-1951(02)00384-0
Hazzard JF, Young RP (2004) Dynamic modelling of induced seismicity. Int J Rock Mech Min Sci 41:1365–1376. https://doi.org/10.1016/j.ijrmms.2004.09.005
Baud P, Wong TF, Zhu W (2014) Effects of porosity and crack density on the compressive strength of rocks. Int J Rock Mech Min Sci 67:202–211. https://doi.org/10.1016/j.ijrmms.2013.08.031
Zhai MY, Xue L, Bu FC, Yang BC, Ding H (2022) Microcracking behaviors and AE characteristics of granite subjected to direct shear based on a novel grain-based model. Comput Geotech. https://doi.org/10.1016/j.compgeo.2022.104955
Yoon JS, Stephansson O, Zang A, Min KB, Lanaro F (2017) Discrete bonded particle modelling of fault activation near a nuclear waste repository site and comparison to static rupture earthquake scaling laws. Int J Rock Mech Min Sci 98:1–9. https://doi.org/10.1016/j.ijrmms.2017.07.008
Zhang Q, Zhang XP, Yang SQ (2022) Numerical Study of fracture failure nature around the circular and horseshoe openings using the bonded-particle model. Geophys J Int 232:725–737. https://doi.org/10.1093/gji/ggac360
Bai QS, Konietzky H, Ding ZW, Cai W, Zhang C (2021) A displacement-dependent moment tensor method for simulating fault-slip induced seismicity. Geomech Geophys Geo-Energy Geo-Resour. https://doi.org/10.1007/s40948-021-00269-y
Zhai MY, Xue L, Chen HR, Xu C, Cui Y (2021) Effects of shear rates on the damaging behaviors of layered rocks subjected to direct shear: Insights from AE characteristics. Eng Fract Mech. https://doi.org/10.1016/j.engfracmech.2021.108046
Hu XJ, Bian K, Liu J, Chen M, Cen Y, Liu ZP (2021) Particle flow simulation of the effect of particle size distribution of granite crystal on AE characteristics. J China Coal Soc 46:721–730. https://doi.org/10.13225/j.cnki.jccs.2021.0581
Xu GW, Hu XY, Tang R, Hou ZK (2022) Fracture evolution of transversely isotropic rocks with a pre-existing flaw under compression tests based on moment tensor analysis. Acta Geotech 17:169–203. https://doi.org/10.1007/s11440-021-01214-9
Yuan GT, Zhang MW, Zhang K, Wei J, Tian ZC, Liu BL (2023) Dynamic mechanical response characteristics and cracking behavior of randomly distributed cracked sandstone. Comput Part Mech. https://doi.org/10.1007/s40571-023-00612-y
Bahrani N, Kaiser PK (2016) Numerical investigation of the influence of specimen size on the unconfined strength of defected rocks. Comput Geotech 77:56–67. https://doi.org/10.1016/j.compgeo.2016.04.004
Huang YH, Yang SQ, Tian WL, Wu SY (2022) Experimental and DEM Study on failure behavior and stress distribution of flawed sandstone specimens under uniaxial compression. Theor Appl Fract Mech. https://doi.org/10.1016/j.tafmec.2022.103266
Shi H, Song L, Zhang HQ, Chen WL, Lin HS, Li DQ, Wang GZ, Zhao HY (2022) Experimental and numerical studies on progressive debonding of grouted rock bolts. Int J Min Sci Technol 32:63–74. https://doi.org/10.1016/j.ijmst.2021.10.002
Liu HL, Wang PT, Yang TH, Xu T, Yu QL, Xia D (2015) AE characteristics of granite uniaxial compression fracture process based on discrete element method. J China Coal Soc 40:1790–1795. https://doi.org/10.13225/j.cnki.jccs.2014.1779
Cheng AP, Shu PF, Deng DQ, Zhou CS, Huang SB, Ye ZY (2021) Microscopic AE simulation and fracture mechanism of cemented tailings backfill based on moment tensor theory. Constr Build Mater. https://doi.org/10.1016/j.conbuildmat.2021.125069
Zhao Y, Yang TH, Zhang PH, Xu HY, Wang SH (2020) Inversion of seepage channels based on mining-induced microseismic data. Int J Rock Mech Min Sci 1:26. https://doi.org/10.1016/j.ijrmms.2019.104180
Zhao Y, Zhao GY, Zhou J, Ma J, Cai X (2021) Failure mechanism analysis of rock in particle discrete element method simulation based on moment tensors. Comput Geotech. https://doi.org/10.1016/j.compgeo.2021.104215
Feignier B, Young RP (1992) Moment tensor inversion of induced microseismic events: evidence of non-shear failures in the − 4 < M < − 2 moment magnitude range. Geophys Res Lett 19:1503–1506. https://doi.org/10.1029/92GL01130
Liu YC, Li SL (2021) Tang, Research on the improvement and application of the criterion of the source mechanism solution type of rock mass fracture. Rock Soil Mech 42:1335–1344. https://doi.org/10.16285/j.rsm.2020.1228
Ohtsu M (1995) AE theory for moment tensor analysis. Res Nondestr Eval 6:169–184. https://doi.org/10.1007/BF01606380
Zhao Y, Yang TH, Zhang PH, Xu HY, Zhou JR, Yu QL (2019) Method for generating a discrete fracture network from microseismic data and its application in analyzing the permeability of rock masses: a case study (February, 10.1007/s00603-018-1712-x, 2019). Rock Mech Rock Eng 52:2021–2021. https://doi.org/10.1007/s00603-019-1742-z
Manouchehrian A, Sharifzadeh M, Marji MF, Gholamnejad J (2014) A bonded particle model for analysis of the flaw orientation effect on crack propagation mechanism in brittle materials under compression. Arch Civ Mech Eng 14:40–52. https://doi.org/10.1016/j.acme.2013.05.008
Marji MF (2014) A bonded particle model for analysis of the flaw orientation effect on crack propagation mechanism in brittle materials under compression. Arch Civ Mech Eng 14:40–52. https://doi.org/10.1088/0953-4075/32/13/101
Castro-Filgueira U, Alejano LR, Arzúa J, Ivars DM (2017) Sensitivity analysis of the micro-parameters used in a PFC analysis towards the mechanical properties of rocks. Procedia Eng 191:488–495. https://doi.org/10.1016/j.proeng.2017.05.208
Chen HR, Qin SQ, Xue L (2017) Characterization of rock brittle failure and application range of Weibull distribution. Progress Geophys 32:2200–2206. https://doi.org/10.6038/pg20170548
Li XB, Zou Y, Zhou ZL (2014) Numerical simulation of the rock SHPB test with a special shape striker based on the discrete element method. Rock Mech Rock Eng 47:1693–1709. https://doi.org/10.1007/s00603-013-0484-6
Zhang QB, Zhao J (2014) A review of dynamic experimental techniques and mechanical behaviour of rock materials. Rock Mech Rock Eng 47:1411–1478. https://doi.org/10.1007/s00603-013-0463-y
Xie HP, Li LY, Ju Y, Peng RD, Yang YM (2011) Energy analysis for damage and catastrophic failure of rocks. Sci China Technol Sci 54:199–209. https://doi.org/10.1007/s11431-011-4639-y
Gong FQ, Yan JY, Li XB, Luo S (2019) A peak-strength strain energy storage index for rock burst proneness of rock materials. Int J Rock Mech Min Sci 117:76–89. https://doi.org/10.1016/j.ijrmms.2019.03.020
Zhao TB, Yin YC, Tan YL (2014) Microscopic simulation test of coal rock burst tendency based on particle flow theory. J Res 39:280–285. https://doi.org/10.13225/j.cnki.jccs.2013.2017
Yan ZL, Dai F, Liu Y, Du HB (2020) Experimental investigations of the dynamic mechanical properties and fracturing behavior of cracked rocks under dynamic loading. B Eng Geol Environ 79:5535–5552. https://doi.org/10.1007/s10064-020-01914-8
Haeri H, Sarfarazi V, Fatehi Marji M (2022) Static and dynamic response of rock engineering models. Iran J Sci Technol Trans Civ Eng 46:327–341. https://doi.org/10.1007/s40996-020-00564-w
Wu C, Gong FQ, Luo Y (2021) A new quantitative method to identify the crack damage stress of rock using AE detection parameters. B Eng Geol Environ 80:519–531. https://doi.org/10.1007/s10064-020-01932-6
Liu J, Ma FS, Guo J, Zhou TT, Song YW, Li FR (2022) Numerical simulation of failure behavior of brittle heterogeneous rock under uniaxial compression test. Materials. https://doi.org/10.3390/ma15197035
Lundberg B (1976) A split Hopkinson bar study of energy absorption in dynamic rock fragmentation. Int J Rock Mech Min Sci Geomech Abstr 13:187–197. https://doi.org/10.1016/0148-9062(76)91285-7
Zhang MT, Wang W, Wang QZ (2021) study on dynamic failure process and strain-damage evolution law of sandstone based on SHPB experiment. Explos Shock Waves 41:40–53. https://doi.org/10.11883/bzycj-2020-0288
Zhou X, Xie YJ, Long GC, Zeng XH, Li JT, Li N, Wang F, Umar HA (2023) Influence of end friction confinement on dynamic mechanical properties and damage evolution of concrete by coupled DEM-FDM method. Eng Fract Mech. https://doi.org/10.1016/j.engfracmech.2023.109150
Liu XL, Liu Z, Li XB, Gong FQ, Du K (2020) Experimental study on the effect of strain rate on rock AE characteristics. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2020.104420
Fu JW, Haeri H, Sarfarazi V, Naderi AA, Marji MF, Xu LG (2023) Influence of arch shaped notch angle, length and opening on the failure mechanism of rock like material and acoustic emission properties: experimental test and numerical simulation. Theor Appl Fract Mech. https://doi.org/10.1016/j.tafmec.2023.103879
Yuan GT, Zhang MW, Zhang K, Duan HY, Jia L, Liu BL (2023) Strain rate effect on the fracture evolution of sandstones under quasi-static loading conditions: Insights from acoustic emission characteristics. Eng Fract Mech 290:109465. https://doi.org/10.1016/j.engfracmech.2023.109465
Heinze T, Galvan B, Miller SA (2015) A new method to estimate location and slip of simulated rock failure events. Tectonophysics 651:35–43. https://doi.org/10.1016/j.tecto.2015.03.009
Liu XL, Li XB, Hong L, Yin TB, Rao M (2015) AE characteristics of rock under impact loading. J Cent South Univ 22:3571–3577. https://doi.org/10.1007/s11771-015-2897-8
Guo TY, Zhao Q (2022) AE characteristics during the microcracking processes of granite, marble and sandstone under mode I loading. Rock Mech Rock Eng 55:5467–5489. https://doi.org/10.1007/s00603-022-02937-1
Amini MS, Sarfarazi V, Hoori MM, Jahanmiri S, Wang X (2023) Effects of un-parallel notches on the granite fracture properties and acoustic emission phenomena under biaxial test: PFC computation and experimental verification. Mech Adv Mater Struct. https://doi.org/10.1080/15376494.2023.2207179
Li BQ, Einstein HH (2020) Normalized radiated seismic energy from laboratory fracture experiments on opalinus clayshale and barre granite. J Geophys Res-Sol Earth. https://doi.org/10.1029/2019JB018544
Zhang H, Chen L, Chen SG, Sun JC, Yang JS (2018) The spatiotemporal distribution law of microseismic events and rockburst characteristics of the deeply buried tunnel group. Energies. https://doi.org/10.3390/en11123257
Lu CP, Dou LM, Wang YF, Du JT (2010) Microseismic effect of coal burst failure induced by hard roof. Chin J Geophys 53:450–456. https://doi.org/10.3969/j.issn.0001-5733.2010.02.024
Jiang FX, Ye GX, Wang CW, Zhang DY (2008) Application of high precision microseismic monitoring technology in coal mine water inrush monitoring. Chin J Rock Mech Eng 202:1932–1938. https://doi.org/10.3321/j.issn:1000-6915.2008.09.023
Acknowledgements
Financial supports from the National Natural Science Foundation of China (No. 52074260); Fundamental Research Funds for the Central Universities of China (No. 2019QNA26).
Author information
Authors and Affiliations
Contributions
GY did conceptualization, methodology, investigation, data curation, validation, formal analysis, and writing. MZ done conceptualization, methodology, writing, and supervision. KZ was involved in methodology, investigation, and data curation. Zhuangcai Tian supervised and validated the study. HD done methodology and investigation. BL investigated the study.
Corresponding author
Ethics declarations
Conflict of 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.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Yuan, G., Zhang, M., Zhang, K. et al. Mechanical response and AE characteristics of heterogeneous rock under dynamic compression tests based on moment tensor analysis. Comp. Part. Mech. 11, 815–838 (2024). https://doi.org/10.1007/s40571-023-00655-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40571-023-00655-1