Application and prospective of 3D printing in rock mechanics: A review

Yong-tao Gao; Tian-hua Wu; Yu Zhou

doi:10.1007/s12613-020-2119-8

Volume 28 Issue 1

Jan. 2021

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Article Navigation > International Journal of Minerals, Metallurgy and Materials > 2021 > 28(1): 1-17

Yong-tao Gao, Tian-hua Wu, and Yu Zhou, Application and prospective of 3D printing in rock mechanics: A review, Int. J. Miner. Metall. Mater., 28(2021), No. 1, pp. 1-17. https://doi.org/10.1007/s12613-020-2119-8

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Yong-tao Gao, Tian-hua Wu, and Yu Zhou, Application and prospective of 3D printing in rock mechanics: A review, Int. J. Miner. Metall. Mater., 28(2021), No. 1, pp. 1-17. https://doi.org/10.1007/s12613-020-2119-8

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Invited Review

Application and prospective of 3D printing in rock mechanics: A review

+ Author Affiliations

Corresponding author:
Yu Zhou E-mail: westboy85@ustb.edu.cn
Received: 27 March 2020; Revised: 22 May 2020; Accepted: 16 June 2020; Available online: 18 June 2020

Abstract

Abstract

This review aims to discuss the application and development of three-dimensional printing (3DP) technology in the field of rock mechanics and the mechanical behaviors of 3D-printed specimens on the basis of various available printing materials. This review begins with a brief description of the concepts and principles associated with 3DP, and then systematically elaborates the five major applications of 3DP technology in the field of rock mechanics, namely, the preparation of rock (including pre-flawed rock) specimens, preparation of joints, preparation of geophysical models, reconstruction of complex rock structures, and performance of bridging experimental testing and numerical simulation. Meanwhile, the mechanical performance of 3D-printed specimens created using six different printing materials, such as polymers, resin, gypsum, sand, ceramics, and rock-like geological materials, is reviewed in detail. Subsequently, some improvements that can make these 3D-printed specimens close to natural rocks and some limitations of 3DP technology in the application of rock mechanics are discussed. Some prospects that are required to be investigated in the future are also proposed. Finally, a brief summary is presented. This review suggests that 3DP technology, especially when integrated with other advanced technologies, such as computed tomography scanning and 3D scanning, has great potential in rock mechanics field.
- three-dimensional printing (3DP);
- rock mechanics;
- 3DP material;
- rock analogue;
- 3DP geotechnical model;
- numerical simulation

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References

[1]	B.H.G. Brady and E.T. Brown, Rock Mechanics: For Underground Mining, George Allen & Unwin Ltd, London, 1985, p. 15.
[2]	R.E. Goodman, Introduction to Rock Mechanics, 2nd ed., Wiley, New York, 1989, p. 28.
[3]	R.D. Lama and V.S. Vutukuri, Handbook on Mechanical Properties of Rocks, Trans Tech Publications, Clausthal, 1978, p. 116.
[4]	W.R. Wawersik and C. Fairhurst, A study of brittle rock fracture in laboratory compression experiments, Int. J. Rock Mech. Min. Sci., 7(1970), No. 5, p. 561. doi: 10.1016/0148-9062(70)90007-0
[5]	Y. Zhou, G. Zhang, S.C. Wu, and L. Zhang, The effect of flaw on rock mechanical properties under the Brazilian test, Kuwait J. Sci., 45(2018), No. 2, p. 94.
[6]	S.W. Feng, Y. Zhou, Y. Wang, and M.D. Lei, Experimental research on the dynamic mechanical properties and damage characteristics of lightweight foamed concrete under impact loading, Int. J. Impact Eng., 140(2020), art. No. 103558. doi: 10.1016/j.ijimpeng.2020.103558
[7]	Y. Zhou, S.C. Wu, Y.T. Gao, and A. Misra, Macro and meso analysis of jointed rock mass triaxial compression test by using equivalent rock mass (ERM) technique, J. Cent. South Univ., 21(2014), No. 3, p. 1125. doi: 10.1007/s11771-014-2045-x
[8]	Y. Zhou, N.B. Chen, L. Wang, J.W. Li, and T.H. Wu, A flat-joint contact model and meso analysis on mechanical characteristics of brittle rock, Kuwait J. Sci., 46(2019), No. 3, p. 71.
[9]	Y. Ju, H.P. Xie, Z.M. Zheng, J.B. Lu, L.T. Mao, F. Gao, and R.D. Peng, Visualization of the complex structure and stress field inside rock by means of 3D printing technology, Chin. Sci. Bull., 59(2014), No. 36, p. 5354. doi: 10.1007/s11434-014-0579-9
[10]	C. Jiang and G.F. Zhao, A preliminary study of 3D printing on rock mechanics, Rock Mech. Rock Eng., 48(2015), No. 3, p. 1041. doi: 10.1007/s00603-014-0612-y
[11]	M. Sharafisafa, L.M. Shen, and Q.F. Xu, Characterisation of mechanical behaviour of 3D printed rock-like material with digital image correlation, Int. J. Rock Mech. Min. Sci., 112(2018), p. 122. doi: 10.1016/j.ijrmms.2018.10.012
[12]	X.T. Feng, Y.H. Gong, Y.Y. Zhou, Z.W. Li, and X.F. Liu, The 3D-printing technology of geological models using rock-like materials, Rock Mech. Rock Eng., 52(2019), p. 2261. doi: 10.1007/s00603-018-1703-y
[13]	C.W. Hull, Apparatus for Production of Three-Dimensional Objects by Stereolithography, United States Patent, Appl. 4575330, 1986.
[14]	S. Bose, S. Vahabzadeh, and A. Bandyopadhyay, Bone tissue engineering using 3D printing, Mater. Today, 16(2013), No. 12, p. 496. doi: 10.1016/j.mattod.2013.11.017
[15]	L.B. Song, Q. Jiang, Y.E. Shi, X.T. Feng, Y.H. Li, F.S. Su, and C. Liu, Feasibility investigation of 3D printing technology for geotechnical physical models: Study of tunnels, Rock Mech. Rock Eng., 51(2018), p. 2617. doi: 10.1007/s00603-018-1504-3
[16]	S. Fereshtenejad and J.J. Song, Fundamental study on applicability of powder-based 3D printer for physical modeling in rock mechanics, Rock Mech. Rock Eng., 49(2016), No. 6, p. 2065. doi: 10.1007/s00603-015-0904-x
[17]	P. Liu, Y. Ju, P.G. Ranjith, Z.M. Zheng, L. Wang, and A. Wanniarachchi, Visual representation and characterization of three-dimensional hydrofracturing cracks within heterogeneous rock through 3D printing and transparent models, Int. J. Coal Sci. Technol., 3(2016), No. 3, p. 284. doi: 10.1007/s40789-016-0145-y
[18]	H. Mazhar, T. Osswald, and D. Negrut, On the use of computational multi-body dynamics analysis in SLS-based 3D printing, Addit. Manuf., 12(2016), p. 291.
[19]	M.G. Mitchell, Cell Biology: Translational Impact in Cancer Biology and Bioinformatics, Elsevier, Cambridge, 2016, p. 122.
[20]	C. Jiang, G.F. Zhao, J.B. Zhu, Y.X. Zhao, and L.M. Shen, Investigation of dynamic crack coalescence using a gypsum-like 3D printing material, Rock Mech. Rock Eng., 49(2016), No. 10, p. 3983. doi: 10.1007/s00603-016-0967-3
[21]	T. Zhou, J.B. Zhu, Y. Ju, and H.P. Xie, Volumetric fracturing behavior of 3D printed artificial rocks containing single and double 3D internal flaws under static uniaxial compression, Eng. Fract. Mech., 205(2019), p. 190. doi: 10.1016/j.engfracmech.2018.11.030
[22]	E.M. Gell, S.M. Walley, and C.H. Braithwaite, Review of the validity of the use of artificial specimens for characterizing the mechanical properties of rocks, Rock Mech. Rock Eng., 52(2019), No. 9, p. 2949. doi: 10.1007/s00603-019-01787-8
[23]	R.M. Bishwal, Scope of 3-D printing in mining and geology: An overview, J. Geol. Soc. India, 93(2019), No. 4, p. 482. doi: 10.1007/s12594-019-1203-z
[24]	Q. Jiang, X.T. Feng, L.B. Song, Y.H. Gong, H. Zheng, and J. Cui, Modeling rock specimens through 3D printing: Tentative experiments and prospects, Acta Mech. Sin., 32(2016), No. 1, p. 101. doi: 10.1007/s10409-015-0524-4
[25]	Y. Ju, L. Wang, H.P. Xie, G.W. Ma, L.T. Mao, Z.M. Zheng, and J.B. Lu, Visualization of the three-dimensional structure and stress field of aggregated concrete materials through 3D printing and frozen-stress techniques, Constr. Build. Mater., 143(2017), p. 121. doi: 10.1016/j.conbuildmat.2017.03.102
[26]	T. Zhou and J.B. Zhu, An experimental investigation of tensile fracturing behavior of natural and artificial rocks in static and dynamic Brazilian disc tests, Procedia Eng., 191(2017), p. 992. doi: 10.1016/j.proeng.2017.05.271
[27]	T. Zhou and J.B. Zhu, Identification of a suitable 3D printing material for mimicking brittle and hard rocks and its brittleness enhancements, Rock Mech. Rock Eng., 51(2018), No. 3, p. 765. doi: 10.1007/s00603-017-1335-7
[28]	L.Y. Kong, M. Ostadhassan, C.X. Li, and N. Tamimi, Can 3-D printed gypsum samples replicate natural rocks? An experimental study, Rock Mech. Rock Eng., 51(2018), No. 10, p. 3061. doi: 10.1007/s00603-018-1520-3
[29]	K.J. Hodder, J.A. Nychka, and R.J. Chalaturnyk, Process limitations of 3D printing model rock, Prog. Addit. Manuf., 3(2018), p. 173. doi: 10.1007/s40964-018-0042-6
[30]	X. Wang, M. Jiang, Z.W. Zhou, J.H. Gou, and D. Hui, 3D printing of polymer matrix composites: A review and prospective, Composites Part B, 110(2017), p. 442. doi: 10.1016/j.compositesb.2016.11.034
[31]	T.D. Ngo, A. Kashani, G. Imbalzano, K.T.Q. Nguyen, and D. Hui, Additive manufacturing (3D printing): A review of materials. methods.applications and challenges, Composites Part B, 143(2018), p. 172. doi: 10.1016/j.compositesb.2018.02.012
[32]	Y. Ju, L. Wang, H.P. Xie, G.W. Ma, Z.M. Zheng, and L.T. Mao, Visualization and transparentization of the structure and stress field of aggregated geomaterials through 3D printing and photoelastic techniques, Rock Mech. Rock Eng., 50(2017), No. 6, p. 1383. doi: 10.1007/s00603-017-1171-9
[33]	J.B. Zhu, T. Zhou, Z.Y. Liao, L. Sun, X.B. Li, and R. Chen, Replication of internal defects and investigation of mechanical and fracture behaviour of rock using 3D printing and 3D numerical methods in combination with X-ray computerized tomography, Int. J. Rock Mech. Min. Sci., 106(2018), p. 198. doi: 10.1016/j.ijrmms.2018.04.022
[34]	T. Zhou and J.B. Zhu, Application of 3D printing and micro-CT scan to rock dynamics, [in] H.B. Li, J.C. Li, Q.B. Zhang, and J. Zhao, eds., Rock Dynamics: From Research to Engineering, 2nd International Conference on Rock Dynamics and Applications, Suzhou, 2016, p. 247.
[35]	L.Y. Kong, M. Ostadhassan, C.X. Li, and N. Tamimi, Rock physics and geomechanics of 3-D printed rocks, [in] 51st U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, 2017, p. 2866.
[36]	S.Q. Yang, P.F. Yin, and P.G. Ranjith, Experimental study on mechanical behavior and brittleness characteristics of Longmaxi formation shale in Changning, Sichuan basin, China, Rock Mech. Rock Eng., 53(2020), p. 2461. doi: 10.1007/s00603-020-02057-8
[37]	S. Osinga, G. Zambrano-Narvaez, and R.J. Chalaturnyk, Study of geomechanical properties of 3D printed sandstone analogue, [in] 49th US Rock Mechanics/Geomechanics Symposium, San Francisco, 2015, p. 3137.
[38]	B. Primkulov, J. Chalaturnyk, R. Chalaturnyk, and G. Zambrano-Narvaez, 3D printed sandstone strength: Curing of furfuryl alcohol resin-based sandstones, 3D Print. Addit. Manuf., 4(2017), No. 3, p. 149. doi: 10.1089/3dp.2017.0032
[39]	D. Vogler, S.D.C. Walsh, E. Dombrovski, and M.A. Perras, A comparison of tensile failure in 3D-printed and natural sandstone, Eng. Geol., 226(2017), p. 221. doi: 10.1016/j.enggeo.2017.06.011
[40]	M.A. Perras and D. Vogler, Compressive and tensile behavior of 3D-printed and natural sandstones, Transp. Porous Media, 129(2019), No. 2, p. 559. doi: 10.1007/s11242-018-1153-8
[41]	J.S. Gomez, R.J. Chalaturnyk, and G. Zambrano-Narvaez, Experimental investigation of the mechanical behavior and permeability of 3D printed sandstone analogues under triaxial conditions, Transp. Porous Media, 129(2019), No. 2, p. 541. doi: 10.1007/s11242-018-1177-0
[42]	W. Tian and N.V. Han, Mechanical properties of rock specimens containing pre-existing flaws with 3D printed materials, Strain, 53(2017), No. 6, art. No. e12240. doi: 10.1111/str.12240
[43]	W. Tian and N.V. Han, Preliminary research on mechanical properties of 3D printed rock structures, Geotech. Test. J., 40(2017), No. 3, p. 483.
[44]	S.Q. Yang, Crack coalescence behavior of brittle sandstone samples containing two coplanar fissures in the process of deformation failure, Eng. Fract. Mech., 78(2011), No. 17, p. 3059. doi: 10.1016/j.engfracmech.2011.09.002
[45]	T.H. Wu, Y.T. Gao, Y. Zhou, and J.W. Li, Experimental and numerical study on the interaction between holes and fissures in rock-like materials under uniaxial compression, Theor. Appl. Fract. Mech., 106(2020), art. No. 102488. doi: 10.1016/j.tafmec.2020.102488
[46]	J.X. Zhou, Y. Zhou, and Y.T. Gao, Effect mechanism of fractures on the mechanics characteristics of jointed rock mass under compression, Arab. J. Sci. Eng., 43(2018), No. 7, p. 3659. doi: 10.1007/s13369-017-2980-6
[47]	J. Hiller and H. Lipson, Design and analysis of digital materials for physical 3D voxel printing, Rapid PrototyJ., 15(2009), No. 2, p. 137. doi: 10.1108/13552540910943441
[48]	C. Jiang and G.F. Zhao, Implementation of a coupled plastic damage distinct lattice spring model for dynamic crack propagation in geomaterials, Int. J. Numer. Anal. Methods Geomech., 42(2018), No. 4, p. 674. doi: 10.1002/nag.2761
[49]	Y. Ju, Z. Zheng, H. Xie, J. Lu, L. Wang, and K. He, Experimental visualisation methods for three-dimensional stress fields of porous solids, Exp. Tech., 41(2017), No. 4, p. 331. doi: 10.1007/s40799-017-0178-1
[50]	G.W. Ma, Q.Q. Dong, L.F. Fan, and J.W. Gao, An investigation of non-straight fissures cracking under uniaxial compression, Eng. Fract. Mech., 191(2018), p. 300. doi: 10.1016/j.engfracmech.2017.12.017
[51]	Y. Ju, H.P. Xie, X. Zhao, L.T. Mao, Z.Y. Ren, J.T. Zheng, F.P. Chiang, Y.L. Wang, and F. Gao, Visualization method for stress-field evolution during rapid crack propagation using 3D printing and photoelastic testing techniques, Sci. Rep., 8(2018), No. 1, art. No. 4353. doi: 10.1038/s41598-018-22773-0
[52]	G.W. Ma, Q.Q. Dong, and L. Wang, Experimental investigation on the cracking behavior of 3D printed kinked fissure, Sci. China Technol. Sci., 61(2018), No. 12, p. 1872. doi: 10.1007/s11431-017-9192-7
[53]	H. Haeri, K. Shahriar, M.F. Marji, and P. Moarefvand, Experimental and numerical study of crack propagation and coalescence in pre-cracked rock-like disks, Int. J. Rock Mech. Min. Sci., 67(2014), p. 20. doi: 10.1016/j.ijrmms.2014.01.008
[54]	H. Haeri, A. Khaloo, and M.F. Marji, Experimental and numerical analysis of Brazilian discs with multiple parallel cracks, Arabian J. Geosci., 8(2015), No. 8, p. 5897. doi: 10.1007/s12517-014-1598-1
[55]	M. Sharafisafa, L.M. Shen, Y.G. Zheng, and J.Z. Xiao, The effect of flaw filling material on the compressive behaviour of 3D printed rock-like discs, Int. J. Rock Mech. Min. Sci., 117(2019), p. 105. doi: 10.1016/j.ijrmms.2019.03.031
[56]	R.E. Goodman, R.L. Taylor, and T.L. Brekke, A model for the mechanics of jointed rock, J. Soil Mech. Found. Div, 94(1968), No. 3, p. 637.
[57]	S. Bandis, A.C. Lumsden, and N.R. Barton, Experimental studies of scales effects on the shear behaviour of rock joints, Int. J. Rock Mech. Min. Sci., 18(1981), No. 1, p. 1.
[58]	J.W. Park and J.J. Song, Numerical simulation of a direct shear test on a rock joint using a bonded-particle model, Int. J. Rock Mech. Min. Sci., 46(2009), No. 8, p. 1315. doi: 10.1016/j.ijrmms.2009.03.007
[59]	Z.T. Bieniawski, Determining rock mass deformability: Experience from case histories, Int. J. Rock Mech. Min. Sci., 15(1978), No. 5, p. 237. doi: 10.1016/0148-9062(78)90956-7
[60]	T.S. Ueng, Y.J. Jou, and I.H. Peng, Scale effect on shear strength of computer-aided-manufactured joints, J. GeoEng., 5(2010), No. 2, p. 29.
[61]	R. Kumar and A.K. Verma, Anisotropic shear behavior of rock joint replicas, Int. J. Rock Mech. Min. Sci., 90(2016), p. 62. doi: 10.1016/j.ijrmms.2016.10.005
[62]	Y. Gui, C.C. Xia, W.Q. Ding, X. Qian, and S.G. Du, A new method for 3D modeling of joint surface degradation and void space evolution under normal and shear loads, Rock Mech. Rock Eng., 50(2017), p. 2827. doi: 10.1007/s00603-017-1242-y
[63]	Y. Fang, D. Elsworth, T. Ishibashi, and F.S. Zhang, Permeability evolution and frictional stability of fabricated fractures with specified roughness, J. Geophys. Res. Solid Earth, 123(2018), No. 11, p. 9355. doi: 10.1029/2018JB016215
[64]	M. Asadizadeh, M. Moosavi, M.F. Hossaini, and H. Masoumi, Shear strength and cracking process of non-persistent jointed rocks: An extensive experimental investigation, Rock Mech. Rock Eng., 51(2018), No. 2, p. 415. doi: 10.1007/s00603-017-1328-6
[65]	M. Asadizadeh, M.F. Hossaini, M. Moosavi, H. Masoumi, and P.G. Ranjith, Mechanical characterisation of jointed rock-like material with non-persistent rough joints subjected to uniaxial compression, Eng. Geol., 260(2019), art. No. 105224. doi: 10.1016/j.enggeo.2019.105224
[66]	Y.J. Xia, C.Q. Zhang, H. Zhou, J. Hou, G.S. Su, Y. Gao, N. Liu, and H.K. Singh, Mechanical behavior of structurally reconstructed irregular columnar jointed rock mass using 3D printing, Eng. Geol., 268(2020), art. No. 105509. doi: 10.1016/j.enggeo.2020.105509
[67]	N. Barton and V. Choubey, The shear strength of rock joints in theory and practice, Rock Mech., 10(1977), p. 1. doi: 10.1007/BF01261801
[68]	D.H. Kim, I. Gratchev, M. Hein, and A. Balasubramaniam, The application of normal stress reduction function in tilt tests for different block shapes, Rock Mech. Rock Eng., 49(2016), No. 8, p. 3041. doi: 10.1007/s00603-016-0989-x
[69]	Q.S. Liu, Y.C. Tian, P.Q. Ji, and H. Ma, Experimental investigation of the peak shear strength criterion based on three-dimensional surface description, Rock Mech. Rock Eng., 51(2018), p. 1005. doi: 10.1007/s00603-017-1390-0
[70]	L.B. Gong, A. Heitor, and B. Indraratna, An approach to measure infill matric suction of irregular infilled rock joints under constant normal stiffness shearing, J. Rock Mech. Geotech. Eng., 10(2018), No. 4, p. 653. doi: 10.1016/j.jrmge.2018.02.006
[71]	Y.B. Huang, Y.J. Zhang, Z.W. Yu, Y.Q. Ma, and C. Zhang, Experimental investigation of seepage and heat transfer in rough fractures for enhanced geothermal systems, Renewable Energy, 135(2019), p. 846. doi: 10.1016/j.renene.2018.12.063
[72]	S. Choi, S. Lee, H. Jeong, and S. Jeon, Development of a new method for the quantitative generation of an artificial joint specimen with specific geometric properties, Sustainability, 11(2019), No. 2, art. No. 373. doi: 10.3390/su11020373
[73]	B. Indraratna, A. Haque, and N. Aziz, Laboratory modelling of shear behaviour of soft joints under constant normal stiffness conditions, Geotech. Geol. Eng., 16(1998), p. 17. doi: 10.1023/A:1008880112926
[74]	J. Woodman, W. Murphy, M.E. Thomas, A. Ougier-Simonin, H. Reeves, and T.W. Berry, A novel approach to the laboratory testing of replica discontinuities: 3D printing representative morphologies, [in] 51st US Rock Mechanics/Geomechanics Symposium. San Francisco, 2017, p. 143.
[75]	Y.J. Xia, C.Q. Zhang, H. Zhou, J.L. Chen, Y. Gao, N. Liu, and P.Z. Chen, Structural characteristics of columnar jointed basalt in drainage tunnel of Baihetan hydropower station and its influence on the behavior of P-wave anisotropy, Eng. Geol., 264(2020), art. No. 105304. doi: 10.1016/j.enggeo.2019.105304
[76]	Q. Jiang, X.T. Feng, Y.H. Gong, L.B. Song, S.G. Ran, and J. Cui, Reverse modelling of natural rock joints using 3D scanning and 3D printing, Comput. Geotech., 73(2016), p. 210. doi: 10.1016/j.compgeo.2015.11.020
[77]	M.R. Shen and Q.Z. Zhang, Experimental study of shear deformation characteristics of rock mass discontinuities, Chin. J. Rock Mech. Eng., 29(2010), No. 4, p. 713.
[78]	Z.X. Zou, H.M. Tang, X. Liu, R. Yong, and W.D. Ni, Quantitative study of structural plane direct shear test results influenced by sample preparation errors, Chin. J. Rock Mech. Eng., 29(2010), No. 8, p. 1664.
[79]	J.C. Li, L.F. Rong, H.B. Li, and S.N. Hong, An SHPB test study on stress wave energy attenuation in jointed rock masses, Rock Mech. Rock Eng., 52(2019), p. 403. doi: 10.1007/s00603-018-1586-y
[80]	Y. Ju, Y.M. Yang, Z.D. Song, and W.J. Xu, A statistical model for porous structure of rocks, Sci. China Ser. E:Technol. Sci., 51(2008), No. 11, p. 2040. doi: 10.1007/s11431-008-0111-z
[81]	Y. Ju, Q.G. Zhang, Y.M. Yang, H.P. Xie, F. Gao, and H.J. Wang, An experimental investigation on the mechanism of fluid flow through single rough fracture of rock, Sci. China Technol. Sci., 56(2013), No. 8, p. 2070. doi: 10.1007/s11431-013-5274-6
[82]	A. Suzuki, S. Sawasdee, H. Makita, T. Hashida, K.W. Li, and R.N. Horne, Characterization of 3D printed fracture networks, [in] Proceedings of the 41st Workshop on Geothermal Reservoir Engineering, Stanford, 2016.
[83]	A. Suzuki, N. Watanabe, K.W. Li, and R.N. Horne, Fracture network created by 3-D printer and its validation using CT images, Water Resour. Res., 53(2017), No. 7, p. 6330. doi: 10.1002/2017WR021032
[84]	Y. Ju, W.B. Gong, and J.T. Zheng, Characterization of immiscible phase displacement in heterogeneous pore structures: Parallel multicomponent lattice Boltzmann simulation and experimental validation using three-dimensional printing technology, Int. J. Multiphase Flow, 114(2019), p. 50. doi: 10.1016/j.ijmultiphaseflow.2019.02.006
[85]	S. Ishutov, 3D Printing Porous Proxies as a New Tool for Laboratory and Numerical Analyses of Sedimentary Rocks [Dissertation], Iowa State University, Ames, 2017, p. 102.
[86]	S. Ishutov, F.J. Hasiuk, C. Harding, and J.N. Gray, 3D printing sandstone porosity models, Interpretation, 3(2015), No. 3, p. SX49. doi: 10.1190/INT-2014-0266.1
[87]	S. Ishutov and F.J. Hasiuk, 3D printing Berea sandstone: Testing a new tool for petrophysical analysis of reservoirs, Petrophysics, 58(2017), No. 6, p. 592.
[88]	S. Ishutov, F.J. Hasiuk, S.M. Fullmer, A.S. Buono, J.N. Gray, and C. Harding, Resurrection of a reservoir sandstone from tomographic data using three-dimensional printing, AAPG Bull., 101(2017), No. 9, p. 1425. doi: 10.1306/11111616038
[89]	S. Ishutov, F.J. Hasiuk, D. Jobe, and S. Agar, Using resin-based 3D printing to build geometrically accurate proxies of porous sedimentary rocks, Groundwater, 56(2018), No. 3, p. 482. doi: 10.1111/gwat.12601
[90]	F. Hasiuk, S. Ishutov, and A. Pacyga, Validating 3D-printed porous proxies by tomography and porosimetry, Rapid PrototyJ., 24(2018), No. 3, p. 630. doi: 10.1108/RPJ-06-2017-0121
[91]	S. Ishutov, Establishing framework for 3D printing porous rock models in curable resins, Transp. Porous Media, 129(2019), p. 431. doi: 10.1007/s11242-019-01297-9
[92]	L.Y. Kong, M. Ostadhassan, C.X. Li, and N. Tamimi, Pore characterization of 3D-printed gypsum rocks: A comprehensive approach, J. Mater. Sci., 53(2018), p. 5063. doi: 10.1007/s10853-017-1953-1
[93]	A. Piovesan, C. Achille, R. Ameloot, B. Nicolai, and P. Verboven, Pore network model for permeability characterization of three-dimensionally-printed porous materials for passive microfluidics, Phys. Rev. E, 99(2019), No. 3, art. No. 033107. doi: 10.1103/PhysRevE.99.033107
[94]	D. Head and T. Vanorio, Effects of changes in rock microstructures on permeability: 3-D printing investigation, Geophys. Res. Lett., 43(2016), No. 14, p. 7494. doi: 10.1002/2016GL069334
[95]	Y. Ju, Z.Y. Ren, L.T. Mao, and F.P. Chiang, Quantitative visualisation of the continuous whole-field stress evolution in complex pore structures using photoelastic testing and 3D printing methods, Opt. Express, 26(2018), No. 5, p. 6182. doi: 10.1364/OE.26.006182
[96]	Y. Ju, Z.Y. Ren, X.L. Li, Y.T. Wang, L.T. Mao, and F.P. Chiang, Quantification of hidden whole-field stress inside porous geomaterials via three-dimensional printing and photoelastic testing methods, J. Geophys. Res. Solid Earth, 124(2019), No. 6, p. 5408. doi: 10.1029/2018JB016835
[97]	M.C. He, W.L. Gong, H.M. Zhai, and H.P. Zhang, Physical modeling of deep ground excavation in geologically horizontal strata based on infrared thermography, Tunnelling Underground Space Technol., 25(2010), No. 4, p. 366. doi: 10.1016/j.tust.2010.01.012
[98]	X.T. Feng, S.F. Pei, Q. Jiang, Y.Y. Zhou, S.J. Li, and Z.B. Yao, Deep fracturing of the hard rock surrounding a large underground cavern subjected to high geostress: In situ observation and mechanism analysis, Rock Mech. Rock Eng., 50(2017), p. 2155. doi: 10.1007/s00603-017-1220-4
[99]	Q.Y. Zhang, K. Duan, Y.Y. Jiao, and W. Xiang, Physical model test and numerical simulation for the stability analysis of deep gas storage cavern group located in bedded rock salt formation, Int. J. Rock Mech. Min. Sci., 94(2017), p. 43. doi: 10.1016/j.ijrmms.2017.02.015
[100]	K. Skrzypkowski, W. Korzeniowski, K. Zagórski, and P. Dudek, Application of long expansion rock bolt support in the underground mines of Legnica–Głogów copper district, Stud. Geotech. Mech., 39(2017), No. 3, p. 47. doi: 10.1515/sgem-2017-0029
[101]	L.Y. Kong, M. Ostadhassan, S. Zamiran, B. Liu, C.X. Li, and G.G. Marino, Geomechanical upscaling methods: Comparison and verification via 3D printing, Energies, 12(2019), No. 3, p. 382. doi: 10.3390/en12030382
[102]	Y.H. Huang, S.Q. Yang, and W.L. Tian, Cracking process of a granite specimen that contains multiple pre-existing holes under uniaxial compression, Fatigue Fract. Eng. Mater. Struct., 42(2019), No. 6, p. 1341. doi: 10.1111/ffe.12990
[103]	A. Farzadi, M. Solati-Hashjin, M. Asadi-Eydivand, and N.A.A. Osman, Effect of layer thickness and printing orientation on mechanical properties and dimensional accuracy of 3D printed porous samples for bone tissue engineering, PLoS One, 9(2014), No. 9, art. No. e108252. doi: 10.1371/journal.pone.0108252
[104]	L. Wang, Y. Ju, H.P. Xie, G.W. Ma, L.T. Mao, and K.X. He, The mechanical and photoelastic properties of 3D printable stress-visualized materials, Sci. Rep., 7(2017), No. 1, art. No. 10918. doi: 10.1038/s41598-017-11433-4
[105]	O. Sano, I. Ito, and M. Terada, Influence of strain rate on dilatancy and strength of Oshima granite under uniaxial compression, J. Geophys. Res. Solid Earth, 86(1981), No. B10, p. 9299. doi: 10.1029/JB086iB10p09299
[106]	C.D. Martin, The Strength of Massive Lac Du Bonnet Granite Around Underground Openings [Dissertation], University of Manitoba, Winnipeg, 1993, p. 12.
[107]	K.J. Hodder, J.A. Nychka, and R.J. Chalaturnyk, Improvement of the unconfined compressive strength of 3D-printed model rock via silica sand functionalization using silane coupling agents, Int. J. Adhes. Adhes., 85(2018), p. 274. doi: 10.1016/j.ijadhadh.2018.07.001
[108]	M. Haftani, B. Bohloli, A. Nouri, M.R.M. Javan, and M. Moosavi, Size effect in strength assessment by indentation testing on rock fragments, Int. J. Rock Mech. Min. Sci., 65(2014), p. 141. doi: 10.1016/j.ijrmms.2013.10.001
[109]	P.T. Wang, T.H. Yang, T. Xu, M.F. Cai, and C.H. Li, Numerical analysis on scale effect of elasticity, strength and failure patterns of jointed rock masses, Geosci. J., 20(2016), No. 4, p. 539. doi: 10.1007/s12303-015-0070-x
[110]	P. Feng, X.M. Meng, J.F. Chen, and L.P. Ye, Mechanical properties of structures 3D printed with cementitious powders, Constr. Build. Mater., 93(2015), p. 486. doi: 10.1016/j.conbuildmat.2015.05.132