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Features of the Energy Balance and Fragmentation Mechanisms at Spontaneous Failure of Class I and Class II Rocks

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Abstract

Practically, all types of rockbursts are accompanied by release of seismic energy, rock bulking (due to fracturing and fragmentation), and ejection of fragmented rocks in the opening. Principles of the energy redistribution during rockbursts in some regards are comparable with principles taking place at spontaneous failure of rock specimens under compression in loading systems. In both cases, the total potential elastic energy accumulated in the failing material and in the loading system (or surrounding rock mass) is converted into such components of dynamic energy as rupture energy, seismic energy (or energy of oscillation of the loading system due to dynamic energy release), and kinetic energy of flying fragments of the failed material. It is known that spontaneous failure takes place at the post-peak failure stage and is determined by the ratio between stiffness of the loading system and stiffness (or brittleness) of the failing material. However, principles of the energy redistribution between different components of the energy balance are still unclear. The paper discusses results of laboratory experiments conducted on rock specimens of different brittleness (including Class I and Class II) that were loaded in testing machines of different loading stiffness. The most brittle of the tested specimens are represented by quartzite and glass, and the less brittle by salt. The loading stiffness of testing machines used in experiments was variable within three decimal orders of magnitude. The specific variations of the dynamic energy balance depending on rock brittleness and loading stiffness were established. The role of each portion of elastic energy stemming from the specimen and from the loading system in determining the dynamic energy balance and fragmentation mechanisms operating at spontaneous failure is analysed. The results obtained contribute to the understanding of dynamic processes taking place during rockbursts.

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Abbreviations

E :

Elastic modulus

M :

Post-peak modulus

σ :

Axial stress

ε :

Axial strain

F :

Axial force

d :

Axial displacement

W e :

Elastic energy stored in the specimen at the peak stress

W r :

Total post-peak rupture energy

W r.in :

Internal component of static post-peak rupture energy

W r.ex :

External component of static post-peak rupture energy

∆W r(d) :

Dynamic increment of the post-peak rupture energy

W d :

Surplus elastic energy responsible for dynamics

W k :

Kinetic energy of rock fragments

W se :

Seismic energy

dW e :

Total elastic energy withdrawn from the specimen during post-peak failure

dW a :

Elastic energy released during spontaneous failure

m o :

Inertial mass of the specimen

m H :

Inertial mass of the loading system

K 1 :

Brittleness index

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Acknowledgements

The authors acknowledge the support provided by the Centre for Offshore Foundation Systems (COFS) at the University of Western Australia.

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Authors and Affiliations

  1. Centre for Offshore Foundation Systems, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Boris G. Tarasov

  2. School of Mining Engineering, University of the Witwatersrand, Private Bag 3, Johannesburg, 2050, South Africa

    Thomas R. Stacey

Authors
  1. Boris G. Tarasov
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  2. Thomas R. Stacey
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Corresponding author

Correspondence to Boris G. Tarasov.

Appendix

Appendix

See Fig. 22.

Fig. 22
figure 22

Stress–strain curves obtained at different strain rates for 1 marble, 2 granite, 3 sandstone-1, 4 sandstone-2, 5 sulphide ore, 6 lignite, 7 rock salt, 8 sylvinite. During each test constant, strain rate was provided before and after peak stress. The magnitude of strain rate \(\acute{\varepsilon}_1\) for each stress–strain curve is presented in the table (from Stavrogin and Tarasov 2001)

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Tarasov, B.G., Stacey, T.R. Features of the Energy Balance and Fragmentation Mechanisms at Spontaneous Failure of Class I and Class II Rocks. Rock Mech Rock Eng 50, 2563–2584 (2017). https://doi.org/10.1007/s00603-017-1251-x

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