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One of the critical properties controlling the service life of concrete
structures is the resistance the concrete provides to the diffusive ingress
of deleterious species such as chloride and sulfate ions [1].
A priori prediction of the chloride diffusivity of a concrete based on its
mixture proportions and expected curing is needed to accurately predict
its service life in its expected service environment and
to allow the development of durability-based (in addition to the current
strength-based) design codes. In fact, specifications are already being
issued which contain quite restrictive chloride diffusivity limits to meet a
100-year service life requirement [2]. In this research,
microstructural modeling techniques are applied to the a priori prediction of
chloride ion diffusion coefficients for conventional
(0.25 < w/c < 0.75)
saturated concretes. Diffusion/sorption in partially saturated concrete,
important in many field exposures, is not addressed in this study, but
computational techniques similar to those developed here should be applicable
to this mixed transport mode as well. In addition, we are only considering
chloride ion diffusion under steady-state conditions, as binding effects
are beyond the scope of the present study.
Because of the wide range of feature sizes in concrete, from nanometer-sized pores to centimeter-sized aggregates, it is difficult to concurrently represent all of these structural features in a single microstructural model. However, multi-scale modelling techniques appear to offer a promising solution to this restriction [3,4]. In this approach, properties computed at one scale, micrometers for instance, are input into a model which encompasses a higher scale, such as millimeters. Here, microstructural models for a) cement paste surrounding a single aggregate with a resolution of micrometers, and for b) a representative volume of concrete on the order of 20 cm3 in volume and containing hundreds of thousands of aggregate particles, are employed. These two microstructural models are interconnected along with computational techniques for computing the relative diffusivity or relative conductivity of a three-dimensional microstructure to ultimately compute the diffusivity of a representative volume of concrete, as has been demonstrated previously for mortars [4].
To determine which mixture proportion and curing parameters most influence the diffusivity of a concrete, a statistically designed computer experiment is conducted. Because we wish to consider seven variables at each of two levels, a fractional factorial experimental design is utilized to reduce the number of computer experiments required from 128 (27) to 16, while still obtaining information on all of the main, and some of the second-order, interaction effects [5]. Once the most significant variables have been identified, a response surface design is executed to better determine the effects of the "major" variables on diffusivity. Based on the results of this design, an equation relating diffusivity to material parameters is developed to approach our goal of the a priori prediction of concrete diffusivity. This equation essentially summarizes, in a simple analytical form, the complicated computations based on the multi-scale models.