Macro- and Micromechanical Behaviors and Energy Variation of Sandstone under Different Unloading Stress Paths with DEM
Publication: International Journal of Geomechanics
Volume 21, Issue 8
Abstract
Various mechanical responses of rocks under a complex stress state have attracted the attention of engineers. A hollow cylinder torsional apparatus (HCA) was constructed using the discrete element method (DEM). A series of conventional triaxial compression tests under different confining pressures and a complex stress path test with torsion were conducted. The numerical results are consistent with laboratory and theoretical findings, which indicates that the microscopic parameters of the DEM sandstone specimens were correct and reasonable. Based on the HCA DEM specimen, the macro–micromechanical response of sandstone specimens under four typical unloading stress paths were studied, and variations in the strain energy density, strain energy, and dissipated energy of sandstone specimens were obtained. These results could provide a reference for the study of the mechanical properties of unloaded sandstone in geotechnical engineering.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work presented in this paper was financially supported by The National Natural Science Foundation of China (Grant Nos. 41831278 and 51679071), the National Basic Research Program of China (973 Program) (Grant No. 2015CB057903), and the Natural Science Foundation of Jiangsu Province (Grant No. BK20171434).
References
Cundall, P. A. 1978. “Distinct element models of rock and soil structure.” Chap. 4 in Analytical and computational methods in engineering rock mechanics, edited by E. T. Brown, 129–163. London: Allen & Unwin.
Cundall, P. A., and O. D. L. Strack. 1980. “Discussion: A discrete numerical model for granular assemblies.” Géotechnique 30 (3): 331–336. https://doi.org/10.1680/geot.1980.30.3.331.
Hight, D. W., M. J. Symes, and A. J. G. Gens. 1983. “The development of a new hollow cylinder apparatus for investigating the effects of principal stress rotation in soils.” Géotechnique 33 (4): 355–383. https://doi.org/10.1680/geot.1983.33.4.355.
Itasca. 2014. PFC3D particle flow code in 3 dimensions, fish in PFC3D. Minneapolis: Itasca Consulting Group.
Kandasami, R. K., and T. G. Murthy. 2015. “Experimental studies on the influence of intermediate principal stress and inclination on the mechanical behaviour of angular sands.” Granular Matter 17 (2): 217–230. https://doi.org/10.1007/s10035-015-0554-4.
Kim, J. S., J. Y. Kim, and S. R. Lee. 1997. “Analysis of soil nailed earth slope by discrete element method.” Comput. Geotech. 20 (1): 1–14. https://doi.org/10.1016/S0266-352X(96)00010-9.
Kwasniewski, M., and K. Mogi. 1990. “Effect of the intermediate principal stress on the failure of a foliated anisotropic rock.” In Mechanics of jointed and faulted rock, edited by H.-P. Rossmanith, 407–416. Boca Raton, FL: CRC Press.
Li, B., L. L. Chen, and M. Gutierrez. 2017. “Influence of the intermediate principal stress and principal stress direction on the mechanical behavior of cohesionless soils using the discrete element method.” Comput. Geotech. 86: 52–66. https://doi.org/10.1016/j.compgeo.2017.01.004.
Li, B., L. Guo, and F. S. Zhang. 2014a. “Macro-micro investigation of granular materials in torsional shear test.” J. Central South Univ. 21 (7): 2950–2961. https://doi.org/10.1007/s11771-014-2262-3.
Li, B., F. S. Zhang, and M. Gutierrez. 2015. “A numerical examination of the hollow cylindrical torsional shear test using DEM.” Acta Geotech. 10 (4): 449–467. https://doi.org/10.1007/s11440-014-0329-9.
Li, J., L. Wang, X. Wang, R. Wang, Z. Cheng, and L. Dang. 2010. “Research on unloading nonlinear mechanical characteristics of jointed rock masses.” J. Rock Mech. Geotech. Eng. 2 (4): 357–364. https://doi.org/10.3724/SP.J.1235.2010.00357.
Li, X. B., W. Z. Cao, Z. L. Zhou, and Y. Zou. 2014b. “Influence of stress path on excavation unloading response.” Tunnelling Underground Space Technol. 42: 237–246. https://doi.org/10.1016/j.tust.2014.03.002.
Liu, Y. M., H. B. Liu, and H. J. Mao. 2017. “DEM investigation of the effect of intermediate principle stress on particle breakage of granular materials.” Comput. Geotech. 84: 58–67. https://doi.org/10.1016/j.compgeo.2016.11.020.
Lu, M., and G. R. McDowell. 2007. “The importance of modelling ballast particle shape in the discrete element method.” Granular Matter 9 (1–2): 69–80. https://doi.org/10.1007/s10035-006-0021-3.
Manouchehrian, A., and M. Cai. 2016. “Simulation of unstable rock failure under unloading conditions.” Can. Geotech. J. 53 (1): 22–34. https://doi.org/10.1139/cgj-2015-0126.
Marina, S., E. K. Imo-Imo, I. Derek, P. Mohamed, and S. Yong. 2014. “Modelling of hydraulic fracturing process by coupled discrete element and fluid dynamic methods.” Environ. Earth Sci. 72 (9): 3383–3399. https://doi.org/10.1007/s12665-014-3244-3.
Ni, Q., W. Powrie, X. Zhang, and R. Harkness. 2000. “Effect of particle properties on soil behavior: 3-D numerical modeling of shearbox tests.” In Numerical Methods in Geotechnical Engineering, Geotechnical Special Publication 96, edited by G. M. Filz, and D. V. Griffiths, 58–70. Reston, VA: ASCE.
Pan, P. Z., X. T. Feng, and J. A. Hudson. 2012. “The influence of the intermediate principal stress on rock failure behaviour: A numerical study.” Eng. Geol. 124: 109–118. https://doi.org/10.1016/j.enggeo.2011.10.008.
Potyondy, D. O. 2015. “The bonded-particle model as a tool for rock mechanics research and application: Current trends and future directions.” Geosyst. Eng. 18 (1): 1–28. https://doi.org/10.1080/12269328.2014.998346.
Potyondy, D. O., and P. A. Cundall. 2004. “A bonded-particle model for rock.” Int. J. Rock Mech. Min. Sci. 41 (8): 1329–1364. https://doi.org/10.1016/j.ijrmms.2004.09.011.
Sayao, A. V., and Y. P. Vaid. 1992. “A critical assessment of stress nonuniformities in hollow cylinder test specimens.” Soils Found. 31 (1): 60–72. https://doi.org/10.3208/sandf1972.31.60.
Scholtes, L., and F. V. Donze. 2012. “Modelling progressive failure in fractured rock masses using a 3D discrete element method.” Int. J. Rock Mech. Min. Sci. 52: 18–30. https://doi.org/10.1016/j.ijrmms.2012.02.009.
Su, O., and N. A. Akcin. 2011. “Numerical simulation of rock cutting using the discrete element method.” Int. J. Rock Mech. Min. Sci. 48 (3): 434–442. https://doi.org/10.1016/j.ijrmms.2010.08.012.
Tao, M., X. B. Li, and C. Q. Wu. 2012. “Characteristics of the unloading process of rocks under high initial stress.” Comput. Geotech. 45: 83–92. https://doi.org/10.1016/j.compgeo.2012.05.002.
Vaid, Y. P., A. Sayao, E. Hou, and D. Negussey. 1990. “Generalized stress-path-dependent soil behaviour with a new hollow cylinder torsional apparatus.” Can. Geotech. J. 27 (5): 601–616. https://doi.org/10.1139/t90-075.
Wang, S., W. Xu, L. Yan, X.-T. Feng, W.-C. Xie, and H. Chen. 2020. “Experimental investigation and failure mechanism analysis for dacite under true triaxial unloading conditions.” Eng. Geol. 264: 105407. https://doi.org/10.1016/j.enggeo.2019.105407.
Wijewickreme, D., and Y. P. Vaid. 2008. “Experimental observations on the response of loose sand under simultaneous increase in stress ratio and rotation of principal stresses.” Can. Geotech. J. 45 (5): 597–610. https://doi.org/10.1139/T08-001.
Yang, S. Q. 2016. “Experimental study on deformation, peak strength and crack damage behavior of hollow sandstone under conventional triaxial compression.” Eng. Geol. 213: 11–24. https://doi.org/10.1016/j.enggeo.2016.08.012.
Yang, Z. X., X. S. Li, and J. Yang. 2007. “Undrained anisotropy and rotational shear in granular soil.” Géotechnique 57 (4): 371–384. https://doi.org/10.1680/geot.2007.57.4.371.
You, Z., and W. G. Buttlar. 2004. “Discrete element modeling to predict the modulus of asphalt concrete mixtures.” J. Mater. Civ. Eng. 16 (2): 140–146. https://doi.org/10.1061/(ASCE)0899-1561(2004)16:2(140).
Zhang, Y. L., J. F. Shao, Z. B. Liu, C. Shi, and G. De Saxce. 2019. “Effects of confining pressure and loading path on deformation and strength of cohesive granular materials: A three-dimensional DEM analysis.” Acta Geotech. 14 (2): 443–460. https://doi.org/10.1007/s11440-018-0671-4.
Zhao, D. W., E. G. Nezami, Y. M. A. Hashash, and J. Ghaboussi. 2006. “Three-dimensional discrete element simulation for granular materials.” Eng. Comput. 23 (7): 749–770. https://doi.org/10.1108/02644400610689884.
Zheng, Y. L., and S. X. Deng. 2015. “Failure probability model considering the effect of intermediate principal stress on rock strength.” Math. Probl. Eng. 2015: 960973. https://doi.org/10.1155/2015/960973.
Zhou, H., Y. Jiang, J. J. Lu, Y. Gao, and J. Chen. 2018. “Development of a hollow cylinder torsional apparatus for rock.” Rock Mech. Rock Eng. 51 (12): 3845–3852. https://doi.org/10.1007/s00603-018-1563-5.
Zhou, X. P. 2005. “Localization of deformation and stress-strain relation for mesoscopic heterogeneous brittle rock materials under unloading.” Theor. Appl. Fract. Mech. 44 (1): 27–43. https://doi.org/10.1016/j.tafmec.2005.05.003.
Zhou, X. P., Q. L. Ha, Y. X. Zhang, and K. S. Zhu. 2004. “Analysis of deformation localization and the complete stress-strain relation for brittle rock subjected to dynamic compressive loads.” Int. J. Rock Mech. Min. Sci. 41 (2): 311–319. https://doi.org/10.1016/S1365-1609(03)00094-7.
Information & Authors
Information
Published In
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Apr 22, 2020
Accepted: Mar 15, 2021
Published online: May 19, 2021
Published in print: Aug 1, 2021
Discussion open until: Oct 19, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Yunhe Ao, Baoxin Jia, Chuang Sun, Fengpu Liu, Fracture characteristics and energy evolution analysis of pre-cracked granite under uniaxial compression based on a 3D-Clump model, Theoretical and Applied Fracture Mechanics, 10.1016/j.tafmec.2023.103756, 124, (103756), (2023).
- Feng Jiao, Jiang Xu, Shoujian Peng, Meixin He, Xinrui Zhang, Experimental Study on Mechanical Properties and Stability Analysis of Structural Plane under Unloading Normal Stress, Sustainability, 10.3390/su142315656, 14, 23, (15656), (2022).