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An Instability Line for Spalling Around Circular Openings and the Limiting Effects of Scale

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Abstract

Depending on the type of failure mechanism, the strength of intact rock may be susceptible to the effects of scale. The influence of scale is apparent in the spalling of rock around underground openings. To reconcile field-scale observations, an understanding of the unconfined rock strength has to be appreciated from the standpoint of energy instability, particularly for instances in which the mechanism of failure involves propagation of fractures. Fracture energy principles were used to create a link between laboratory-measured uniaxial compressive strength (UCS) and rock failure as observed in spalling around circular openings. An Instability Line (IL) is proposed to predict the stresses above which spalling could occur with different opening diameters. Good comparisons were obtained for a range of dimensions from small boreholes to large tunnels. Based on field observations and analytical study, the results suggest that two conditions are required for spalling to occur. The first is that the crack initiation stress has to be exceeded, and the second is that the stress needs to be above the IL. The findings suggest that the effects of scale are limited by the crack initiation stress. For large-diameter openings, instability occurs immediately at crack initiation stress, whereas for smaller-diameter openings instability occurs at higher stresses post-crack initiation stress.

Highlights

  • This paper aims to explain the discrepancies in the rock mechanics literature to predict spalling for small-diameter boreholes as against large-diameter tunnels.

  • The failure mechanism of spalling is studied based on the framework of energy stability. An Instability Line is proposed based on the analytical study.

  • The results of the analytical study compared well with published laboratory and field observations.

  • The results suggest that two conditions are required for spalling to occur. The first is that the crack initiation stress has to be exceeded, and the second is that the stress needs to be above the Instability Line.

  • The findings suggest that the effects of scale are limited by the crack initiation stress.

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Abbreviations

σ ci :

Crack initiation stress

σ cd :

Crack damage stress

σ max :

Maximum stress

σ θθ :

Tangential stress at borehole wall

σ il :

Stress threshold for instability

τ :

Shear stress

τ oct :

Octahedral shear stress

ϕ :

Friction angle

γ :

Specific surface energy

v :

Poisson’s ratio

db:

Half-length of microcracks

c :

Half-crack length

D :

Scale

db:

Half-length of microcrack

h :

Efficiency parameter

k :

Factor to maximum stress for driving stress

R :

Radius of circular opening

UCS:

Uniaxial compressive strength

E :

Young’s modulus

G :

Shear modulus

IL:

Instability Line

J 2 :

Second deviatoric stress invariant

\(\Delta P\) :

Energy release

U :

Energy stored around a crack

W :

Energy demand or absorbed

W D :

Limiting distortional energy

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Acknowledgements

The views in this paper are those of the author and not the affiliated organization. Discussions with the late Professor John Hudson in 2013 on his views of a rock failure criterion are acknowledged.

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  1. Gamuda Engineering Sdn Bhd, 47820, Petaling Jaya, Selangor, Malaysia

    Chia Weng Boon

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Boon, C.W. An Instability Line for Spalling Around Circular Openings and the Limiting Effects of Scale. Rock Mech Rock Eng 55, 5759–5772 (2022). https://doi.org/10.1007/s00603-022-02943-3

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