RESULTS AND DISCUSSION

Numerical results obtained with the NIST CEMHYD3D cement hydration and microstructure development model clearly indicate that leaching has a significant effect on the diffusivity of cement pastes. The diffusivity values calculated with the model for the original and completely leached microstructures are summarized in Table (2). In agreement with previous results for simpler C₃S systems¹⁴, the increase in diffusivity due to leaching is seen to be a factor of 20 or more, depending on the initial w/c ratio and the degree of hydration achieved prior to leaching. Additionally, the increase in diffusivity is seen to be much more dramatic for the lower w/c ratio systems, due mainly to the re-percolation of the capillary pore network during the leaching of the CH. For the higher w/c ratio systems, the depercolation of the capillary porosity is never achieved during the initial hydration (since the critical percolation threshold for the capillary porosity is on the order of 0.20) ^{14, 17, 18}. Thus, the relative increase in diffusivity caused by leaching is significantly less since both the hydrated and hydrated/leached microstructures contain a continuous capillary pore system.

Table 2: Model results for increase in diffusivity of cement pastes due to CH leaching

Cement	w/c	$\alpha$	$\phi_{orig}$orig	(D/D0)orig	$\phi_{leach}$leach	(D/D0 )leach	Dl /Do
A	0.40	0.6823	0.216133	0.00465	0.365127	0.0726	15.62
A	0.40	0.7985	0.164761	0.00222	0.333371	0.0535	24.1
A	0.60	0.7234	0.383334	0.0647	0.502002	0.1877	2.90
A	0.60	0.8879	0.328439	0.0322	0.467383	0.1506	4.68
B	0.40	0.7141	0.200007	0.00338	0.346106	0.0569	16.86
B	0.40	0.8101	0.159915	0.00204	0.320229	0.0423	20.77
B	0.60	0.790	0.342954	0.0377	0.466465	0.141	3.74
B	0.60	0.9010	0.308901	0.0223	0.444681	0.1207	5.41
C	0.40	0.7364	0.188660	0.00286	0.353968	0.0617	21.57
C	0.40	0.8142	0.153031	0.0022	0.330547	0.0493	22.4
C	0.60	0.7583	0.356682	0.0438	0.489645	0.1689	3.86
C	0.60	0.8917	0.307971	0.0222	0.456563	0.1366	6.15

 

In addition to leaching all of the CH from a hydrated microstructure, a fraction of the CH can be leached by specifying a leaching probability and a number of leaching cycles to be executed in the leaching program. For each leaching cycle, the microstructure is first scanned to identify all CH pixels which are in contact with capillary porosity. In a second scan, these pixels are randomly leached in proportion to the user-specified leaching probability. For six of the microstructures summarized in Table ( 2), "partial" leaching of the microstructures has been executed. The results for the ratio of the diffusivity of the leached to that of the original hydrated microstructure as a function of the amount of CH leached are provided in Figure 2. As observed previously¹⁴ and in agreement with the available experimental data³⁰, initially the removal of a small portion of the CH due to leaching has only minor effects on the computed diffusivities. Then, as 30 % to 60 % of the CH is leached, the effects on diffusivity are more dramatic. Finally, above 90 % leached, the increase in diffusivity tends to level off once more. Once again, it is clearly observed that the relative increase in diffusivity due to leaching is significantly greater for the lower 0.4 w/c ratio systems. Conversely, the differences between the three different cements at a constant w/c ratio are relatively minor, especially for CH leached fractions below about 50 %.

  

Figure 2: Model results for increase in diffusivity of cement pastes due to leaching of CH

In order to develop a simple equation for predicting the diffusivity ratio as a function of the fraction of CH leached from a microstructure, all of the data in Figure 2 were normalized using the diffusivity ratios for the original, ( DR(CH = 0)), and completely leached, ( DR(CH = 100)), microstructures and the following equation:

$$D_N(CH) = 1~+~\frac{DR(CH)-DR(CH=0)}{DR(CH=100)-DR(CH=0)}$$ (5)

It can be easily observed that this will result in normalized diffusivities (D_N ) with values between 1 and 2 for every case.

These normalized diffusivity ratios are plotted vs. the fraction of CH leached for each of the six cement paste systems in Figure (3). While there is still some scatter amongst the different systems, particularly for small values of the CH leached, for engineering purposes, all of the data in Figure (3) has been fitted to the following equation:

$$D_N(CH) = 1~+~\frac{1.1 \times CH^2}{0.28~+~0.79 \times CH}$$ (6)

where CH is the fraction of CH leached, having values in the range of [0,1]. As indicated by the dashed line in Figure (3), this equation gives an acceptable "average" fit to all of the data and will provide a simple method for estimating the diffusivity ratio for intermediate CH leaching when the values for the original and completely leached microstructures have been measured or computed.

  

Figure 3: Model results for normalized diffusivity ratio as a function of amount of CH leached from the microstructure. Solid lines indicate series/parallel bounds for a simple two-phase composite, dotted lines are the Hashin-Shtrikman upper and lower bounds, and dashed line is the fit of equation 7 to all of the computer simulation data.

Also included in Figure (3) are the upper and lower bounds computed using both the series/parallel and Hashin-Shtrikman equations³¹. In this case, it is assumed that the partially leached microstructure is composed of two components: original unleached cement paste with a normalized diffusivity of 1 and totally leached cement paste with a normalized diffusivity of 2. The fact that many of the plotted data points lie outside of these bounds (particularly the more restrictive Hashin-Shtrikman bounds) indicates that the simple consideration of a partially leached microstructure as a composite of unleached and totally leached phases is not totally appropriate but still serves as a useful abstraction.

The data provided by the NIST model were implemented in STADIUM and simulations were run for the 0.6 water/cement ratio mixture made of the CSA Type 10 cement (cement A) tested in saturated and unsaturated conditions. All the input data used in the simulations are summarized in Tables ( 3) and (4).

 

Table 3: Physical characteristics of the two mixtures

Mixture	Diffusion coefficient		Porosity	$\alpha$
	(m2/s)		(%)	(%)
	OH-	7.6e-11
W/C=0.40	Na+	1.9e-11
	SO42-	2.2e-11	37	68
	K+	2.8e-11
	Ca2+	1.1e-11
	OH-	17.6e-11
W/C=0.60	Na+	4.5e-11
	SO42-	5.2e-11	52	75
	K+	6.5e-11
	Ca2+	2.6e-11

 

 

Table 4: Pore solution chemistry

Ion	Concentration (mmol/L)
	W/C = 0.40	W/C = 0.60
OH-	700	434
Na+	192	111
SO42-	44	4
K+	592	327
Ca2+	2	2

 

Results of the simulations are given in Figures (4) and (5). The total concentrations in calcium (expressed in g/kg of paste) yielded by the model are compared to the experimental calcium profiles provided by the microprobe analyses. The curve labeled "with damage factor" corresponds to the results calculated by taking into account the effect of CH dissolution on the transport properties of the paste mixtures (see Table (2) and Figure (2)). Microprobe data are given in counts per second (Cps).

As can be seen, whatever the moisture state of the samples, the calcium profiles predicted by the model are in good agreement with the profiles obtained by the microprobe analyses. Not only does the model accurately predict the depth of CH penetration, but it also reproduces quite well the total distribution in calcium over the entire thickness of the samples. It should be emphasized that the model has no "fitting parameter", and that the numerical simulations are solely based on the properties of the mixture and the chemical damage equation derived from numerical data provided by the NIST model. However, since the model predicts an averaged concentration per unit volume (or unit mass) of material, the numerical results do not reproduce the local variations in calcium measured by the microprobe analyses. These variations are due to the experimental "noise" of the technique and the presence of CH crystals within the hydrated cement paste matrix.

  

Figure 4: Total calcium profile after three months of immersion - CSA Type 10, W/C = 0.6, saturated conditions

  

Figure 5: Total calcium profile after three months of exposure - CSA Type 10, W/C = 0.6, unsaturated conditions

Both series of results also indicate that the increase in diffusivity induced by the removal of CH has a limited influence on the kinetics of degradation. This phenomenon can be explained by the fact that the duration of the experiments was limited to only 3 months. As can be seen, degradation is limited to the first 2 mm near the surface. For longer exposure periods (and thicker samples), the influence of CH dissolution would most certainly has a more significant effect on the degradation kinetics. Simulations for a 100 mm thick sample clearly indicate that chemical damage (i.e. the microstructural alterations induced by the dissolution of CH) does have a strong influence on the kinetics of penetration of the degradation front.

It should also be emphasized that experiments were carried out using a relatively porous mixture (prepared at a w/c ratio of 0.6) which is less likely to be affected by the dissolution of CH. As previously mentioned, the pore structure of the 0.6 w/c ratio mixture was already percolated, thus reducing the detrimental influence of CH dissolution on the transport properties of the material.

Additional simulations were run for the 0.4 w/c ratio mixture prepared with the CSA Type 10 cement (cement A). Numerical results are given in Figure (6). Although the relative increase in diffusivity caused by leaching was found to be significantly more important for the 0.4 w/c ratio mixtures, both series of results are similar. This phenomenon can be explained by the fact that the initial diffusion coefficient of the 0.4 w/c ratio mixture was low, thus reducing the rate of diffusion of calcium and hydroxide ions out of the sample. As can be seen in the figure, degradation is mainly limited to the first millimeter near the surface. These results clearly emphasize the importance of the diffusion coefficient of the material on the kinetics of degradation.

  

Figure 6: Total calcium profile after three months of immersion - CSA Type 10 W/C = 0.4