Abstract
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.
Similar content being viewed by others
Abbreviations
- 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)
- JRC:
-
Joint roughness coefficient
- JCS:
-
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
References
Ajoku U, Saleh N, Hopkinson N, Hague R, Erasenthiran P (2006) Investigating mechanical anisotropy and end-of-vector effect in laser-sintered nylon parts. Proc Inst Mech Eng Part B: J Eng Manuf 220(7):1077–1086
Aydan Ö, Shimizu Y, Ichikawa Y (1989) The effective failure modes and stability of slopes in rock mass with two discontinuity sets. Rock Mech Rock Eng 22:163–188
Bandis SC, Lumsden AC, Barton NR (1983) Fundamentals of rock joint deformation. In: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts. Elsevier, pp 249–268
Barton N (1973) Review of a new shear-strength criterion for rock joints. Eng Geol 7:287–332
Barton N (1976) The shear strength of rock and rock joints. In: International Journal of rock mechanics and mining sciences & geomechanics abstracts. Elsevier, pp 255–279
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. https://doi.org/10.1016/j.jrmge.2013.05.008
Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech 10:1–54
Belem T, Souley M, Homand F (2009) Method for quantification of wear of sheared joint walls based on surface morphology. Rock Mech Rock Eng 42:883–910. https://doi.org/10.1007/s00603-008-0023-z
Bieniawski ZT, Bernede MJ (1979) Suggested methods for determining the uniaxial compressive strength and deformability of rock materials. Int J Rock Mech Min Sci Geomech Abstr 16(2):137–140
Bonilla-Sierra V, Scholtès L, Donzé F, Elmouttie M (2015) DEM analysis of rock bridges and the contribution to rock slope stability in the case of translational sliding failures. Int J Rock Mech Min Sci 80:67–78. https://doi.org/10.1016/j.ijrmms.2015.09.008
Brady BHG, Brown ET (2004) Rock mechanics: for underground mining, 3rd edn. Kluwer, Dordrecht
Buckingham E (1914) On physically similar systems, illustration of the use of dimensional equations. Phys Rev 4(4):345–376
Buzzi O, Casagrande D (2018) A step towards the end of the scale effect conundrum when predicting the shear strength of large in situ discontinuities. Int J Rock Mech Min Sci 105:210–219. https://doi.org/10.1016/j.ijrmms.2018.01.027
Caulfield B, McHugh PE, Lohfeld S (2006) Dependence of mechanical properties of polyamide components on build parameters in the SLS process. J Mater Process Technol 183(1/3):477–488
Clark GB (1981) Geotechnical centrifuges for model studies and physical property testing of rock and rock structures. Colarado School of Mines Quarterly, 76(4)
Davy P, Darcel C, Le Goc R, Mas Ivars D (2018) Elastic properties of fractured rock masses with frictional properties and power law fracture size distributions. J Geophys Res Solid Earth. https://doi.org/10.1029/2017JB015329
Deckard C, Beaman J J, Darrah J (1988) Patent cooperation treaty application. WO 9208567
Einstein HH, Veneziano D, Baecher GB, O’reilly KJ (1983) The effect of discontinuity persistence on rock slope stability. In: International journal of rock mechanics and mining sciences and geomechanics abstracts. Elsevier, pp 227–236
Fereshtenejad S, Song J-J (2016) Fundamental study on applicability of powder-based 3D printer for physical modeling in rock mechanics. Rock Mech Rock Eng 49:2065–2074. https://doi.org/10.1007/s00603-015-0904-x
Fuenkajorn K, Phueakphum D (2010) Physical model simulation of shallow openings in jointed rock mass under static and cyclic loadings. Eng Geol 113:81–89. https://doi.org/10.1016/j.enggeo.2010.03.003
Gerrard CM (1982) Equivalent elastic moduli of a rock mass consisting of orthorhombic layers. In: International journal of rock mechanics and mining sciences and geomechanics abstracts. Elsevier, pp 9–14
Ghabraie B, Ren G, Smith J, Holden L (2015a) Application of 3D laser scanner, optical transducers and digital image processing techniques in physical modelling of mining-related strata movement. Int J Rock Mech Min Sci 80:219–230. https://doi.org/10.1016/j.ijrmms.2015.09.025
Ghabraie B, Ren G, Zhang X, Smith J (2015b) Physical modelling of subsidence from sequential extraction of partially overlapping longwall panels and study of substrata movement characteristics. Int J Coal Geol 140:71–83. https://doi.org/10.1016/j.coal.2015.01.004
Goodman RE (1976) Methods of geological engineering in discontinuous rocks. West New York
Grasselli G, Egger P (2003) Constitutive law for the shear strength of rock joints based on three-dimensional surface parameters. Int J Rock Mech Min Sci 40:25–40. https://doi.org/10.1016/S1365-1609(02)00101-6
Grasselli G, Wirth J, Egger P (2002) Quantitative three-dimensional description of a rough surface and parameter evolution with shearing. Int J Rock Mech Min Sci 39:789–800. https://doi.org/10.1016/S1365-1609(02)00070-9
He M, Jia X, Gong W, Faramarzi L (2010) Physical modeling of an underground roadway excavation in vertically stratified rock using infrared thermography. Int J Rock Mech Min Sci 47:1212–1221. https://doi.org/10.1016/j.ijrmms.2010.06.020
Heuze FE (1979) Dilatant effects of rock joints. In: Proceedings of the 4th ISRM Congress, Montreux, p 169e75
Hoek E, Brown ET (1980) Underground excavations in rock. Institution of Mining and Metallurgy
Homand F, Belem T, Souley M (2001) Friction and degradation of rock joint surfaces under shear loads. Int J Numer Anal Methods Geomech 25:973–999. https://doi.org/10.1002/nag.163
Jiang C, Zhao G-F (2015) A preliminary study of 3D printing on rock mechanics. Rock Mech Rock Eng 48:1041–1050. https://doi.org/10.1007/s00603-014-0612-y
Jiang C, Zhao G-F, Zhu J et al (2016a) Investigation of dynamic crack coalescence using a gypsum-like 3D printing material. Rock Mech Rock Eng 49:3983–3998. https://doi.org/10.1007/s00603-016-0967-3
Jiang Q, Feng X, Gong Y et al (2016b) Reverse modelling of natural rock joints using 3D scanning and 3D printing. Comput Geotech 73:210–220. https://doi.org/10.1016/j.compgeo.2015.11.020
Jiang Q, Feng X, Song L et al (2016c) Modeling rock specimens through 3D printing: tentative experiments and prospects. Acta Mech Sin 32:101–111. https://doi.org/10.1007/s10409-015-0524-4
Jiang Q, Li LF, Song LB (2018) Application of 3D Printing technology in geotechnical-physical modeling: Tentative experiment practice. In: 9th International conference physics modelling geotechnics. London, pp 395–400
Kenzari S, Bonina D, Marie Dubois J, Fournée V (2014) Complex metallic alloys as new materials for additive manufacturing. Sci Technol Adv Mater 15:024802. https://doi.org/10.1088/1468-6996/15/2/024802
Kulatilake PHSW, Shou G, Huang TH, Morgan RM (1995) New peak shear strength criteria for anisotropic rock joints. Int J Rock Mech Min Sci Geomech Abstr 32:673–697
Kulhawy FH (1975) Stresses and displacements around openings in homogeneous rock. In: International journal of rock mechanics and mining sciences & geomechanics abstracts. Elsevier, pp 43–57
Kulhawy FH (1978) Geomechanical model for rock foundation settelment. ASCE 104(GT2):211–227
Ladanyi B, Archambault G (1970) Simulation of the shear behavior of a jointed rock mass. In: Proceedings of the 11th US symposium on rock mechanics. Berkeley, pp 105–12
Leichnitz W (1985) Mechanical properties of rock joints. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts; 22(5):313e21
Li SC, Wang Q, Wang HT et al (2015) Model test study on surrounding rock deformation and failure mechanisms of deep roadways with thick top coal. Tunn Undergr Space Technol 47:52–63. https://doi.org/10.1016/j.tust.2014.12.013
Lin P, Liu H, Zhou W (2015) Experimental study on failure behaviour of deep tunnels under high in situ stresses. Tunn Undergr Space Technol 46:28–45. https://doi.org/10.1016/j.tust.2014.10.009
Mandel J (1962) Essais sur modèle réduits en mécanique des terrain - Etude des conditions de similitude, Revue d’industrie minérale: no 9, 611–620
Mestat P (1993) Lois de comportement des géomatériaux et modélisation par la méthode des éléments finis. Collection « Etudes et recherche des laboratoires des Ponts et Chaussées » , série Géotechnique, ISSN 1157–3910
Min K-B, Jing L (2003) Numerical determination of the equivalent elastic compliance tensor for fractured rock masses using the distinct element method. Int J Rock Mech Min Sci 40:795–816. https://doi.org/10.1016/S1365-1609(03)00038-8
Olsson R, Barton N (2001) An improved model for hydromechanical coupling during shearing of rock joints. Int J Rock Mech Min Sci 38:317–329
Panet M (1976) La Mécanique des roches appliquée aux ouvrages du génie civil, p. 226 Presses de l’Ecole Nationale des Ponts et Chaussées
Patton FD (1966) Multiple modes of shear failure in rock. In: Proceedings 1st Congress of International Society of Rock Mechanics. Lisbon: Vol. 1, 509-513
Pouya A, Chalhoub M (2011) Ellipsoidal anisotropy in elasticity for rocks and rock masses. arXiv Prepr ArXiv11033033
Pouya A, Ghoreychi M (2001) Determination of rock mass strength properties by homogenization. Int J Numer Anal Methods Geomech 25:1285–1303
Pua LM, Caicedo B, Castillo D, Caro S (2018) Development of a 3D clay printer for the preparation of heterogeneous models. In: 9th Int. Conf. Phys. Modelling Geotechnics. London: 155-160
Rachez X (1997) Les fondations au rocher de grands viaducs: l’apport de la méthode des éléments distincts. Ph.D. Thesis, Ecole Nationale des Ponts et Chaussées
Reik G, Zacas M (1978) Strength and deformation characteristics of jointed media in true triaxial compression. Int J Rock Mech Min Sci Geomech Abstr 15(6):295–303
Ritter S, DeJong MJ, Giardina G, Mair RJ (2018) 3D printing of masonry structures for centrifuge modelling. In: 9th Int. Conf. Phys. Modelling Geotechnics. London: 449–454
Saeb S, Amadei B (1992) Modelling rock joints under shear and normal loading. In: International journal of rock mechanics and mining sciences & geomechanics abstracts. Elsevier, pp 267–278
Sharafisafa M, Shen L, Xu Q (2018) Characterisation of mechanical behaviour of 3D printed rock-like material with digital image correlation. Int J Rock Mech Min Sci 112:122–138. https://doi.org/10.1016/j.ijrmms.2018.10.012
Son M, Park J (2014) Physical and numerical tests of the excavation walls in jointed rock masses. Can Geotech J 51:554–569. https://doi.org/10.1139/cgj-2013-0081
Song L, Jiang Q, Shi Y-E et al (2018) Feasibility investigation of 3D printing technology for geotechnical physical models: study of tunnels. Rock Mech Rock Eng 51:2617–2637. https://doi.org/10.1007/s00603-018-1504-3
Stathas D, Xu L, Wang JP, Ling HI, Li L (2018) Concave segmental retaining walls. In: 9th Int. Conf. Phys.Modelling Geotechnics. London
Sturzenegger M, Stead D (2012) The Palliser Rockslide, Canadian Rocky Mountains: characterization and modeling of a stepped failure surface. Geomorphology 138:145–161. https://doi.org/10.1016/j.geomorph.2011.09.001
Sui W, Hang Y, Ma L et al (2015) Interactions of overburden failure zones due to multiple-seam mining using longwall caving. Bull Eng Geol Environ 74:1019–1035. https://doi.org/10.1007/s10064-014-0674-9
Wei J, Men Y, Sun S et al (2018) Experimental study on 3D roughness and shear failure mechanism of rock mass discontinuity. Adv Civ Eng 2018:1–20. https://doi.org/10.1155/2018/7358205
Xia C-C, Tang Z-C, Xiao W-M, Song Y-L (2014) New peak shear strength criterion of rock joints based on quantified surface description. Rock Mech Rock Eng 47:387–400. https://doi.org/10.1007/s00603-013-0395-6
Xie GX, Chang JC, Yang K (2009) Investigations into stress shell characteristics of surrounding rock in fully mechanized top-coal caving face. Int J Rock Mech Min Sci 46:172–181. https://doi.org/10.1016/j.ijrmms.2008.09.006
Yang J, Rong G, Hou D et al (2016) Experimental study on peak shear strength criterion for rock joints. Rock Mech Rock Eng 49:821–835. https://doi.org/10.1007/s00603-015-0791-1
Zarringhalam H, Hopkinson N, Kamperman NF, de Vlieger JJ (2006) Effects of processing on microstructure and properties of SLS Nylon 12. Mater Sci Eng, A 435–436:172–180. https://doi.org/10.1016/j.msea.2006.07.084
Zhao J, Zhu W (2004) Stability analysis and modelling of underground excavations in fractured rocks. Elsevier Geo-Engineering book series vol 1
Zhou P, Johansson F (2014) On the use of the continuity factor for rock mass properties based on a literature review of the representative elementary volume. International Society for Rock Mechanics and Rock Engineering
Zhou T, Zhu JB, Ju Y, Xie HP (2019) Volumetric fracturing behavior of 3D printed artificial rocks containing single and double 3D internal flaws under static uniaxial compression. Eng Fract Mech 205:190–204. https://doi.org/10.1016/j.engfracmech.2018.11.030
Acknowledgements
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Appendix
See Table 11.
Rights and permissions
About this article
Cite this article
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). https://doi.org/10.1007/s00603-020-02064-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-020-02064-9