Undrained Responses of Anisotropic Granular Material under Rotational Shear by DEM
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 148, Issue 12
Abstract
The undrained response of sand under complex loading conditions involving principal stress rotation (PSR) is of particular interest in practical engineering. Although this subject has been studied extensively through laboratory experiments, more in-depth investigations of the microscopic mechanism underlying the macroscale observations under PSR have not been reported adequately. The discrete element method (DEM) plays an important role in the investigation of the elementary behavior of sand subjected to various complex loading conditions. It could enable us to comprehend the evolution of particle-scale quantities. Therefore, an advanced discrete element approach that can apply an arbitrary undrained loading path is implemented in this study. Based on this approach, numerical algorithms that implement undrained rotational shear are elucidated, and undrained pure PSR tests are conducted on anisotropic specimens with varying stress ratios, densities, and intermediate principal stress ratios. The evolution of the fabric anisotropy of specimens under PSR is quantified by a contact normal fabric tensor. The macroscopic mechanical results are found to be consistent with the experimental results. The interplay between fabric evolution with stress and strain increments is examined. The findings provide effective microscopic insights into the anisotropic responses of granular materials under rotational shear.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The research described in this paper was supported by the Department of Transport of Zhejiang Province through Project No. 2021019 and Natural Science Foundation of China (Nos. 51825803 and 52020105003), which are gratefully acknowledged.
References
Chang, C. S., and K. Bennett. 2017. “Micromechanical modeling for the deformation of sand with noncoaxiality between the stress and material axes.” J. Eng. Mech. 143 (1): C4015001. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000966.
Fang, H., Y. Shen, and Y. Zhao. 2019. “Multishear bounding surface modelling of anisotropic sands accounting for fabric and its evolution.” Comput. Geotech. 110 (Jun): 57–70. https://doi.org/10.1016/j.compgeo.2019.02.015.
Gao, Z., and J. Zhao. 2017. “A non-coaxial critical-state model for sand accounting for fabric anisotropy and fabric evolution.” Int. J. Solids Struct. 106–107 (Feb): 200–212. https://doi.org/10.1016/j.ijsolstr.2016.11.019.
Gutierrez, M., K. Ishihara, and I. Towhata. 1991. “Flow theory for sand during rotation of principal stress direction.” Soils Found. 31 (4): 121–132. https://doi.org/10.3208/sandf1972.31.4_121.
Horne, M. R. 1965. “The behaviour of an assembly of rotund, rigid, cohesionless particles. I.” Proc. R. Soc. London, Ser. A 286 (1404): 62–78. https://doi.org/10.1098/rspa.1965.0130.
Huang, X., K. J. Hanley, C. O’Sullivan, C. Y. Kwok, and M. A. Wadee. 2014. “DEM analysis of the influence of the intermediate stress ratio on the critical-state behaviour of granular materials.” Granular Matter 16 (5): 641–655. https://doi.org/10.1007/s10035-014-0520-6.
Huang, X., C. O’Sullivan, Z. X. Zhang, C. Y. Kwok, and K. J. Hanley. 2017. “Exploring the undrained cyclic behaviour of sand using DEM.” In Proc., 7th Int. Conf. on Discrete Element Methods (DEM), 757–765. Singapore: Springer-Verlag.
Ishihara, K. 1993. “Liquefaction and flow failure during earthquakes.” Géotechnique 43 (3): 351–451. https://doi.org/10.1680/geot.1993.43.3.351.
Ishihara, K., and I. Towhata. 1983. “Sand response to cyclic rotation of principal stress directions as induced by wave loads.” Soils Found. 23 (4): 11–26. https://doi.org/10.3208/sandf1972.23.4_11.
Jiang, M. J., J. M. Konrad, and S. Leroueil. 2003. “An efficient technique for generating homogeneous specimens for DEM studies.” Comput. Geotech. 30 (7): 579–597. https://doi.org/10.1016/S0266-352X(03)00064-8.
Kanatani, K.-I. 1984. “Distribution of directional data and fabric tensors.” Int. J. Eng. Sci. 22 (2): 149–164. https://doi.org/10.1016/0020-7225(84)90090-9.
Lashkari, A., and M. Latifi. 2008. “A non-coaxial constitutive model for sand deformation under rotation of principal stress axes.” Int. J. Numer. Anal. Methods Geomech. 32 (9): 1051–1086. https://doi.org/10.1002/nag.659.
Li, X., D. Yang, and H.-S. Yu. 2016. “Macro deformation and micro-structure of 3D granular assemblies subjected to rotation of principal stress axes.” Granular Matter 18 (3): 53. https://doi.org/10.1007/s10035-016-0632-2.
Li, X., and H.-S. Yu. 2009. “Influence of loading direction on the behavior of anisotropic granular materials.” Int. J. Eng. Sci. 47 (11–12): 1284–1296. https://doi.org/10.1016/j.ijengsci.2009.03.001.
Li, X., and H.-S. Yu. 2010. “Numerical investigation of granular material behaviour under rotational shear.” Géotechnique 60 (5): 381–394. https://doi.org/10.1680/geot.2010.60.5.381.
Li, X., H.-S. Yu, and X.-S. Li. 2013. “A virtual experiment technique on the elementary behaviour of granular materials with discrete element method.” Int. J. Numer. Anal. Methods Geomech. 37 (1): 75–96. https://doi.org/10.1002/nag.1086.
Li, X. S., and Y. F. Dafalias. 2004. “A constitutive framework for anisotropic sand including non-proportional loading.” Géotechnique 54 (1): 41–55. https://doi.org/10.1680/geot.2004.54.1.41.
Li, X. S., and Y. F. Dafalias. 2012. “Anisotropic critical state theory: Role of fabric.” J. Eng. Mech. 138 (3): 263–275. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000324.
Liu, D. Y., C. O’Sullivan, J. Antonio, and H. Carraro. 2021. “Influence of particle size distribution on the proportion of stress-transmitting particles and implications for measures of soil state.” J. Geotech. Geoenviron. Eng. 147 (3): 04020182. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002466.
Miura, K., S. Miura, and S. Toki. 1986. “Deformation behavior of anisotropic dense sand under principal stress rotation.” Soils Found. 26 (1): 36–52. https://doi.org/10.3208/sandf1972.26.36.
Nakata, Y., M. Hyodo, H. Murata, and N. Yasufuku. 1998. “Flow deformation of sands subjected to principal stress rotation.” Soils Found. 38 (2): 115–128. https://doi.org/10.3208/sandf.38.2_115.
Rahman, M. M., H. B. K. Nguyen, A. B. Fourie, and M. R. Kuhn. 2021. “Critical state soil mechanics for cyclic liquefaction and postliquefaction behavior: DEM study.” J. Geotech. Geoenviron. Eng. 147 (2): 04020166. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002453.
Rothenburg, L., and R. J. Bathurst. 1989. “Analytical study of induced anisotropy in idealized granular materials.” Géotechnique 39 (4): 601–614. https://doi.org/10.1680/geot.1989.39.4.601.
Sun, J., and S. Sundaresan. 2011. “A constitutive model with microstructure evolution for flow of rate-independent granular materials.” J. Fluid Mech. 682 (Sep): 590–616. https://doi.org/10.1017/jfm.2011.251.
Symes, M. J., A. Gens, and D. W. Hight. 1988. “Drained principal stress rotation in saturated sand.” Géotechnique 38 (1): 59–81. https://doi.org/10.1680/geot.1988.38.1.59.
Tian, Y., and Y. P. Yao. 2018. “Constitutive modeling of principal stress rotation by considering inherent and induced anisotropy of soils.” Acta Geotech. 13 (6): 1299–1311. https://doi.org/10.1007/s11440-018-0680-3.
Tong, Z., P. Fu, Y. F. Dafalias, and Y. Yao. 2014. “Discrete element method analysis of non-coaxial flow under rotational shear.” Int. J. Numer. Anal. Methods Geomech. 38 (14): 1519–1540. https://doi.org/10.1002/nag.2290.
Tong, Z.-X., J.-M. Zhang, Y.-L. Yu, and G. Zhang. 2010. “Drained deformation behavior of anisotropic sands during cyclic rotation of principal stress axes.” J. Geotech. Geoenviron. Eng. 136 (11): 1509–1518. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000378.
Towhata, I., and K. Ishihara. 1985. “Undrained strength of sand undergoing cyclic rotation of principal stress axes.” Soils Found. 25 (2): 135–147. https://doi.org/10.3208/sandf1972.25.2_135.
Triantafyllos, P. K., V. N. Georgiannou, Y. F. Dafalias, and I. O. Georgopoulos. 2021. “Novel findings on the dilatancy and non-coaxiality of sand under generalised loading.” Acta Geotech. 16 (Jun): 1699–1734. https://doi.org/10.1007/s11440-020-01100-w.
Wang, R., Y. F. Dafalias, P. C. Fu, and J. M. Zhang. 2020. “Fabric evolution and dilatancy within anisotropic critical state theory guided and validated by DEM.” Int. J. Solids Struct. 188–189 (Apr): 210–222. https://doi.org/10.1016/j.ijsolstr.2019.10.013.
Wang, R., P. Fu, J.-M. Zhang, and Y. F. Dafalias. 2019. “Deformation of granular material under continuous rotation of stress principal axes.” Int. J. Geomech. 19 (4): 04019017. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001383.
Wang, R., G. Pinzón, E. Andò, and G. Viggiani. 2022. “Modeling combined fabric evolution in an anisometric granular material driven by particle-scale X-ray measurements.” J. Eng. Mech. 148 (1): 04021120. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002032.
Wang, Z.-L., Y. F. Dafalias, and C.-K. Shen. 1990. “Bounding surface hypoplasticity model for sand.” J. Eng. Mech. 116 (5): 983–1001. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:5(983).
Wei, J., D. Huang, and G. Wang. 2020. “Fabric evolution of granular soils under multidirectional cyclic loading.” Acta Geotech. 15 (9): 2529–2543. https://doi.org/10.1007/s11440-020-00942-8.
Wu, Q. X., K. Pan, and Z. X. Yang. 2021a. “Undrained cyclic behavior of granular materials considering initial static shear effect: Insights from discrete element modeling.” Soil Dyn. Earthquake Eng. 143 (Apr): 106597. https://doi.org/10.1016/j.soildyn.2021.106597.
Wu, Q. X., T. T. Xu, and Z. X. Yang. 2020. “Diffuse instability of granular material under various drainage conditions: Discrete element simulation and constitutive modeling.” Acta Geotech. 15 (7): 1763–1778. https://doi.org/10.1007/s11440-019-00885-9.
Wu, Q. X., L. Y. Yan, and Z. X. Yang. 2021b. “Discrete element simulations of drained granular material response under multidirectional rotational shear.” Comput. Geotech. 139 (Nov): 104375. https://doi.org/10.1016/j.compgeo.2021.104375.
Wu, Q. X., and Z. X. Yang. 2021. “Novel undrained servomechanism in discrete-element modeling and its application in multidirectional cyclic shearing simulations.” J. Eng. Mech. 147 (3): 04020155. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001896.
Wu, Q. X., Z. X. Yang, and X. Li. 2019. “Numerical simulations of granular material behavior under rotation of principal stresses: Micromechanical observation and energy consideration.” Meccanica 54 (4–5): 723–740. https://doi.org/10.1007/s11012-018-00939-4.
Xue, L., N. P. Kruyt, R. Wang, and J.-M. Zhang. 2019. “3D DEM simulation of principal stress rotation in different planes of cross-anisotropic granular materials.” Int. J. Numer. Anal. Methods Geomech. 43 (14): 2227–2250. https://doi.org/10.1002/nag.2945.
Yang, D. S. 2014. “Microscopic study of granular material behaviors under general stress paths.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Nottingham.
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.
Yang, Z. X., D. Liao, and T. T. Xu. 2020. “A hypoplastic model for granular soils incorporating anisotropic critical state theory.” Int. J. Numer. Anal. Methods Geomech. 44 (6): 723–748. https://doi.org/10.1002/nag.3025.
Yang, Z. X., and Y. Wu. 2017. “Critical state for anisotropic granular materials: A discrete element perspective.” Int. J. Geomech. 17 (2): 04016054. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000720.
Yang, Z. X., T. T. Xu, and Y. N. Chen. 2018. “Unified modeling of the influence of consolidation conditions on monotonic soil response considering fabric evolution.” J. Eng. Mech. 144 (8): 04018073. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001499.
Yoshimine, M., K. Ishihara, and W. Vargas. 1998. “Effects of principal stress direction and intermediate principal stress on undrained shear behavior of sand.” Soils Found. 38 (3): 179–188. https://doi.org/10.3208/sandf.38.3_179.
Zhao, C.-F., and N. P. Kruyt. 2020. “An evolution law for fabric anisotropy and its application in micromechanical modelling of granular materials.” Int. J. Solids Struct. 196–197 (Jul): 53–66. https://doi.org/10.1016/j.ijsolstr.2020.04.007.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 148 • Issue 12 • December 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Dec 20, 2021
Accepted: Jul 6, 2022
Published online: Oct 3, 2022
Published in print: Dec 1, 2022
Discussion open until: Mar 3, 2023
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
- Sheng Zhang, Qingsong Zhao, Xueqian Ni, Numerical explanation of microscopic/macroscopic behavior of reliquefied sand using 3D DEM with non-spherical particles, Powder Technology, 10.1016/j.powtec.2023.118274, 417, (118274), (2023).
- Q. X. Wu, K. Pan, Z. X. Yang, Effects of initial static shear on undrained cyclic behavior of granular materials: energy evolution and micromechanical interpretation, Granular Matter, 10.1007/s10035-022-01291-x, 25, 1, (2022).