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Creep and Long-Term Permeability of a Red Sandstone Subjected to Cyclic Loading After Thermal Treatments

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A Correction to this article was published on 24 September 2018

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Abstract

Long-term experiments were performed on red sandstones after different thermal treatments (25, 300, 700 and 1000 °C) under multi-step loading and unloading cycles and a confining pressure of 25 MPa. Furthermore, to quantitatively analyse the temperature influence on the deformation behaviours of the specimens, the concept of the temperature–strain rate was proposed to describe the relationship between strain and temperature, and the experimental results were corrected to identical temperatures (i.e., 20 °C), to overcome the influence of periodic fluctuations in ambient temperature. The results show that the axial mean temperature–strain rate first increased as temperature increased from 25 to 300 °C and then decreased with increasing temperature, whereas the lateral mean temperature–strain rate decreased with increasing temperature. The total strain was divided into the instantaneous elastic strain, the instantaneous plastic strain, the visco-elastic strain and the visco-plastic strain. The total axial strain increased with increasing deviatoric stress, and the irrecoverable strain increased with increasing loading and unloading history. Furthermore, the total axial strain increased with increasing temperature; specifically, at 1000 °C, it was approximately two times that at 700 °C and three times those at 25 and 300 °C. The instantaneous elastic strain and the instantaneous plastic strain increased approximately linearly with increasing deviatoric stress, whereas the creep strain varied with deviatoric stress in complicated ways at different temperatures. However, under identical deviatoric stress, the instantaneous elastic strain and the instantaneous plastic strain increased slightly as temperature increased from 25 to 700 °C and then increased substantially as temperature reached 1000 °C, whereas the variations in the creep strain, the visco-elastic strain and the visco-plastic strain were dependent on temperature and stress level. Finally, the permeability first decreased slightly as temperature increased from 25 to 300 °C and then increased with increasing temperature.

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Change history

  • 24 September 2018

    In Figs. 14 and 15, the unit (m2) of permeability (k) is mistaken, which should be replaced with (10− 6 m2).

Abbreviations

AE:

Acoustic emission

A :

Sample cross-sectional area

A, B, m :

Fitting parameters

C 1 :

Volume of upstream reservoir

C 2 :

Volume of downstream reservoir

E me :

Instantaneous elastic modulus

E mp :

Instantaneous plastic modulus

k :

Permeability

L :

Sample length

P 3(t):

Upstream gas pressure at time t

P 4(t):

Downstream gas pressure at time t

\(P_{3}^{0}\) :

Initial upstream gas pressure

\(P_{4}^{0}\) :

Initial downstream gas pressure

P e :

Effective porosity

SEM:

Scanning electron microscopy

t :

Time

V :

Sample volume at high temperature

V 0 :

Sample volume at 25 °C

XRD:

X-ray diffraction

Δk u :

Heating temperature–strain rate

Δk d :

Cooling temperature–strain rate

ΔP t :

Differential gas pressure (P3(t) − P4(t)) at time t

ΔP t + Δt :

Differential gas pressure (P3(t) − P4(t)) at time increment Δt

ΔP 0 :

Initial differential gas pressure

ΔT u :

Temperature increment

ΔT d :

Temperature decrement

Δt u :

Heating time

Δt d :

Cooling time

ε :

Total strain

ε m :

Instantaneous strain

ε c :

Creep strain

ε me :

Instantaneous elastic strain

ε mp :

Instantaneous plastic strain

ε cve :

Visco-elastic strain

ε cvp :

Visco-plastic strain

ε r :

Calculated creep strain rate

µ :

Dynamic viscosity

ρ :

Sample density at high temperature

ρ 0 :

Sample density at 25 °C

σ cd :

Crack damage stress

σ 1, σ 3 :

Principal stresses (σ1 ≥ σ3 compression positive)

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Acknowledgements

This research was supported by the Fundamental Research Funds for the Central Universities (2015XKZD05). The authors would like to express their sincere gratitude to the editor and the anonymous reviewers for their valuable comments, which have greatly improved this paper.

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  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, 221116, People’s Republic of China

    Sheng-Qi Yang & Bo Hu

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Yang, SQ., Hu, B. Creep and Long-Term Permeability of a Red Sandstone Subjected to Cyclic Loading After Thermal Treatments. Rock Mech Rock Eng 51, 2981–3004 (2018). https://doi.org/10.1007/s00603-018-1528-8

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