Constitutive Model for Brittle Granular Materials Considering Competition between Breakage and Dilation
Publication: Journal of Engineering Mechanics
Volume 146, Issue 1
Abstract
A constitutive model is presented for brittle granular materials based on a recent reformulation of the breakage mechanics theory. The primary objective of the study is to capture peak strength with subsequent strain softening in dilatant specimens under shearing and the simultaneous evolution of breakage and dilation. The predictive performance of the model is assessed relative to two experimental datasets from the literature. The influence of the model parameters on the overall material response is described through a detailed calibration procedure based on a benchmark experimental dataset. Comparison of the results of drained triaxial compression experiments on two sands with the predictions of the model indicates that the enriched model can successfully capture the evolution of stress-strain behavior at different confinement levels. The predicted response of dilatant specimens exhibits stress- and density-dependent peak strength and strain softening toward the critical state, which is in agreement with experimental evidence. The simulations of Kurnell sand can reproduce the transition of the volumetric strain from to 0.14 as the confining pressure increases from 760 to 7,800 kPa. The predicted breakage of specimens subjected to different confining pressures is slightly higher than experimental measurements, whereas they exhibit similar trends. The proposed framework is capable of qualitatively reproducing many aspects of the experimentally observed stress-dilatancy-breakage relationship in brittle granular materials.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement No. W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
References
Alshibli, K. A., and M. B. Cil. 2018. “Influence of particle morphology on the friction and dilatancy of sand.” J. Geotech. Geoenviron. Eng. 144 (3): 04017118. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001841.
Alshibli, K. A., M. F. Jarrar, A. M. Druckrey, and R. I. Al-Raoush. 2017. “Influence of particle morphology on 3D kinematic behavior and strain localization of sheared sand.” J. Geotech. Geoenviron. Eng. 143 (2): 04016097. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001601.
Altuhafi, F. N., and M. R. Coop. 2011. “Changes to particle characteristics associated with the compression of sands.” Géotechnique 61 (6): 459–471. https://doi.org/10.1680/geot.9.P.114.
Andò, E., G. Viggiani, S. A. Hall, and J. Desrues. 2013. “Experimental micro-mechanics of granular media studied by x-ray tomography: Recent results and challenges.” Géotechnique Lett. 3 (3): 142–146. https://doi.org/10.1680/geolett.13.00036.
Bandini, V., and M. R. Coop. 2011. “The influence of particle breakage on the location of the critical state line of sands.” Soils Found. 51 (4): 591–600. https://doi.org/10.3208/sandf.51.591.
Ben-Nun, O., and I. Einav. 2010. “The role of self-organization during confined comminution of granular materials.” Philos. Trans. R. Soc. London, Ser. A. 368 (1910): 231–247. https://doi.org/10.1098/rsta.2009.0205.
Bolton, M. D. 1986. “The strength and dilatancy of sands.” Géotechnique 36 (1): 65–78. https://doi.org/10.1680/geot.1986.36.1.65.
Cecconi, M., A. DeSimone, C. Tamagnini, and G. M. B. Viggiani. 2002. “A constitutive model for granular materials with grain crushing and its application to a pyroclastic soil.” Int. J. Numer. Anal. Methods Geomech. 26 (15): 1531–1560. https://doi.org/10.1002/nag.257.
Ciantia, M. O., M. Arroyo, C. O’Sullivan, A. Gens, and T. Liu. 2019. “Grading evolution and critical state in a discrete numerical model of Fontainebleau sand.” Géotechnique 69 (1): 1–15. https://doi.org/10.1680/jgeot.17.P.023.
Cil, M. B., and G. Buscarnera. 2016. “DEM assessment of scaling laws capturing the grain size dependence of yielding in granular soils.” Granular Matter 18 (3): 36. https://doi.org/10.1007/s10035-016-0638-9.
Das, A., G. D. Nguyen, and I. Einav. 2011. “Compaction bands due to grain crushing in porous rocks: A theoretical approach based on breakage mechanics.” J. Geophys. Res. Solid Earth 116 (B8): B08203. https://doi.org/10.1029/2011JB008265.
Einav, I. 2007a. “Breakage mechanics—Part I: Theory.” J. Mech. Phys. Solids 55 (6): 1274–1297. https://doi.org/10.1016/j.jmps.2006.11.003.
Einav, I. 2007b. “Breakage mechanics—Part II: Modelling granular materials.” J. Mech. Phys. Solids 55 (6): 1298–1320. https://doi.org/10.1016/j.jmps.2006.11.004.
Einav, I., and A. M. Puzrin. 2004. “Pressure-dependent elasticity and energy conservation in elastoplastic models for soils.” J. Geotech. Geoenviron. Eng. 130 (1): 81–92. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:1(81).
Frossard, E., W. Hu, C. Dano, and P.-Y. 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.
Gens, A., and D. M. Potts. 1988. “Critical state models in computational geomechanics.” Eng. Comput. 5 (3): 178–197. https://doi.org/10.1108/eb023736.
Ghafghazi, M., D. A. Shuttle, and J. T. DeJong. 2014. “Particle breakage and the critical state of sand.” Soils Found. 54 (3): 451–461. https://doi.org/10.1016/j.sandf.2014.04.016.
Houlsby, G. T., and A. M. Puzrin. 2007. Principles of hyperplasticity: An approach to plasticity theory based on thermodynamic principles. London: Springer.
Hurley, R. C., J. Lind, D. C. Pagan, M. C. Akin, and E. B. Herbold. 2018. “In situ grain fracture mechanics during uniaxial compaction of granular solids.” J. Mech. Phys. Solids 112 (Mar): 273–290. https://doi.org/10.1016/j.jmps.2017.12.007.
Indraratna, B., and S. Nimbalkar. 2013. “Stress-strain degradation response of railway ballast stabilized with geosynthetics.” J. Geotech. Geoenviron. Eng. 139 (5): 684–700. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000758.
Kan, M. E., and H. A. Taiebat. 2014. “A bounding surface plasticity model for highly crushable granular materials.” Soils Found. 54 (6): 1188–1201. https://doi.org/10.1016/j.sandf.2014.11.012.
Karatza, Z., E. Andò, S.-A. Papanicolopulos, J. Y. Ooi, and G. Viggiani. 2018. “Evolution of deformation and breakage in sand studied using X-ray tomography.” Géotechnique 68 (2): 107–117. https://doi.org/10.1680/jgeot.16.P.208.
Kikumoto, M., D. M. Wood, and A. Russell. 2010. “Particle crushing and deformation behaviour.” Soils Found. 50 (4): 547–563. https://doi.org/10.3208/sandf.50.547.
Lade, P. V., and P. A. Bopp. 2005. “Relative density effects on drained sand behavior at high pressures.” J. Jpn. Geotech. Soc. 45 (1): 1–13.
Lade, P. V., J. A. Yamamuro, and P. A. Bopp. 1996. “Significance of particle crushing in granular materials.” J. Geotech. Eng. 122 (4): 309–316. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:4(309).
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, M., Y. Zhang, and H. Zhu. 2017. “3D elastoplastic model for crushable soils with explicit formulation of particle crushing.” J. Eng. Mech. 143 (12): 04017140. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001361.
Luzzani, L., and M. R. Coop. 2002. “On the relationship between particle breakage and the critical state of sands.” Soils Found. 42 (2): 71–82. https://doi.org/10.3208/sandf.42.2_71.
Marone, C., and C. H. Scholz. 1989. “Particle-size distribution and microstructures within simulated fault gouge.” J. Struct. Geol. 11 (7): 799–814. https://doi.org/10.1016/0191-8141(89)90099-0.
Nguyen, G. D., and I. Einav. 2009. “The energetics of cataclasis based on breakage mechanics.” Pure Appl. Geophys. 166 (10–11): 1693–1724. https://doi.org/10.1007/s00024-009-0518-x.
Pestana, J. M., and A. J. Whittle. 1999. “Formulation of a unified constitutive model for clays and sands.” Int. J. Numer. Anal. Methods Geomech. 23 (12): 1215–1243. https://doi.org/10.1002/(SICI)1096-9853(199910)23:12%3C1215::AID-NAG29%3E3.0.CO;2-F.
Petrakis, E., and R. Dobry. 1987. Micromechanical modeling of granular soil at small strain by arrays of elastic spheres. Rep. Troy, NY: Dept. of Civil Engineering, Rensselaer Polytechnic Institute.
Rubin, M. B., and I. Einav. 2011. “A large deformation breakage model of granular materials including porosity and inelastic distortional deformation rate.” Int. J. Eng. Sci. 49 (10): 1151–1169. https://doi.org/10.1016/j.ijengsci.2011.05.002.
Russell, A. R. 2004. “Cavity expansion in unsaturated soils.” Ph.D. thesis, School of Civil and Environmental Engineering, Univ. of New South Wales.
Russell, A. R., and N. Khalili. 2004. “A bounding surface plasticity model for sands exhibiting particle crushing.” Can. Geotech. J. 41 (6): 1179–1192. https://doi.org/10.1139/t04-065.
Sadrekarimi, A., and S. M. Olson. 2010. “Particle damage observed in ring shear tests on sands.” Can. Geotech. J. 47 (5): 497–515. https://doi.org/10.1139/T09-117.
Salim, W., and B. Indraratna. 2004. “A new elastoplastic constitutive model for coarse granular aggregates incorporating particle breakage.” Can. Geotech. J. 41 (4): 657–671. https://doi.org/10.1139/t04-025.
Sammis, C., G. King, and R. Biegel. 1987. “The kinematics of gouge deformation.” Pure Appl. Geophys. 125 (5): 777–812. https://doi.org/10.1007/BF00878033.
Schofield, A., and W. Peter. 1968. Critical state soil mechanics. London: McGraw-Hill.
Sohn, C., Y. D. Zhang, M. Cil, and G. Buscarnera. 2017. “Experimental assessment of continuum breakage models accounting for mechanical interactions at particle contacts.” Granular Matter 19 (4): 67. https://doi.org/10.1007/s10035-017-0750-5.
Taiebat, M., and Y. F. Dafalias. 2008. “SANISAND: Simple anisotropic sand plasticity model.” Int. J. Numer. Anal. Methods Geomech. 32 (8): 915–948. https://doi.org/10.1002/nag.651.
Tengattini, A., A. Das, and I. Einav. 2016. “A constitutive modelling framework predicting critical state in sand undergoing crushing and dilation.” Géotechnique 66 (9): 695–710. https://doi.org/10.1680/jgeot.14.P.164.
Wang, P., and C. Arson. 2016. “Breakage mechanics modeling of the brittle-ductile transition in granular materials.” In Proc., 50th US Rock Mechanics/Geomechanics Symp., 6. Houston: American Rock Mechanics Association.
Wood, D. M., and K. Maeda. 2008. “Changing grading of soil: Effect on critical states.” Acta Geotech. 3 (1): 3. https://doi.org/10.1007/s11440-007-0041-0.
Xiao, Y., H. Liu, Y. Chen, J. Jiang, and W. Zhang. 2015. “State-dependent constitutive model for rockfill materials.” Int. J. Geomech. 15 (5): 04014075. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000421.
Xiao, Y., H. Liu, X. Ding, Y. Chen, J. Jiang, and W. Zhang. 2016. “Influence of particle breakage on critical state line of rockfill material.” Int. J. Geomech. 16 (1): 04015031. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000538.
Xiao, Y., L. Long, T. M. 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.
Yamamuro, J. A. 1993. “Instability and behavior of granular materials at high pressures.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of California.
Yamamuro, J. A., and P. V. Lade. 1996. “Drained sand behavior in axisymmetric tests at high pressures.” J. Geotech. Eng. 122 (2): 109–119. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:2(109).
Yao, Y.-P., H. Yamamoto, and N.-D. Wang. 2008. “Constitutive model considering sand crushing.” Soils Found. 48 (4): 603–608. https://doi.org/10.3208/sandf.48.603.
Yasufuku, N., and A. F. L. Hyde. 1995. “Pile end-bearing capacity in crushable sands.” Géotechnique 45 (4): 663–676. https://doi.org/10.1680/geot.1995.45.4.663.
Youd, T. 1973. “Factors controlling maximum and minimum densities of sands.” In Evaluation of relative density and its role in geotechnical projects involving cohesionless soils, 98–112. West Conshohocken, PA: ASTM.
Yu, F. 2017a. “Particle breakage and the drained shear behavior of sands.” Int. J. Geomech. 17 (8): 04017041. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000919.
Yu, F. W. 2017b. “Particle breakage and the critical state of sands.” Géotechnique 67 (8): 713–719. https://doi.org/10.1680/jgeot.15.P.250.
Zhang, Y. D., and G. Buscarnera. 2017. “A rate-dependent breakage model based on the kinetics of crack growth at the grain scale.” Géotechnique 67 (11): 953–967. https://doi.org/10.1680/jgeot.16.P.181.
Information & Authors
Information
Published In
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jan 16, 2019
Accepted: Apr 30, 2019
Published online: Oct 28, 2019
Published in print: Jan 1, 2020
Discussion open until: Mar 28, 2020
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.