Skip to main content

Advertisement

SpringerLink
Log in

Effects of Loading Rate on Rockburst Proneness of Granite from Energy Storage and Surplus Perspectives

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

Rockburst is a kind of rock failure phenomenon during which the internal elastic strain energy of surrounding rock mass is released dynamically under external load, and the loading rate is an essential influencing factor of potential for bursting. To investigate the effects of loading rate on rockburst proneness from energy storage and surplus perspectives, conventional uniaxial compression tests are conducted on granite under four orders of magnitude loading rate. The failure process and mode of granite specimens were recorded in real time with a high-speed camera with microsecond shooting speed. The variation trend of the internal elastic strain energy of granite specimens under four loading rates was obtained by performing the single-cycle loading–unloading uniaxial compression test. The experimental results show that the elastic strain energy linearly increases as the input strain energy increases under each loading rate, which meet the linear energy storage law. Based on the linear energy storage law, the peak elastic strain energy of each granite specimen can be accurately obtained. According to the mass and range of ejected rock debris after specimen failure, the bursting liability of each specimen was evaluated by the far-field ejection mass ratio (MF) from a qualitative point of view. Meanwhile, the residual elastic energy index (AEF) and the other three criteria were used to evaluate the potential for bursting of granite specimens under different loading rates. The comparison results show the rockburst proneness of granite specimens increases with the loading rate and that the evaluation results of MF and AEF are unified from qualitative and quantitative aspects, respectively. The fundamental reason for the consistent results is that these two indexes have a common essence of elastic strain energy release.

Highlights

  • The mechanical properties of granite are significantly influenced by loading rate.

  • The loading rate does not affect the existence of linear energy storage law and the compression energy storage coefficient is independent of loading rate.

  • The rockburst liability of granite increases with the loading rate.

  • At different loading rates, the far-field ejection mass ratio and residual elastic energy index offer consistent qualitative and quantitative evaluations for the rockburst proneness of granite.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Abbreviations

\(\sigma_{{\text{c}}}\) :

Peak strength

\(k\) :

Preset unloading stress level

\(i\) :

Actual unloading stress level

\(\sigma_{{\text{c}}}^{k}\) :

Peak strength of specimens with preset unloading stress level k

\(k\sigma_{{\text{c}}}\) :

Preset unloading stress

\(u_{{\text{i}}}\) :

Input strain energy

\(u_{{\text{d}}}\) :

Dissipated strain energy

\(u_{{\text{e}}}\) :

Elastic strain energy

\(u_{{\text{a}}}\) :

Post-failure strain energy

\(u_{{\text{i}}}^{i}\) :

Input strain energy at the actual unloading stress level i

\(u_{{\text{e}}}^{i}\) :

Elastic strain energy at the actual unloading stress level i

\(u_{{\text{d}}}^{i}\) :

Dissipated strain energy at the actual unloading stress level i

\(u_{{\text{i}}}^{{\text{p}}}\) :

Peak input strain energy, that is, input strain energy at peak strength

\(u_{{\text{e}}}^{{\text{p}}}\) :

Peak elastic strain energy, that is, elastic strain energy at peak strength

\(u_{{\text{d}}}^{{\text{p}}}\) :

Peak dissipated strain energy, that is, dissipated strain energy at peak strength

\(\varepsilon_{0}\) :

Permanent strain after unloading

\(\varepsilon_{{\text{u}}}\) :

Strain at unloading point

\(\varepsilon_{{\text{p}}}\) :

Peak strain

\(\varepsilon_{{\text{a}}}\) :

Total strain

\(v\) :

Experimental loading velocity

\(\dot{\sigma }\) :

Loading rate

\(\dot{\varepsilon }\) :

Strain rate

\(E\) :

Elastic modulus

a :

Compression energy storage coefficient

b :

Fitting coefficient

c :

Compression energy dissipation coefficient

\(A_{{{\text{EF}}}}\) :

Residual elastic energy index

\(M_{{\text{F}}}\) :

Far-field ejection mass ratio

\({\text{PES}}^{{\text{P}}}\) :

Peak-strength potential energy of elastic strain

\(A_{{{\text{CF}}}}^{^{\prime}}\) :

Peak-strength energy impact index

\(W_{{{\text{et}}}}^{{\text{p}}}\) :

Peak-strength strain energy storage index

CoV:

Coefficient of variation

\(\beta\) :

Standard deviation

\(\mu\) :

Average value

UC:

Uniaxial compression

SCLUC:

Single-cycle loading–unloading uniaxial compression

ISE:

Input strain energy

ESE:

Elastic strain energy

DSE:

Dissipated strain energy

LES:

Linear energy storage

LED:

Linear energy dissipation

ESC:

Compression energy storage coefficient

EDC:

Compression energy dissipation coefficient

ULES:

Unified linear energy storage

ULED:

Unified linear energy dissipation

References

  • Chen GQ, Feng XT, Zhang CQ, Jiang Q, Su GS (2008) Research on prevention measures for failure induced by tunneling in deep hard rock. Chin J Rock Mech Eng 27(10):2064–2071

    Google Scholar 

  • Chen ZY, Su GS, Woody JuJ, Jiang JQ (2019) Experimental study on energy dissipation of fragments during rockburst. B Eng Geol Environ 78(7):5369–5386

    Google Scholar 

  • Cook NGW (1963) The basic mechanics of rockbursts. J S Afr I Min Metall 64(3):71–81.

  • Cook NGW (1965) A note on rockbursts considered as a problem of stability. J S Afr I Min Metall 65:437–446

    Google Scholar 

  • Diederichs MS, Kaiser PK, Eberhardt E (2004) Damage initiation and propagation in hard rock during tunnelling and the influence of nearface stress rotation. Int J Rock Mech Min Sci 41:785–812

    Google Scholar 

  • Fairhurst CE, Hudson JA (1999) Draft ISRM suggested method for the complete stress–strain curve for intact rock in uniaxial compression. Int J Rock Mech Min Sci 36(3):279–289

    Google Scholar 

  • Feng XT, Chen BR, Ming HJ, Zhou H, Zeng XH, Feng GL, Xiao YX (2012) Evolution law and mechanism of rockbursts in deep tunnels: Immediate rockburst. Chin J Rock Mech Eng 31(3):433–444

    Google Scholar 

  • Feng GL, Feng XT, Chen BR, Xiao YX, Yu Y (2015) A microseismic method for dynamic warning of rockburst development processes in tunnels. Rock Mech Rock Eng 48(5):2061–2076

    Google Scholar 

  • Gong FQ, Luo S, Yan JY (2018a) Energy storage and dissipation evolution process and characteristics of marble in three tension-type failure tests. Rock Mech Rock Eng 51:3613–3624

    Google Scholar 

  • Gong FQ, Wang J, Li XB (2018b) The rate effect of compression characteristics and a unified model of dynamic increasing factor for rock materials. Chin J Rock Mech Eng 37(7):1586–1595

    Google Scholar 

  • Gong FQ, Yan JY, Li XB (2018c) A new criterion of rock burst proneness based on the linear energy storage law and the residual elastic energy index. Chin J Rock Mech Eng 37(9):1993–2014

    Google Scholar 

  • Gong FQ, Yan JY, Li XB, Luo S (2019a) A peak-strength strain energy storage index for rock burst proneness of rock materials. Int J Rock Mech Min Sci 117:76–89

    Google Scholar 

  • Gong FQ, Yan JY, Luo S, Li XB (2019b) Investigation on the linear energy storage and dissipation laws of rock materials under uniaxial compression. Rock Mech Rock Eng 52(11):4237–4255

    Google Scholar 

  • Gong FQ, Wang YL, Luo S (2020) Rockburst proneness criteria for rock materials: review and new insights. J Cent South Univ 27(10):2793–2821

    Google Scholar 

  • Gong FQ, Wang YL, Wang ZG, Pan JF, Luo S (2021) A new criterion of coal burst proneness based on the residual elastic energy index. Int J Min Sci Techno 31(4):553-563

    Google Scholar 

  • Gong FQ, Luo S, Jiang Q, Xu L (2022a) Theoretical verification of the rationality of strain energy storage index as rockburst criterion based on linear energy storage law. J Rock Mech Geotech. https://doi.org/10.1016/j.jrmge.2021.12.015

    Article  Google Scholar 

  • Gong FQ, Shi RH, Xu L (2022) Linear energy storage and dissipation laws of concrete under uniaxial compression at different ages. Constr Build Mater 318: 125963

  • Gong FQ, Zhao YJ, Wang YL, Peng K (2022b) Research progress of coal bursting liability indices and coal burst “Human-Coal-Environment” three elements mechanism. J Chin Coal Soc 47(5):1976–2010

    Google Scholar 

  • Hashiba K, Fukui K (2015) Index of loading-rate dependency of rock strength. Rock Mech Rock Eng 48(2):859–865

    Google Scholar 

  • He MC, Zhao F, Du S, Zheng MJ (2014) Rockburst characteristics based on experimental tests under different unloading rates. Rock Soil Mech 35(10):2737–2747 (2793)

    Google Scholar 

  • He MM, Zhang ZQ, Zhu JW, Li N, Li G, Chen YS (2021) Correlation between the rockburst proneness and friction characteristics of rock materials and a new method for rockburst proneness prediction: Field demonstration. J Pet Sci Eng 205:10899

    Google Scholar 

  • Hu F, Chen JZ, Li CY (2019) Experiment study on rockburst of granite roadway under the loading rate effect. Min Metall 28(4):7–23

    Google Scholar 

  • Huang BX, Liu ZW (2013) The effect of loading rate on the behavior of samples composed of coal and rock. Int J Rock Mech Min Sci 61:23–30

    Google Scholar 

  • Jia HY (2021) Study on size effect and loading rate effect of energy storage and dissipation law during uniaxial experiment. Changsha, Central South University, China

    Google Scholar 

  • Jiang BY, Gu ST, Wang LG, Zhang GC, Li WS (2019) Strainburst process of marble in tunnel-excavation-induced stress path considering intermediate principal stress. J Cent South Univ 26(4):984–999

    Google Scholar 

  • Keneti A, Sainsbury BA (2018) Review of published rockburst events and their contributing factors. Eng Geol 246:361–373

    Google Scholar 

  • Kidybinski A (1981) Bursting liability indices of coal. Int J Rock Mech Min Sci 18(6):295–304

    Google Scholar 

  • Li CC (2021) Principles and methods of rock support for rockburst control. J Rock Mech Geotech. https://doi.org/10.1016/j.jrmge.2020.11.001

    Article  Google Scholar 

  • Li SL, Feng XT, Wang YJ, Yang NG (2001) Evaluation of rockburst proneness in a deep hard rock mine. J Northeastern Univ (nat Sci) 22(1):60–63

    Google Scholar 

  • Li XB, Lok TS, Zhao J (2005) Dynamic characteristics of granite subjected to intermediate loading rate. Rock Mech Rock Eng 38(1):21–39

    Google Scholar 

  • Li ZJ, Zhang L, Li Q, Chen HJ (2021) Influence of loading rates under true triaxial stress on the mechanical properties and rockburst characteristics of granite. Arab J Geosci 14(24):2850

    Google Scholar 

  • Liang CY, Li X, Wang SX, Li SD, Hao JM, Ma CF (2012) Experimental investigations on rate-dependent stress–strain characteristics and energy mechanism of rock under uniaxial compression. Chin J Rock Mech Eng 31(9):1830–1838

    Google Scholar 

  • Liu P, Yu B, Cao H (2021) Study on the countermeasures for the prevention and control of rock burst in the over-kilometer shaft. Nonferr Metal Eng 11(1):92–100

    Google Scholar 

  • Luo S, Gong FQ (2020a) Linear energy storage and dissipation laws of rocks under preset angle shear conditions. Rock Mech Rock Eng 53:3303–3323

    Google Scholar 

  • Luo S, Gong FQ (2020b) Linear energy storage and dissipation laws during rock fracture under three-point flexural loading. Eng Fract Mech 234:107102

    Google Scholar 

  • Miao SJ, Cai MF, Guo QF, Huang ZJ (2016) Rock burst prediction based on in-situ stress and energy accumulation theory. Int J Rock Mech Min Sci 83:86–94

    Google Scholar 

  • Ortlepp WD, Stacey TR (1994) Rockburst mechanisms in tunnels and shafts. Tunn Undergr Sp Tech 9(1):59–65

    Google Scholar 

  • Si XF, Huang LQ, Gong FQ, Liu XL, Li XB (2020) Experimental investigation on influence of loading rate on rockburst in deep circular tunnel under true-triaxial stress condition. J Cent South Univ 27(10):2914–2929

    Google Scholar 

  • Singh SP (1987) The influence of rock properties on the occurrence and control of rockbursts. Min Sci Tech 5:11–18

    Google Scholar 

  • Singh SP (1988) Burst energy release index. Rock Mech Rock Eng 21:149–155

    Google Scholar 

  • Singh SP (1989) Classification of mine workings according to their rockburst proneness. Min Sci Tech 8:253–262

    Google Scholar 

  • Su GS, Jiang JQ, Feng XT, Jiang Q, Chen ZY, Mo JH (2019) Influence of loading rate on strainburst: an experimental study. B Eng Geol Environ 78(5):3559–3573

    Google Scholar 

  • Tan YA (1992) Discussion on the energy impact index of rockburst. Hydroge Eng Geol 19(2):10–12

    Google Scholar 

  • Tang LZ, Wang WX (2002) New rock burst proneness index. Chin J Rock Mech Eng 21(6):874–878

    Google Scholar 

  • Wang JA, Park HD (2001) Comprehensive prediction of rockburst based on analysis of strain energy in rocks. Tunn Undergr Sp Tech 16(1):49–57

    Google Scholar 

  • Wang YH, Chen LW, Shen F (2008) Numerical modeling of energy release in rockburst. Rock Soil Mech 29(3):790–794

    Google Scholar 

  • Wang SM, Zhou J, Li CQ, Danial JA, Li XB, Hani SM (2021) Rockburst prediction in hard rock mines developing bagging and boosting tree-based ensemble techniques. J Cent South Univ 28(2):527–542

    Google Scholar 

  • Xie HP, Ju Y, Li LY (2005) Criteria for strength and structural failure of rocks based on energy dissipation and energy release principles. Chin J Rock Mech Eng 24(17):3003–3010

    Google Scholar 

  • Xu LS, Wang LS, Li TB (1999) Present situation of rockburst research at home and abroad. J Yangtze River Sci Res Inst 16(4):25–28 (39)

    Google Scholar 

  • Xu C, Liu XL, Wang EZ, Zheng YL, Wang SJ (2018) Rockburst prediction and classification based on the ideal-point method of information theory. Tunn Undergr Sp Tech 81:382–390

    Google Scholar 

  • Xu L, Gong FQ, Liu ZX (2021) Experiments on rockburst proneness of pre-heated granite at different temperatures: Insights from energy storage, dissipation and surplus. J Rock Mech Geotech. https://doi.org/10.1016/j.jrmge.2021.08.004

    Article  Google Scholar 

  • Zhang JJ, Fu BJ (2008) Rockburst and its criteria and control. Chin J Rock Mech Eng 27(10):2034–2042

    Google Scholar 

  • Zhang QB, Zhao J (2014) A review of dynamic experimental techniques and mechanical behaviour of rock materials. Rock Mech Rock Eng 47(4):1411–1478

    Google Scholar 

  • Zhao XG, Wang J, Cai M (2014) Influence of unloading rate on the strainburst characteristics of Beishan granite under true-triaxial unloading conditions. Rock Mech Rock Eng 47(2):467–483

    Google Scholar 

  • Zhao K, Yu X, Zhou Y, Wang Q, Wang JQ, Hao JL (2020) Energy evolution of brittle granite under different loading rates. Int J Rock Mech Min Sci 132:104392

    Google Scholar 

  • Zhou YQ, Sheng Q, Li NN, Fu XD (2020) The influence of strain rate on the energy characteristics and damage evolution of rock materials under dynamic uniaxial compression. Rock Mech Rock Eng 53(8):3823–3834

    Google Scholar 

  • Zhu ZF (1985) Rigidity testing machine. Beijing, China Coal Industry Publishing House

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 42077244), the Open Research Fund of State Key Laboratory of Deep Earth Science and Engineering (Sichuan University) (Grant No.DESE 202201) and the Fundamental Research Funds for the Central Universities (Grant No. 2242022k30054).

Author information

Authors and Affiliations

  1. Engineering Research Center of Safety and Protection of Explosion & Impact of Ministry of Education (ERCSPEIME), Southeast University, Nanjing, 211189, China

    Fengqiang Gong

  2. Southeast University-Monash University Joint Graduate School, Southeast University, Suzhou, 215123, Jiangsu, China

    Fengqiang Gong & Yuxin Ni

  3. Key Laboratory of Deep Earth Science and Engineering (Sichuan University), Ministry of Education, Chengdu, 610065, China

    Fengqiang Gong & Li Ren

Authors
  1. Fengqiang Gong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuxin Ni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Li Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fengqiang Gong.

Ethics declarations

Conflict of interest

We would like to declare that the work described is original research that has not been published previously, and is not under consideration for publication elsewhere, in whole or in part. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. The manuscript is approved by all authors for publication.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gong, F., Ni, Y. & Ren, L. Effects of Loading Rate on Rockburst Proneness of Granite from Energy Storage and Surplus Perspectives. Rock Mech Rock Eng 55, 6495–6516 (2022). https://doi.org/10.1007/s00603-022-02990-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-022-02990-w

Keywords

Search

Navigation