Diffusion $($Fick$\text{'}$s second law$)$

A concrete bridge is under construction in a brackish water environment $($chloride concentration

in water $10,000ppm.$ The cover depth over the black steel reinforcement in the footings and

piles will be $75mm($the minimum amount for this environment, see CSA A$23\mathrm{.}1$:$19$ Table $17).$

Assume that corrosion of the reinforcement will begin when the chloride content reaches $0\mathrm{.}10\%$

at the depth of the reinforcement $(C_t=0\mathrm{.}10\%)$

$($a$)$ If the diffusion coefficient is $D=6{10}^{-13}\frac{m^2}{s}$ how long will it take for corrosion of the

reinforcement to initiate?

$($b$)$ What is the maximum allowable diffusion coefficient if you're designing for a $100$ year

service life $(t=100$ years$)?$

a$.$ Suggest two things the concrete producer might try to achieve the decrease in

diffusion coefficient.

$($c$)$ In situation $($b$)$ above what's the chloride concentration at the depth of the steel after

$200$ years?

$($d$)$ If $D=6{10}^{-13}\frac{m^2}{s}$ and the concrete mixture design includes a corrosion$-$inhibiting

admixture which effectively increases the corrosion threshold to $C_t=0\mathrm{.}30\%,$ how long

will it take for corrosion to initiate?