Example Results

The computer code described herein has been used extensively at NIST to simulate a variety of cement-based systems [6-13 ]. A brief survey of various results generated using the computer codes will be presented here.

The most basic application of the code would be to a system of monosize spheres, where the ratio of the soft shell thickness to the hard core radius is systematically varied. Figure 3 shows the results obtained for the volume fractions of hard cores and soft shells needed to just form a percolated pathway across the microstructure. For the case of totally overlapping particles (i.e., hard core radius=0), the classical result of 0.29 volume fraction is obtained [7]. As the ratio of hard core to total radius increases, less soft shell volume is needed to form a percolated pathway. For comparison, for a mortar (sand and cement paste), typically a volume fraction of soft shells on the order of 0.10 is needed to achieve percolation [24].

Figure 3: Computer model hard core soft shell percolation results for monosize spheres with variable ratios of hard core radius b to total (hard core + soft shell) radius a. The data points indicate the volume fractions of hard core grains and soft shells needed for percolation and the dashed lines indicate the predicted results of a self-consistent effective medium theory (SC-EMT) [7]. The solid horizontal line indicates the random parking limit for monosize spheres (about 0.38).

In another study [6], the HCSS model was applied to determine the best value for the thickness of the ITZ regions to match mercury intrusion porosimetry (MIP) experimental results. In this study, a series of mortars of variable hard core volume fraction were prepared and examined using the MIP technique. As the hard core volume fraction increased, a point was reached where the soft shells (which contain more and larger pores) achieved percolation. In MIP, this percolation was indicated by the appearance of a new class of pores of larger size than those determined for the bulk paste. Since the size distribution of the sand (hard cores) was measured experimentally, the simulation was conducted matching the sieve classification and varying the thickness of the soft shells. The results presented in Fig. 4 show the connected fraction of soft shells plotted vs. the volume fraction of hard core particles. Experimentally, the percolation was observed to occur between 45 % and 49 % sand volume fraction. From Fig. 4, this would best correspond to an ITZ (soft shell) thickness of 15 µm , in general agreement with experimental microscopy observations [2,3].

Figure 4: Computer model interfacial zone percolation results for varying sand volume fractions and interfacial zone thicknesses. Labels provide the interfacial transition zone thicknesses in µm.

A further issue which can be addressed by varying the thickness of the soft shells is the determination of the volume fraction of matrix within a given distance of the hard core particles. Using realistic size distributions for the aggregate particles, Fig. 5 provides a plot of the percentage of the cement paste within a given distance of an aggregate for both a typical mortar and a typical concrete. Because of the higher surface area of the aggregate particles in a mortar relative to those in a concrete, a larger volume fraction of paste is found within a fixed distance of the aggregate for the mortar. Given an ITZ thickness on the order of 20 µm, one finds that an appreciable volume fraction of the cement paste (on the order of 20 %) is contained in the ITZ regions, which could have a significant influence on transport and mechanical properties. The equations of Lu and Torquato [16] can also be used to very accurately predict these volume fractions of paste within a given distance of an aggregate [17].

Figure 5: Fraction of total cement paste within a given distance of aggregate surface, for a mortar (V_HC=0.552) and for a concrete (V_HC=0.646).

This concept can be extended in the case of air voids in concrete to consider the distribution of void to void distances [12]. Figure 6 provides a plot of the mean void-void spacing as a function of the void radius (for voids of radius r, what is the average surface to surface distance to the nearest neighbor void). It can be seen that the larger the void radius, the more likely that there exists another void within a short distance of its surface. The predictions of Lu and Torquato [16] are seen to be in excellent agreement with the simulation results.

Figure 6: Mean void-void spacing (l_p) for lognormally distributed sphere radii with a density of 240 mm^-3 [ 12]. Measured values are shown as solid circles; the solid line is the estimate of Lu and Torquato [ 16].

The random walker diffusivity code has been used to predict the diffusivity of concrete as a function of mixture proportions [9] and also to evaluate the diffusivity of a series of mortars of variable sand contents [26]. Figure 7 shows a comparison of experimental and model results for a series of mortars prepared using a water-to-cement (w/c) ratio of 0.5. In general, the agreement between experimental and model values is quite reasonable, as the difficulties in making accurate experimental measurements usually result in a coefficient of variation on the order of 20 %.

Figure 7: Comparison of experimental and model diffusion coefficients for w/c=0.50 [26].