Title:
Global Size Effect Model—A Variant for Type-2 Size Effect Model
Author(s):
Dong Li, Liu Jin, and Xiuli Du
Publication:
Materials Journal
Volume:
118
Issue:
3
Appears on pages(s):
117-130
Keywords:
cementitious system; maximum aggregate size; morphological structure; quasi-brittle fracture mechanics; size effect
DOI:
10.14359/51730425
Date:
5/1/2021
Abstract:
The concept of global size effect theory from material level to structural level is raised. The material level is described by a Universal Morphological Model (UMM) that accounts for the size effect behaviors introduced by the mixture variables of concrete, whereas the structural level is linked to the size effect theory based on quasi-brittle fracture mechanics. First, the UMM that is eligible for the description of material-level size effect is established and verified. Parametric study on the UMM shows that the mechanical properties of concrete are insensitive to the maximum aggregate size (MAS) at a critical interface crack index ηc. Secondly, by introducing the UMM into the formulation of structural-level size effect, a global size effect model (GSEM) expressed as a variant for the Type-2 size effect model (SEM) is proposed. Parametric study on the GSEM shows that the properties and the scales of mesostructures have significant influences on the size effect behaviors of concrete at the structural level. The critical interface crack index ηc determined by the UMM should receive sufficient attention in large-scale structural concrete design in practice.
Related References:
1. Kani, G. N. J., “How Safe Are Our Large Reinforced Concrete Beams?” ACI Journal Proceedings, V. 64, No. 3, Mar. 1967, pp. 128-141.
2. Weibull, W., “Phenomenon of Rupture in Solids,” Proceedings, Royal Swedish Institute of Engineering Research, V. 53, 1939, pp. 1-55.
3. Weibull, W., “A Statistical Theory of Strength of Materials,” Ingvetensk Akad Handl, V. 151, 1939, pp. 5-45.
4. Weibull, W., “A Statistical Distribution Function of Wide Applicability,” Journal of Applied Mechanics, V. 18, No. 3, 1951, pp. 293-297. doi: 10.1115/1.4010337
5. JSCE Subcommitee on English Version of Standard Specifications for Concrete Structures, “JSCE Guidelines for Concrete No. 15: Design,” Japan Society of Civil Engineering, Tokyo, Japan, 2007.
6. Bažant, Z. P., and Planas, J., Fracture and Size Effect in Concrete and Other Quasibrittle Materials, CRC Press, Boca Raton, FL, 1998.
7. Bažant, Z. P., “Size Effect in Blunt Fracture: Concrete, Rock, Metal,” Journal of Engineering Mechanics, ASCE, V. 110, No. 4, 1984, pp. 518-535. doi: 10.1061/(ASCE)0733-9399(1984)110:4(518)
8. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19),” American Concrete Institute, Farmington Hills, MI, 2019, 624 pp.
9. Fédération Internationale du Béton, (fib), “Model Code 2010,” Lausanne, Switzerland, 2012.
10. Carloni, C.; Cusatis, G.; Salviato, M.; Le, J. L.; Hoover, C. G.; and Bažant, Z. P., “Critical Comparison of the Boundary Effect Model with Cohesive Crack Model and Size Effect Law,” Engineering Fracture Mechanics, V. 215, 2019, pp. 193-210. doi: 10.1016/j.engfracmech.2019.04.036
11. Muttoni, A., and Fernandez Ruiz, M., “Shear Strength of Members without Transverse Reinforcement as Function of Critical Shear Crack Width,” ACI Structural Journal, V. 105, No. 2, Mar.-Apr. 2008, pp. 163-172.
12. Dönmez, A., and Bažant, Z. P., “Critique of Critical Shear Crack Theory for fib Model Code Articles on Shear Strength and Size Effect of Reinforced Concrete Beams,” Structural Concrete, V. 20, No. 4, 2019, pp. 1-14. doi: 10.1002/suco.201800315
13. Carpinteri, A., “Fractal Nature of Material Microstructure and Size Effects on Apparent Mechanical Properties,” Mechanics of Materials, V. 18, No. 2, 1994, pp. 89-101. doi: 10.1016/0167-6636(94)00008-5
14. Carpinteri, A., “Scaling Laws and Renormalization Groups for Strength and Toughness of Disordered Materials,” International Journal of Solids and Structures, V. 31, No. 3, 1994, pp. 291-302. doi: 10.1016/0020-7683(94)90107-4
15. Carpinteri, A., and Ferro, G., “Size Effects on Tensile Fracture Properties: A Unified Explanation Based on Disorder and Fractality of Concrete Microstructure,” Materials and Structures, V. 27, No. 10, 1994, pp. 563-571. doi: 10.1007/BF02473124
16. Carpinteri, A., and Chiaia, B., “Multifractal Scaling Law for the Fracture Energy Variation of Concrete Structures,” Fracture Mechanics of Concrete Structures: Proceedings, FRAMCOS-2, 1995, pp. 581-596.
17. Carpinteri, A.; Chiaia, B.; and Ferro, G., “Size Effects on Nominal Tensile Strength of Concrete Structures: Multifractality of Material Ligaments and Dimensional Transition from Order to Disorder,” Materials and Structures, V. 28, No. 6, 1995, pp. 311-317. doi: 10.1007/BF02473145
18. Carpinteri, A., and Chiaia, B., “Size Effects on Concrete Fracture Energy: Dimensional Transition from Order to Disorder,” Materials and Structures, V. 29, No. 5, 1996, pp. 259-266. doi: 10.1007/BF02486360
19. Carpinteri, A., and Ferro, G., “Scaling Behaviour and Dual Renormalization of Experimental Tensile Softening Responses,” Materials and Structures, V. 31, No. 5, 1998, pp. 303-309. doi: 10.1007/BF02480671
20. Hu, X., and Wittmann, F., “Size Effect on Toughness Induced by Crack Close to Free Surface,” Engineering Fracture Mechanics, V. 65, No. 2-3, 2000, pp. 209-221. doi: 10.1016/S0013-7944(99)00123-X
21. Duan, K.; Hu, X.; and Wittmann, F. H., “Boundary Effect on Concrete Fracture and Non-Constant Fracture Energy Distribution,” Engineering Fracture Mechanics, V. 70, No. 16, 2003, pp. 2257-2268. doi: 10.1016/S0013-7944(02)00223-0
22. Duan, K.; Hu, X.; and Wittmann, F. H., “Scaling of Quasi-Brittle Fracture: Boundary and Size Effect,” Mechanics of Materials, V. 38, No. 1-2, 2006, pp. 128-141. doi: 10.1016/j.mechmat.2005.05.016
23. Hu, X., and Duan, K., “Size Effect and Quasi-Brittle Fracture: The Role of FPZ,” International Journal of Fracture, V. 154, No. 1-2, 2008, pp. 3-14. doi: 10.1007/s10704-008-9290-7
24. Hu, X., and Duan, K., “Mechanism Behind the Size Effect Phenomenon,” Journal of Engineering Mechanics, ASCE, V. 136, No. 1, 2010, pp. 60-68. doi: 10.1061/(ASCE)EM.1943-7889.0000070
25. Bažant, Z. P.; Xi, Y.; and Reid, S. G., “Statistical Size Effect in Quasi-Brittle Structures: I. Is Weibull Theory Applicable?” Journal of Engineering Mechanics, ASCE, V. 117, No. 11, 1991, pp. 2609-2622. doi: 10.1061/(ASCE)0733-9399(1991)117:11(2609)
26. Bažant, Z. P., and Xi, Y., “Statistical Size Effect in Quasi-Brittle Structures: II. Nonlocal Theory,” Journal of Engineering Mechanics, ASCE, V. 117, No. 11, 1991, pp. 2623-2640. doi: 10.1061/(ASCE)0733-9399(1991)117:11(2623)
27. Bažant, Z. P., “Scaling of Quasi-Brittle Fracture and the Fractal Question,” Journal of Engineering Materials and Technology, V. 117, No. 4, 1995, pp. 361-367. doi: 10.1115/1.2804726
28. Bažant, Z. P., and Yu, Q., “Size Effect in Fracture of Concrete Specimens and Structures: New Problems and Progress,” Acta Polytechnica, V. 44, No. 5-6, 2004, pp. 153-162. doi: 10.14311/608
29. Bažant, Z. P., and Yavari, A., “Is the Cause of Size Effect on Structural Strength Fractal or Energetic–Statistical?” Engineering Fracture Mechanics, V. 72, No. 1, 2005, pp. 1-31. doi: 10.1016/j.engfracmech.2004.03.004
30. Yu, Q.; Le, J. L.; Hoover, C. G.; and Bažant, Z. P., “Problems with Hu-Duan Boundary Effect Model and its Comparison to Size-Shape Effect Law for Quasi-Brittle Fracture,” Journal of Engineering Mechanics, ASCE, V. 136, No. 1, 2010, pp. 40-50. doi: 10.1061/(ASCE)EM.1943-7889.89
31. Hoover, C. G., and Bažant, Z. P., “Comparison of the Hu-Duan Boundary Effect Model with the Size-Shape Effect Law for Quasi-Brittle Fracture Based on New Comprehensive Fracture Tests,” Journal of Engineering Mechanics, ASCE, V. 140, No. 3, 2014, pp. 480-486. doi: 10.1061/(ASCE)EM.1943-7889.0000632
32. Hu, X.; Guan, J.; Wang, Y.; Keating, A.; and Yang, S., “Comparison of Boundary and Size Effect Models Based on New Developments,” Engineering Fracture Mechanics, V. 175, 2017, pp. 146-167. doi: 10.1016/j.engfracmech.2017.02.005
33. Li, D.; Jin, L.; Du, X.; and Liu, J., “A Theoretical Method to Determine the Tortuous Crack Length and the Mechanical Parameters of Concrete in Direct Tension—A Particle Size Effect Analysis,” Engineering Fracture Mechanics, V. 197, 2018, pp. 128-150. doi: 10.1016/j.engfracmech.2018.04.039
34. Saouma, V. E.; Broz, J. J.; Brühwiler, E.; and Boggs, H. L., “Effect of Aggregate and Specimen Size on Fracture Properties of Dam Concrete,” Journal of Materials in Civil Engineering, ASCE, V. 3, No. 3, 1991, pp. 204-218. doi: 10.1061/(ASCE)0899-1561(1991)3:3(204)
35. Wu, Z., and Zhao, G., “Influences of Aggregate Sizes on Fracture Parameters of Concrete,” Journal of Dalian University of Technology, V. 34, No. 5, 1994, pp. 583-588.
36. Stock, A. F.; Hannant, D. J.; Williams, R. I. T.; Hobbs, D. W.; Akman, M. S.; and Bartoš, P., “The Effect of Aggregate Concentration upon the Strength and Modulus of Elasticity of Concrete,” Magazine of Concrete Research, V. 32, No. 113, 1980, pp. 246-250. doi: 10.1680/macr.1980.32.113.246
37. Amparano, F. E.; Xi, Y.; and Roh, Y., “Experimental Study on the Effect of Aggregate Content on Fracture Behavior of Concrete,” Engineering Fracture Mechanics, V. 67, No. 1, 2000, pp. 65-84. doi: 10.1016/S0013-7944(00)00036-9
38. Gangnant, A.; Saliba, J.; La Borderie, C.; and Morel, S., “Modeling of the Quasibrittle Fracture of Concrete at Meso-Scale: Effect of Classes of Aggregates on Global and Local Behavior,” Cement and Concrete Research, V. 89, 2016, pp. 35-44. doi: 10.1016/j.cemconres.2016.07.010
39. Siregar, A. P. N.; Rafiq, M. I.; and Mulheron, M., “Experimental Investigation of the Effects of Aggregate Size Distribution on the Fracture Behaviour of High Strength Concrete,” Construction and Building Materials, V. 150, 2017, pp. 252-259. doi: 10.1016/j.conbuildmat.2017.05.142
40. Vishalakshi, K. P.; Revathi, V.; and Reddy, S. S., “Effect of Type of Coarse Aggregate on the Strength Properties and Fracture Energy of Normal and High Strength Concrete,” Engineering Fracture Mechanics, V. 194, 2018, pp. 52-60. doi: 10.1016/j.engfracmech.2018.02.029
41. Ninčević, K.; Boumakis, I.; Marcon, M.; and Wan-Wendner, R., “Aggregate Effect on Concrete Cone Capacity,” Engineering Structures, V. 191, 2019, pp. 358-369. doi: 10.1016/j.engstruct.2019.04.028
42. Rocco, C. G., and Elices, M., “Effect of Aggregate Shape on the Mechanical Properties of a Simple Concrete,” Engineering Fracture Mechanics, V. 76, No. 2, 2009, pp. 286-298. doi: 10.1016/j.engfracmech.2008.10.010
43. Akcaoğlu, T., “Determining Aggregate Size & Shape Effect on Concrete Microcracking under Compression by Means of a Degree of Reversibility Method,” Construction and Building Materials, V. 143, 2017, pp. 376-386. doi: 10.1016/j.conbuildmat.2017.03.128
44. Mindess, S., and Diamond, S., “A Preliminary SEM Study of Crack Propagation in Mortar,” Cement and Concrete Research, V. 10, No. 4, 1980, pp. 509-519. doi: 10.1016/0008-8846(80)90095-2
45. Zhang, H.; Šavija, B.; Xu, Y.; and Schlangen, E., “Size Effect on Splitting Strength of Hardened Cement Paste: Experimental and Numerical Study,” Cement and Concrete Composites, V. 94, 2018, pp. 264-276. doi: 10.1016/j.cemconcomp.2018.09.018
46. Ollivier, J. P.; Maso, J. C.; and Bourdette, B., “Interfacial Transition Zone in Concrete,” Advanced Cement Based Materials, V. 2, No. 1, 1995, pp. 30-38. doi: 10.1016/1065-7355(95)90037-3
47. Trende, U., and Büyüköztürk, O., “Size Effect and Influence of Aggregate Roughness in Interface Fracture of Concrete Composites,” ACI Materials Journal, V. 95, No. 4, July-Aug. 1998, pp. 331-338.
48. Zhou, F. P.; Barr, B. I. G.; and Lydon, F. D., “Fracture Properties of High Strength Concrete with Varying Silica Fume Content and Aggregates,” Cement and Concrete Research, V. 25, No. 3, 1995, pp. 543-552. doi: 10.1016/0008-8846(95)00043-C
49. Donza, H.; Cabrera, O.; and Irassar, E. F., “High-Strength Concrete with Different Fine Aggregate,” Cement and Concrete Research, V. 32, No. 11, 2002, pp. 1755-1761. doi: 10.1016/S0008-8846(02)00860-8
50. Nallathambi, P.; Karihaloo, B. L.; and Heaton, B. S., “Effect of Specimen and Crack Sizes, Water/Cement Ratio and Coarse Aggregate Texture upon Fracture Toughness of Concrete,” Magazine of Concrete Research, V. 36, No. 129, 1984, pp. 227-236. doi: 10.1680/macr.1984.36.129.227
51. Nallathambi, P.; Karihaloo, B. L.; and Heaton, B. S., “Various Size Effects in Fracture of Concrete,” Cement and Concrete Research, V. 15, No. 1, 1985, pp. 117-126. doi: 10.1016/0008-8846(85)90016-X
52. Alam, S. Y.; Zhu, R.; and Loukili, A., “A New Way to Analyse the Size Effect in Quasi-Brittle Materials by Scaling the Heterogeneity Size,” Engineering Fracture Mechanics, V. 225, 2020, p. 106864. doi: 10.1016/j.engfracmech.2019.106864
53. DL/T 5330-2015, “Code for Mix Design of Hydraulic Concrete,” Ministry of Construction of the People’s Republic of China (MCPRC), Beijing, China, 2015.
54. Fuller, W. B., and Thompson, S. E., “The Laws of Proportioning Concrete,” Transactions of the American Society of Civil Engineers, V. 59, No. 2, 1907, pp. 67-143. doi: 10.1061/TACEAT.0001979
55. Walraven, J. C., and Reinhardt, H. W., “Theory and Experiments on the Mechanical Behaviour of Cracks in Plain and Reinforced Concrete Subjected to Shear Loading,” Heron, V. 26, 1981, pp. 26-39.
56. Neville, A. M., Properties of Concrete, Longman, London, UK, 1995.
57. Shi, J.; Xu, Y.; and Ye, Z., “Mesoanalysis of Concrete Behavior due to Effect of Aggregate Gradation,” Engineering Mechanics, V. 26, No. 4, 2009, pp. 134-138.
58. Meddah, M. S.; Zitouni, S.; and Belâabes, S., “Effect of Content and Particle Size Distribution of Coarse Aggregate on the Compressive Strength of Concrete,” Construction and Building Materials, V. 24, No. 4, 2010, pp. 505-512. doi: 10.1016/j.conbuildmat.2009.10.009
59. Rosselló, C.; Elices, M.; and Guinea, G. V., “Fracture of Model Concrete: 2. Fracture Energy and Characteristic Length,” Cement and Concrete Research, V. 36, No. 7, 2006, pp. 1345-1353. doi: 10.1016/j.cemconres.2005.04.016
60. Grassl, P.; Wong, H. S.; and Buenfeld, N. R., “Influence of Aggregate Size and Volume Fraction on Shrinkage Induced Micro-Cracking of Concrete and Mortar,” Cement and Concrete Research, V. 40, No. 1, 2010, pp. 85-93. doi: 10.1016/j.cemconres.2009.09.012
61. Beygi, M. H. A.; Kazemi, M. T.; Nikbin, I. M.; Amiri, J. V.; Rabbanifar, S.; and Rahmani, E., “The Influence of Coarse Aggregate Size and Volume on the Fracture Behavior and Brittleness of Self-Compacting Concrete,” Cement and Concrete Research, V. 66, 2014, pp. 75-90. doi: 10.1016/j.cemconres.2014.06.008
62. Lilliu, G., and van Mier, J. G. M., “3D Lattice Type Fracture Model for Concrete,” Engineering Fracture Mechanics, V. 70, No. 7-8, 2003, pp. 927-941. doi: 10.1016/S0013-7944(02)00158-3
63. Shah, S. P., and Chandra, S., “Critical Stress, Volume Change and Micro Cracking of Concrete,” ACI Journal Proceedings, V. 65, No. 9, Sept. 1968, pp. 770-781.
64. Akçaoğlu, T.; Tokyay, M.; and Çelik, T., “Effect of Coarse Aggregate Size and Matrix Quality on ITZ and Failure Behavior of Concrete Under Uniaxial Compression,” Cement and Concrete Composites, V. 26, No. 6, 2004, pp. 633-638. doi: 10.1016/S0958-9465(03)00092-1
65. Hillerborg, A.; Modéer, M.; and Petersson, P. E., “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements,” Cement and Concrete Research, V. 6, No. 6, 1976, pp. 773-781. doi: 10.1016/0008-8846(76)90007-7
66. Bažant, Z. P., and Oh, B. H., “Crack Band Theory for Fracture of Concrete,” Materiales de Construcción, V. 16, No. 3, 1983, pp. 155-177.
67. Bažant, Z. P., and Yu, Q., “Universal Size Effect Law and Effect of Crack Depth on Quasi-Brittle Structure Strength,” Journal of Engineering Mechanics, ASCE, V. 135, No. 2, 2009, pp. 78-84. doi: 10.1061/(ASCE)0733-9399(2009)135:2(78)
68. Hoover, C. G., and Bažant, Z. P., “Universal Size-Shape Effect Law Based on Comprehensive Concrete Fracture Tests,” Journal of Engineering Mechanics, ASCE, V. 140, No. 3, 2014, pp. 473-479. doi: 10.1061/(ASCE)EM.1943-7889.0000627
69. Hoover, C. G.; Bažant, Z. P.; Vorel, J.; Wendner, R.; and Hubler, M. H., “Comprehensive Concrete Fracture Tests: Description and Results,” Engineering Fracture Mechanics, V. 114, 2013, pp. 92-103. doi: 10.1016/j.engfracmech.2013.08.007
70. Hoover, C. G., and Bažant, Z. P., “Comprehensive Concrete Fracture Tests: Size Effects of Types 1 & 2, Crack Length Effect and Postpeak,” Engineering Fracture Mechanics, V. 110, 2013, pp. 281-289. doi: 10.1016/j.engfracmech.2013.08.008
71. Li, D.; Jin, L.; Du, X.; Fu, J.; and Lu, A., “Size Effect Tests of Normal-Strength and High-Strength RC Columns Subjected to Axial Compressive Loading,” Engineering Structures, V. 109, 2016, pp. 43-60. doi: 10.1016/j.engstruct.2015.11.022
72. Zhu, R.; Alam, S. Y.; and Loukili, A., “An Experimental Investigation on the Correlation between the Aggregate Size Effect and the Structural Size Effect,” Engineering Fracture Mechanics, V. 234, 2020, p. 107101. doi: 10.1016/j.engfracmech.2020.107101