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3D Particle-Based DEM Investigation into the Shear Behaviour of Incipient Rock Joints with Various Geometries of Rock Bridges

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A 3D particle-based DEM model was established taking into account the geometries of rock bridges. The model was used to investigate the shear behaviour of incipient rock joints. Fifty-seven direct shear tests were conducted under constant normal load (CNL) boundary conditions using the established model, in which rock bridges with 19 different geometries and incipient joints with various areal persistence (between 0.2 and 0.96) were involved. Our results show that, for the cases having a single rock bridge, cracks often initiated around the edges of the rock bridges and coalesced first in the middle of the rock bridge areas. While for other cases containing multiple rock bridges, cracks initially appeared at the connection points (located in the middle of the joint planes) of the rock bridges and then propagated to the edges. High crack initiation stresses were measured, which were often more than 60% of the shear strength of the tested incipient rock joints. Sudden failures of the rock bridges subjected to shearing were observed, accompanying dramatic increases in the number of cracks. Another important conclusion derived from this research is that both joint areal persistence and rock bridge geometry played significant roles in the shear failure of the simulated Horton Formation Siltstone joints. The present study has shown that shear strength increased gradually when joint areal persistence was decreased. Interestingly, different shear strength values were measured for rock joints with the same areal persistence (e.g. K = 0.5). Shear velocity was also found to have a significant influence on the shear characteristics of the Horton Formation Siltstone joints. A higher shear strength was measured when the shearing velocity was increased from 0.01 to 1 m/s.

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Fig. 1

After Shang et al. (2016)

Fig. 2

Adapted from Lajtai (1969a)

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A :

Cross-sectional area of parallel bond

A B :

Total area of rock bridges on an incipient joint plane

A j1, A j2, …, A jn :

Persistent areas along an incipient joint plane

a, b :

Two side lengths of a rectangle rock bridge

c sj :

Cohesion of smooth-joint bond

d v, d h :

Vertical and horizontal spacings between adjacent joint planes

E :

Young’s modulus

E c :

Young’s modulus of particle linear contact

E c_ :

Young’s modulus of parallel bond

F c :

Vector of contact force

F n :

Normal force acting on parallel bond

F s :

Shear force acting on parallel bond

I :

Moment of inertia of the cross section of parallel bond

J :

Total length of an incipient joint


Polar moment of inertia of the cross section of parallel bond

j 1, j 2, …, j n :

Joint segments measured along an incipient joint

K :

Joint areal persistence

K n/K s :

Particle linear contact normal to shear stiffness ratio

K n_/K s_ :

Parallel bond contact normal to shear stiffness ratio

K nsj :

Normal stiffness of smooth joint contact

K ssj :

Shear stiffness of smooth joint contact

k :

Moment-contribution factor to strength

L c :

Branch vector

R max :

Maximum particle radius

R min :

Minimum particle radius

V :

Volume of a measurement region

α :

Strike of an incipient joint

β :

Dip of an incipient joint

v :

Poisson’s ratio

σ :

Tensile stress in parallel-bond periphery

σ c :

Tensile strength of parallel bond

σ sj :

Tensile strength of smooth-joint bond

\(\bar {\sigma }\) :

Average stress measured in a measurement region

τ :

Shear stress in parallel-bond periphery

\(\phi\) :

Friction angle of parallel bond

µ :

Coefficient of particle friction

µ sj :

Coefficient of smooth-joint contact

ΔF n, ΔF s :

Increments of normal and shear forces in parallel bond

ΔM n, ΔM s :

Increments of components of parallel bond moment

\(\Delta {\partial _{\text{n}}}\), \(\Delta {\partial _{\text{s}}}\) :

Increments of normal and shear displacement, respectively


Constant normal load


Discrete Element Method


Flat joint contact model


International Society for Rock Mechanics and Rock Engineering


Loading rate


Parallel bond model


Particle Flow Code


Rock failure process analysis


Smooth joint model


Uniaxial compressive strength


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The research was partially funded by the National Natural Science Foundation of China: Mechanism and test of time-varying and multi-scale behaviours of rock mass under deep mining (no. 41672298). The stereonet developed by Prof. Richard Allmendinger of Cornell University was used to interpret orientations of cracks. The editor-in-chief Prof. Giovanni Barla and the two anonymous reviewers are thanked for their valuable comments.

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Shang, J., Zhao, Z., Hu, J. et al. 3D Particle-Based DEM Investigation into the Shear Behaviour of Incipient Rock Joints with Various Geometries of Rock Bridges. Rock Mech Rock Eng 51, 3563–3584 (2018).

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