A model for non-linear rock deformation under compression due to sub-critical crack growth

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Abstract

Time dependency in rock deformation under compression is modelled by considering an elastic body containing cracks that grow under compressive stresses due to sub-critical crack growth. This is considered the prime mechanism for the time-dependent deformation of brittle rocks at low temperatures. The growth of cracks under compressive stresses is formulated using the "sliding crack" model, which considers extensile crack growth due to stress concentrations around pre-existing flaws. Subcritical crack growt is included into the sliding crack model by utilizing the empirical Charles power law relation between crack velocity and the crack tip stress intensity factor. The model is able to predict the dependence of the stress-strain curve on the applied strain rate, and agrees extremely well with experimental data. Also, the model is able to predict the occurrence of both transient and tertiary creep. The transient creep behavior is derived in closed-form, and is found to give creep that depends on the logarithm of time, which is similar to many empirical formulae for creep in brittle rocks. Tertiary creep in the model is due to crack interaction, and is found to occur at a critical value of crack density. This allows time-to-failure predictions to be made, which could be useful for underground structures required to remain open for long periods of time.

Original languageEnglish (US)
Pages (from-to)459-467
Number of pages9
JournalInternational Journal of Rock Mechanics and Mining Sciences and
Volume28
Issue number6
DOIs
StatePublished - 1991

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Crack propagation
crack
Compaction
compression
Rocks
Cracks
Creep
rock
creep
Compressive stress
Underground structures
sliding
Stress-strain curves
Stress intensity factors
Crack tips
Stress concentration
Strain rate
strain rate
Defects
power law

ASJC Scopus subject areas

  • Economic Geology
  • Earth and Planetary Sciences(all)
  • Environmental Science(all)
  • Engineering(all)

Cite this

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title = "A model for non-linear rock deformation under compression due to sub-critical crack growth",
abstract = "Time dependency in rock deformation under compression is modelled by considering an elastic body containing cracks that grow under compressive stresses due to sub-critical crack growth. This is considered the prime mechanism for the time-dependent deformation of brittle rocks at low temperatures. The growth of cracks under compressive stresses is formulated using the {"}sliding crack{"} model, which considers extensile crack growth due to stress concentrations around pre-existing flaws. Subcritical crack growt is included into the sliding crack model by utilizing the empirical Charles power law relation between crack velocity and the crack tip stress intensity factor. The model is able to predict the dependence of the stress-strain curve on the applied strain rate, and agrees extremely well with experimental data. Also, the model is able to predict the occurrence of both transient and tertiary creep. The transient creep behavior is derived in closed-form, and is found to give creep that depends on the logarithm of time, which is similar to many empirical formulae for creep in brittle rocks. Tertiary creep in the model is due to crack interaction, and is found to occur at a critical value of crack density. This allows time-to-failure predictions to be made, which could be useful for underground structures required to remain open for long periods of time.",
author = "Kemeny, {John M}",
year = "1991",
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N2 - Time dependency in rock deformation under compression is modelled by considering an elastic body containing cracks that grow under compressive stresses due to sub-critical crack growth. This is considered the prime mechanism for the time-dependent deformation of brittle rocks at low temperatures. The growth of cracks under compressive stresses is formulated using the "sliding crack" model, which considers extensile crack growth due to stress concentrations around pre-existing flaws. Subcritical crack growt is included into the sliding crack model by utilizing the empirical Charles power law relation between crack velocity and the crack tip stress intensity factor. The model is able to predict the dependence of the stress-strain curve on the applied strain rate, and agrees extremely well with experimental data. Also, the model is able to predict the occurrence of both transient and tertiary creep. The transient creep behavior is derived in closed-form, and is found to give creep that depends on the logarithm of time, which is similar to many empirical formulae for creep in brittle rocks. Tertiary creep in the model is due to crack interaction, and is found to occur at a critical value of crack density. This allows time-to-failure predictions to be made, which could be useful for underground structures required to remain open for long periods of time.

AB - Time dependency in rock deformation under compression is modelled by considering an elastic body containing cracks that grow under compressive stresses due to sub-critical crack growth. This is considered the prime mechanism for the time-dependent deformation of brittle rocks at low temperatures. The growth of cracks under compressive stresses is formulated using the "sliding crack" model, which considers extensile crack growth due to stress concentrations around pre-existing flaws. Subcritical crack growt is included into the sliding crack model by utilizing the empirical Charles power law relation between crack velocity and the crack tip stress intensity factor. The model is able to predict the dependence of the stress-strain curve on the applied strain rate, and agrees extremely well with experimental data. Also, the model is able to predict the occurrence of both transient and tertiary creep. The transient creep behavior is derived in closed-form, and is found to give creep that depends on the logarithm of time, which is similar to many empirical formulae for creep in brittle rocks. Tertiary creep in the model is due to crack interaction, and is found to occur at a critical value of crack density. This allows time-to-failure predictions to be made, which could be useful for underground structures required to remain open for long periods of time.

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