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

Abstract

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.

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Abbreviations

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

JCR:

joint roughness coefficient

JCS:

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 :

density

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 :

viscosity

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Correspondence to Kenneth Imo-Imo Israel Eshiet.

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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). https://doi.org/10.1007/s10064-020-01933-5

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Keywords

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