 | (96) |
Two different transport parameters appear in Eq. (88). There is the diffusion coefficient Di associated with the diffusion process and the liquid water diffusivity DL to characterize the effect of the fluid velocity on the ionic transport. A discussion of DL was already given in Section 2.5.
The diffusion coefficient is evaluated with the migration experiment test. It consists in accelerating chloride ions with an applied external potential through a disk of cement-based materials glued between two cells filled with ionic solutions. The analysis of the results yields the diffusion coefficients. Different analysis methods are found in the literature. One is based on steady-state measurements of chloride having crossed the sample [47] and [48]. Another [49] is based on measuring non-steady-state chloride profiles by grinding the sample after a short exposure. A recent paper by Samson et al. [50] describes a method based on current measurements during the migration test. The measurements are analyzed with the extended Nernst-Planck model to yield the diffusion coefficient of each ionic species in the material.
All these methods are performed in saturated conditions. As shown in Eq. (76), the diffusion coefficient Di depends, through τL, on the saturation condition. No method could be found in the literature to evaluate this parameter for unsaturated conditions. However, it is possible that Di might not be affected by the saturation state of the material above a given saturation level, the latter being defined as s=θL/φ, where φ is the porosity. Revil [32] showed that for shaly sand, the diffusion of the ions is almost unaffected for a water saturation above 0.6. We thus infer that for concrete structures exposed to high relative humidity environment, the diffusion coefficient is independent of the water content.
In the flux Eq. (75), the recurring quantity τLθL, which could also be written τLsφ is analogous to a saturation-dependent formation factor for the liquid phase of the pore system. The saturation s results from the averaging over the REV. The tortuosity τL is also a function of the saturation and reflects the connectedness of the moisture phase. At a critical moisture content sc, the liquid phase is no longer connected, the tortuosity τL goes to zero, and the transport within the liquid phase ceases.
The remaining question is the dependence of the tortuosity
τL on the saturation. Although no precise data exist for
cementitious systems, there exist qualitative data from which inferences can be made.
These data typically express the relative total conduction as a function of the
saturation s. The relative total conduction
σ/σo is analogous to the product of the saturation
and the relative tortuosity:
The work of Martys [19] suggests that, for a preferentially wetting liquid being displaced by a nonwetting one, the limiting behavior of τL near saturation can be approximated by the dilute effective medium theory result:
