*3.2. Effect of Crack Geometry on the Chloride Diffusion Process in Cracked Concrete*

The non-steady-state chloride diffusion process in cracked concrete was simulated using the finite difference method. Rectangular, V-shaped and real cracks were adopted in the simulations. The detailed geometries of these cracks are shown in Figure 7. The rectangular cracks had different crack depths (i.e., 25 mm, 35 mm and 45 mm). The depth of the V-shaped and real cracks was set to be 45 mm. The geometry of real crack was adopted from [33]. All of the cracks had a crack width of 0.6 mm at the left surface of the specimen.

**Figure 7.** The crack geometries used in non-steady-state diffusion simulation (crack width at the left surface: 0.6 mm).

The simulated chloride concentration distributions in concrete with rectangular cracks after one year of immersion in NaCl solution are shown in Figure 8. The chloride penetrated the concrete specimen quickly through the crack, and the chloride penetration depth was largely dependent on the crack depth. A higher crack depth led to a deeper chloride penetration depth. Hence, the crack depth is the key factor that influences the service life of concrete structures in chloride environments. The chlorides also penetrated concrete through the crack surfaces; hence, the chloride concentration in concrete near the crack surfaces was also increased due to the presence of cracks.

**Figure 8.** The simulated chloride concentration in cracked concrete with rectangular cracks after one year of immersion in NaCl solution.

The chloride concentration distributions in cracked concrete with different crack geometries are shown in Figure 9. At the immersion age of 0.01 years, it was quite obvious that the chloride concentration in the real tortuous crack was lower than that in the rectangular and V-shaped cracks. The tortuous crack inhibited the fast chlorides' diffusion in concrete cracks. When the immersion age increased, the chloride concentration distributions in different cracked concretes were close to each other. The chloride concentrations at the height of 25 mm in cracked concrete (i.e., at the center of the cracked concrete in the vertical direction) are shown in Figure 10. At the immersion age of 0.01 years, the

chloride concentration at the real crack tip was much lower than that in the rectangular and V-shaped cracks, and for the real crack, the chloride concentration beyond the crack tip was also lower than that in the other two. At the immersion age of one year, the chloride concentration distributions in cracked concrete with rectangular and V-shaped cracks were almost the same. The chloride concentration in the real crack was only slightly lower than that in the rectangular and V-shaped cracks. This suggested that the crack geometry influenced the chloride diffusion process in cracked concrete soon after the chloride penetrated the crack. However, for a long-term immersion with a given crack depth, the crack geometry did not show much influence on the chloride penetration depth in cracked concrete. In comparison, the influence of crack depth was more significant than that of crack geometry on the chloride penetration depth in cracked concrete in the long term.

**Figure 9.** The chloride concentration distribution in concrete with different crack geometries.

**Figure 10.** The chloride concentrations at the height of 25 mm in cracked concrete: (**a**) at the immersion age of 0.01 years; (**b**) at the immersion age of one year.

Generally, in cracked concrete, the crack width influences the short-term chloride diffusion process, but for long-term chloride diffusion, the influence of crack depth is more significant. That is, the crack depth is the main factor that influences the residual service life of a cracked concrete structure in chloride environments. Moreover, when predicting the residual service life of cracked concrete structures with numerical methods, the real crack could be simplified as rectangular (or other shaped) crack in the simulations.
