Abstract
It is well known that particle breakage plays a critical role in the mechanical behavior of granular materials and has been a topic subject to intensive studies. This paper presents a three dimensional fracture model in the context of combined finite-discrete element method (FDEM) to simulate the breakage of irregular shaped granular materials, e.g., sands, gravels, and rockfills. In this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted non-thickness cohesive interface elements with a progressive damage model. The Mohr–Coulomb model with tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode at the particle scale. The particle breakage modeling using combined FDEM is validated by the qualitative agreement between the results of simulated single particle crushing tests and those obtained from laboratory tests and prior DEM simulations. A comprehensive numerical triaxial tests are carried out on both the unbreakable and breakable particle assemblies with varied confining pressure and particle crushability. The simulated stress–strain–dilation responses of breakable granular assembly are qualitatively in good agreement with the experimental observations. The effects of particle breakage on the compressibility, shear strength, volumetric response of the fairly dense breakable granular assembly are thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis. This paper also reports the energy input and dissipation behavior and its relation to the mechanical response.
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References
Hardin, B.O.: Crushing of soil particles. J. Geotech. Eng. 111(10), 1177–1192 (1985)
Lade, P.V., Yamamuro, J.A., Bopp, P.A.: Significance of particle crushing in granular materials. J. Geotech. Eng. 122(4), 309–316 (1996)
Coop, M.R., Sorensen, K.K., Freitas, T.B., et al.: Particle breakage during shearing of a carbonate sand. Géotechnique 54(3), 157–163 (2004)
Xiao, Y., Liu, H., Chen, Y., et al.: Strength and deformation of rockfill material based on large-scale triaxial compression tests. II: influence of particle breakage. J. Geotech. Geoenviron. Eng. 140(12), 04014071 (2014)
Robertson, D., Bolton, M.D.: DEM simulations of crushable grains and soils. In: Kishino, Y. (ed.) Powders and Grains, pp. 623–626. Balkema, Lisse (2001)
Cheng, Y.P., Nakata, Y., Bolton, M.D.: Discrete element simulation of crushable soil. Geotechnique 53(7), 633–641 (2003)
Bolton, M.D., Nakata, Y., Cheng, Y.P.: Micro-and macro-mechanical behaviour of DEM crushable materials. Géotechnique 58(6), 471–480 (2008)
Donohue, S., O’sullivan, C., Long, M.: Particle breakage during cyclic triaxial loading of a carbonate sand. Géotechnique 59(5), 477–482 (2009)
Cil, M.B., Alshibli, K.A.: 3D assessment of fracture of sand particles using discrete element method. Geotech. Lett. 2(3), 161–166 (2012)
Alaei, E., Mahboubi, A.: A discrete model for simulating shear strength and deformation behaviour of rockfill material, considering the particle breakage phenomenon. Granul Matter 14(6), 707–717 (2012)
Wang, J., Yan, H.: On the role of particle breakage in the shear failure behavior of granular soils by DEM. Int. J. Numer. Anal. Methods Geomech. 37(8), 832–854 (2013)
Lobo-Guerrero, S., Vallejo, L.E.: Discrete element method evaluation of granular crushing under direct shear test conditions. J. Geotech. Geoenviron. Eng. 131(10), 1295–1300 (2005)
Brosh, T., Kalman, H., Levy, A.: Fragments spawning and interaction models for DEM breakage simulation. Granul. Matter 13(6), 765–776 (2011)
de Bono, J.P., McDowell, G.R.: DEM of triaxial tests on crushable sand. Granul. Matter 16(4), 551–562 (2014)
Zhou, W., Yang, L., Ma, G., et al.: Macro–micro responses of crushable granular materials in simulated true triaxial tests. Granul. Matter 17(4), 497–509 (2015)
Munjiza, A., Owen, D.R.J., Bicanic, N.: A combined finite-discrete element method in transient dynamics of fracturing solids. Eng. Comput. 12(2), 145–174 (1995)
Munjiza, A.: The Combined Finite-Discrete Element Method. Wiley, New York (2004)
Latham, J.P., Munjiza, A.: The modelling of particle systems with real shapes. Philos. Trans. R. Soc. Lond. Ser. Math. Phys. Eng. Sci. 362, 1953–1972 (2004)
Mahabadi, O.K., Cottrell, B.E., Grasselli, G.: An example of realistic modelling of rock dynamics problems: FEM/DEM simulation of dynamic Brazilian test on Barre granite. Rock Mech. Rock Eng. 43(6), 707–716 (2010)
Vyazmensky, A., Stead, D., Elmo, D., et al.: Numerical analysis of block caving-induced instability in large open pit slopes: a finite element/discrete element approach. Rock Mech. Rock Eng. 43(1), 21–39 (2010)
Smoljanović, H., Živaljić, N., Nikolić, Ž.: A combined finite-discrete element analysis of dry stone masonry structures. Eng. Struct. 52(7), 89–100 (2013)
Chang, X.L., Hu, C., Zhou, W., et al.: A combined continuous–discontinuous approach for failure process of quasi-brittle materials. Sci. China Technol. Sci. 57(3), 550–559 (2014)
Ma, G., Zhou, W., Chang, X.L., et al.: Combined FEM/DEM modeling of triaxial compression tests for rockfills with polyhedral particles. Int. J. Geomech. 14(4), 1–14 (2014)
Ma, G., Zhou, W., Chang, X.L.: Modeling the particle breakage of rockfill materials with the cohesive crack model. Comput. Geotech. 61(9), 132–143 (2014)
Latham, J.P., Anastasaki, E., Xiang, J.: New modelling and analysis methods for concrete armour unit systems using FEMDEM. Coast. Eng. 77(7), 151–166 (2013)
Guo, L., Latham, J.P., Xiang, J.: Numerical simulation of breakages of concrete armour units using a three-dimensional fracture model in the context of the combined finite-discrete element method. Comput. Struct. 146, 117–142 (2015)
Latham, J.P., Munjiza, A., Garcia, X., et al.: Three-dimensional particle shape acquisition and use of shape library for DEM and FEM/DEM simulation. Miner. Eng. 21(11), 797–805 (2008)
ABAQUS 6.10. ABAQUS Analysis User’s Manual. Dassault Systèmes Simulia Corp, Providence (2010)
Xu, X.P., Needleman, A.: Numerical simulations of dynamic crack growth along an interface. Int. J. Fract. 74(4), 289–324 (1995)
Chandra, N., Li, H., Shet, C., et al.: Some issues in the application of cohesive zone models for metal–ceramic interfaces. Int. J. Solids Struct. 39(10), 2827–2855 (2002)
Alfano, G.: On the influence of the shape of the interface law on the application of cohesive-zone models. Compos. Sci. Technol. 66(6), 723–730 (2006)
Lisjak, A., Liu, Q., Zhao, Q., et al.: Numerical simulation of acoustic emission in brittle rocks by two-dimensional finite-discrete element analysis. Geophys. J. Int. 195(1), 423–443 (2013)
Day, R.A., Potts, D.M.: Zero thickness interface elements–numerical stability and application. Int. J. Numer. Anal. Methods Geomech. 18(10), 689–708 (1994)
Zou, Z., Reid, S.R., Li, S., et al.: Modelling interlaminar and intralaminar damage in filament-wound pipes under quasi-static indentation. J. Compos. Mater. 36(4), 477–499 (2002)
Camanho, P.P., Davila, C.G., De Moura, M.F.: Numerical simulation of mixed-mode progressive delamination in composite materials. J. Compos. Mater. 37(16), 1415–1438 (2003)
Diehl, T.: On using a penalty-based cohesive-zone finite element approach, part I: elastic solution benchmarks. Int. J. Adhes. Adhes. 28(4), 237–255 (2008)
Song, S.H., Paulino, G.H., Buttlar, W.G.: A bilinear cohesive zone model tailored for fracture of asphalt concrete considering viscoelastic bulk material. Engi. Fract. Mech. 73(18), 2829–2848 (2006)
Turon, A., Davila, C.G., Camanho, P.P., et al.: An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models. Eng. Fract. Mech. 74(10), 1665–1682 (2007)
Lens, L.N., Bittencourt, E., d’Avila, V.M.R.: Constitutive models for cohesive zones in mixed-mode fracture of plain concrete. Eng. Fract. Mech. 76(14), 2281–2297 (2009)
Camacho, G.T., Ortiz, M.: Computational modelling of impact damage in brittle materials. Int. J. Solids Struct. 33(20), 2899–2938 (1996)
Cheshomi, A., Sheshde, E.A.: Determination of uniaxial compressive strength of microcrystalline limestone using single particles load test. J. Pet. Sci. Eng. 111(11), 121–126 (2013)
Huang, J., Xu, S., Yi, H., et al.: Size effect on the compression breakage strengths of glass particles. Powder Technol. 268(12), 86–94 (2014)
Carmona, H.A., Wittel, F.K., Kun, F., et al.: Fragmentation processes in impact of spheres. Phys. Rev. E 77(5), 463–470 (2008)
Russell, A., Aman, S., Tomas, J.: Breakage probability of granules during repeated loading. Powder Technol. 269(1), 541–547 (2015)
Nakata, A.F.L., Hyde, M., Hyodo, H.: A probabilistic approach to sand particle crushing in the triaxial test. Geotechnique 49(5), 567–583 (1999)
McDowell, G.R., Amon, A.: The application of Weibull statistics to the fracture of soil particles. Soils Found. 40(5), 133–141 (2000)
Lim, W.L., McDowell, G.R., Collop, A.C.: The application of Weibull statistics to the strength of railway ballast. Granul. Matter 6(4), 229–237 (2004)
Ergenzinger, C., Seifried, R., Eberhard, P.: A discrete element model predicting the strength of ballast stones. Comput. Struct. 108(10), 3–13 (2012)
Cui, L., O’sullivan, C., O’neill, S.: An analysis of the triaxial apparatus using a mixed boundary three-dimensional discrete element model. Geotechnique 57(10), 831–844 (2007)
Wang, Y., Tonon, F.: Modeling triaxial test on intact rock using discrete element method with membrane boundary. J. Eng. Mech. 135(9), 1029–1037 (2009)
Li, X.S., Dafalias, Y.F., Wang, Z.L.: State-dependant dilatancy in critical-state constitutive modelling of sand. Can. Geotech. J. 36(4), 599–611 (1999)
Sayeed, M.A., Suzuki, K., Rahman, M.M., et al.: Strength and deformation characteristics of granular materials under extremely low to high confining pressures in triaxial compression. Int. J. Civil Environ. Eng. 11(4), 1–6 (2011)
Bi, Z., Sun, Q., Jin, F., et al.: Numerical study on energy transformation in granular matter under biaxial compression. Granul. Matter 13(4), 503–510 (2011)
Wang, J., Yan, H.: DEM analysis of energy dissipation in crushable soils. Soils Found. 52(4), 644–657 (2012)
Acknowledgments
This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51379161 and 51509190) and China Postdoctoral Science Foundation (2015M572195), and the Fundamental Research Funds for the Central Universities.
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Ma, G., Zhou, W., Chang, XL. et al. A hybrid approach for modeling of breakable granular materials using combined finite-discrete element method. Granular Matter 18, 7 (2016). https://doi.org/10.1007/s10035-016-0615-3
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DOI: https://doi.org/10.1007/s10035-016-0615-3