Technical Papers
Mar 10, 2023

Orthotropic Elastic Model and Its Parameters in Anchored Layered Rock Mass under Varying Incident Angles: Development and Validation

Publication: International Journal of Geomechanics
Volume 23, Issue 5

Abstract

Rock bolting is one of the most effective and economical methods for jointed rock mass reinforcement. Therefore, the elastic constitutive relationship in an anchored rock mass, which could well reflect the rules of strength and deformation, should be studied. An orthotropic elastic model, which considered varying anchorage angles (α) and the corresponding mechanical parameters, was investigated based on the theory of mechanics of composite materials. To verify the suitability of the model and the mechanical parameters, a WAW-3,000 kN servo universal hydraulic testing machine was used to undertake a series of uniaxial compression tests on the anchored layered rock specimens. The mechanical parameters of composite specimens, such as elastic modulus (E), Poisson’s ratio (ν), peak strength, and its variation with α were obtained. The results showed that the anchored effect of a bolt on the layered rock mass was very significant and anisotropic, for instance, increments in the elastic parameters in three orthogonal directions were quite different with the increase in α from 0° to 90°, which mainly depended on the relative volume content of the component materials in a certain direction. Comparing the calculated E with the experimental values, the variation rules for the mechanical parameters maintained good consistency, and this proved that the calculated equations in this work were reasonable and had acceptable precision. The spillway slope of a reservoir was simplified and simulated and the optimal α was obtained, which further demonstrated the reasonability and applicability of the proposed model from the viewpoint of engineering practice.

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Acknowledgments

This research was financially supported by the National Natural Science Foundation Project of China (No. 42167025), Major Science and Technology Special Project of Guizhou Province, China (No. [2018]3011), Science and Technology Foundation Project of Guizhou Province, China (No. [2020]1Z052, [2020]1Y185). They are gratefully acknowledged.

References

De Figueiredo, J. J. S., M. J. S. do Nascimento, E. Hartmann, B. F. Chiba, C. B. da Silva, M. C. de Sousa, C. Silva, and L. K. Santos. 2018. “On the application of Eshelby-Cheng effective model in a porous cracked medium with background anisotropy: An experimental approach.” Geophysics 83: 1–51. https://doi.org/10.1190/geo2018-0625-tiogeo.1.
Dinzart, F., H. Sabar, and S. Berbenni. 2016. “Homogenization of multi-phase composites based on a revisited formulation of the multi-coated inclusion problem.”. Int. J. Eng. Sci. 100: 136–151. https://doi.org/10.1016/j.ijengsci.2015.12.001.
Do, D. P., D. Hoxha, and T. S. Bui. 2015. “Assessment of mechanical properties of interphase in composite like geomaterials by ultrasonic measurement and the extended multi-inclusion model.” J. Appl. Mech. 82: 3. https://doi.org/10.1115/1.4029487.
Dorhmi, K., K. Derrien, Z. Hadjem-Hamouche, L. Morin, and J. P. Chevalier. 2021. “Experimental study and micromechanical modelling of the effective elastic properties of Fe-TiB2 composites.” Compos. Struct. 272: 114122. https://doi.org/10.1016/j.compstruct.2021.114122.
Eshelby, J. D. 1957. “Determination of the elastic field of an ellipsoidal inclusion, and related problems.” Proc. R. Soc. London, Ser. A 24: 2–3. https://doi.org/10.1098/rspa.1957.0133.
Fortsakis, P., K. Nikas, V. Marinos, and P. Marinos. 2012. “Anisotropic behaviour of stratified rock masses in tunnelling.” Eng. Geol. 141: 74–83. https://doi.org/10.1016/j.enggeo.2012.05.001.
Ghazvinian, A., and M. R. Hadei. 2012. “Effect of discontinuity orientation and confinement on the strength of jointed anisotropic rocks.” Int. J. Rock Mech. Min. Sci. 55: 117–124. https://doi.org/10.1016/j.ijrmms.2012.06.008.
Grasselli, G. 2005. “3D behaviour of bolted rock joints: Experimental and numerical study.” Int. J. Rock Mech. Min. Sci. 42 (1): 13–24. https://doi.org/10.1016/j.ijrmms.2004.06.003.
Guo, D. Z. 2001. Layered elastic system mechanics. Harbin, China: Harbin Institute of Technology Press.
He, X., S. Y. Zuo, J. Zhang, Q. Pu, and C. Huang. 2021. “Experimental study on mechanical parameters of unidirectionally reinforced two-way enhanced rock similar materials.” Chin. J. Underground Space Eng. 17: 365–373.
Kang, H., Y. Wu, F. Gao, P. Jiang, P. Cheng, and X. Meng. 2016. “Mechanical performances and stress states of rock bolts under varying loading conditions.” Tunnelling Underground Space. Technol. 52 (Feb.): 138–146. https://doi.org/10.1016/j.tust.2015.12.005.
Lee, S., J. Lee, and S. Ryu. 2019. “Modified Eshelby tensor for an anisotropic matrix with interfacial damage.” Math. Mech. Solids 24 (6): 1749–1762. https://doi.org/10.1177/1081286518805521.
Lee, S., and S. Ryu. 2018. “Theoretical study of the effective modulus of a composite considering the orientation distribution of the fillers and the interfacial damage.” Eur. J. Mech. A. Solids 72: 79–87. https://doi.org/10.1016/j.euromechsol.2018.02.008.
Li, L., P. C. Hagan, S. Saydam, B. Hebblewhite, and Y. Li. 2016. “Parametric study of rock bolt shear behaviour by double shear test.” Rock Mech. Rock Eng. 49 (12): 4787–4797. https://doi.org/10.1007/s00603-016-1063-4.
Li, Y., and C. Liu. 2019. “Experimental study on the shear behavior of fully grouted bolts.” Rock Mech. Rock Eng. 223: 1123–1134. https://doi.org/10.1016/j.conbuildmat.2019.06.207.
Liu, H., and B. Wang. 2019. “Characteristics of geological minerals in northwestern China under polarized light microscope.” World Nonferrous Met. 17: 201–202. https://doi.org/10.3969/j.issn.1002-5065.2019.17.120.
National Standards Writing Group. 2010. Code for design of concrete structures. GB/T50010-2010. Beijing: China Planning Press.
National Standards Writing Group. 2013. Standard for test methods of engineering rock mass. GB/T50266-2013. Beijing: China Planning Press.
Park, I., J. Moon, S. Bae, J. E. Oh, and S. Yoon. 2020. “Application of micro-CT to Mori-Tanaka method for non-randomly oriented pores in air-entrained cement pastes.” Constr. Build. Mater. 255: 119342. https://doi.org/10.1016/j.conbuildmat.2020.119342.
Perazzelli, P., and G. Anagnostou. 2013. “Stress analysis of reinforced tunnel faces and comparison with the limit equilibrium method.” Tunnelling Underground Space Technol. 38: 87–98. https://doi.org/10.1016/j.tust.2013.05.008.
Ren, M. Y., Q. Y. Zhang, S. Y. Chen, L. Y. Zhang, Y. Y. Jiao, and W. Xiang. 2020. “Experimental study on mechanical properties of anchored rock-like material with weak interlayer under uniaxial compression.” Geotech. Geol. Eng. 38 (5): 4545–4556. https://doi.org/10.1007/s10706-020-01309-2.
Shen, G. L., K. G. Hu, and B. Liu. 2006. Mechanical of composite materials. Beijing: Tsinghua University Press.
Shil’ko, S. V., D. A. Chernous, S. V. Panin, and H. Choe. 2021. “A method for predicting the parameters of plastic deformation of dispersedly reinforced materials by using a modified Mori-Tanaka model.” Mech. Compos. Mater. 57 (2): 153–160. https://doi.org/10.1007/s11029-021-09942-5.
Singh, H. K., and A. Basu. 2017. “A comparison between the shear behavior of ‘real’ natural rock discontinuities and their replicas.” Rock Mech. Rock Eng. 51: 329–340. https://doi.org/10.1007/s00603-017-1334-8.
Song, G. H. 2006. Study on the integral mechanical properties of bolted joint rockmass. Wuhan, China: Wuhan Univ. of Technology.
Tang, X., Q. Zhang, Y. Zhou, and D. Ma. 2021. “Damage and acoustic emission characteristics of combined rock mass with anchor under different inclination angles and combination modes.” Geotech. Geol. Eng. 39: 5895–5906. https://doi.org/10.1007/s10706-021-01903-y.
Teng, J. Y., Y. N. Zhang, J. X. Tang, C. Zhang, and C. L. Li. 2017. “Mechanical behaviors of anchored bedding rock under uniaxial compression.” Rock Soil Mech. 8 (7): 1974–1982 and 1998. https://doi.org/10.16285/j.rsm.2017.07.017.
Teymen, A., and A. Kilic. 2018. “Effect of grout strength on the stress distribution (tensile) of fully-grouted rockbolts.” Tunnelling Underground Space Technol. 77 (JUL.): 280–287. https://doi.org/10.1016/j.tust.2018.04.022.
Wang, Z., Q. Zhang, J. Liu, and L. Y. Fu. 2021. “Effective moduli of rocks predicted by the Kuster-Toksöz and Mori-Tanaka models.” J. Geophys. Eng. 18 (4): 539–557. https://doi.org/10.1093/jge/gxab034.
Xie, H. P. 2019. “Research review of the state key research development program of China: Deep rock mechanics and mining theory.” Chin. J. Coal Soc. 5: 1283–1305. https://doi.org/CNKI:SUN: MTXB.0.2019-05-002.
Yang, Y. Y., and S. Y. Wang. 1995. “Study on toughening of jointed rock masses reinforced with bolts.” Chin. J. Geotech. Eng. 17: 9–17. https://doi.org/10.1007/BF02943584.
Zhang, J., S. Zuo, Y. Zhang, H. E. Xing, and L. Wang. 2019. “Study on orthogonal experiment of proportion of rock similar material.” Water Resour. Hydropower Eng. 50 (3): 161–168. https://doi.org/10.13928/j.cnki.wrahe.2019.03.022.
Zhang, Y. J., and Y. P. Liu. 2002a. “Constitute relation and failure criterion of anchored orthotropic rock mass.” Chin. Acta Mech. Sin. 34: 812–819. https://doi.org/CNKI:SUN:LXXB.0.2002-05-019.
Zhang, Y. J., and Y. P. Liu. 2002b. “3D elasto-plastic fem analysis for bolted orthotropic rock mass.” Chin. J. Rock Mech. Eng. 21 (2002): 1115–1119. https://doi.org/CNKI:SUN:YSLX.0.2002-08-002.
Zhao, L., Q. Yao, D. H. Han, F. Yan, and M. Nasser. 2016. “Characterizing the effect of elastic interactions on the effective elastic properties of porous, cracked rocks.” Geophys. Prospect. 64 (1): 157–169. https://doi.org/10.1111/1365-2478.12243.
Zhao, Z., W. Sun, S. Chen, W. Wang, and Q. Wang. 2020. “Coupling model of jointed rock mass and rock bolt in offshore LPG underground storage.” Energy Sci. Eng. 88 (5): 1468–1483. https://doi.org/10.1002/ese3.605.
Zhou, Y. Y., X. T. Feng, D. P. Xu, and Q. X. Fan. 2016. “Experimental investigation of the mechanical behavior of bedded rocks and its implication for high sidewall caverns.” Rock Mech. Rock Eng. 49 (9): 3643–3669. https://doi.org/10.1007/s00603-016-1018-9.
Zhu, W. S., and W. Z. Ren. 2001. “Research on reinforcing effect for jointed rock masses of shiplock slope by physical modeling.” Chin. J. Rock Mech. Eng. 20 (5): 720–725. https://doi.org/10.3321/j.issn:1000-6915.2001.05.024.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 23Issue 5May 2023

History

Received: May 23, 2022
Accepted: Nov 20, 2022
Published online: Mar 10, 2023
Published in print: May 1, 2023
Discussion open until: Aug 10, 2023

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Graduate Student, Key Laboratory of Karst Geological Resources and Environment, Ministry of Education, Guizhou Univ., Guiyang 550025, China. ORCID: https://orcid.org/0000-0001-7074-4273. Email: [email protected]
Shuang-ying Zuo [email protected]
Professor, College of Resource and Environmental Engineering, Guizhou Univ., Guiyang 550025, China; Key Laboratory of Karst Geological Resources and Environment, Ministry of Education, Guizhou Univ., Guiyang 550025, China (corresponding author). Email: [email protected]
Shi-wan Chen [email protected]
Associate Professor, College of Resource and Environmental Engineering, Guizhou Univ., Guiyang 550025, China; Key Laboratory of Karst Geological Resources and Environment, Ministry of Education, Guizhou Univ., Guiyang 550025, China. Email: [email protected]
Graduate Student, College of Resource and Environmental Engineering, Guizhou Univ., Guiyang 550025, China. Email: [email protected]

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