Abstract
Significant nonlinear material behavior of concrete subjected to compression is to be avoided in reinforced concrete structures subjected to regular service loads. Herein, initiation of prepeak nonlinearities under multiaxial compression is predicted using a multiscale model. The latter is based on a microscopic criterion for pressure-sensitive shear failure of micron-sized hydrate-gel needles that are part of the microstructure of the thin interfacial transition zones surrounding the aggregates. Model predictions agree well with starting points of significant nonlinearities in macroscopic stress-strain curves from several multiaxial compression tests. Corresponding limit stress surfaces are illustrated in a principal stress space, for general stress paths of multiaxial compression. Sensitivity analyses with respect to the initial composition of concrete and its maturity are described. The study confirms that the microstructural mechanism governing failure of concrete under uniaxial compression triggers initiation of prepeak nonlinearities under multiaxial compression.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Abrams, D. A. 1919. Design of concrete mixtures, Vol. 1. Chicago: Lewis Institute.
Acker, P. 2001. “Micromechanical analysis of creep and shrinkage mechanisms.” In Creep, shrinkage and durability mechanics of concrete and other quasi-brittle materials, 15–25. Cambridge, MA: Elsevier.
Ansari, F., and Q. Li. 1998. “High-strength concrete subjected to triaxial compression.” Mater. J. 95 (6): 747–755.
Benveniste, Y. 1987. “A new approach to the application of Mori-Tanaka’s theory in composite materials.” Mech. Mater. 6 (2): 147–157. https://doi.org/10.1016/0167-6636(87)90005-6.
Bernard, O., F. J. Ulm, and E. Lemarchand. 2003. “A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials.” Cem. Concr. Res. 33 (9): 1293–1309. https://doi.org/10.1016/S0008-8846(03)00039-5.
Bigoni, D., and A. Piccolroaz. 2004. “Yield criteria for quasibrittle and frictional materials.” Int. J. Solids Struct. 41 (11–12): 2855–2878. https://doi.org/10.1016/j.ijsolstr.2003.12.024.
Candappa, D. C., J. G. Sanjayan, and S. Setunge. 2001. “Complete triaxial stress-strain curves of high-strength concrete.” J. Mater. Civ. Eng. 13 (3): 209–215. https://doi.org/10.1061/(ASCE)0899-1561(2001)13:3(209).
CEN. 2013. Eurocode: Basis of structural design. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2011. Eurocode 2: Design of concrete structures—Part 1-1: General rules and rules for buildings. Brussels, Belgium: CEN.
Chen, D., X. Yu, R. Liu, S. Li, and Y. Zhang. 2019. “Triaxial mechanical behavior of early age concrete: Experimental and modelling research.” Cem. Concr. Res. 115 (Jan): 433–444. https://doi.org/10.1016/j.cemconres.2018.09.013.
Constantinides, G., and F.-J. Ulm. 2004. “The effect of two types of C-S-H on the elasticity of cement-based materials: Results from nanoindentation and micromechanical modeling.” Cem. Concr. Res. 34 (1): 67–80. https://doi.org/10.1016/S0008-8846(03)00230-8.
de Wolski, S. C., J. E. Bolander, and E. N. Landis. 2014. “An in-situ X-ray microtomography study of split cylinder fracture in cement-based materials.” Exp. Mech. 54 (7): 1227–1235. https://doi.org/10.1007/s11340-014-9875-1.
Diamond, S. 2001. “Considerations in image analysis as applied to investigations of the ITZ in concrete.” Cem. Concr. Compos. 23 (2–3): 171–178. https://doi.org/10.1016/S0958-9465(00)00085-8.
Dormieux, L., D. Kondo, and F.-J. Ulm. 2006. “A micromechanical analysis of damage propagation in fluid-saturated cracked media.” C.R. Mec. 334 (7): 440–446. https://doi.org/10.1016/j.crme.2006.05.007.
Drugan, W., and J. Willis. 1996. “A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites.” J. Mech. Phys. Solids 44 (4): 497–524. https://doi.org/10.1016/0022-5096(96)00007-5.
Féret, R. 1892. “Sur la compacité des mortiers hydrauliques.” [In French.] Paris: Dunod.
Fritsch, A., L. Dormieux, and C. Hellmich. 2006. “Porous polycrystals built up by uniformly and axisymmetrically oriented needles: Homogenization of elastic properties.” C.R. Mec. 334 (3): 151–157. https://doi.org/10.1016/j.crme.2006.01.008.
Garboczi, E. J., and D. P. Bentz. 1997. “Analytical formulas for interfacial transition zone properties.” Adv. Cem. Based Mater. 6 (3–4): 99–108. https://doi.org/10.1016/S1065-7355(97)90016-X.
Glucklich, J. 1968. “The effect of microcracking on time-dependent deformations and the long-term strength of concrete.” In Proc., Int. Conf. on the Structure of Concrete, 176–189. London: Technion Research and Development Foundation.
Hampel, T., K. Speck, S. Scheerer, R. Ritter, and M. Curbach. 2009. “High-performance concrete under biaxial and triaxial loads.” J. Eng. Mech. 135 (11): 1274–1280. https://doi.org/10.1061/(ASCE)0733-9399(2009)135:11(1274).
Hellmich, C., A. Fritsch, and L. Dormieux. 2011. Multiscale homogenization theory: An analysis tool for revealing mechanical design principles in bone and bone replacement materials, 81–103. Berlin: Springer.
Hershey, A. 1954. “The elasticity of an isotropic aggregate of anisotropic cubic crystals.” J. Appl. Mech. 21 (3): 236–240. https://doi.org/10.1115/1.4010899.
Hill, R. 1965. “A self-consistent mechanics of composite materials.” J. Mech. Phys. Solids 13 (4): 213–222. https://doi.org/10.1016/0022-5096(65)90010-4.
Hofstetter, G., and H. Mang. 1995. Computational mechanics of reinforced concrete structures. Brunswick, Germany: Vieweg Verlag.
Hsu, T. T. C., F. O. Slate, G. M. Sturman, and G. Winter. 1963. “Microcracking of plain concrete and the shape of the stress-strain curve.” ACI J. Proc. 60 (5): 209–224.
Hussein, A. 1998. “Behaviour of high-strength concrete under biaxial loading conditions.” Ph.D. thesis, Faculty of Engineering and Applied Science, Memorial Univ. of Newfoundland.
Hussein, A., and H. Marzouk. 2000. “Behavior of high-strength concrete under biaxial stresses.” ACI Mater. J. 97 (1): 27–36.
Imran, I. 1994. “Applications of nonassociated plasticity in modeling the mechanical response of concrete.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Toronto.
Imran, I., and S. J. Pantazopoulou. 1996. “Experimental study of plain concrete under triaxial stress.” ACI Mater. J. 93 (6): 589–601.
ISO. 2012. Durability—Service life design of concrete structures. ISO 16204. Geneva: ISO.
ISO. 2015. General principles on reliability for structures. ISO 2394. Geneva: ISO.
Jennings, H. M. 2004. “Colloid model of C-S-H and implications to the problem of creep and shrinkage.” Mater. Struct. 37 (1): 59–70. https://doi.org/10.1007/BF02481627.
Kohlhauser, C., and C. Hellmich. 2013. “Ultrasonic contact pulse transmission for elastic wave velocity and stiffness determination: Influence of specimen geometry and porosity.” Eng. Struct. 47 (Feb): 115–133. https://doi.org/10.1016/j.engstruct.2012.10.027.
Königsberger, M. 2012. “Onset of cracking in concrete: Debonding or ITZ failure? A micromechanical approach.” Master’s thesis, Faculty for Civil Engineering, TU Wien.
Königsberger, M., M. Hlobil, B. Delsaute, S. Staquet, C. Hellmich, and B. Pichler. 2018. “Hydrate failure in ITZ governs concrete strength: A micro-to-macro validated engineering mechanics model.” Cem. Concr. Res. 103 (Jan): 77–94. https://doi.org/10.1016/j.cemconres.2017.10.002.
Königsberger, M., B. Pichler, and C. Hellmich. 2014a. “Micromechanics of ITZ-aggregate interaction in concrete: Crack initiation.” In Proc., RILEM Int. Symp. on Concrete Modelling (CONMOD’2014). Marne la Vallée, France: RILEM.
Königsberger, M., B. Pichler, and C. Hellmich. 2014b. “Micromechanics of ITZ–aggregate interaction in concrete Part I: Stress concentration.” J. Am. Ceram. Soc. 97 (2): 535–542. https://doi.org/10.1111/jace.12591.
Königsberger, M., B. Pichler, and C. Hellmich. 2014c. “Micromechanics of ITZ-aggregate interaction in concrete Part II: Strength upscaling.” J. Am. Ceram. Soc. 97 (2): 543–551. https://doi.org/10.1111/jace.12606.
Kröner, E. 1958. “Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls.” [In German.] Z. für Phys. A Hadrons Nuclei 151 (4): 504–518. https://doi.org/10.1007/BF01337948.
Liu, M., Y. Gao, and H. Liu. 2012. “A nonlinear Drucker-Prager and Matsuoka-Nakai unified failure criterion for geomaterials with separated stress invariants.” Int. J. Rock Mech. Min. Sci. 50 (Feb): 1–10. https://doi.org/10.1016/j.ijrmms.2012.01.002.
Mondal, P., S. P. Shah, and L. D. Marks. 2009. “Nanomechanical properties of interfacial transition zone in concrete.” In Nanotechnology in construction 3, edited by Z. Bittnar, P. J. M. Bartos, J. Němeček, V. Šmilauer, and J. Zeman, 315–320. Heidelberg, Germany: Springer.
Mori, T., and K. Tanaka. 1973. “Average stress in matrix and average elastic energy of materials with misfitting inclusions.” Acta Metall. 21 (5): 571–574. https://doi.org/10.1016/0001-6160(73)90064-3.
Muller, A. C. A., K. L. Scrivener, A. M. Gajewicz, and P. J. McDonald. 2013. “Densification of C-S-H measured by 1H NMR relaxometry.” J. Phys. Chem. C 117 (1): 403–412. https://doi.org/10.1021/jp3102964.
Ollivier, J., J. Maso, and B. Bourdette. 1995. “Interfacial transition zone in concrete.” Adv. Cem. Based Mater. 2 (1): 30–38. https://doi.org/10.1016/1065-7355(95)90037-3.
Perry, C., and J. Gillott. 1977. “The influence of mortar-aggregate bond strength on the behaviour of concrete in uniaxial compression.” Cem. Concr. Res. 7 (5): 553–564. https://doi.org/10.1016/0008-8846(77)90117-X.
Pichler, B., and C. Hellmich. 2011. “Upscaling quasi-brittle strength of cement paste and mortar: A multi-scale engineering mechanics model.” Cem. Concr. Res. 41 (5): 467–476. https://doi.org/10.1016/j.cemconres.2011.01.010.
Pichler, B., C. Hellmich, and J. Eberhardsteiner. 2009. “Spherical and acicular representation of hydrates in a micromechanical model for cement paste: Prediction of early-age elasticity and strength.” Acta Mech. 203 (3): 137–162. https://doi.org/10.1007/s00707-008-0007-9.
Pichler, B., C. Hellmich, J. Eberhardsteiner, J. Wasserbauer, P. Termkhajornkit, R. Barbarulo, and G. Chanvillard. 2013. “Effect of gel-space ratio and microstructure on strength of hydrating cementitious materials: An engineering micromechanics approach.” Cem. Concr. Res. 45 (Mar): 55–68. https://doi.org/10.1016/j.cemconres.2012.10.019.
Poinard, C., E. Piotrowska, Y. Malecot, L. Daudeville, and E. N. Landis. 2012. “Compression triaxial behavior of concrete: The role of the mesostructure by analysis of X-ray tomographic images.” Supplement, Eur. J. Environ. Civ. Eng. 16 (S1): s115–s136. https://doi.org/10.1080/19648189.2012.682458.
Powers, T., and T. Brownyard. 1948. “Studies of the physical properties of hardened Portland cement paste.” Res. Lab. Portland Cem. Assoc. Bull. 22 (Jan): 101–992.
Richardson, I. 2004. “Tobermorite/jennite- and tobermorite/calcium hydroxide-based models for the structure of C-S-H: Applicability to hardened pastes of tricalcium silicate, -dicalcium silicate, Portland cement, and blends of Portland cement with blast-furnace slag, metakaolin, or silica fume.” Cem. Concr. Res. 34 (9): 1733–1777. https://doi.org/10.1016/j.cemconres.2004.05.034.
Salençon, J. 2001. Handbook of continuum mechanics: General concepts thermoelasticity. New York: Springer.
Sarris, E., and G. Constantinides. 2013. “Finite element modeling of nanoindentation on C–S–H: Effect of pile-up and contact friction.” Cem. Concr. Compos. 36 (Feb): 78–84. https://doi.org/10.1016/j.cemconcomp.2012.10.010.
Scrivener, K. L., A. K. Crumbie, and P. Laugesen. 2004. “The interfacial transition zone (ITZ) between cement paste and aggregate in concrete.” Interface Sci. 12 (4): 411–421. https://doi.org/10.1023/B:INTS.0000042339.92990.4c.
Scrivener, K. L., and K. M. Nemati. 1996. “The percolation of pore space in the cement paste/aggregate interfacial zone of concrete.” Cem. Concr. Res. 26 (1): 35–40. https://doi.org/10.1016/0008-8846(95)00185-9.
Sfer, D., I. Carol, R. Gettu, and G. Etse. 2002. “Study of the behavior of concrete under triaxial compression.” J. Eng. Mech. 128 (2): 156–163. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:2(156).
Taerwe, L., and S. Matthys. 2013. Fib model code for concrete structures 2010. New York: Wiley.
Taylor, R., I. G. Richardson, and R. M. D. Brydson. 2007. “Nature of C–S–H in 20 year old neat ordinary Portland cement and 10% Portland cement–90% ground granulated blast furnace slag pastes.” Adv. Appl. Ceram. 106 (6): 294–301. https://doi.org/10.1179/174367607X228106.
Van Geel, H. 1998. “Concrete behaviour in multiaxial compression: Experimental research.” Ph.D. thesis, Dept. of the Built Environment, Eindhoven Univ. of Technology.
Vorel, J., V. Šmilauer, and Z. Bittnar. 2012. “Multiscale simulations of concrete mechanical tests.” J. Comput. Appl. Math. 236 (18): 4882–4892. https://doi.org/10.1016/j.cam.2012.01.009.
Vu, X. H., Y. Malecot, and L. Daudeville. 2009. “Strain measurements on porous concrete samples for triaxial compression and extension tests under very high confinement.” J. Strain Anal. Eng. Des. 44 (8): 633–657. https://doi.org/10.1243/03093247JSA547.
Wang, H., C. Hellmich, Y. Yuan, H. Mang, and B. Pichler. 2018. “May reversible water uptake/release by hydrates explain the thermal expansion of cement paste?—Arguments from an inverse multiscale analysis.” Cem. Concr. Res. 113 (Nov): 13–26. https://doi.org/10.1016/j.cemconres.2018.05.008.
Wang, Y.-B., J. Y. Liew, S. C. Lee, and D. X. Xiong. 2016. “Experimental study of ultra-high-strength concrete under triaxial compression.” ACI Mater. J. 113 (1): 105–112. https://doi.org/10.14359/51688071.
Wastiels, J. 1979. “Behaviour of concrete under multiaxial stresses—A review.” Cem. Concr. Res. 9 (1): 35–44. https://doi.org/10.1016/0008-8846(79)90092-9.
Zaoui, A. 2002. “Continuum micromechanics: Survey.” J. Eng. Mech. 128 (8): 808–816. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:8(808).
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 1 • January 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Feb 18, 2022
Accepted: Jul 20, 2022
Published online: Nov 12, 2022
Published in print: Jan 1, 2023
Discussion open until: Apr 12, 2023
ASCE Technical Topics:
- Analysis (by type)
- Compression
- Concrete
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering materials (by type)
- Engineering mechanics
- Failure analysis
- Hydration
- Laminating
- Material failures
- Material mechanics
- Material properties
- Materials characterization
- Materials engineering
- Materials processing
- Reinforced concrete
- Sensitivity analysis
- Solid mechanics
- Stress (by type)
- Stress strain relations
- Structural analysis
- Structural dynamics
- Structural engineering
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.