Rock Mechanics and Rock Engineering

, Volume 50, Issue 6, pp 1529–1549 | Cite as

Experimental and Numerical Investigation of Permeability Evolution with Damage of Sandstone Under Triaxial Compression

  • Xu Chen
  • Jin Yu
  • Chun’an Tang
  • Hong Li
  • Shanyong Wang
Original Paper
First Online:
Received:
Accepted:

Abstract

A series of triaxial compression tests with permeability measurements was carried out under different confining pressure and pore pressure difference coupling conditions to investigate some mechanical properties and permeability evolution with damage of sandstone. It is found that the shapes of stress–strain curves, permeability evolution curves, and failure patterns are significantly affected by the confining pressure but are only slightly affected by the pore pressure difference. In addition, the corresponding numerical simulations of the experiments were then implemented based on the two-dimensional Realistic Failure Process Analysis-Flow (RFPA2D-Flow) code. In this simulator, the heterogeneity of rock is considered by assuming the material properties of the mesoscopic elements conform to a Weibull distribution and a statistical damage constitutive model based on elastic damage mechanics and the flow–stress–damage (FSD) coupling model. The numerical simulations reproduced the failure processes and failure patterns in detail, and the numerical results about permeability–strain qualitatively agree with the experimental results by assigning different parameters in the FSD model. Finally, the experimental results about relationship between permeability evolution and volumetric strain are discussed.

Keywords

Triaxial compression Hydromechanical coupling Permeability evolution Failure process Numerical simulation Rock mechanics 

List of symbols

\( A \)

Cross-sectional area

\( D \)

Damage variable

\( E \)

Young’s moduli of damaged material

\( E_{0} \)

Young’s moduli of undamaged material

\( f_{\text{c}} \)

Uniaxial compressive strength

\( f_{\text{cr}} \)

Compressive residual stress

\( f_{j} \)

Body force in the jth direction

\( f_{\text{t}} \)

Tensile strength

\( f_{\text{tr}} \)

Tensile residual stress

\( G \)

Shear modulus

\( k \)

Absolute permeability

\( K \)

Hydraulic conductivity

\( K_{0} \)

Initial hydraulic conductivity

\( L \)

Sample height

\( m \)

Homogeneity index

\( p \)

Pore pressure

\( P(\alpha ) \)

Cumulative probability function of Weibull distribution

\( Q \)

Volumetric water flow rate

\( Q_{\text{B}} \)

Biot’s constant

t

Time

\( u_{i} \)

Displacement in the ith direction

\( \alpha \)

A given material property (such as the elastic modulus or strength)

\( \alpha_{0} \)

Scale parameter denoting the average value of the material property α

\( \beta \)

Pore pressure coefficient

\( \gamma \)

Unit weight of the fluid

\( \delta_{ij} \)

Kronecker delta

\( \Delta p \)

Pore pressure difference applied between both end planes of the rock sample

\( \varepsilon \)

Elastic strain

\( \varepsilon_{\text{ax}} \)

Axial strain

\( \varepsilon_{c0} \)

Maximum principal strain

\( \varepsilon_{ij} \)

Components of the Cauchy strain tensor

\( \varepsilon_{\text{rad}} \)

Radial strain

\( \varepsilon_{\text{tu}} \)

Ultimate tensile strain

\( \varepsilon_{\text{v}} \)

Volumetric strain

\( \eta \)

A material constant

\( \lambda \)

Lamé coefficient

\( \mu \)

Fluid dynamic viscosity coefficient

\( \nu \)

Poisson’s ratio

\( \xi \)

Damage factor of the hydraulic conductivity

σ

Stress

\( \sigma_{1} \)

Major principal stress

\( \sigma_{2} \)

Intermediate principal stress

\( \sigma_{3} \)

Minor principal stress

\( \sigma_{ij} \)

Components of the Cauchy stress tensor

\( \sigma_{j}^{{\prime }} \)

Components of the effective stress tensor

\( \varphi \)

Friction angle of the element

\( \varphi (\alpha ) \)

Probability density function of Weibull distribution

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Notes

Acknowledgements

The research shown in this paper is financially supported by the National Basic Research Program of China (973 Program) (Grant No. 2014CB047100), the National Basic Research Program of China (973 Program) (Grant No. 2011CB013503), the National Natural Science Foundation of China (Grant No. 51374112), and the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (No. ZQN-PY112), China. This paper is also supported by the National Natural Science Foundation of China (Grant No. 51679093).

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Copyright information

© Springer-Verlag Wien 2017

Authors and Affiliations

  • Xu Chen
    • 1
  • Jin Yu
    • 2
  • Chun’an Tang
    • 1
    • 3
  • Hong Li
    • 3
  • Shanyong Wang
    • 4
  1. 1.School of Resources and Civil EngineeringNortheastern UniversityShenyangChina
  2. 2.Institute of Geotechnical EngineeringHuaqiao UniversityXiamenChina
  3. 3.School of Civil and Hydraulic EngineeringDalian University of TechnologyDalianChina
  4. 4.ARC Centre of Excellence for Geotechnical Science and Engineering, Civil, Surveying and Environmental EngineeringThe University of NewcastleCallaghanAustralia

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