Multi-Scale Digital-Image-Based Modelling of Cement-Based Materials
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ABSTRACT
Computer modelling of the properties and performance of cement-based materials is complicated by the large range of relevant size scales. Processes occurring in the nanometersized pores ultimately affect the performance of these materials at the structural level of meters and larger. One approach to alleviating this complication is the development of a suite of models, consisting of individual digital-image-based structural models for the calcium silicate hydrate gel at the nanometer level, the hydrated cement paste at the micrometer level, and a mortar or concrete at the millimeter level. Computations performed at one level provide input properties to be used in simulations of performance at the next higher level. This methodology is demonstrated for the property of ionic diffusivity in saturated concrete. The more complicated problem of drying shrinkage is also addressed.
INTRODUCTION
Predicting the performance of concrete structures is made difficult by the complexity of the material, which has a complex microstructure [1] and exhibits composite behavior at a series of length scales. At the scale of millimeters, one can view the concrete as a composite of aggregates and air voids embedded in a continuous cement paste matrix. Even here, one may need to account for the difference in cement paste microstructure and properties in the interfacial zones surrounding each inclusion [2, 3, 4, 5, 6]. At the scale of micrometers, the cement paste is a composite of unhydrated cement particles, hydration products (crystalline and amorphous), and capillary porosity. Finally, the major hydration product of calcium silicate cements, calcium silicate hydrate (C-S-H) gel, is itself a composite of nanometer-sized "particles" and pores. A better understanding of the physical processes occurring at each of these scales and their interactions is necessary to increase the predictability of the performance of concrete. For example, it is the capillary forces which develop in the capillary and gel pores that are mainly responsible for the drying shrinkage of concrete. Thus, to reliably predict the drying shrinkage of a field concrete, one must understand the material at the scale of micrometers and even nanometers [7]. While this large scale range cannot be easily incorporated into a single model for concrete microstructure, it is possible to develop an integrated model in 33 Mat. Res. Soc. Symp. Proc. Vol. 370 01995 Materials Research Society
which information gained at one scale level is used in computing characteristics at the next higher level [2, 8, 9], as is demonstrated in this paper.
COMPUTER MODELLING TECHNIQUES At each scale of interest, a method for generating appropriate representative threedimensional microstructures must be chosen. Computational techniques are then employed to compute the physical properties (diffusivity, elastic moduli, etc.) of these composite microstructures. It should be noted that application of these property computation techniques is not limited to model microstructures, as they can b
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