Rock Mechanics and Rock Engineering

, Volume 52, Issue 1, pp 277–281 | Cite as

Consideration of the Volumetric Changes that Accompany Rock Mass Failure

  • Bre-Anne Louise SainsburyEmail author
Technical Note


Some numerical modelling packages are able to calculate numerical solutions in both a large-strain and small-strain mode. In small-strain mode, grid-point co-ordinates are not updated during mechanical calculations; in large-strain mode, grid-point coordinates are constantly updated. The application of a small-strain mode is most useful when controlling boundary and applied conditions and large displacements are expected in relation to the grid size. As a result of the small-strain calculation mode, modification of the density and bulking/dilational behaviour of the rock mass during volumetric expansion is required to be considered as constitutive model behaviour. A summary of validated volumetric behaviours that can be used for large-deformational modelling in small-strain calculation mode is provided below.

Rock Mass Constitutive Behaviour


Volumetric expansion of a rock mass can occur as a result of fracture, separation and rotation during dilation under shear...


Volumetric change Numerical model Small strain Constitutive behaviour 

List of symbols

\({\rho _{\text{d}}}\)

Dynamic rock mass density (kg/m3)

\({\rho _{\text{s}}}\)

Initial rock mass in situ density (kg/m3)



\({\eta _{{\text{eqiv}}}}\)

Equivalent porosity

\({\eta _{{\text{max}}}}\)

Maximum porosity achieved by a rock mass. Default 0.4.

\({\varepsilon _{{\text{vsi}}}}\)

Volumetric strain increment

\({\varepsilon _{{\text{vsi(max)}}}}\)

Maximum volumetric strain achievable by a rock mass


Dilation angle (degrees)

\({\psi _{{\text{dyn}}}}\)

Dynamic dilation angle (degrees)


Friction angle (degrees)

\({\sigma _{{\text{ci}}}}\)

Intact Unconfined Compressive Strength (MPa)

\({\sigma _3}\)

Minor principal stress magnitude (MPa)


Dynamic deformation modulus (GPa)


Initial peak in situ rock mass deformation modulus (MPa)



  1. Adler L (1970) Double elasticity in drill cores under flexure. Int J Rock Mech Min Sci Geomech Abstr 7:357–370CrossRefGoogle Scholar
  2. Alejano L, Alonso E (2005) Considerations of the dilatancy angle in rocks and rock masses. Int J Rock Mech Min Sci 42:481–507CrossRefGoogle Scholar
  3. Al-Harthi AA, Al-Amri RM, Shehata W (1999) The porosity and engineering properties of vesicular basalt in Saudi Arabia. Eng Geol 54(3–4):313–320CrossRefGoogle Scholar
  4. Andersson CA (1996) Derivation of the exponential relation for the effect of ellipsoidal porosity on elastic modulus. J Am Ceram Soc. CrossRefGoogle Scholar
  5. Avar BB, Hudyma N, Karakouzian M (2003) Porosity dependence of the elastic modulus of lithophysaerich tuff: numerical and experimental investigations. Int J Rock Mech Min Sci, 40:919–928CrossRefGoogle Scholar
  6. Barton N, Bandis S (1982) Effects of block size on the shear behaviour of jointed rocks. 23rd US symposium on rock mechanics, Vol. 10, Balkema, Rotterdam, pp. 739–760Google Scholar
  7. Barton N, Pandey SK (2011) Numerical modelling of two stoping methods in two Indian mines using degradation of c and mobilisation of friction based on Q-parameters. Int J Rock Mech Min Sci, 48:1095–1112CrossRefGoogle Scholar
  8. Boccaccini AR, Fan Z (1997) A new approach for the Young’s modulus-porosity correlation of ceramic materials. Ceram Int 23(3):239–245CrossRefGoogle Scholar
  9. Chen R, Stimpson B (1993) Interpretation of indirect tensile strength tests when moduli of deformation in compression and in tension are different. Rock Mech Rock Eng 26:(2):183–189. CrossRefGoogle Scholar
  10. Detournay E (1986) Elastoplastic model of a deep tunnel for a rock with variable dilatancy. Rock Mech Rock Eng 19:99–108CrossRefGoogle Scholar
  11. Duncan-Fama ME (2003) Numerical modelling of yield zones in weak rock. In: Hudson J (ed) Comprehensive rock engineering, vol 2. Pergamon Press; 1993, Oxford, pp 49–75Google Scholar
  12. Fairhurst C (1961) Laboratory measurement of some physical properties of rock. In: Proceedings 4th symposium of rock mechanics, pp 105–118Google Scholar
  13. Haimson BC, Tharp T (1974) Real stresses around boreholes. Soc Petrol Engr J 14:145–151CrossRefGoogle Scholar
  14. Hill R (1950) The mathematical theory of plasticity. ClarendonPress;1950, OxfordGoogle Scholar
  15. Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Mineral Sci 34:8 1997Google Scholar
  16. Hoek E, Diederichs MS (2006) Empirical estimation of rock mass modulus. Int J Rock Mech Min Sci 43:203–215CrossRefGoogle Scholar
  17. Hutchinson DJ, Diederichs MS (1996) Cablebolting in underground mines. Bitech Publishers Ltd., Vancouver, 416pGoogle Scholar
  18. Katz JL (1972) Elastic Properties of Urinary Stones: Some experimental and theoretical observations. In: proceedings of the conference on urolithiasis: physical aspects. National Academy of Sciences, WashingtonGoogle Scholar
  19. Khan AS, Yuan S (1988) A three-dimensional finite element program for brittle bimodular rock-like material. Int J Numer Anal Methods Geomech 12:599–609CrossRefGoogle Scholar
  20. Kováčik J (2001) Correlation between shear modulus and porosity in porous materials. J Mater Sci Lett 20(21):1953–1955CrossRefGoogle Scholar
  21. Lorig L (2000) The roel of numerical modelling in assessing caveabilty, itasca consulting group Inc., Report to the International Caving Study, ICG00-099-3-16, October 2000Google Scholar
  22. Medhurst TP (1996) Estimation of the in situ strength and deformation of coal for engineering design. PhD Thesis. University of QueenslandGoogle Scholar
  23. Nielsen L (1990) Strength and stiffness of porous materials. J Am Ceram Soc 73(9):2684–2689CrossRefGoogle Scholar
  24. Palchik V, Hatzor YH (2002) Crack damage stress as a composite function of porosity and elastic matrix stiffness in dolomites and limestones. Eng Geol 63(3–4):233–245CrossRefGoogle Scholar
  25. Pappas D, Mark C (1993) Behaviour of Simulated Longwall Gob Material. Report of Investigations 9458. United States Department of the Interior, Bureau of MinesGoogle Scholar
  26. Passaris EKS (1977) The effect of directional anisotropy on the mechanical behaviour of rocksalt. In: Proceedings, conference rock engineering, British Geotechnical Society, Department of Mining Engineering. Newcastle upon Tyne, U.K., pp 11–31Google Scholar
  27. Pierce M, Cundall P, Potyondy D, Mas Ivars D (2006) A synthetic rock mass model for jointed rock. In: Eberhart E, Stead D, Morrison T Rock mechanics: meeting society’s challenges and Demands (2007). Taylor and Francis Group, London, ISBN 978-0-415-44401-9, pp 341–349Google Scholar
  28. Reyes-Montes J, Sainsbury B, Andrews J, Young RP (2016) Application of cave-scale rock degradation models in the imaging of the seismogenic zone. CIM J Paper 9178:Q2, 2016Google Scholar
  29. Ribacchi R (2000) Mechanical tests on pervasively jointed rock material: insight into rock mass behaviour. Rock Mech Rock Engng (2000) 33(4):243–266CrossRefGoogle Scholar
  30. Sainsbury B, Sainsbury D (2017) Practical use of the ubiquitous-joint constitutive model for the simulation of anisotropic rock masses. Int J Rock Mech Min Sci 50(6):1507–1528Google Scholar
  31. Sterpi D (1999) An analysis of geotechnical problems involving strain softening effects. Int J Numer Anal Meth Geomech 23(13):1427–1454CrossRefGoogle Scholar
  32. Sundaram RN, Corrales JM (1980) Brazilian tensile strength of rocks with different elastic properties in tension and compression. Int J Rock Mech Min Geomech Abstr 17:131–133CrossRefGoogle Scholar
  33. Vermeer PA, de Borst R (1984) Non-associated plasticity for soils, concrete and rock. Heron 29(3)Google Scholar
  34. Walsh JB (1965) The effect of cracks on the compressibility of rock. J Geophys Res. CrossRefGoogle Scholar
  35. Zohdi TI, Monteiro PJM, Lamour V (2002) Extraction of elastic moduli from granular compacts. Int J Fracture June 2002 115(3):49–54CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Science, Engineering and Built EnvironmentDeakin UniversityWaurn PondsAustralia

Personalised recommendations