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Concrete Durability

Concrete Carbonation Depth Prediction Simulator

Predict how atmospheric CO₂ lowers the pH of concrete using Fick's diffusion law. Move the cement type, W/C, humidity, CO₂ concentration and cover thickness, and see the rebar corrosion-initiation year and the cover required for a 100-year design life update in real time.

Parameters
Cement type
Sets the carbonation-rate multiplier on the baseline k₀
Water-cement ratio W/C
Dominant control on pore volume and CO₂ diffusivity
Age
year
Relative humidity RH
%
Peak rate at 50-70%; dry or water-saturated concrete is slower
CO₂ concentration
ppm
Outdoor air ≈420; higher indoors, underground or industrial
Rebar cover
mm
Distance from concrete surface to the reinforcing steel
Exposure class
Dry indoor carbonates fastest; splash zones are slowest
Results
—
Rate constant k (mm/√y)
—
Current depth d (mm)
—
Years to rebar
—
Strength loss (%)
—
Cover for 100 y (mm)
—
Corrosion state
—
Concrete cross-section & carbonation front — animation

Blue is the alkaline (sound) zone; grey is the carbonated region. The red bars mark the rebar location and the white particles represent CO₂ diffusing in.

Carbonation depth vs age
Carbonation rate by cement type
Theory & Key Formulas

$$d = k\sqrt{t},\quad k = k_0 \cdot f_{cement} \cdot f_{W/C} \cdot f_{RH} \cdot f_{CO_2} \cdot f_{exposure}$$

d = carbonation depth (mm), t = age (years), k = carbonation-rate constant (mm/√year), k₀ = 3.0 (baseline). Each factor captures the acceleration or deceleration from material and environment.

$$f_{W/C}=\left(\frac{W/C}{0.5}\right)^{2.5},\quad f_{RH}=4\cdot\frac{RH}{100}\left(1-\frac{RH}{100}\right)$$

W/C dependence is steep (2.5 power around 0.5). The humidity term is a bell curve that peaks at RH = 50%.

$$t_{rebar}=\left(\frac{cover}{k}\right)^{2},\quad cover_{100y}=k\sqrt{100}$$

Years to rebar corrosion initiation and the cover required for a 100-year service life — the headline equations of durability design.

Concrete Carbonation Depth Prediction — Durability Design Against Rebar Corrosion

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What is actually happening when concrete "carbonates"? People say CO₂ is bad for it — but how exactly?
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In short: atmospheric CO₂ diffuses through the connected pores of the concrete and reacts with the calcium hydroxide Ca(OH)₂ inside, turning it into calcium carbonate CaCO₃. That drags the pH down from about 12.5 to roughly 8. While the pH is high, a very thin "passive" oxide film protects the steel reinforcement. The instant the carbonation front reaches the bar, that film breaks down and the rebar starts rusting in earnest.
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So that's why cover thickness matters. What controls how fast CO₂ gets into the concrete?
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The water-cement ratio W/C is the biggest lever. The higher it is, the more open the pore network, and CO₂ travels much faster. This tool uses a 2.5-power dependence around W/C = 0.5, so moving from W/C = 0.40 to 0.60 roughly doubles k. Humidity is the surprise second factor: carbonation is fastest at RH 50-70%. Too dry, and there is no water for the reaction; too wet, and CO₂ cannot diffuse through water-filled pores. That is why a partly dry indoor wall carbonates much faster than an underwater pier.
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I've also heard blast-furnace slag cement carbonates faster. Isn't it supposed to be the eco-friendly choice?
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That trade-off is one of the hardest parts of durability design. Slag and fly ash give big gains in long-term strength, chloride resistance and heat-of-hydration, but they consume Ca(OH)₂, so the alkaline buffer is smaller and apparent k goes up. This tool uses 1.5× for Slag-B and 2.0× for Slag-C. For a coastal bridge pier where chloride attack dominates, slag cement is still the right call; for an indoor parking deck where carbonation is the main threat, OPC or silica-fume mixes win.
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Can I just use the "recommended cover for 100 years" as my design value?
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It is only the analytical minimum. The number on the right is k·√100 = 10·k, the thickness that — on average materials and conditions — would let the carbonation front just barely reach the rebar at year 100. Real design layers on tolerances for construction (bars drift, formwork bulges), climate scatter and the ~10-year crack-propagation phase, adding another 10-20 mm on top. So with k = 2.80 the calculated 28 mm becomes a built cover of 40-50 mm for typical Japanese highway bridges and tunnels.
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How would I use this simulator on an existing structure that has already been in service?
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The field workflow is to spray phenolphthalein on a freshly broken surface — magenta = sound, colourless = carbonated — and measure the actual depth. Combined with the structure's age t, you back out the in-situ rate constant as k_actual = d/√t. Then plug that k into this tool to project the remaining distance to the bar and the future corrosion year. For diagnostics, measured k from cores is far more reliable than any textbook value, so we always combine the two.

Frequently Asked Questions

From Fick's first law of diffusion as d = k·√t, where d is the carbonation depth (mm), t is the age (years) and k is the carbonation-rate constant (mm/√year). k is obtained by multiplying a baseline value of 3.0 by correction factors for cement type, W/C, humidity, CO₂ concentration and exposure class. For ordinary Portland cement, W/C=0.5, RH=65%, CO₂=420ppm under outdoor-sheltered conditions, k ≈ 2.80 mm/√y, giving a carbonation depth of about 19.8 mm after 50 years.
Slag consumes some of the calcium hydroxide Ca(OH)₂ in the cement through its latent hydraulic reaction, reducing the alkaline reserve that would otherwise neutralise incoming CO₂. With less Ca(OH)₂ available per unit volume, the apparent carbonation front advances faster for the same CO₂ flux. This tool applies a 1.5× factor for Slag-B (40-70% replacement) and 2.0× for Slag-C (>70%). Silica fume, in contrast, densifies the pore structure and is treated as 0.7×.
Corrosion is taken to begin the moment the carbonation depth reaches the rebar cover. The passive oxide film that protects the steel in alkaline concrete (pH ≈ 12.5) breaks down once the pH at the bar surface falls below 9. This tool's "years to rebar = (cover/k)²" reports that initiation time. The subsequent crack-propagation phase usually lasts another 10 years, so engineers commonly take initiation + 10 years as the end of the service life.
From the condition cover ≥ k·√T for the target life T, the minimum required cover for 100 years is k·√100 = 10·k. With k=2.80 mm/√y under the standard conditions, the recommended cover is 28 mm. In Japanese civil practice this calculated minimum is then increased by 10-15 mm to absorb construction tolerances and local climate variability, so the final design cover for bridges and tunnels typically sits at 40-50 mm.

Real-World Applications

Highway bridges and viaducts: 100-year service life is standard for major civil structures, where coastal sites face combined chloride attack and inland sites face carbonation as the dominant deterioration. Rate-constant models such as this one are used to assign part-by-part cover thicknesses — piers, beam ends, deck soffits — typically in the 40-70 mm range depending on the local micro-environment.

Nuclear facilities and underground structures: For 50-100 year service requirements where rebar corrosion and spalling are unacceptable, designers reach for low-W/C concrete (W/C = 0.35-0.40) with fly ash or silica fume to deliberately halve the carbonation rate. Tools like this one are used at the mix-design stage to verify that the chosen recipe meets the durability target.

Diagnostics of existing structures: For 30-50 year-old bridges and tunnels, engineers measure carbonation depth on cores with phenolphthalein, back out the in-situ k, and use this tool to project the remaining life. If rebar reach is forecast within 10 years, surface coatings (cathodic protection, silane sealers) are deployed to extend service, or the structure is moved up the repair/replacement schedule.

Indoor car parks and underground warehouses: CO₂ concentration easily reaches 2-5× outdoor air (800-2000 ppm) thanks to vehicle exhaust and limited ventilation, and the combined temperature and humidity are ideal for carbonation. Running this tool at 1500 ppm CO₂ exposes the spalling risk on indoor garage ceilings and is a useful sanity check on ventilation-design assumptions.

Common Misconceptions and Pitfalls

The biggest pitfall is ignoring cracks in the cover concrete. The d = k·√t model in this tool assumes intact, one-dimensional diffusion. With cracks wider than about 0.2 mm, CO₂ rushes straight into the depth and the local carbonation front races ahead at 3-10× the bulk rate. Most rebar corrosion in the field actually starts at cracks and spreads outward, so crack-width control through shrinkage, thermal and load detailing is just as important as the surface-rate calculations you do here.

Second, do not confuse "carbonation depth" with "rebar corrosion rate". Corrosion starts the moment the front arrives, but how fast steel actually loses section is then governed by oxygen supply, moisture, chloride ions and temperature. Coastal members may show modest carbonation and yet fail by chloride attack first; permanently submerged elements may sit fully carbonated for decades with very little corrosion because there is no oxygen. The "years to rebar" output is an initiation time, not a failure time — add another 5-30 years of propagation for the true life.

Third, field data beats any textbook k. The carbonation-rate constant depends strongly on materials, curing, weather and workmanship, so analytical predictions carry a ±30% spread. The right way to manage long-life structures is to combine an initial accelerated-carbonation test on the mix with periodic core sampling and phenolphthalein measurements at 10-20 year intervals, updating the in-situ k as the asset ages. Use this tool for early design and sensitivity studies, but base diagnostic decisions on measured data first.

How to Use

  1. Enter water-cement ratio (0.40–0.65 typical for structural concrete; lower ratios reduce permeability)
  2. Input concrete age in years and ambient relative humidity (40–90% affects carbonation rate; 50–70% is critical zone)
  3. Set CO₂ concentration in ppm (ambient ~400 ppm, industrial/urban 600–1000 ppm)
  4. Simulator calculates carbonation depth using Fick's second law, predicts years until pH drops below 9 at rebar depth, and estimates corrosion initiation risk

Worked Example

Reinforced concrete column: w/c ratio 0.50, age 10 years, 60% RH, 500 ppm CO₂, 40 mm cover. Simulator yields k = 2.8 mm/√year, current depth d = 8.9 mm, years to rebar = 18 years, strength loss = 3.2%, recommended cover for 100-year durability = 65 mm. With existing 40 mm cover, carbonation reaches rebar around year 28, requiring protective coatings or increased concrete density to extend service life.

Practical Notes

  1. w/c ratio dominates carbonation rate: 0.40 ratio reduces k by ~35% versus 0.60 ratio in same environment
  2. RH near 70% accelerates carbonation; both very dry (<40%) and saturated (>85%) slow the process
  3. Minimum cover in EN 206: 40 mm for ordinary exposure; increase to 55–75 mm in high-CO₂ urban/coastal zones or when w/c >0.55
  4. Corrosion initiates at carbonation front; once started, attack rate ~0.1–0.3 mm/year in moist conditions
  5. Dense concrete (self-compacting, low porosity) and pozzolanic binders (fly ash, silica fume) reduce k by 40–60%