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Influence of Loading System Stiffness on Post-peak Stress–Strain Curve of Stable Rock Failures

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Abstract

It is well known from laboratory testing that the rock failure process becomes unstable in a soft test machine due to excessive energy released from the machine. Great efforts had been devoted to increasing the loading system stiffness (LSS) of laboratory test machines to ensure that the post-peak stress–strain curve of rock can be obtained for underground rock engineering design. A comprehensive literature review on the development of stiff test machines reveals that because of the differences in the manufacturing arrangement of the test machines, LSS values of the test machines used for rock property testing are always finite and vary in a large range, and the influence of LSS on stable rock failure is less understood. A FEM-based numerical experiment is carried out to study the influence of LSS on the stress–strain curves of stable rock failure in uniaxial compression, with a focus on the post-peak deformation stage. Three test machine loadings including idealized rigid loading, platen loading, and frame–platen loading with finite LSS are considered, and the simulation results are analyzed and compared. The modeling results obtained from the simulations indicate that even if the LSS value is large enough to inhibit unstable rock failure, as long as LSS is finite, it has an influence on the post-peak stress–strain curve of rock. It is revealed that because the input energy supplied by the external energy source to drive the stable rock failure process is affected by the finite LSS of a test machine, the post-peak descending slopes of the stress–strain curves are all steeper than the post-peak descending slope obtained under an ideal loading condition of infinite LSS. An insight from this numerical experiment is that it might be more feasible to develop laboratory test machines with variable LSS that can match the local mine stiffness in the field for rock property testing.

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Notes

  1. Note that the displacement rate applied using an explicit algorithm for solving quasi-static problems is not comparable to that used real rock testing because it is computationally impractical to model the loading process in its physical time when the explicit algorithm is used. Instead, an optimal displacement rate was selected through a parametric study to ensure that the computation is cost-effective by increasing the displacement rate, while it does not cause serious oscillation that normally leads to dynamic loading to the specimen.

  2. Note that no loading components other than the thermal loading platen are defined with the thermal property for heat conduction; thus, there is no heat conduction between the thermal platen and the specimen.

Abbreviations

A :

Cross-sectional area

δ :

Displacement

E in :

Accumulative energy input from an external energy source at peak load

E t :

Energy stored in a test machine at peak load

E r :

Accumulative energy consumed in a rock specimen at peak load

E *in :

Accumulative energy input from an external energy source at the post-peak deformation stage

E *t :

Energy stored in a test machine at the post-peak deformation stage

E *r :

Accumulative energy consumed in a rock specimen at the post-peak deformation stage

ΔE in :

Energy input from an external energy source during post-peak deformation

ΔE t :

Energy released from a test machine during post-peak deformation

ΔE r :

Energy consumed in a rock specimen during post-peak deformation

ΔE Br :

Energy item ΔE r under the ideal loading condition

E p :

Post-peak stiffness of a rock specimen in stress–strain curve

H :

Height

k :

Stiffness of a column-shaped structure

λ :

Post-peak stiffness of a rock specimen

LSSP :

Stiffness of a platen loading test machine

LSSF :

Stiffness of a frame–platen loading test machine

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Acknowledgements

This work was financially supported by NSERC (Natural Science and Engineering Research Council of Canada, Grant No. 249620-2011) and the Open Research Fund of the State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (Grant No. Z015001).

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Authors and Affiliations

  1. Bharti School of Engineering, Laurentian University, Sudbury, ON, P3E 2C6, Canada

    Y. H. Xu & M. Cai

  2. MIRARCO, Laurentian University, Sudbury, ON, P3E 2C6, Canada

    Y. H. Xu & M. Cai

  3. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, China

    M. Cai

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  1. Y. H. Xu
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Xu, Y.H., Cai, M. Influence of Loading System Stiffness on Post-peak Stress–Strain Curve of Stable Rock Failures. Rock Mech Rock Eng 50, 2255–2275 (2017). https://doi.org/10.1007/s00603-017-1231-1

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