This is the 2D companion to the 3D carbonation slab: the same governing physics, computed independently as a bank of parallel front-tracking columns spanning the slab's width instead of one global scalar. Each column solves its own quasi-steady CO₂ diffusion-reaction (Stefan-problem) mass balance,
a·x·dx/dt = D_e·C_s ⇒ d(x²)/dt = 2·D_e·C_s/a = 2Q (constant)
Integrating x² directly (rather than x itself) is what makes this numerically well-posed: x² grows linearly in time with no singularity at x=0, and the exact solution x(t)=√(2Qt) reduces to the same engineering x_c=K·√t law used by the 3D model, with K=√(2Q). Each column is given an independent random porosity multiplier (±35%) on Q, so the carbonation front is rugged across the slab's width instead of a flat plane — exactly the spatial variability real concrete cover shows, something a single global depth can't represent.
Once a column's front reaches the cover depth locally, that column depassivates independently: Faraday's law drives local steel penetration, rust bulges the local bar, and once local rust product exceeds a critical thickness that column cracks — so cracking starts patchily at the weakest (most porous) points along the bar, not uniformly everywhere at once.
dr/dt [mm/yr] = 0.0116 · i_corr [µA/cm²] rust = steel_loss · (2.5−1)
The small inset chart plots the slab-average front depth against √(elapsed years) alongside the fitted line through the origin — the emergent √t scaling law falls directly out of the per-column integration rather than being drawn from a formula.
- CO₂ exposure — scales the CO₂ diffusion driving term from ordinary urban air up to accelerated carbonation-chamber levels.
- Cover depth — doubling cover roughly quadruples time to depassivation (x²∝t).
- Water/cement ratio — the biggest mix-design lever on porosity and CO₂ diffusivity.
- Time speed — fast-forwards a process that plays out over decades in reality.