Keywords: micromechanical analysis, hydration model, heat of hydration, elastic properties, viscoelastic properties, autogeneous shrinkage.

Hydration of concrete is a complex process that can be modelled using a multiscale approach. Several dominant mechanisms occur at the level of cement paste which evolution may be simulated by microstructural evolution model CEMHYD3D [1]. Application of the cement hydration model is demonstrated in the following areas; heat of hydration, elastic and viscoelastic properties, and autogeneous shrinkage of cement paste. The examples presented show invaluable approach of micromechanical analysis, using intrinsic properties of constituents rather than phenomenological laws.

Evolving microstructure of cement paste liberates the heat of hydration, which is of importance in massive structures. Aggregates in concrete do not influence significantly the hydration process, therefore the cement paste level may be considered on the concrete scale. Foundation slab of 1 m thickness is validated, coupling the structural level with the hydration in terms of released heat and actual temperature. The validation shows perfect correlation up to 48 hours of hydration, the climatic boundary conditions distort later results slightly.

The linear elastic homogenisation relies on intrinsic properties of cement paste, which were obtained by means of nanoindentation. Recent homogenisation method based on FFT is used directly on the evolving microstructures from the CEMHYD3D model. Homogenised data from seven previously homogenised cement pastes were used to fit a newly formulated relationship between Young's modulus and the degree of hydration. A new formula preserves asymptotic behaviour and shows that Young's modulus does not exceed approximately 50 GPa in cement paste.

The viscoelastic properties of cement paste may be formulated via a quasi-static multiscale approach, using the power of FFT-based homogenisation method. The B3 model, used often in civil engineering, is used for the assignment of non-aging creep behaviour of C-S-H phase [2]. Validation is aimed at finding the "intrinsic" creep function of C-S-H from known data of 30 years old cement paste. The redistribution of stress between creeping C-S-H and other elastic solid phases clearly demonstrates the multiscale nature of creep.

The finite element method will be employed for the simulation of capillary underpressure and corresponding displacements in autogeneous shrinkage. Since the simulation starts at an early stage of cement paste, it is necessary to introduce solid percolation filtering with additional split nodes in sharp corners within the microstructure. The validation focuses on a cement paste, where capillary underpressure is obtained directly from known intrusion pressure of mercury [3]. The underpressure is used as a load for the evolving microstructure of cement paste, including known creep function. Validation shows that creep plays a dominant role in autogeneous shrinkage, much larger than elastic part caused by underpressure load, e.g. simulation revealed that the elastic part creates only 14% of the total strain at 25 days of hydration.

The hydration model CEMHYD3D, designed for the level of cement paste, finds its application as well at the level of concrete. A multiscale approach enables the use of intrinsic properties of constituents rather than phenomenological laws. Since cement paste represents a dominant level in the analysis of concrete, the results from the paste may be upscaled to the concrete level.

[1]

D.P. Bentz, "CEMHYD3D: A Three-Dimensional Cement Hydration and Microstructure Development Modeling Package. Version 3.0.", Tech. Rep., {NIST Building and Fire Research Laboratory}, Gaithersburg, Maryland, 2005.

[2]

Z.P. Bazant, A.B. Hauggaard, S. Baweja, and F.-J. Ulm, "Microprestress-solidification theory for concrete creep. I. aging and drying effects", Journal of Engineering Mechanics, 123, 1188-1194, 1997. doi:10.1061/(ASCE)0733-9399(1997)123:11(1188)

[3]

C. Hua, P. Acker, and A. Ehrlacher, "Analyses and models of the autogenous shrinkage of hardening cement paste. I. Modelling at macroscopic scale", Cem. Concr. Res., 25, 1457-1468, 1995. doi:10.1016/0008-8846(95)00140-8

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