Investigation of the Mechanical Behavior of 3D Printed Polyamide-12 Joints for Reduced Scale Models of Rock Mass


This study presents the experimental results of the mechanical characterization of artificial rock joints constructed by 3D-printing (3DP). The mechanical behavior of rock masses is controlled by the presence of joints. Understanding the mechanical behavior of rock joints is essential to predict their influence on a rock mass. The application of innovative 3DP technology in rock mechanics to model artificial rock-like joints allows strict control of joint geometry (orientation, roughness, number of rock bridges, etc.), and thus of its mechanical behavior. The 3DP technology used in this work is selective laser sintering, and the material is Polyamide 12. Geometric characterization shows that this technology gives high dimensional precision for details smaller than 0.4 mm. More than 30 discontinuous samples were printed to investigate the global mechanical properties of a joint relative to its geometric features including Young’s Modulus (E), shear stiffness (ks), cohesion (cj), friction angle (φj) and dilation (i). The results show that the number of rock bridges (Nrb) and the roughness significantly influence the mechanical properties. A failure criterion that considers these parameters is proposed. These 3D-printed joints can be used in physical modeling of rock mass to understand the influence of the fractures on its stability by applying scaling laws. The application of scale factors to the experimental results shows the possibility of representing actual rocks with artificial 3DP joints.

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τ :

Shear stress (MPa)

σ n :

Normal stress (MPa)

σ T :

Transitional normal stress (MPa)

c j :

Joint cohesion (MPa)

φ j :

Joint friction angle (°)

φ j,r :

Joint residual friction angle (°)

φ b :

Basic joint friction angle (°)

τ peak :

Peak shear stress (MPa)

τ res :

Residual shear stress (MPa)

u_n :

Normal displacement (mm)

u_t :

Shear displacement (mm)

k s :

Joint shear stiffness (MPa/mm)

k n :

Joint normal stiffness (MPa/mm)

θ :

Asperity angle (°)

a s :

Shear area ratio

\(\dot{\upsilon }\) :

Dilation rate

S r :

Intact rock strength, (MPa)


Joint roughness coefficient


Joint compressive strength (MPa)

N rb :

Number of rock bridges

ɛ :

Axial deformation (mm/mm)

E :

Young modulus (MPa)

c :

Cohesion (MPa)

i peak :

Dilation angle at τpeak (°)

i post-peak :

Dilation angle after the peak (°)

D p :

Printed sample diameter (mm)

D t :

Theoretical sample diameter (mm)

H p :

Printed sample height (mm)

H t :

Theoretical sample height (mm)

σ*, ρ*, L*, g*, k *s , \(c^{*}\), \(\varphi^{*}\), \(\tau^{*}\), \(E^{*}\) :

Scaling factor, respectively, for the normal stress, density, dimensions, gravity, shear stiffness, cohesion, friction angle, shear stress and Young modulus


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This work is a part of the research project “Stone3d” realized in collaboration with GeoRessources and Institut Jean Lamour. It was funded by the “Ministry of Higher Education, Research and Innovation”, and by the “Carnot Institute, ICÉEL”. We acknowledge “Ateliers CINI SA” for their help in the 3D-Printing of samples, Mountaka Souley for the fruitful discussions, and the members of GeoRessources who helped in samples preparation and shear tests (Christophe Auvray, Clément Granclaude et Laurent Schoumacker).

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Correspondence to Jana Jaber.

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See Table 11.

Table 11 Ratio between theoretical (index t) and printed dimensions (index p) of SLS constructed samples

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Jaber, J., Conin, M., Deck, O. et al. Investigation of the Mechanical Behavior of 3D Printed Polyamide-12 Joints for Reduced Scale Models of Rock Mass. Rock Mech Rock Eng 53, 2687–2705 (2020).

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  • 3D-printing
  • Rock joints
  • Shear tests
  • Physical modelling