Particle Breakage Model for Granular Geomaterials Considering Stress Paths
Publication: International Journal of Geomechanics
Volume 23, Issue 12
Abstract
Particle breakage, which is affected by the stress path, is a key factor influencing the mechanical properties of granular geomaterials. According to the results of triaxial tests conducted on granular geomaterials under different stress paths, a particle breakage model considering the effects of the stress path was established in this study, and a mathematical expression of the model and a method to determine the model parameters were established. The results indicated that the integral function of the plastic strain increment can be used to describe the variation in the particle breakage of granular geomaterials under different stress paths; however, the influence of the stress path on the plastic strain increment should be eliminated by introducing a stress-path-related parameter. Because it was difficult to obtain such a parameter directly, particle breakage models under a proportional loading path and a triaxial compression test path were established, and functional expressions of the particle breakage model of granular geomaterials under different stress paths were derived by combining the concepts of constant-breakage surface and stress path decomposition. A comparison of the calculated results with the experimental results showed that the proposed model can not only reasonably predict the particle breakage under different shear strains applied in the loading process but can also describe the variation in the particle breakage under different stress paths, thus validating the proposed model.
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Data Availability Statement
The data of this study are available from the corresponding author upon request.
Acknowledgments
The authors would like to acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 42172295), the Hubei Provincial Education Department Science and Technology Research Project (Grant No. Q20222701), and the project funded by the Natural Science Foundation of Xiaogan (Grant No. XGKJ2022010101). The authors would also like to thank all reviewers who participated in the review process, as well as MJEditor, for providing English editing services during the preparation of this manuscript.
Notation
The following symbols are used in this paper:
- a
- breakage number;
- Br
- relative breakage index;
- Br,p
- particle breakage caused by p;
- Br,q
- particle breakage caused by q;
- B(p, q)
- stress-path-related parameter;
- b
- intermediate variable parameter;
- d
- dilatancy ratio; d = dεv/dεs;
- dp
- average principal stress increment;
- dq
- deviatoric stress increment;
- dW
- total input energy increment;
- dεv
- volumetric strain increment;
- dεs
- shear strain increment;
- f
- constant-breakage surface;
- h
- parameter related to εs;
- M
- critical stress ratio;
- m, n
- parameters related to the critical state;
- p
- average principal stress;
- p0
- initial average principal stress;
- pmax
- maximum average principal stress;
- Q
- parameter set related to q;
- q
- deviatoric stress;
- q0
- initial deviatoric stress;
- q1
- average effective stress corresponding to qmax;
- qcs
- critical deviatoric stress;
- qm
- maximum deviatoric stress;
- qmax
- peak deviatoric stress; deviatoric stress at peak state;
- R
- principal stress ratio; R = Δσ1/Δσ3;
- W
- total input energy;
- wa
- fitting parameter;
- wb
- fitting parameter;
- ε1
- axial strain;
- εcs
- shear strain value of the specimen when the critical state is reached;
- εs
- shear strain;
- εs0
- initial shear strain;
- εv
- volumetric strain;
- η
- stress ratio;
- ηmax
- peak stress ratio; stress ratio at peak state;
- σ1
- axial stress;
- σ3
- confining pressure; and
- ν
- critical-state-related parameter.
References
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.
Cao, Z., J. Chen, X. Ye, C. Gu, Z. Guo, and Y. Cai. 2021. “Experimental study on particle breakage of carbonate gravels under cyclic loadings through large-scale triaxial tests.” Transp. Geotech. 30: 100632. https://doi.org/10.1016/j.trgeo.2021.100632.
Carraro, J. A. H., M. Prezzi, and R. Salgado. 2009. “Shear strength and stiffness of sands containing plastic or nonplastic fines.” J. Geotech. Geoenviron. Eng. 135 (9): 1167–1178. https://doi.org/10.1061/(ASCE)1090-0241(2009)135:9(1167).
Chavez, C., and E. E. Alonso. 2003. “A constitutive model for crushed granular aggregates which includes suction effects.” Soils Found. 43 (4): 215–227. https://doi.org/10.3208/sandf.43.4_215.
Chen, Q., B. Indraratna, J. P. Carter, and S. Nimbalkar. 2016. “Isotropic–kinematic hardening model for coarse granular soils capturing particle breakage and cyclic loading under triaxial stress space.” Can. Geotech. J. 53 (4): 646–658. https://doi.org/10.1139/cgj-2015-0166.
Ciantia, M., 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.
Coop, M. R. 1990. “The mechanics of uncemented carbonate sands.” Géotechnique 40 (4): 607–626. https://doi.org/10.1680/geot.1990.40.4.607.
Daouadji, A., P. Y. Hicher, and A. Rahma. 2001. “An elastoplastic model for granular materials taking into account grainbreakage.” Eur. J. Mech. A. Solids 20 (1): 113–137. https://doi.org/10.10 16/S0997-7538(00)01130-X.
Ding, L. N., and G. Y. Li. 2022. “SBG model for particle breakage of rockfills based on fractal gradation equation.” Chin. J. Geotech. Eng. 44 (2): 264–270. https://doi.org/10.11779/CJGE202202007.
Dong, Z. L., C. X. Tong, S. Zhang, and D. C. Sheng. 2021. “Study on breakage transition matrix of granular soils.” Chin. J. Rock Mech. Eng. 40 (7): 1504–1512. https://doi.org/10.13722/j.cnki.jrme.2020.1109.
Einav, I. 2007. “Breakage mechanics—Part I: Theory.” J. Mech. Phys. Solids 55 (6): 1274–1297. https://doi.org/10.1016/j.jmps.2006.11.003.
Fan, K. W., Y. H. Zheng, B. A. Baudet, and Y. P. H. Cheng. 2021. “Investigation of the ultimate particle size distribution of a carbonate sand.” Soils Found. 61 (6): 1708–1717. https://doi.org/10.1016/j.sandf.2021. 10.002.
Guo, W. L., and L. Chen. 2019a. “A stress–dilatancy relationship for rockfill incorporating particle breakage and intermediate principal-stress ratio.” KSCE J. Civ. Eng. 23 (7): 2847–2851. https://doi.org/ 10.1007/s12205-019-0279-8.
Guo, W. L., J. G. Zhu, B. Qian, and D. Zhang. 2019b. “Particle breakage evolution model of coarse-grained soil and its experimental verification.” Rock Soil Mech. 40 (3): 1023–1029. https://doi.org/10.16285/j.rsm.2017. 2005.
Han, H. Q., S. S. Chen, H. Fu, and C. F. Zheng. 2017. “Particle breakage of rockfill materials under cyclic loadings.” Chin. J. Geotech. Eng. 39 (10): 1753–1760. https://doi.org/10.11779/CJGE201710001.
Hardin, B. O. 1985. “Crushing of soil particles.” J. Geotech. Eng. 111 (10): 1177–1192. https://doi.org/10.1061/(asce)0733-9410(1985)111:10(1177).
Hu, W., Z. Y. Yin, G. Scaringi, C. Dano, and P. Y. Hicher. 2018. “Relating fragmentation, plastic work and critical state in crushable rock clasts.” Eng. Geol. 246: 326–336. https://doi.org/10.1016/j.enggeo.2018.10.012.
Indraratna, B., Q. D. Sun, and S. Nimbalkar. 2015. “Observed and predicted behaviour of rail ballast under monotonic loading capturing particle breakage.” Can. Geotech. J. 52 (1): 73–86. https://doi.org/10.1139/cg j-2013-0361.
Ji, W. D., Y. T. Zhang, W. B. Pei, and D. J. Zuo. 2018. “Influence of loading method and stress level on the particle crushing of coral calcareous sand.” Chin. J. Rock Mech. Eng. 37 (8): 182–190. https://doi.org/10.13722/j.cnki.jrme.2017.1646.
Jia, Y. F., S. C. Chi, and G. Lin. 2010. “Dilatancy unified constitutive model for coarse granular aggregates incorporating particle breakage.” Rock Soil Mech. 331 (5): 1381–1388. https://doi.org/10.16285/j.rsm.2010.05.039.
Jia, Y. F., S. C. Chi, J. Yang, and G. Lin. 2009. “Measurement of breakage energy of coarse granular aggregates.” Rock Soil Mech. 30 (7): 1960–1966. https://doi.org/10.16285/j.rsm.2009. 07.032.
Jia, Y. F., B. Xu, S. C. Chi, B. Xiang, D. Xiao, and Y. Zhou. 2019. “Particle breakage of rockfill material during triaxial tests under complex stress paths.” Int. J. Geomech. 19 (12): 04019124. https://doi.org/10.1061/(asce)gm.1943-5622.0001517.
Jia, Y. F., B. Xu, S. C. 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.1943-562 2.0000977.
Karimpour, H., and P. V. Lade. 2013. “Creep behavior in Virginia Beach sand.” Can. Geotech. J. 50 (11): 1159–1178. https://doi.org/10.1139/cgj-2012-0467.
Kikumoto, M., D. M. Wood, and A. Russell. 2010. “Particle crushing and deformation behavior.” Soils Found. 50 (4): 547–563. https://doi.org/10.1201/noe0415804820.ch39.
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).
Lin, N., S. Li, L. Q. Sun, T. T. Li, and J. S. Yin. 2021. “Study on evolution of particle breakage of carbonate soils based on fractal theory.” Chin. J. Rock Mech. Eng. 40 (3): 640–648. https://doi.org/10.13722/j.cnki.jrme.2020.0591.
Liu, H. B., K. F. Zeng, and Y. Zou. 2020. “Particle breakage of calcareous sand and its correlation with input energy.” Int. J. Geomech. 20 (2): 04019151. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001541.
Liu, M. C., and Y. F. Gao. 2017. “Constitutive modeling of coarse-grained materials incorporating the effect of particle breakage on critical state behavior in a framework of generalized plasticity.” Int. J. Geomech. 17 (5): 04016113. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000759.
Liu, X., S. Li, J. S. Yin, and T. T. Li. 2022. “The effect of drying and wetting cycles on the mechanical properties and particle breakage of carbonate sand.” Acta Geotech. 17 (10): 4641–4654. https://doi.org/10.1007/s114 40-022-01556-y.
Luo, M. X., J. R. Zhang, X. X. Liu, and D. D. Xu. 2021. “Critical state elastoplastic constitutive model of angular-shaped and fragile granular materials.” Mar. Georesour. Geotechnol. 39 (8): 937–950. https://doi.org/10.1080/1064119X.2020.1785065.
McDowell, G. R. 2002. “On the yielding and plastic compression of sand.” Soils Found. 42 (1): 139–145. https://doi.org/10.3208/sandf.42.139.
McDowell, G. R., M. D. Bolton, and D. Robertson. 1996. “The fractal crushing of granular materials.” J. Mech. Phys. Solids 44 (12): 2079–2102. https://doi.org/10.1016/S0022-5096(96)00058-0.
Miura, N., and S. O-Hara. 1979. “Particle crushing of a decomposed granite soil under shear stresses.” Soils Found. 19 (3): 1–14. https://doi.org/10.3208/sandf1972.19.3_1.
Murthy, T. G., D. Loukidis, J. A. H. Carraro, M. Prezzi, and R. Salgado. 2007. “Undrained monotonic response of clean and silty sands.” Géotechnique 57 (3): 273–288. https://doi.org/10.1680/geot.2007.57.3.273.
Ning, F. W., J. M. Liu, X. J. Kong, and D. G. Zou. 2020. “Critical state and grading evolution of rockfill material under different triaxial compression tests.” Int. J. Geomech. 20 (2): 04019154. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001550.
Ovalle, C., and P. Y. Hicher. 2020. “Modeling the effect of wetting on the mechanical behavior of crushable granular materials.” Geosci. Front. 11 (2): 487–494. https://doi.org/10.1016/j.gsf. 2019.06.009.
Qin, S. L., L. Q. Yang, H. Gao, S. X. Chen, and W. J. Luo. 2014. “Experimental study of mechanical properties of coarse aggregates of sericite schist under different stress paths.” Chin. J. Rock Mech. Eng. 33 (9): 1932–1938. https://doi.org/10.13722/j.cnki.jrme.2014.09.025.
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.
Sadrekarimi, A., and S. M. Olson. 2011. “Critical state friction angle of sands.” Géotechnique 61 (9): 771–783. https://doi.org/10.1680/geot.9.P.090.
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.
Shen, C. K., S. C. Chi, and Y. F. Jia. 2010. “A constitutive model for coarse granular soil incorporating particle breakage.” Rock Soil Mech. 31 (7): 2111–2115. https://doi.org/10.16285/j.rsm.2010.07.021.
Shi, J., Y. Xiao, J. Hu, H. Wu, H. Liu, and W. Haegeman. 2022. “Small-strain shear modulus of calcareous sand under anisotropic consolidation.” Can. Geotech. J. 59 (6): 878–888. https://doi.org/10.1139/cgj-2021-0329.
Sun, Y. F., H. L. Liu, and G. Yang. 2013. “Yielding function for coarse aggregates considering gradation evolution induced by particle breakage.” Rock Soil Mech. 34 (12): 3479–3484. https://doi.org/10.16285/j.rsm.2013. 12.006.
Sun, Y. F., Y. Xiao, and W. Ju. 2014. “Bounding surface model for ballast with additional attention on the evolution of particle size distribution.” Sci. China Technol. Sci. 57 (7): 1352–1360. https://doi.org/10.1007/s11431-014-5575-4.
Tengattini, A., A. Das, and I. Einav. 2016. “A constitutive modelling framework predicting critical state in sand undergoing crushing and dilation.” Géotechnique 66 (9): 695–616. https://doi.org/10.1680/jgeot.14.P.164.
Ueng, T. S., and T. J. Chen. 2000. “Energy aspects of particle breakage in drained shear of sands.” Géotechnique 50 (1): 65–72. https://doi.org/10.1680/geot.2000.50.1.65.
Vilhar, G., V. Jovic, and M. R. Coop. 2013. “The role of particle breakage in the mechanics of a non-plastic silty sand.” Soils Found. 53 (1): 91–104. https://doi.org/10.1016/j.sandf.2012.12.006.
Wang, G., Z. N. Wang, Q. G. Ye, and J. J. Zha. 2021a. “Particle breakage evolution of coral sand using triaxial compression tests.” J. Rock Mech. Geotech. Eng. 13: 321–334. https://doi.org/ 10.1016/j.jrmge.2020.06.010.
Wang, X. Z., Y. L. Weng, H. Z. Wei, Q. S. Meng, and M. J. Hu. 2019. “Particle obstruction and crushing of dredged calcareous soil in the Nansha Islands, South China Sea.” Eng. Geol. 261: 105274. https://doi.org/10.1016/j.enggeo.2019.105274.
Wang, Y., S. Zhang, D. H. Ao, Y. Z. Yu, and X. Sun. 2018. “Particle breakage characteristics of rockfills under complex stress paths.” Chin. J. Geotech. Eng. 40 (4): 698–7062. https://doi.org/10.11779/CJGE201804014.
Wang, Z. N., G. Wang, Q. G. Ye, and H. Yin. 2021b. “Particle breakage model for coral sand under triaxial compression stress paths.” Chin. J. Geotech. Eng. 43 (3): 540–546. https://doi.org/10.11779/CJGE2021030.17.
Wei, H. Z., X. X. Li, S. D. Zhang, T. Zhao, M. Yin, and Q. S. Meng. 2021. “Influence of particle breakage on drained shear strength of calcareous sands.” Int. J. Geomech. 21 (7): 04021118. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002078.
Wei, H. Z., Z. Tao, J. He, Q. Meng, and X. Wang. 2018. “Evolution of particle breakage for calcareous sands during ring shear tests.” Int. J. Geomech. 18 (2): 04017153. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001073.
Wei, S. 2006. “Study on wetting deformation behaviour and numerical model of coarse-grained materials.” Ph.D. thesis, College of Civil Engineering, Hohai Univ.
Wu, Y., H. Yamamoto, J. Cui, and H. Cheng. 2020. “Influence of load mode on particle crushing characteristics of silica sand at high stresses.” Int. J. Geomech. 20 (3): 04019194. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001600.
Xiao, Y., H. Liu, Y. Chen, and J. Chu. 2014. “Strength and dilatancy of silty sand.” J. Geotech. Geoenviron. Eng. 140 (7): 06014007. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001136.
Xiao, Y., H. L. Liu, C. S. Desai, Y. F. Sun, and H. Liu. 2016a. “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, P. Xiao, and J. Xiang. 2016b. “Fractal crushing of carbonate sands under impact loading.” Geotech. Lett. 6 (3): 199–204. https://doi.org/10.1680/jgele.16.00056.
Xiao, Y., M. Q. Meng, A. Daouadji, Q. S. Chen, Z. J. Wu, and X. Jiang. 2020. “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, W. Zhou, J. Q. Shi, and C. S. Desai. 2022a. “Evolution of particle shape produced by sand breakage.” Int. J. Geomech. 22 (4): 4022003. https://doi.org/10.1061/(ASCE)GM.19 43-5622.0002333.
Xiao, Y., C. G. Wang, J. Q. Shi, L. H. Long, and H. L. Liu. 2022b. “Fracturing and ultimate state of binary carbonate sands.” Int. J. Geomech. 22 (7): 04022089. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002450.
Xu, M., E. Song, and J. Chen. 2012. “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.
Yang, G., B. Y. Zhang, Y. Z. Yu, and X. Sun. 2010. “An experimental study on particle breakage of coarse-grained materials under various stress paths.” J. Hydraul. Eng. 41 (3): 338–342. https://doi.org/10.13243/j.cnki.slxb.2010.03.014.
Yang, Y., Y. H. Tian, C. H. Zhang, L. Wang, M. Zhou, and J. B. He. 2022. “An approach to predict soil particle breakage and gradation evolution for carbonate sands.” Powder Technol. 404: 117404. https://doi.org/10.1016/j.powtec.2022.117404.
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.
Yu, F. W. 2018. “Particle breakage and the undrained shear behavior of sands.” Int. J. Geomech. 18 (7): 04018079. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001203.
Yu, F. W. 2019. “Particle breakage in granular soils: A review.” Part. Sci. Technol. 39 (1): 91–100. https://doi.org/10.1080/02726351.2019.1666946.
Zhang, J. R., C. Hua, M. X. Luo, and B. W. Zhang. 2020. “Behavior of particle breakage in calcareous sands during drained triaxial shearing.” Chin. J. Geotech. Eng. 42 (9): 1593–1602. https://doi.org/10.11779/CJG E202009003.
Zhang, J. R., and M. X. Luo. 2020. “Dilatancy and critical state of calcareous sand incorporating particle breakage.” Int. J. Geomech. 20 (4): 04020030. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001637.
Zhang, J. R., M. X. Luo, W. K. Peng, and B. W. Zhang. 2021. “Drained triaxial tests on mechanical properties of calcareous sand under various stress paths.” Chin. J. Geotech. Eng. 43 (4): 593–602. https://doi.org/10.11779/CJGE202104001.
Zhang, J. R., B. W. Zhang, Y. Hu, and X. H. Liao. 2016. “Predicting the particle breakage of granular geomaterials.” Chin. J. Rock Mech. Eng. 35 (9): 1898–1905. https://doi.org/10.13722/j.cnki.jrme.2015.1568.
Zhang, T., C. Zhang, and T. T. Luo. 2022. “Effect of stress anisotropy on deformation and particle breakage of silica sand at high-pressure compression tests.” Constr. Build. Mater. 316: 125835. https://doi.org/10.1016/j.conbuildmat.2021.125835.
Zhu, F. Y. 2017a. “Experimental study on the mechanical properties of rockfill material under different loading stress paths.” Ph.D. thesis, School of Hydraulic Engineering, Dalian Univ. of Technology.
Zhu, M. L. 2017b. “Research on particle breakage of coarse granular soil under complex stress path.” Ph.D. thesis, Dalian Univ. of Technology.
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Published In
International Journal of Geomechanics
Volume 23 • Issue 12 • December 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jan 4, 2023
Accepted: Jun 11, 2023
Published online: Sep 26, 2023
Published in print: Dec 1, 2023
Discussion open until: Feb 26, 2024
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