Elastoplastic Constitutive Model of Sand–Gravel Composites Considering the Whole Shearing Process
Publication: Journal of Engineering Mechanics
Volume 148, Issue 9
Abstract
In the framework of generalized plasticity theory, this paper presents a new elastoplastic model to characterize complicated softening/hardening and dilation/contraction behaviors of sand–gravel composites in triaxial tests. The model has six parameters that are determined by the conventional triaxial test directly, which is of great practical interest to engineers. The dilatancy equation that is able to describe the dilatancy of sand–gravel composites during the whole shearing process is incorporated into the model. The advantage of the proposed model in predicting the dilatancy behavior of sand–gravel composites is demonstrated by comparing it with three widely used dilatancy equations. A set of drained triaxial compression tests were launched to examine the performance of the proposed model. In addition, the applicability of the model is also confirmed by sand–gravel composites tests covering a wider range of confining pressure in previous literature. The generality of the model on other granular materials including rockfill, Ottawa sand, calcareous sand, cement-sand–gravel material, and glass beads mixtures is also verified by comparing the experimental results with the corresponding fitting results. Furthermore, the proposed model is programmed into the nonlinear finite element program GEODYNA and applied to the numerical simulation of high concrete-faced sand–gravel dams. Summarizing the fitting and numerical results comprehensively, the constitutive model proposed in this study is capable of characterizing the mechanical behaviors of granular materials and can provide a powerful tool for geotechnical engineering.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51979026 and 52009017), National Key R&D Program of China (2021YFB2601102), and the Fundamental Research Funds for the Central Universities (DUT21TD106). These financial supports are gratefully acknowledged. We also thank Prof. Degao Zou and Prof. Jingmao Liu for their guidance and help in the numerical implementation of the model.
References
Altuhafi, F. N., M. R. Coop, and V. N. Georgiannou. 2016. “Effect of particle shape on the mechanical behavior of natural sands.” J. Geotech. Geoenviron. Eng. 142 (12): 04016071. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001569.
Been, K., M. G. Jefferies, and J. Hachey. 1991. “The critical state of sands.” Géotechnique 41 (3): 365–381. https://doi.org/10.1680/geot.1991.41.3.365.
Cai, X., J. Yang, X. W. Guo, and Y. L. Wu. 2016. “Elastoplastic constitutive model for cement-sand-gravel material.” Chin. J. Geotech. Eng. 38 (9): 1569–1577. https://doi.org/10.11779/CJGE201609003.
Chen, C., X. Lu, J. Li, J. Chen, Z. Zhou, and L. Pei. 2021a. “A novel settlement forecasting model for rockfill dams based on physical causes.” Bull. Eng. Geol. Environ. 80 (10): 7973–7988. https://doi.org/10.1007/s10064-021-02403-2.
Chen, G., Q. Wu, T. Sun, K. Zhao, E. Zhou, L. Xu, and Y. Zhou. 2021b. “Cyclic behaviors of saturated sand-gravel mixtures under undrained cyclic triaxial loading.” J. Earthquake Eng. 25 (4): 756–789. https://doi.org/10.1080/13632469.2018.1540370.
Chinese Standard. 2019. Standard for soil test method. GB/T 50123-2019. Beijing: China Planning Press.
Chiu, C. F., and X. J. Fu. 2008. “Interpreting undrained instability of mixed soils by equivalent intergranular state parameter.” Géotechnique 58 (9): 751–755. https://doi.org/10.1680/geot.2008.58.9.751.
Cho, G. C., J. Dodds, and J. C. Santamarina. 2006. “Particle shape effects on packing density, stiffness, and strength: Natural and crushed sands.” J. Geotech. Geoenviron. 132 (5): 591–602. https://doi.org/10.1680/geot.2008.58.9.751.
Dafalias, Y. F., and M. T. Manzari. 2004. “Simple plasticity sand model accounting for fabric change effects.” J. Eng. Mech. 130 (6): 622–634. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:6(622).
Daouadji, A., P. Hicher, and A. Rahma. 2001. “An elastoplastic model for granular materials taking into account grain breakage.” Eur. J. Mech. A. Solids 20 (1): 113–137. https://doi.org/10.1016/S0997-7538(00)01130-X.
Desai, C. S., S. Somasundaram, and G. Frantziskonis. 1986. “A hierarchical approach for constitutive modelling of geologic materials.” Int. J. Numer. Anal. Methods 10 (3): 225–257. https://doi.org/10.1002/nag.1610100302.
Duncan, J. M., and C. Chang. 1970. “Nonlinear analysis of stress and strain in soils.” J. Soil Mech. Found. Div. 96 (5): 1629–1653. https://doi.org/10.1061/JSFEAQ.0001458.
Frossard, E., W. Hu, C. Dano, and P. Hicher. 2012. “Rockfill shear strength evaluation: A rational method based on size effects.” Géotechnique 62 (5): 415–427. https://doi.org/10.1680/geot.10.P.079.
Gao, Y., W. Li, and T. Shi. 2021. “Particle breakage and micromechanical characteristics of calcareous sand during shearing.” In Vol. 787 of IOP Conf. Ser.: Earth Environ. Sci. 787 (1): 012047. https://doi.org/10.1088/1755-1315/787/1/012047.
Guo, W., Z. Cai, Y. Wu, C. Zhang, and J. Wang. 2022. “Dilatancy behaviour of rockfill materials and its description.” Eur. J. Environ. Civ. Eng. 26 (5): 1883–1896. https://doi.org/10.1080/19648189.2020.1739562.
Guo, W., J. Zhu, and W. Peng. 2018. “Dilatancy equation and generalized plastic constitutive model for coarse-grained soils.” Chin. J. Geotech. Eng. 40 (6): 1103–1110. https://doi.org/10.11779/CJGE201806016.
Honkanadavar, N. P., and K. G. Sharma. 2013. “Testing and modeling the behavior of riverbed and blasted quarried rockfill materials.” Int. J. Geomech. 14 (6): 04014028. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000378.
Hu, J. 2021. “Data cleaning and feature selection for gravelly soil liquefaction.” Soil Dyn. Earthquake Eng. 145 (Jun): 106711. https://doi.org/10.1016/j.soildyn.2021.106711.
Huang, S., X. Ding, Y. Zhang, and W. Cheng. 2015. “Triaxial test and mechanical analysis of rock-soil aggregate sampled from natural sliding mass.” Adv. Mater. Sci. Eng. 2015 (Mar): 238095. https://doi.org/10.1155/2015/238095.
Jia, Y., B. Xu, S. Chi, B. Xiang, and Y. Zhou. 2017. “Research on the particle breakage of rockfill materials during triaxial tests.” Int. J. Geomech. 17 (10): 04017085. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000977.
Kuang, D., Z. Long, R. Guo, and P. Yu. 2021. “Experimental and numerical investigation on size effect on crushing behaviors of single calcareous sand particles.” Mar. Georesour. Geotechnol. 39 (5): 543–553. https://doi.org/10.1080/1064119X.2020.1725194.
Lade, P. V., and J. M. Duncan. 1975. “Elastoplastic stress-strain theory for cohesionless soil.” J. Geotech. Eng. Div. 101 (10): 1037–1053. https://doi.org/10.1061/AJGEB6.0000204.
Lade, P. V., and R. B. Nelson. 1987. “Modelling the elastic behaviour of granular materials.” Int. J. Numer. Anal. Methods 11 (5): 521–542. https://doi.org/10.1002/nag.1610110507.
Li, T., and H. Zhang. 2010. “Dynamic parameter verification of PZ model and its application of dynamic analysis on rockfill dam.” In Earth and space 2010: Engineering, science, construction, and operations in challenging environments, 2706–2713. Reston, VA: ASCE.
Li, X., L. Han, and Y. Guan. 2018. “State-dependent dilatancy theory and numerical modelling of rockfills.” J. Civ. Eng. Constr. 7 (2): 100–106. https://doi.org/10.32732/jcec.2018.7.2.100.
Li, X., and Y. Wang. 1998. “Linear representation of steady-state line for sand.” J. Geotech. Geoenviron. Eng. 124 (12): 1215–1217. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:12(1215).
Li, X. S., and Y. F. Dafalias. 2000. “Dilatancy for cohesionless soils.” Géotechnique 50 (4): 449–460. https://doi.org/10.1680/geot.2000.50.4.449.
Ling, H. I., and H. Liu. 2003. “Pressure-level dependency and densification behavior of sand through generalized plasticity model.” J. Eng. Mech. 129 (8): 851–860. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:8(851).
Ling, H. I., and S. Yang. 2006. “Unified sand model based on the critical state and generalized plasticity.” J. Eng. Mech. 132 (12): 1380–1391. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:12(1380).
Liu, H., and D. Zou. 2013. “Associated generalized plasticity framework for modeling gravelly soils considering particle breakage.” J. Eng. Mech. 139 (5): 606–615. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000513.
Liu, J., and M. G. Iskander. 2010. “Modelling capacity of transparent soil.” Can. Geotech. J. 47 (4): 451–460. https://doi.org/10.1139/T09-116.
Liu, J., H. Liu, D. Zou, and X. Kong. 2015. “Particle breakage and the critical state of sand.” Soils Found. 55 (1): 220–222. https://doi.org/10.1016/j.sandf.2014.12.018.
Liu, Y., D. Stolle, P. Guo, and J. Emery. 2014. “Stress-path dependency of resilient behaviour of granular materials.” Int. J. Pavement Eng. 15 (7): 614–622. https://doi.org/10.1080/10298436.2013.808340.
Marachi, N. 1969. Strength and deformation characteristics of rockfill materials. Berkeley, CA: Univ. of California, Berkeley.
Ning, F. 2020. Research on the scale effect of coarse grained materials based on super large triaxial apparatus. Dalian, China: Dalian Univ. of Technology.
Pastor, M. 1991. “A generalized plasticity model for anisotropic behaviour of sand.” In Proc., Int. Conf. on Computer Methods and Advances in Geomechanics, 661–668. Rotterdam, Netherlands: A.A. Balkema.
Pastor, M., and O. C. Zienkiewicz. 1986. “A generalized plasticity, hierarchical model for sand under monotonic and cyclic loading.” Proc., 2nd Int. Symp. on Numerical Models in Geomechanics, edited by G. N. Pande and W. F. Van Impe, 131–150. Ghent, Belgium: Jackson and Son.
Pastor, M., O. C. Zienkiewicz, and A. Chan. 1990. “Generalized plasticity and the modelling of soil behavior.” Int. J. Numer. Anal. Methods 14 (3): 151–190. https://doi.org/10.1002/nag.1610140302.
Richart, F. E., J. R. Hall, and R. D. Woods. 1970. “Vibrations of soils and foundations.” In International series in theoretical and applied mechanics. Englewood Cliffs, NJ: Prentice-Hall.
Roscoe, K. H. 1963. “Mechanical behaviour of an idealized ‘wet’ clay.” In Vol. 1 of Proc., 3rd European Conf. on Soil Mechanical, 47–54. Berlin: Springer.
Rowe, P. W. 1962. “The stress-dilatancy relation for static equilibrium of an assembly of particles in contact.” Proc. R. Soc. London, Ser. A 269 (1339): 500–527. https://doi.org/10.1098/rspa.1962.0193.
Shen, C., S. Liu, and L. Wang. 2021. “Elasto-plastic constitutive modelling of compacted rockfill materials: A physically based approach.” Géotechnique 1–41. https://doi.org/10.1680/jgeot.21.00100.
Shi, J., W. Haegeman, and J. Andries. 2021. “Investigation on the mechanical properties of a calcareous sand: The role of the initial fabric.” Mar. Georesour. Geotechnol. 39 (7): 859–875. https://doi.org/10.1080/1064119X.2020.1775327.
Strahler, A., A. W. Stuedlein, and P. W. Arduino. 2016. “Stress-strain response and dilatancy of sandy gravel in triaxial compression and plane strain.” J. Geotech. Geoenviron. Eng. 142 (4): 04015098. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001435.
Strahler, A. W., A. W. Stuedlein, and P. Arduino. 2018. “Three-dimensional stress-strain response and stress-dilatancy of well-graded gravel.” Int. J. Geomech. 18 (4): 04018014. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001118.
Varadarajan, A., K. G. Sharma, S. M. Abbas, and A. K. Dhawan. 2006. “Constitutive model for rockfill materials and determination of material constants.” Int. J. Geomech. 6 (4): 226–237. https://doi.org/10.1061/(ASCE)1532-3641(2006)6:4(226).
Vasko, A. 2015. An investigation into the behavior of Ottawa sand through monotonic and cyclic shear tests. Washington, DC: George Washington Univ.
Wan, R. G., and P. J. Guo. 1998. “A simple constitutive model for granular soils: Modified stress-dilatancy approach.” Comput. Geotech. 22 (2): 109–133. https://doi.org/10.1016/S0266-352X(98)00004-4.
Wang, X., B. Xu, X. Meng, and Q. Fan. 2022. “Experimental study on the dilatancy characteristics and equation of saturated sand–gravel composites during the whole shearing process.” Int. J. Geomech. 22 (3): 04021310. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002306.
Wang, Y., X. Rao, and Z. Wang. 2015. “Effect of gravel content on liquefaction characteristics of saturated sandy gravels.” Chin. Earthquake Eng. J. 37 (2): 390–396. https://doi.org/10.3969/j.issn.1000-0844.2015.02.0390.
Wei, K. M., S. S. Chen, and G. Y. Li. 2019. “Elastoplastic model for cemented coarse-grained materials and its application.” Chin. J. Geotech. Eng. 41 (5): 797–805. https://doi.org/10.11779/CJGE201905001.
Wu, Y., N. Li, X. Wang, J. Cui, Y. Chen, Y. Wu, and H. Yamamoto. 2021. “Experimental investigation on mechanical behavior and particle crushing of calcareous sand retrieved from South China Sea.” Eng. Geol. 280 (Jan): 105932. https://doi.org/10.1016/j.enggeo.2020.105932.
Xiao, Y., M. R. Coop, H. Liu, H. Liu, and J. Jiang. 2016a. “Transitional behaviors in well-graded coarse granular soils.” J. Geotech. Geoenviron. Eng. 142 (12): 06016018. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001551.
Xiao, Y., and H. Liu. 2017. “Elastoplastic constitutive model for rockfill materials considering particle breakage.” Int. J. Geomech. 17 (1): 04016041. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000681.
Xiao, Y., H. Liu, Y. Chen, and J. Jiang. 2014. “Strength and deformation of rockfill material based on large-scale triaxial compression tests. I: Influences of density and pressure.” J. Geotech. Geoenviron. Eng. 140 (12): 04014070. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001176.
Xiao, Y., H. Liu, C. S. Desai, Y. Sun, and H. Liu. 2016b. “Effect of intermediate principal-stress ratio on particle breakage of rockfill material.” J. Geotech. Geoenviron. Eng. 142 (4): 06015017. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001433.
Xiao, Y., H. Liu, Y. Sun, H. Liu, and Y. Chen. 2015. “Stress–dilatancy behaviors of coarse granular soils in three-dimensional stress space.” Eng. Geol. 195 (Sep): 104–110. https://doi.org/10.1016/j.enggeo.2015.05.029.
Xiao, Y., L. Long, T. Matthew Evans, H. Zhou, H. Liu, and A. W. Stuedlein. 2019. “Effect of particle shape on stress-dilatancy responses of medium-dense sands.” J. Geotech. Geoenviron. Eng. 145 (2): 04018105. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001994.
Xiao, Y., M. Meng, A. Daouadji, Q. Chen, Z. Wu, and X. Jiang. 2020a. “Effects of particle size on crushing and deformation behaviors of rockfill materials.” Geosci. Front. 11 (2): 375–388. https://doi.org/10.1016/j.gsf.2018.10.010.
Xiao, Y., Y. Sun, F. Yin, H. Liu, and J. Xiang. 2017. “Constitutive modeling for transparent granular soils.” Int. J. Geomech. 17 (7): 04016150. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000857.
Xiao, Y., Z. Sun, A. W. Stuedlein, C. Wang, Z. Wu, and Z. Zhang. 2020b. “Bounding surface plasticity model for stress-strain and grain-crushing behaviors of rockfill materials.” Geosci. Front. 11 (2): 495–510. https://doi.org/10.1016/j.gsf.2019.06.010.
Xu, B., D. Zou, and H. Liu. 2012a. “Three-dimensional simulation of the construction process of the Zipingpu concrete face rockfill dam based on a generalized plasticity model.” Comput. Geotech. 43 (Jun): 143–154. https://doi.org/10.1016/j.compgeo.2012.03.002.
Xu, M., E. Song, and J. Chen. 2012b. “A large triaxial investigation of the stress-path-dependent behavior of compacted rockfill.” Acta Geotech. 7 (3): 167–175. https://doi.org/10.1007/s11440-012-0160-0.
Xu, Y., X. Feng, H. Zhu, and F. Chu. 2015. “Fractal model for rockfill shear strength based on particle fragmentation.” Granular Matter 17 (6): 753–761. https://doi.org/10.1007/s10035-015-0591-z.
Yang, J., and X. D. Luo. 2015. “Exploring the relationship between critical state and particle shape for granular materials.” J. Mech. Phys. Solids 84 (Nov): 196–213. https://doi.org/10.1016/j.jmps.2015.08.001.
Zhang, J., Y. Li, B. Xu, Q. Meng, Q. Zhang, and R. Wang. 2020. “Testing and constitutive modelling of the mechanical behaviours of gravelly soil material.” Arabian J. Geosci. 13 (13): 1–15. https://doi.org/10.1007/s12517-020-05385-9.
Zhang, Y. D., G. Buscarnera, and I. Einav. 2016. “Grain size dependence of yielding in granular soils interpreted using fracture mechanics, breakage mechanics and Weibull statistics.” Géotechnique 66 (2): 149–160. https://doi.org/10.1680/jgeot.15.P.119.
Zhao, M., G. Liu, L. Deng, and Y. Li. 2021. “Optimizing the compaction characteristics and strength properties of gravelly soils in terms of fine contents.” Adv. Mater. Sci. Eng. 2021 (Jan): 6634237. https://doi.org/10.1155/2021/6634237.
Zhou, W., L. Yang, G. Ma, X. Chang, Z. Lai, and K. Xu. 2016. “DEM analysis of the size effects on the behavior of crushable granular materials.” Granular Matter 18 (1): 1–11. https://doi.org/10.1007/s10035-015-0597-6.
Zienkiewicz, O. C. 1982. “Generalized plasticity and some models for geomechanics.” Numerical methods in geomechanics, 57–78. Dordrecht, Netherlands: Springer.
Zou, D., X. Kong, and B. Xu. 2005. Geotechnical dynamic nonlinear analysis GEODYNA. Dalian, China: Faculty of Infrastructure Engineering, Dalian Univ. of Technology.
Zou, D., B. Xu, X. Kong, H. Liu, and Y. Zhou. 2013. “Numerical simulation of the seismic response of the Zipingpu concrete face rockfill dam during the Wenchuan earthquake based on a generalized plasticity model.” Comput. Geotech. 49 (Apr): 111–122. https://doi.org/10.1016/j.compgeo.2012.10.010.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 148 • Issue 9 • September 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 25, 2022
Accepted: May 8, 2022
Published online: Jul 13, 2022
Published in print: Sep 1, 2022
Discussion open until: Dec 13, 2022
ASCE Technical Topics:
- Composite materials
- Dilatancy
- Engineering fundamentals
- Engineering materials (by type)
- Fluid mechanics
- Granular materials
- Gravels
- Hydrologic engineering
- Infrastructure
- Laboratory tests
- Material mechanics
- Material properties
- Materials engineering
- Models (by type)
- Numerical models
- Pavements
- Sand (material)
- Tests (by type)
- Transportation engineering
- Triaxial tests
- Water and water resources
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.