DOI QR코드

DOI QR Code

Aspects of size effect on discrete element modeling of normal strength concrete

  • Gyurko, Zoltan (Department of Construction Materials and Technologies, Budapest University of Technology and Economics) ;
  • Nemes, Rita (Department of Construction Materials and Technologies, Budapest University of Technology and Economics)
  • Received : 2020.02.12
  • Accepted : 2021.11.17
  • Published : 2021.11.25

Abstract

Present paper focuses on the modeling of size effect on the compressive strength of normal concrete with the application of Discrete Element Method (DEM). Test specimens with different size and shape were cast and uniaxial compressive strength test was performed on each sample. Five different concrete mixes were used, all belonging to a different normal strength concrete class (C20/25, C30/37, C35/45, C45/55, and C50/60). The numerical simulations were carried out by using the PFC 5 software, which applies rigid spheres and contacts between them to model the material. DEM modeling of size effect could be advantageous because the development of micro-cracks in the material can be observed and the failure mode can be visualized. The series of experiments were repeated with the model after calibration. The relationship of the parallel bond strength of the contacts and the laboratory compressive strength test was analyzed by aiming to determine a relation between the compressive strength and the bond strength of different sized models. An equation was derived based on Bazant's size effect law to estimate the parallel bond strength of differently sized specimens. The parameters of the equation were optimized based on measurement data using nonlinear least-squares method with SSE (sum of squared errors) objective function. The laboratory test results showed a good agreement with the literature data (compressive strength is decreasing with the increase of the size of the specimen regardless of the shape). The derived estimation models showed strong correlation with the measurement data. The results indicated that the size effect is stronger on concretes with lower strength class due to the higher level of inhomogeneity of the material. It was observed that size effect is more significant on cube specimens than on cylinder samples, which can be caused by the side ratios of the specimens and the size of the purely compressed zone. A limit value for the minimum size of DE model for cubes and cylinder was determined, above which the size effect on compressive strength can be neglected within the investigated size range. The relationship of model size (particle number) and computational time was analyzed and a method to decrease the computational time (number of iterations) of material genesis is proposed.

Keywords

Acknowledgement

Authors are grateful to the Hungarian Scientific Research Fund (OTKA) for the financial support of the OTKA K 109233 research project and to the Itasca Consulting Group for providing applied the DEM software (PFC3D).

References

  1. Bagi, K. (1993), "A quasi-static numerical model for micro-level analysis of granular assemblies", Mech. Mater., 16, 101-110. https://doi.org/10.1016/0167-6636(93)90032-m.
  2. Bazant, Z.P. (1984), "Size effect in blunt fracture; concrete, rock, metal", J. Eng. Mech. Am. Soc. Civil Eng., 110, 518-535. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:4(518).
  3. Bazant, Z.P. (1987), "Fracture energy of heterogeneous material and similitude", SEM-RILEM Int. Conf. Fract. Concrete Rock, 390-402. https://doi.org/10.1007/978-1-4612-3578-1_23.
  4. Bazant, Z.P. (1989), "Identification of strain-softening constitutive relation from uniaxial tests by series coupling model for localization", Cement Concrete Res., 19, 973-977. https://doi.org/10.1016/0008-8846(89)90111-7.
  5. Bazant, Z.P. (1993), "Size effect in tensile and compressive quasibrittle failures I. part", JCI Int. Workshop Size Effect Concrete Struct., 141-160.
  6. Bazant, Z.P. (1993), "Size effect in tensile and compressive quasibrittle failure II. part", Proc. Int. Workshop Size Effect Concrete Struct., Sendai, Japan.
  7. Bazant, Z.P. and Chen, E.P. (1997), "Scaling of structural failure", Appl. Mech. Rev., 50, 593-627. https://doi.org/10.1115/1.3101672.
  8. Bazant, Z.P. and Xi, Y. (1991), "Statistical size effect in quasi-brittle structures: II. Nonlocal theory", J. Eng. Mech. Am. Soc. Civil Eng., 117, 2623-2640. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:11(2623).
  9. Bazant, Z.P. and Xiang, Y. (1994), "Compression failure of quasibrittle materials and size effect", ASME Appl. Mech. Div., 185, 143-143.
  10. Bazant, Z.P. and Xiang, Y. (1997), "Size effect in compression fracture: Splitting crack band propagation", J. Eng. Mech. Am. Soc. Civil Eng., 123, 162-172. https://doi.org/10.1061/(asce)0733-9399(1997)123:2(162).
  11. Bazant, Z.P., Xi, Y. and Reid, S.G. (1991), "Statistical size effect in quasi-brittle structures: I. Is Weibull theory applicable?", J. Eng. Mech. Am. Soc. Civil Eng., 117, 2609-2622. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:11(2609).
  12. Camborde, F., Mariotti, C. and Donze, F.V. (2000), "Numerical study of rock and concrete behaviour by discrete element modelling", Comput. Geotech., 27, 225-247. https://doi.org/10.1016/s0266-352x(00)00013-6.
  13. Cundall, P.A. (1971), "A computer model for simulating progressive large scale movements in blocky rock systems", Proc. Symp. Int. Soc. Rock Mech., Nancy.
  14. Cundall, P.A. (1988), "Formulation of a three-dimensional distinct element model-Part I: A scheme to detect and represent contacts in a system composed of many polyhedral blocks", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 25, 107-116. https://doi.org/10.1016/0148-9062(88)91214-4.
  15. del Viso, J.R., Carmona, J.R. and Ruiz, G. (2008), "Shape and size effects on the compressive strength of high-strength concrete", Cement Concrete Res., 38, 386-395. https://doi.org/10.1016/j.cemconres.2007.09.020.
  16. Dombi, J. (1979), "Epitoanyagok szilardsaga es szilardsagvizsgalata-1", Nyomoszilardsag SZIKKTI Tudomanyos Kozlemenyek. (in Hungarian)
  17. European Committee for Standardization (CEN) (2010), CEN/TS 12390-9 Testing Hardened Concrete-Part 9: Freeze-Thaw Resistance-Scaling, 24.
  18. Gulsan, M.E., Abdulhaleem, K.N., Kurtoglu, A.E. and Cevik, A. (2018), "Size effect on strength of Fiber-Reinforced SelfCompacting Concrete (SCC) after exposure to high temperatures", Comput. Concrete, 21(6), 681-695. https://doi.org/10.12989/cac.2018.21.6.681.
  19. Gyurko, Z and Nemes, R. (2019), "Fracture modelling of normal concrete using different types of aggregates", Eng. Fail. Anal., 101, 464-472. http://doi.org/10.1016/j.engfailanal.2019.04.008.
  20. Gyurko, Z. and Borosnyoi, A. (2015), "Brinell-hardness testing and discrete element modelling of hardened concrete", Epitoanyag-J. Silicate Base. Compos. Mater., 67(1), 8-11. http://doi.org/10.14382/epitoanyag-jsbcm.2015.2.
  21. Gyurko, Z. and Nemes, R. (2016), "Effect of standard deviation of contact normal strength in dem for concrete", Conf. Proc. 4th Int. Conf. Contemporary Achievement. Civil Eng., Subotica, April.
  22. Gyurko, Z. and Nemes, R. (2016), "Size effect on cylinder and cube strength of concrete", Concrete Struct., 17, 18-22.
  23. Gyurko, Z. and Nemes, R. (2018), "Discrete element modelling of compressive strength testing of no-fines concrete", Multidisciplinary Digital Pub. Inst. Proc., 2(8), 555. http://doi.org/10.3390/icem18-05470.
  24. Gyurko, Z., Bagi, K. and Borosnyoi, A. (2014), "Discrete Element Modelling of uniaxial compression test of hardened concrete", Epitoanyag-J. Silicate Base. Compos. Mater., 66(4), 113-119. https://doi.org/10.14382/epitoanyag-jsbcm.2014.21.
  25. Haeri, H., Sarfarazi, V. and Zhu, Z. (2017), "Effect of normal load on the crack propagation from pre-existing joints using Particle Flow Code (PFC)", Comput. Concrete, 19(1), 99-110. https://doi.org/10.12989/cac.2017.19.1.099.
  26. Haeri, H., Sarfarazi, V. and Zhu, Z. (2018), "PFC3D simulation of the effect of particle size on the single edge-notched rectangle bar in bending test", Struct. Eng. Mech., 68(4), 497-505. https://doi.org/10.12989/sem.2018.68.4.497.
  27. Haeri, H., Sarfarazi, V., Zhu, Z. and Lazemi, H.A. (2018), "Investigation of the effects of particle size and model scale on the UCS and shear strength of concrete using PFC2D", Struct. Eng. Mech., 67(5), 505-516. https://doi.org/10.12989/sem.2018.67.5.505.
  28. Itasca Consulting Group (2008), Particle Flow Code in Three Dimensions, Users Guide, Minneapolis, Minnesota, USA.
  29. Karamloo, M., Roudak, M.A. and Hosseinpour, H. (2019), "Size effect study on compressive strength of SCLC", Comput. Concrete, 23(6), 409-419. https://doi.org/10.12989/cac.2019.23.6.409.
  30. Kim, J.K. and Eo, S.H. (1990), "Size effect in concrete specimens with dissimilar initial cracks", Mag. Concrete Res., 42, 233-238. https://doi.org/10.1680/macr.1990.42.153.233.
  31. Kim, J.K. and Yi, S.T. (2002), "Application of size effect to compressive strength of concrete members", Sadhana, 27(4), 467-484. https://doi.org/10.1007/bf02706995.
  32. Kim, J.K. and Yi, S.T. (2004), "Size effect on compressive strength of concrete", Spec. Pub., 118, 179-196.
  33. Kim, J.K., Eo, S.H. and Park, H.K. (1989), "Size effect in concrete structures without initial crack", Fract. Mech. Applicat. Concrete, 118, 179-196.
  34. Kim, J.K., Yi, S.T. and Tang, E.I. (2000), "Size effect on flexural compressive strength of concrete specimens", ACI Struct. J., 97, 291-296. https://doi.org/10.14359/859.
  35. Kim, J.K., Yi, S.T., Park, H.K. and Eo, S.H. (1999), "Size effect on compressive strength of plain and spirally reinforced concrete cylinders", ACI Struct. J., 96, 88-94. https://doi.org/10.14359/599.
  36. Kuhn, M.R. and Bagi, K. (2009), "Specimen size effect in discrete element simulations of granular assemblies", J. Eng. Mech., 135(6), 485-492. http://doi.org/10.1061/(asce)0733-9399(2009)135:6(485).
  37. Kumar, S. and Barai, S.V. (2012), "Size-effect of fracture parameters for crack propagation in concrete: A comparative study", Comput. Concrete, 9(1), 1-19. https://doi.org/10.12989/cac.2012.9.1.001.
  38. Kun, F., Varga, I., Lennartz-Sassinek, S. and Main, I.G. (2013), "Approach to failure in porous granular materials under compression", Phys. Rev., 88(6), 062207.
  39. Liu, Y., You, Z. and Zhao, Y. (2012), "Three-dimensional discrete element modeling of asphalt concrete: Size effects of elements", Constr. Build. Mater., 37, 775-782. https://doi.org/10.1016/j.conbuildmat.2012.08.007.
  40. Marketos, G. and Bolton M. (2009), "Compaction bands simulated in discrete element models", J. Struct. Geol., 31(5), 479-490. https://doi.org/10.1016/j.jsg.2009.03.002.
  41. MSZ EN 4798:2016 (2016), Concrete, Specification, Performance, Production, Conformity, and Rules of Application of EN 206 in Hungary.
  42. O'Sullivan, C. (2011), Particulate Discrete Element Modelling, CRC Press.
  43. Palotas, L. (1947), "A vasbeton", (Reinforced concrete-in Hungarian), Magyar Epitomesterek Egyesulete.
  44. Pollard, D. and Radchenko, P. (2006), "Nonlinear least-squares estimation", J. Multivarate Anal., 97, 548-562. https://doi.org/10.1016/j.jmva.2005.04.002.
  45. Potyondy, D.O. and Cundall, P.A. (2004), "A bonded-particle model for rock", Int. J. Rock Mech. Min. Sci., 41(8), 1329-1364. https://doi.org/10.1016/j.ijrmms.2004.09.011.
  46. Rangari, S., Murali, K. and Deb, A. (2018), "Effect of meso-structure on strength and size effect in concrete under compression", Eng. Fail. Mech., 195, 162-185. https://doi.org/10.1016/j.engfracmech.2018.04.006.
  47. Rousseau, J., Frangin, E., Marin, P. and Daudeville, L. (2008), "Damage prediction in the vicinity of an impact on a concrete structure: A combined FEM/DEM approach", Comput. Concrete, 5(4), 343-358. https://doi.org/10.12989/cac.2008.5.4.343.
  48. Saad, L., Aissani, A., Chateauneuf, A. and Raphael, W. (2016), "Reliability-based optimization of direct and indirect LCC of RC bridge elements under coupled fatigue-corrosion deterioration processes", Eng. Fail. Anal., 59, 570-587. https://doi.org/10.1016/j.engfailanal.2015.11.006.
  49. Schafer, B.C., Quigley, S.F. and Chan, A.H. (2004), "Acceleration of the discrete element method (dem) on a reconfigurable co-processor", Comput. Struct., 82(20), 1707-1718. https://doi.org/10.1016/j.compstruc.2004.03.004.
  50. Shiu, W., Donze, F.V. and Daudeville, L. (2008), "Compaction process in concrete during missile impact: A DEM analysis", Comput. Concrete, 5(4), 329-342. https://doi.org/10.12989/cac.2008.5.4.329.
  51. Sinaie, S. (2016), "Application of the discrete element method for the simulation of size effects in concrete samples", Int. J. Solid. Struct., 108, 224-253. https://doi.org/10.1016/j.ijsolstr.2016.12.022.
  52. Suchorzewski, J. and Tejchman, J. (2019), "Investigations of size effect in concrete during splitting using DEM combined with X-Ray Micro-CT scans", Proc. 10th Int. Conf. Fract. Mech. Concrete Concrete Struct., Berkeley, June. https://doi.org/10.21012/fc10.233583.
  53. Suchorzewski, J., Tejchman, J., Nitka, M. and Bobinski, J. (2019), "Meso-scale analyses of size effect in brittle materials using DEM", Granular Matter, 21(1), 1-19. https://doi.org/10.1007/s10035-018-0862-6.
  54. Tanigawa, Y. and Yamada, K. (1978), "Size effect in compressive strength of concrete", Cement Concrete Res., 8, 181-190. https://doi.org/10.1016/0008-8846(78)90007-8.
  55. Wang, Z., Lin, F. and Gu, X. (2008), "Numerical simulation of failure process of concrete under compression based on mesoscopic discrete element model", Tsinghua Sci. Technol., 13, 19-25. https://doi.org/10.1016/s1007-0214(08)70121-4.
  56. Wang, Z., Ruiken, A., Jacobs, F. and Ziegler, M. (2014), "A new suggestion for determining 2D porosities in DEM studies", Geomech. Eng., 7(6), 665-678. https://doi.org/10.12989/gae.2014.7.6.665.
  57. Yi, S.T., Yang, E.I. and Choi, J.C. (2006), "Effect of specimen sizes, specimen shapes, and placement directions on compressive strength of concrete", Nucl. Eng. Des., 236, 115-127. https://doi.org/10.1016/j.nucengdes.2005.08.004.
  58. Zhao, Y., Chang, J. and Gao, H. (2015), "On geometry dependent R-curve from size effect law for concrete-like quasibrittle materials", Comput. Concrete, 15(4), 673-686. https://doi.org/10.12989/cac.2015.15.4.673.
  59. Zheng, J., An, X. and Huang, M. (2012), "Gpu-based parallel algorithm for particle contact detection and its application in self-compacting concrete flow simulations", Comput. Struct., 112, 193-204. https://doi.org/10.1016/j.compstruc.2012.08.003.