Strength Anisotropy of Rock with Crossing Joints: Results of Physical and Numerical Modeling with Gypsum Models

  • Lifu ChangEmail author
  • Heinz Konietzky
  • Thomas Frühwirt
Original Paper


The geometric and mechanical characteristics of multiple intersecting joints can govern the strength anisotropy behavior of a rock mass. Laboratory uniaxial compression tests with artificial rock-like material (gypsum) were conducted to investigate the strength anisotropy behavior of jointed specimens. Three special kinds of gypsum were used to ensure that the handmade joints have a user-defined-strength for all samples. Specimens with one or two crossing joints covering more than 20 angle configurations and two different property sets were prepared and tested. The strength anisotropy behaviors of specimens with constant joint angles (90°, 80°, 60°, 45°, and 30°) were investigated, and the failure mechanisms were assessed through the damage pattern of the colored gypsum. The details of the design scheme and figures of the evaluated experimental results are presented in this paper. A new equivalent continuum model, called the multi-joint model, is developed for jointed rock masses that contain up to three arbitrary persistent joint sets. The Mohr–Coulomb yield criterion is used to check failure of the intact rock and the joints. The multi-joint model is implemented into the finite difference method code FLAC and compared with the distinct element method code UDEC. The experimental results are used to verify the developed multi-joint constitutive model and to investigate the behavior of jointed specimen. Experimental observations agree well with the simulation results and analytical solutions.


Joint interconnectivity Multi-joint sample Lab testing Numerical simulation Strength anisotropy 

List of Symbols

c, cji (i = 1,2.3)

Cohesion of the intact rock and joint cohesion, respectively

fi,i (i = 0,1, 2, 3)

Shear failure envelopes for rock matrix and joint set, respectively.

fi,i (i = 0,1, 2, 3)

Tensile failure envelopes for rock matrix and joint set, respectively


Slope of the line relating maximum and minimum principal stresses


Joint inclination angle measured from vertical

βi (i = 1, 2, 3)

Inclination angle of weak plane

ϕ, ϕʹ

Friction angle and effective friction angle of the intact rock, respectively

ϕji (i = 1, 2, 3)

Friction angle for the joint set i


Inclination angle measured from horizontal

θji (i = 1, 2, 3)

Joint angles measured counterclockwise from the global x-axis


Density of rock

σ, σn, σt

Tensile stress, normal stress, and intact rock tensile strength, respectively


Maximum and minimum principal stresses, respectively


Uniaxial compressive strength and uniaxial compression stress, respectively

τ, τ′, τji

Shear stress components in the global and local coordinates, respectively


Uniaxial compressive strength



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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Civil Engineering and ArchitectureZhejiang Sci-Tech UniversityHangzhouChina
  2. 2.Geotechnical Institute TU Bergakademie FreibergFreibergGermany

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