Stress influence on the permeability of a sample heterogeneous rock

  • Hossein AgheshluiEmail author
Original Article


In this study, a numerical methodology has been developed and discussed to investigate the influence of in situ stresses, including normal and tractional stresses, on the permeability of a heterogeneous intact rock. Flow properties of a representative rock sample composed of three different rock types, randomly located in a rock block, is studied under different stress regimes. Porosity and permeability within each rock type is distributed using statistical distributions. Different stress regimes corresponding to the rock sample located at surface, and at subsurface with horizontal stresses applied in two different orientations are investigated. The stress distribution in the rock sample under different stress scenarios is calculated and is used to update the permeability and porosity at different locations within the rock sample. The ensemble permeability tensors are calculated by running flow simulations in three perpendicular directions and upscaling the permeability from the element level (5 mm) to the sample scale (5 m). It is demonstrated that the flow properties of the studied heterogeneous rock sample reduce considerably when the sample is taken from the surface to a depth of 1 km. More importantly, it is shown that when the horizontal stresses are not perpendicular to the sidewalls of the rock sample, they create shear stresses which further reduce the permeability.


Stress dependent flow properties Heterogeneity Porosity Permeability Upscaling 

List of symbols


Fourth-order stiffness tensor


Young’s modulus (GPa)


Vector of body forces (N)


Shear modulus (GPa)


Identity matrix


Median initial permeability (m2)


Permeability tensor


Pore fluid pressure (MPa)


Initial pressure (MPa)


Effective pressure (MPa)


Overburden stress (MPa)


Maximum horizontal stress (MPa)


Minimum horizontal stress (MPa)


Velocity vector

u, v, w

Displacements in x, y, and z directions (m)


Volume (m3)


Virtual velocity field


Shear stress vector


Porosity sensitivity exponent


Pressure sensitivity coefficient (MPa−1)




Pore fluid viscosity (m2/s)


Poisson’s ratio


Rock density (kg/m3)


Cauchy stress tensor


Cauchy effective stress tensor


Porosity (%)


Average initial porosity (%)



Caroline Milliotte (FEI Inc., Canberra, Australia) is thanked for the generation of the complex geometry of rock types. Also, Dr. Mohammad Sedaghat is thanked for his advice on the flow simulation processes.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


  1. Abaqus Theory Guide (2016) Dassault Systèmes, Providence, RI, USAGoogle Scholar
  2. Agheshlui H, Sedaghat MH, Matthai S (2018) Stress influence on fracture aperture and permeability of fragmented rocks. J Geophys Res Solid Earth. Google Scholar
  3. Agheshlui H, Sedaghat MH, Azizmohammadi S (2019) A comparative study of stress influence on fracture apertures in fragmented rocks. J Rock Mech Geotech Eng 11(1):38–45. CrossRefGoogle Scholar
  4. Azizmohammadi S, Matthäi SK (2017) Is the permeability of naturally fractured rocks scale dependent? Water Resour Res. Google Scholar
  5. Baghbanan A, Jing L (2008) Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture. Int J Rock Mech Min Sci 45(8):1320–1334. CrossRefGoogle Scholar
  6. Bhandari AR, Flemings PB, Polito PJ, Cronin MB, Bryant SL (2015) Anisotropy and stress dependence of permeability in the barnett shale. Transp Porous Media 108(2):393–411. CrossRefGoogle Scholar
  7. David C, Wong T-F, Zhu W, Zhang J (1994) Laboratory measurement of compaction-induced permeability change in porous rocks: implications for the generation and maintenance of pore pressure excess in the crust. Pure Appl Geophys 143(1):425–456. CrossRefGoogle Scholar
  8. Dong J-J, Hsu J-Y, Wu W-J, Shimamoto T, Hung J-H, Yeh E-C, Sone H (2010) Stress-dependence of the permeability and porosity of sandstone and shale from TCDP Hole-A. Int J Rock Mech Min Sci 47(7):1141–1157. CrossRefGoogle Scholar
  9. Fernandez G, Moon J (2010) Excavation-induced hydraulic conductivity reduction around a tunnel—Part 1: guideline for estimate of ground water inflow rate. Tunn Undergr Space Technol 25(5):560–566. CrossRefGoogle Scholar
  10. Gan Q, Elsworth D (2016) A continuum model for coupled stress and fluid flow in discrete fracture networks. Geomech Geophys Geo-Energy Geo-Resour 2(1):43–61. CrossRefGoogle Scholar
  11. Guo H, Yuan L, Shen B, Qu Q, Xue J (2012) Mining-induced strata stress changes, fractures and gas flow dynamics in multi-seam longwall mining. Int J Rock Mech Min Sci 54:129–139. CrossRefGoogle Scholar
  12. Kazemi H, Gilman JR (1993) Multiphase flow in fractured petroleum reservoirs. In: Bear J, Tsang CF, d. Marsily G (eds) Flow and contaminant transport in fractured rocks. Academic Press, San Diego, pp 267–323CrossRefGoogle Scholar
  13. Latham J-P, Xiang J, Belayneh M, Nick HM, Tsang C-F, Blunt MJ (2013) Modelling stress-dependent permeability in fractured rock including effects of propagating and bending fractures. Int J Rock Mech Min Sci 57:100–112. CrossRefGoogle Scholar
  14. Lei Q, Wang X, Xiang J, Latham JP (2017) Polyaxial stress-dependent permeability of a three-dimensional fractured rock layer. Hydrogeol J 25(8), 2251–2262. CrossRefGoogle Scholar
  15. Liu HH, Ranjith PG, Georgi DT, Lai BT (2016) Some key technical issues in modelling of gas transport process in shales: a review. Geomech Geophys Geo-Energy Geo-Resour 2(4):231–243. CrossRefGoogle Scholar
  16. Min K-B, Rutqvist J, Tsang C-F, Jing L (2004) Stress-dependent permeability of fractured rock masses: a numerical study. Int J Rock Mech Min Sci 41(7):1191–1210. CrossRefGoogle Scholar
  17. Neretnieks I (1993) Solute transport in fractured rock: application to radionuclide waste repositories. In: Bear J, Tsang C-F, d. Marsily G (eds) Flow and contaminant transport in fractured rock. Academic Press, San Diego, pp 39–127CrossRefGoogle Scholar
  18. Ranathunga AS, Perera MSA, Ranjith PG, De Silva GPD (2017) A macro-scale view of the influence of effective stress on carbon dioxide flow behaviour in coal: an experimental study. Geomechan Geophys Geo-Energy Geo-Resour 3(1):13–28. CrossRefGoogle Scholar
  19. Zheng J, Zheng L, Liu H-H, Ju Y (2015) Relationships between permeability, porosity and effective stress for low-permeability sedimentary rock. Int J Rock Mech Min Sci 78:304–318. CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Infrastructure EngineeringThe University of MelbourneParkvilleAustralia

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