42907 Chap.5 Service life design for chloride ingress
Service life design for chloride ingress
Week 3 turns Fick’s second law into a cover. The analytical solution gives the chloride profile as an error function of depth and time, and the design splits into a load, the surface concentration, against a resistance, the apparent diffusion coefficient and the cover. Time to initiation goes as the square of the cover.
The chapter carries the Maage ageing correction with its one year to ten year convention, the published performance data for six binder and ratio combinations, the conversion of the threshold to 0.065 per cent of concrete mass, and the derivation of the submerged surface value of 0.2 per cent.
What this chapter covers
- 01
The error function solution of Fick's second law, and the six symbols in it
- 02
Surface concentration as the durability load, diffusion coefficient and cover as the resistance
- 03
Time to initiation as a function of the square of the cover
- 04
Reading a required cover off the profile at the design life
- 05
The ageing correction and the decay index that quantifies the fall in diffusivity
- 06
The design convention: one year to ten years, and no credit for ageing beyond ten
- 07
Published performance data for general purpose, high slag and high fly ash binders at two ratios
- 08
Converting the threshold from 0.4 per cent of cement mass to 0.065 per cent of concrete mass
- 09
Deriving the submerged surface concentration from sea water chemistry and 15 per cent permeable voids
- 10
Why the tidal surface concentration is several times the submerged one
- 11
The performance based route: four principles and three families of test
- 12
Direct tests against accelerated indirect tests, and what speed is bought with
Minimum cover for a permanently submerged member over one hundred years
- +1Set the surface load. The member is permanently submerged, so the tidal table value does not apply and the surface concentration is 0.20 per cent of concrete mass from the sea water derivation.
- +1Age the coefficient once, across the one year to ten year window: 1.04 times ten to the minus 0.60 gives 0.2612 times ten to the minus twelve square metres per second. No further credit is taken out to a hundred years.
- +1Convert the design life and compute the spread term. One hundred years is 3.1536 times ten to the ninth seconds, and twice the square root of the coefficient times the time is 0.0574 metres, that is 57.4 mm.
- +1Invert at the threshold. One minus the error function equals 0.065 divided by 0.20, which is 0.325, so the error function is 0.675 and its argument is 0.696. The cover is 0.696 times 57.4, which is 40 mm.
- +1Compare with the code. A permanently submerged surface is class B2, and the bridge code requires 50 mm at 55 MPa and above. The prescriptive cover is therefore 10 mm more conservative than the model for this member, so the code governs.
Key terms
- Error function solution
- The analytical solution of Fick's second law for a semi infinite body whose surface is held at a constant concentration. It gives the chloride content at any depth and time from three inputs and is the basis of the first principles method.
- Surface concentration
- The chloride content held at the exposed face, which the design treats as the durability load. It is a property of the exposure rather than of the mix, which is why the submerged and coastal values override the tabulated tidal ones.
- Decay index
- The exponent in the ageing correction, quantifying how fast the apparent diffusion coefficient falls with exposure time. It is largest for blended binders at high water to binder ratio, where the pozzolanic reaction continues for years.
- Ageing correction
- The power law that carries a measured diffusion coefficient from one exposure time to another. This subject applies it only from one year to ten and ignores any further improvement out to fifty or a hundred years.
- Critical threshold
- The chloride content at which the steel depassivates, expressed for calculation as 0.065 per cent by mass of concrete. That figure comes from 0.4 per cent of cement mass assuming 400 kilograms of binder per cubic metre and a density of 2500.
- Spread term
- Twice the square root of the diffusion coefficient multiplied by the time, the single length against which every depth in a profile is measured. It grows as the square root of the exposure time.
- Direct test
- A long term laboratory test that actually drives chloride into concrete and measures the resulting profile, such as bulk diffusion or ponding. It measures the same quantity the model uses.
- Indirect test
- An accelerated laboratory test that measures something correlated with chloride transport, such as charge passed or resistivity, and converts. Speed is bought with an assumption about that correlation.
Service life design for chloride ingress FAQ
Why does cover appear squared in the time to initiation?
Because the diffusion front advances as the square root of time, so inverting the relationship for time puts the depth in as a square. The practical consequence is that small cover gains are worth more than they look: ten per cent more cover buys about twenty one per cent more time.
The subject pairs this with a field observation, that lack of adequate cover is the overwhelming cause of premature corrosion, which makes site attention to cover a cheaper lever than a better binder.
Why is ageing ignored beyond ten years when the concrete keeps improving?
For two reasons, both conservative. The published data extends only to about ten years of exposure, so any extrapolation beyond that is unsupported by measurement; and the power law would keep driving the coefficient towards zero, which is physically wrong. Ignoring the improvement puts it on the safe side of the calculation instead of spending it, and it is a design convention rather than a claim about the physics.
Why is the surface concentration for a submerged member so much lower than for a tidal one?
Because wetting and drying concentrates salt at the surface. Water evaporates from a tidal surface and leaves its dissolved chloride behind, so the concentration builds up well above that of the sea itself. A permanently wet surface only ever sees the sea water concentration. The derived submerged value is 0.2 per cent of concrete mass, against tabulated tidal values running from 0.5 up to 2.8 per cent.
What do I do when the model asks for less cover than the code?
Build to the code. The prescriptive value is a floor, and the model result below it is a statement about margin rather than a licence to reduce. Where the model asks for more, the model governs and you specify the larger figure. Either way the report states the signed difference and the reason for it, because that comparison is the finding the whole exercise exists to produce.
Does the performance based route replace the model?
No, it feeds it. Performance testing measures the concrete's own transport properties, such as the diffusion coefficient or the permeable voids, and compares them against a reference concrete whose field behaviour is known. It still needs a model or a table to turn a measured property into a cover.
Its four stated principles are that you test the concrete and not the mix design, that the test suits the exposure targeted, that you compare against a suitable reference, and that the concrete must perform as well or better than that reference.
Assessment move
Drill the calculation chain until the order is automatic: surface concentration from the exposure, age the coefficient once, convert the design life to seconds, compute the spread term, invert at the threshold, then compare with the code. Write the units beside every quantity as you go, because the method runs in metres and seconds while it reports in millimetres and years.
Practise reading an out of range answer as information rather than as an arithmetic error, since an infeasible cover is the model telling you the mix is wrong. Learn the two derivations, the threshold conversion and the submerged surface value, well enough to reproduce them, because both are short, both are examinable and both are places where an unexplained number would otherwise appear in your report.
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