# Corrosion Modelling

Chloride ingress into concrete is generally held to follow Fick's second law of diffusion, forming a chloride profile with depth into the concrete.

d[Cl]/dt=Dc.d²[Cl]/dx²

where [Cl- ] is the chloride concentration, at depth x and time t and Dc is the diffusion coefficient (usually of the order of 10-8 cm2.s-1). The solution to the differential equation for chlorides diffusing in from a surface is:

(Cmax - Cx,t)lCmac - Cmin)=erf[(x)/(4Dct)½

where Cmax is the surface or near surface concentration Cx,t is the chloride concentration at depth x at time t Cmin is the background chloride concentration erf is the error function

Cmax must be constant which is why a near surface measurement is used, to avoid fluctuations in surface levels on wetted and dried surfaces.

An alternative to the error function calculation is to calculate the progress of a threshold chloride concentration as a parabolic function of time using a similar function to that used for the carbonation front progression.

Carbonation rates generally follow parabolic kinetics:

d = At0.5

where d = carbonation depth, t = time and A is a constant, generally of the order 0.25 to 1.0 mm.year-½

Carbonation rates are a function of the environment where indoor concrete will carbonate faster than outdoor concrete in North American and Northern European environments, but wet/dry cycling in warm conditions can accelerate carbonation in more southerly latitudes. As corrosion will not proceed in the absence of water, carbonation rates are usually unimportant inside buildings except in bathrooms, kitchens and other situations where there is wet/dry cycling and sufficient moisture to cause corrosion after carbonation to rebar depth.

The actual corrosion rate can be measured using the techniques discussed in Corrosion Rate Measurement or in Corrosion Monitoring.

There is far more detail on these and other techniques in the latest edition of my book. Details for ordering are on the home page of the website.

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