Skip to main content

Evaluating the corollary of the interdependency of rock joint properties on subsurface fracturing


The characteristics of structural discontinuities in the subsurface environment often play a key role in the overall behaviour of such systems and their response to externally imposed conditions. Rock joints are one of such features that constitute the heterogeneity of rock masses. Akin to other forms of discontinuities, the characteristics of rock joints affect the performance of their parent rock masses, which are constituents of rock formations. The fracturing process is one of such key geo-mechanical phenomena that is inevitably influenced by pre-existing joints. A numerical technique implemented via a discrete element method (DEM) is herein adopted to evaluate two fundamental properties that control the shear and dilatancy responses of discontinuities. Though these properties are also assessed in isolation, their interdependency, which is a dominant factor, is investigated. As joint frictional resistance increases, it escalates the potential of the joint to attenuate the rate of fracture growth. On the other hand, an increase in joint dilatancy increases the intensity of fracturing. The impact of joint frictional resistance is more pronounced at high friction magnitudes, and in this range, the predominant influence of joint friction overwhelms any effect of joint dilatancy. Contrarily, at low joint frictional resistance, contributions from even a small magnitude of joint dilatancy increases the degree of fracturing. The inter-relationship between joint friction and dilatancy has influencing implications that govern the performance of rock masses. An inquiry into their combined contributions provides information prerequisite for a more accurate estimation and appraisal of fracture behaviour in underground systems.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33


c :

cohesive strength

E :

Young’s modulus

E :

Young’s modulus in plane strain

e y :

axial strain

e x :

lateral strain

ε v :

volumetric strain

ε 1 :

major principal strain

ε 3 :

minor principal strain


joint roughness coefficient


joint wall compressive strength

k n :

particle normal stiffness

k s :

particle shear stiffness

k n :

normal stiffness

k s :

shear stiffness

K f :

bulk modulus

\( {\hat{n}}_{\mathrm{j}} \) :

unit normal vector defining the joint plane

N tc :

estimated rate of development of tensile cracks

N sc :

estimated rate of development of shear cracks

\( \hat{q} \) :

compressive strength

q u :

unconfined compressive strength

T :

tensile strength

t :

elapsed time

τ p :

peak shear strength

τ r :

residual value of shear strength

τ θ :

the shear stress required to overcome the volumetric expansion

ρ f :


υ :

Poisson’s ratio

υ :

Poisson’s ratio in plane strain

γ :

plastic shear strain

γ max :

maximum plastic shear strain

θ :

dip angle

θ d :

average angle of deviation of the joint plane/joint surface particles from the direction of applied shear stress

ϑ :

dip direction

σ D :

deviatoric stress

σ n :

normal stress

σ y :

axial stress

σ x :

lateral stress

\( {\sigma}_1^{\prime } \) :

major effective principal stress

\( {\sigma}_3^{\prime } \) :

minor effective principal stress

ϕ :

angle of internal friction (friction angle)

ϕ r :

residual value of friction angle

ϕ b :

basic friction angle

ϕ crit :

critical friction angle

ϕ f :

interparticle friction angle corrected for work done or energy dissipated due to expansion

ϕ t :

the true angle of friction between the mineral surfaces of the particles

ϕ cv :

angle of friction under constant volume

φ :

dilation of a material, joint or discontinuity

φ p :

peak dilation, which is the same as the maximum dilation

μ :



  1. Amadei B, Saeb S (1990) Constitutive models of rock joints. Proceedings of the international symposium on rock joints. Leon, Norway, p 581–594

  2. Athavale AS, Miskimins JL (2008) Laboratory hydraulic fracturing on small homogeneous and laminated blocks. 42nd US Rock Mechanics Symposium, San Francisco June 29-July 2

  3. Barton N (1973) Review of a new shear-strength criterion for rock joints. Eng Geol 7:287–332

    Google Scholar 

  4. Barton N (1976) The shear strength of rock and rock joints. Int J Rock Mech Min Sci Geomech Abstr 19(9):255–279

    Google Scholar 

  5. Barton N (2013) Shear strength criteria for rock, rock joints, rockfill and rock masses: problems and some solutions. J Rock Mech Geotech Eng 5:249–261.

    Article  Google Scholar 

  6. Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech 10:1–54

    Google Scholar 

  7. Bolton MD (1986) The strength and dilatancy of sands. Geotechnique 36(1):65–78

    Google Scholar 

  8. Byerlee J (1978) Friction of rocks. In: Byerlee J, Wyss M (eds) Rock friction and earthquake prediction. Birkhäuser, Basel

  9. Cacace M, Blocher G (2015) MeshIt - a software for three dimensional volumetric meshing of complex faulted reservoirs. Environ Earth Sci 74(6):5191–5209

    Google Scholar 

  10. Cai M, Horii H (1992) A constitutive model of highly jointed rock masses. Mech Mater 13:217–246

    Google Scholar 

  11. Casas L, Miskimins JL, Black A, Green S (2006) Laboratory hydraulic fracturing test on a rock with artificial discontinuities. SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 24–27 September

  12. Chang CS, Misra A (1990) Packing structure and mechanical properties of granulates. J Eng Mech 116(5):1077–1093

    Google Scholar 

  13. Chuprakov DA, Akulich AV, Siebrits E, Thiercelin M (2010) Hydraulic fracture propagation in a naturally fractured reservoir. SPE Oil and Gas India Conference and Exhibition in Mumbai, India, 20-22 January

  14. Cieslik J (2018) Dilatancy as a measure of fracturing development in the process of rock damage. Open Geosci 10:484–490

    Google Scholar 

  15. De Josselin de Jong G (1976) Rowe’s stress-dilatancy relation based on friction. Geotechnique 26(1):527–534

    Google Scholar 

  16. Desai CS, Zaman MM, Lightner JG, Siriwardane HJ (1984) Thin-layer element for interfaces and joints. Int J Numer Anal Methods Geomech 8(1):19–43

    Google Scholar 

  17. Eshiet K, Sheng Y (2014) Investigation of geomechanical responses of reservoirs induced by carbon dioxide storage. Environ Earth Sci 71:3999–4020

    Google Scholar 

  18. Eshiet KI, Sheng Y (2015) Inter-relationship between joint dilatancy and frictional resistance: impact on fracture behaviour. IOP Conf Ser Earth Environ Sci 26(2015):012053

    Google Scholar 

  19. Eshiet KI, Sheng Y (2017) The role of rock joint frictional strength in the containment of fracture propagation. Acta Geotech 12(4):897–920.

  20. Eshiet KI-I, Welch M, Sheng Y (2018) Numerical modelling to predict fracturing rock (Thanet chalk) due to naturally occurring faults and fluid pressure. J Struct Geol 116:12–33.

    Article  Google Scholar 

  21. Han G, Jing H, Jiang Y, Lui R, Wu J (2020) Effect of cyclic loading on the shear behaviours of both unfilled and infilled rough rock joints under constant normal stiffness conditions. Rock Mech Rock Eng 53:31–57.

    Article  Google Scholar 

  22. Hossaini KA, Babanouri N, Nasab SK (2014) The influence of asperity deformability on the mechanical behavior of rock joints. Int J Rock Mech Min Sci 70:154–161

    Google Scholar 

  23. Huang HY (1999) Discrete element modeling of tool-rock interaction. PhD thesis, University of Minnesota, Minneapolis, MN

  24. Huang Q, Angelier J (1989) Fracture spacing and its relation to bed thickness. Geol Mag 126:355–362

    Google Scholar 

  25. Huang H, Lecampion B, Detournay E (2013) Discrete element modeling of tool-rock interaction I: rock cutting. Int J Numer Anal Methods Geomech 37:1913–1192

    Google Scholar 

  26. Indraratna B, Oliveira D, Jayanathan M (2008) Revised shear strength model for infilled rock joints considering overconsolidation effect. Proceedings of the 1st Southern Hemisphere International Rock Mechanics Symposium SHIRMS, 16-19 September, Perth

  27. Itasca Consulting Group Inc (2014) Particle flow code — PFC (2 and 3 dimension), version 5.0, user’s manual. Minneapolis, Minnesota

  28. Ivars DM, Pierce ME, Darcel C, Reyes-Montes J, Potyondy DO, Young RP, Cundall PA (2011) The synthetic rock mass approach for jointed rock mass modelling. Int J Rock Mech Min Sci 48:219–244

    Google Scholar 

  29. Jacquey AB, Cacace M, Blocher G (2017) Modelling coupled fluid flow and heat transfer in fractured reservoir; description of a 3D benchmark numerical case. Energy Procedia 125:612–621

    Google Scholar 

  30. Ji S, Suruwatari K (1998) A revised model for the relationship between joint spacing and layer thickness. J Struct Geol 20:1495–1508

    Google Scholar 

  31. Ji S, Zhu Z, Wang Z (1998) Relationship between joint spacing and bed thickness in sedimentary rocks: effect of interbed slip. Geol Mag 135:637–655

    Google Scholar 

  32. Johansson F (2016) Influence of scale and matedness on the peak shear strength of fresh, unweathered rock joints. Int J Rock Mech Min Sci 82:36–47.

    Article  Google Scholar 

  33. Johansson F, Stille H (2014) A conceptual model for the peak shear strength of fresh and unweathered rock joints. Int J Rock Mech Min Sci 69:31–38.

    Article  Google Scholar 

  34. Kachanov, M. 1980. Continuum model of medium cracks. Journal of the Engineering Mechanics Division. ASCE, Vol. 106, No. EM5. Proc. Paper 15750, October 1980, 1039–1051

  35. Kachanov M (1982a) Microcrack model of rock inelasticity. Part I: frictional sliding on pre-existing microcracks. Mech Mater 1:19–27

    Google Scholar 

  36. Kachanov M (1982b) Microcrack model of rock inelasticity. Part II: propagation of microcracks. Mech Mater 1:29–41

    Google Scholar 

  37. Kachanov M (1982c) Microcrack model of rock inelasticity. Part III: time-dependent growth of microcracks (stress corrosion cracking). Mech Mater 1:123–129

    Google Scholar 

  38. Kachanov M, Montagut ELE, Laures JP (1990) Mechanics of crack – microcrack interactions. Mech Mater 10:59–71

    Google Scholar 

  39. Kachanov M, Prioul R, Jocker J (2010) Incremental linear-elastic response of rocks containing multiple rough fractures: similarities and differences with traction-free cracks. Geophysics 75(1):D1–D11

    Google Scholar 

  40. Kamonphet T, Khamrat S, Fuenkajorn K (2015) Effects of cyclic shear loads on strength, stiffness and dilation of rock fractures. Songklanakarin J Sci Technol 37(6):683–690

    Google Scholar 

  41. Kulatilake PHSW, Malama B, Wang J (2001) Physical and particle flow modeling of jointed rock block behaviour under uniaxial loading. Int J Rock Mech Min Sci 38:641–657

    Google Scholar 

  42. Ladiera FL, Price NJ (1981) Relationship between fracture spacing and bed thickness. J Struct Geol:3

  43. Lambert C, Coli C (2014) Discrete modeling of rock joints with a smooth-joint contact model. J Rock Mech Geotech Eng 6:1–12.

    Article  Google Scholar 

  44. Lee H, Moon T, Haimson BC (2016) Borehole breakouts induced in Arkosic sandstones and a discrete element analysis. Rock Mech Rock Eng 49(4):1369–1388

    Google Scholar 

  45. Lehner F, Kachanov M (1996) On modelling of “winged” cracks forming under compression. Int J Fract 77:R69–R75

    Google Scholar 

  46. Lei Q, Latham J-P, Xiang J (2016) Implementation of an empirical joint constitutive model into finite-discrete element analysis of the geomechanical behaviour of fractured rocks. Rock Mech Rock Eng.

  47. Li Y, Wu W, Tang C, Liu B (2019) Predicting the shear characteristics of rock joints with asperity degradation and debris backfilling under cyclic loading conditions. Int J Rock Mech Min Sci 120:108–118.

    Article  Google Scholar 

  48. Maciejewski J, Bąk S, Ciężkowski P (2020) Modelling of rock joints interface under cyclic loading. Studia Geotechnica et Mechanica 42(1):36–47.

    Article  Google Scholar 

  49. Mohammadnejad T, Khoei AR (2013) An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model. Finite Elem Anal Des 73:77–95

    Google Scholar 

  50. Narr W, Suppe J (1991) Joint spacing in sedimentary rocks. J Struct Geol 13(9):1037–1048

    Google Scholar 

  51. Newland PL, Allely BH (1957) Volume changes in drained triaxial tests on granular materials. Geotechnique 7:17–34

    Google Scholar 

  52. Ohnishi Y, Chan T, Jing L (1996) Constitutive models for rock joints. Dev Geotech Eng 79:57–92

    Google Scholar 

  53. Park J-W, Song J-J (2009) Numerical simulation of a direct shear test on a rock joint using a bonded-particle model. Int J Rock Mech Min Sci 46:1315–1328

    Google Scholar 

  54. Patton FD (1966) Multiple modes of shear failure in rock. Proc. Ist Congress of International Society of Rock Mechanics, Lisbon, Portugal, p 509–513

  55. Philipp, S., Gudmundsson, A., Meier, S. and Reyer, D. 2009. Field studies and numerical models of hydrofracture propagation layered fractures reservoirs. Geophysical Research Abstracts 11

  56. Plesha M (1987) Constitutive models for rock discontinuities with dilatancy and surface degradation. Int J Numer Anal Methods Geomech 11:345–362

    Google Scholar 

  57. Plesha M (1995) Rock joints: theory, constitutive equations. Stud Appl Mech 42:375–393

    Google Scholar 

  58. Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364

    Google Scholar 

  59. Priest ST (1993) Discontinuity analysis for rock mechanics. Chapman & Hall, London [chapter 10]

    Google Scholar 

  60. Puntel E, Saouma VE (2008) Experimental behavior of concrete joint interfaces under reversed cyclic loading. J Struct Eng 134(9):1558–1568

    Google Scholar 

  61. Roko RO, Daemen JJK, Myers DE (1997) Variogram characterization of joint surface morphology and asperity deformation during shearing. Int J Rock Mech Min Sci 34(1):71–84

    Google Scholar 

  62. Rowe PW (1962) The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proc R Soc Lond A Math Phys Sci 269:500–527

    Google Scholar 

  63. Rowe PW (1969) The relation between the shear strength of sands in triaxial compression, plane strain and direct shear. Geotechnique 19(1):75–86

    Google Scholar 

  64. Saadat M, Taheri A (2019) A cohesive discrete element based approach to characterizing the shear behavior of cohesive soil and clay-infilled rock joints. Comput Geotech 114:103109.

    Article  Google Scholar 

  65. Saadat M, Taheri A (2020) A cohesive grain based model to simulate shear behaviour of rock joints with asperity damage in polycrystalline rock. Comput Geotech 117:103254.

    Article  Google Scholar 

  66. Salgado R (2006) The engineering of foundations. McGraw-Hill Education

  67. Schopfer MPJ, Arslan A, Walsh JJ, Childs C (2011) Reconciliation of contrasting theories for fracture spacing in layered rocks. J Struct Geol 33:551–565

    Google Scholar 

  68. Segura JM, Carol I (2004) On zero-thickness interface elements for diffusion problems. Int J Numer Anal Methods Geomech 28(9):947–962

    Google Scholar 

  69. Segura JM, Carol I (2008) Coupled HM analysis using zero-thickness interface elements with double nodes. Part I: theoretical model. Int J Numer Anal Methods Geomech 32(18):2083–2101

    Google Scholar 

  70. Shimizu H, Murata S, Ishida T (2011) The distinct element analysis for hydraulic fracturing in hard rock considering fluid viscosity and particle size distribution. Int J Rock Mech Min Sci Geomech 48:712–727

    Google Scholar 

  71. Tang CA, Liang ZZ, Zhang YB, Chang X, Tao X, Wang DG, Zhang JX, Liu JS, Zhu WC, Elsworth D (2008) Fracture spacing in layered materials: a new explanation based on two-dimensional failure process modeling. Am J Sci 308:49–72

    Google Scholar 

  72. Thiercelin M, Makkhyu E (2007) Stress field in the vicinity of a natural fault activated by the propagation of an induced hydraulic fracture., Proc First Canada-US Rock Mechanics Symposium-Rock Mechanics Meeting Society's Challenge and Demands, 2 1617–1624

  73. Trivedi A (2010) Strength and dilatancy of jointed rocks with granular fill. Acta Geotech 5(1):15–31

    Google Scholar 

  74. Vallejos JA, Suzuki K, Brzovic A, Ivars DM (2016) Application of synthetic rock mass modeling to veined core-size samples. Int J Rock Mech Min Sci 81:47–61

    Google Scholar 

  75. Wang JG, Ichikawa Y, Leung CF (2003) A constitutive model for rock interfaces and joints. Int J Rock Mech Min Sci 40:41–53

    Google Scholar 

  76. Welch MJ, Souque C, Davies RK, Knipe RJ (2015) Using mechanical models to investigate the controls on fracture geometry and distribution in chalk. Geol Soc Lond, Spec Publ 406:281–309

    Google Scholar 

  77. Wen ZJ, Wang X, Li QH, Lin G, Chen SJ, Jiang YJ (2016) Simulation analysis on the strength and acoustic emission characteristics of jointed rock mass. Tech Gazette 23(5):1277–1284

    Google Scholar 

  78. Wu H, Pollard DD (1995) An experimental study of the relationship between joint spacing and layer thickness. J Struct Geol 17

  79. Yang B, Jiao Y, Lei S (2006) A study on the effects of microparameters on macroproperties for specimens created by bonded particles. Int J Comput Aided Eng Softw 23:607–631

    Google Scholar 

  80. Zare M, Kakaie SR, Jalali SME (2008) A new empirical criterion for prediction of the shear strength of natural infilled rock joints under constant normal load (CNL) conditions. ISRM international symposium - 5th Asian rock mechanics symposium (ARMS5), 24–26 November, Tehran, Iran

  81. Zhang X, Jeffrey RG (2006) The role of friction and secondary flaws on deflection and reinitiation of hydraulic fractures at orthogonal pre-existing fractures. Geophys J Int 166:1454–1465

    Google Scholar 

  82. Zhang, X. and Jeffrey, R. G. 2008. Reinitiation or termination of fluid-driven fractures at frictional bedding interfaces. J Geophys Res, 113, B08416, 16 PP.

    Google Scholar 

  83. Zhao XG, Cai M (2010) A mobilized dilation angle model for rocks. Int J Rock Mech Min Sci 47:368–384.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Kenneth Imo-Imo Israel Eshiet.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Eshiet, K.II.I., Sheng, Y. & Yang, D. Evaluating the corollary of the interdependency of rock joint properties on subsurface fracturing. Bull Eng Geol Environ 80, 567–597 (2021).

Download citation


  • Rock joint
  • Joint frictional resistance
  • Joint dilatancy
  • Fracturing
  • Flow through porous media
  • Subsurface