Multi-scale modeling of the effective chloride ion diffusion coefficient in cement-based composite materials

N-layered spherical inclusions model was used to calculate the effective diffusion coefficient of chloride ion in cement-based materials by using multi-scale method and then to investigate the relationship between the diffusivity and the microstructure of cement-basted materials where the microstructure included the interfacial transition zone (ITZ) between the aggregates and the bulk cement pastes as well as the microstructure of the bulk cement paste itself. For the convenience of applications, the mortar and concrete were considered as a four-phase spherical model, consisting of cement continuous phase, dispersed aggregates phase, interface transition zone and their homogenized effective medium phase. A general effective medium equation was established to calculate the diffusion coefficient of the hardened cement paste by considering the microstructure. During calculation, the tortuosity (n) and constrictivity factors (D _s /D ₀) of pore in the hardened pastes are n≈3.2, D _s /D ₀=1.0×10^?4 respectively from the test data. The calculated results using the n-layered spherical inclusions model are in good agreement with the experimental results; The effective diffusion coefficient of ITZ is 12 times that of the bulk cement for mortar and 17 times for concrete due to the difference between particle size distribution and the volume fraction of aggregates in mortar and concrete.