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SIZE EFFECT IN DISCRETE ELEMENT SIMULATIONS

SIZE EFFECT IN DISCRETE ELEMENT SIMULATIONS. Katalin Bagi Hungarian Academy of Sciences kbagi@mail.bme.hu. Matthew R. Kuhn Portland Universit y kuhn@up.edu. AIMS & MOTIVATIONS  Representative domain: “ a small, finite subset of the assembly which contains enough

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SIZE EFFECT IN DISCRETE ELEMENT SIMULATIONS

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  1. SIZE EFFECT IN DISCRETE ELEMENT SIMULATIONS Katalin Bagi Hungarian Academy of Sciences kbagi@mail.bme.hu Matthew R. Kuhn Portland University kuhn@up.edu

  2. AIMS & MOTIVATIONS Representative domain: “a small, finite subset of the assembly which contains enough grains to reflect the material behavior” How many grains are “enough”? If more grains are taken, how it affects the behavior? Discrete Element Modeling of real problems:  identify the parameters of a small sample to a lab test;  Can we use this DEM model for the real (i.e. large) problem? 2 / 21

  3. THE PRESENTATION Literature overview What is size effect? Size effect in cemented granular materials  Experiences  Sources of size effect Our simulations several assemblies of different sizes; different sample preparation methods biaxial loading:  Shear strength?  Initial Young-modulus?  Deformation patterns? Summary 3 / 21

  4. SIZE EFFECT Meaning:a property of the structure/sample e.g. strength Young-modulus etc. which should beindependent of the size of the structure/sample according to the usual deterministic theories (“simple materials”), still depends on thesize of the structure/sample Examples: large strength small strength 4 / 21

  5. strength usual determi-nistic theories linear elastic fracture mechanics size SIZE EFFECT IN CEMENTED GRANULAR MATERIALS e.g. Bazant, 1998 (etc): 5 / 21

  6. !! !! SIZE EFFECT IN CEMENTED GRANULAR MATERIALS Possible sources of size effect:  The wall effect boundary layer:  different stress state different material properties  “Fracture mechanics size effect” fracture process zone size: depends on the particle size  Statistical size effect Weibull: strength of a chain = strength of its weakest link for metals etc.; not for cemented granular media [stress redistribution]  Others diffusion phenomena; hydratation heat etc. 6 / 21

  7. THE PRESENTATION Literature overview What is size effect? Size effect in cemented granular materials  Experiences  Sources of size effect Our simulations laboratory experiments computer simulations OVAL; PFC several assemblies ofdifferent sizes;  grain size distribution: same for all assemblies  two different methods to prepare the initial arrangements walls  periodic boundaries biaxial loading: Shear strength?  Initial Young-modulus?  Deformation patterns? 7 / 21

  8. OUR SIMULATIONS Sample preparation: samples with the same porosity, coordination #, pressure Method 1: Assemblies with periodic boundaries Initial assemblies of different sizes Biaxial shear tests Compare: shear strength, stiffness, deformation patterns Method 2: Assemblies with walls Initial assemblies of different sizes Biaxial shear tests Compare: shear strength, stiffness, deformation patterns 8 / 21

  9. ASSEMBLIES WITH PERIODIC BOUNDARIES Sample preparation: size 15  15 size 30  30 size 60  60 size 97,5  97,5 100 assemblies of 100 assemblies of 100 assemblies of 20 assemblies of 256 grains 1024 grains 4096 grains 10816 grains the same grain size distribution ; the same porosity  different pressure  9 / 21

  10. ASSEMBLIES WITH PERIODIC BOUNDARIES Sample preparation:  Assemblies with size  97,5  97,5 :  20 assemblies of 10816 grains  average coordination number: 3,9885 average porosity:0,1444 average normalized pressure:1,04110-3  Assemblies with size  60  60 : 4096 grains average coord.number  select a subset of assemblies whose average porosity is the same! average pressure  Assemblies with size  30  30 : 1024 grains do the same selection!  Assemblies with size  15  15 : 256 grains do the same selection! 10 / 21

  11. shear stress ?? strain ASSEMBLIES WITH PERIODIC BOUNDARIES Biaxial shear tests: linear contacts; Coulomb friction; quasi-static loading 256 grains 1024 grains 4096 grains 10816 grains 11 / 21

  12. ASSEMBLIES WITH PERIODIC BOUNDARIES Biaxial shear tests: Deformation patterns: blue: volume increase 10816 grains: red: volume decrease 4096 grains: 1024 grains: 256 grains: 12 / 21

  13. ASSEMBLIES WITH PERIODIC BOUNDARIES Effect of size on the shear strength & Young modulus: Conclusions: increasing size  decreasing shear strength ( 4 %)  slightly increasing stiffness (  0,3 % ) 13 / 21

  14. ASSEMBLIES WITH WALLS Sample preparation: size 30  30 size  60  60 size  120  120 size  240  240 7 assemblies of 7 assemblies of 7 assemblies of 7 assemblies of  1040 grains  4150 grains  16 600 grains  66 600 grains the same grain size distribution the same porosity 14 / 21

  15. ASSEMBLIES WITH WALLS Biaxial shear tests:  30  30  60  60  120  120  240  240 7 assemblies of 7 assemblies of 7 assemblies of 7 assemblies of  1040 grains  4150 grains  16 600 grains  66 600 grains 15 / 21

  16. ASSEMBLIES WITH WALLS Biaxial shear tests: Deformation patterns:  66 600 grains blue: volume increase red: volume decrease  16 600 grains  4150 grains 1040 grains 16 / 21

  17. ASSEMBLIES WITH WALLS Effect of size on the shear strength & Young modulus: Conclusion: increasing size  decreasing shear strength ( 4 % ) 17 / 21

  18. ASSEMBLIES WITH WALLS Effect of size on the shear strength & Young modulus: modified assemblies to have the same coordination number: Conclusion: increasing size  slightly increasing stiffness (  0,8 % ) 18 / 21

  19. ASSEMBLIES WITH WALLS The problem of DEM modeling: to fill up the same domain with increasing number of grains Sample preparation: size 240  240 size  240  240 size  240  240 size  240  240 7 assemblies of 7 assemblies of 7 assemblies of 7 assemblies of  66 600 grains  16 600 grains  4150 grains  1040 grains grain size  1 grain size  2 grain size  4 grain size  8 the same porosity 19 / 21

  20. ASSEMBLIES WITH WALLS The problem of DEM modeling : to fill up the same domain with increasing number of grains Shear strength: Conclusion: increasing number of grains  slightly decreasing strength 20 / 21

  21. SUMMARY Size effect on shear strength a few thousand hundred thousands discrete elements discrete elements: the shear strength decreases only a few % Size effect on stiffness a few thousand hundred thousands discrete elements discrete elements: negligible increase of the stiffness Our message for DEM simulations:  use at least a few thousand elements; and then DO NOT WORRY ABOUT THE SIZE EFFECT 21 / 21

  22. SUMMARY Our doubts The size effect is perhaps more significant for non-circular elements? anisotropic arrangements?  samples deposited under gravity? TO BE CONTINUED Acknowledgements: OTKA 48998, Bolyai grant 22 / 21

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