Arrhenius Equivalent Age (Freiesleben Hansen and Pedersen)

If hydration is a chemical reaction, it should follow the rate law chemistry uses for reactions — Arrhenius' exponential in reciprocal absolute temperature — rather than the straight line Saul assumed. Freiesleben Hansen and Pedersen wrote that version down in 1977, and it is what most maturity instrumentation now runs on. The equivalent age comes out as $t_e = t \exp[-(E/R)(1/T - 1/T_r)]$, and the whole difference from the linear form is that the acceleration curves upward with temperature instead of running straight.

Over a narrow range the two agree well enough that the choice does not matter. Over a wide one they part company, and they part company in the direction that matters most: at the elevated temperatures of steam curing and at the low temperatures of winter concreting, which is exactly where anybody bothers to run a maturity calculation in the first place. The exponential form also has the pleasant property of being founded on something — an activation energy is a physically meaningful quantity — where the datum temperature is frankly a fitting device.

The temperature must be absolute, and this is not a stylistic preference. The exponent contains $1/T$. The reciprocal of a Celsius reading is not approximately right; it is meaningless, and at 0 °C it is undefined. This is the single most common error in every Arrhenius calculation in every field, and it is invisible when it happens, because the arithmetic still runs and still produces a plausible-looking number. That is why this site pins these temperatures to kelvin rather than letting them default to degrees Celsius, and it is why the equivalent-age pages differ from one another in this respect: Nurse-Saul uses only differences from a datum, and a difference is the same number in kelvin as in Celsius, so its affine offset cancels harmlessly. The Arrhenius form has no such protection.

The activation energy is the parameter that has to be measured, and the one that gets borrowed. $E$ here is an apparent activation energy, and the word is carrying real weight. Cement hydration is not one reaction with one energy barrier — it is a set of competing reactions among several clinker phases whose relative rates themselves change with temperature. $E$ is a fitted parameter that summarises all of it over the range it was fitted in, and it is not strictly constant even for a single mixture. It is good enough to be extremely useful, which is a different claim from being true.

It also moves a great deal from mix to mix. Cement chemistry and fineness change it; fly ash, slag and silica fume change it; accelerators and retarders change it. A slag-blended mixture behaves quite differently from straight portland cement, which is precisely why one borrowed figure cannot serve both. ASTM C1074 sets out the laboratory procedure for determining it — mortar specimens of the mixture in question cured at several controlled temperatures, with rate constants extracted and the energy taken from the slope of their logarithm against reciprocal absolute temperature. That standard is the authority, it is copyrighted, and nothing from it is reproduced here. The value that circulates in textbooks and gets typed into loggers as though it were a constant of nature is the maturity method's most reliable source of error.

Two field points that decide whether a maturity system earns its keep. Where the sensor goes is part of the answer. Maturity is local. A thick section runs hot at its core from its own heat of hydration and cold at its faces and corners, and the difference over the first day is easily twenty kelvin — which through this exponent is a factor of two in rate. The governing location is the coldest structurally significant part of the element: an edge, a corner, a thin flange, the face against a windward form. A sensor in the warm middle of a raft measures the fastest concrete on site and tells you nothing about when anything can be stripped. And curing hot has a price: elevated-temperature curing lowers ultimate strength, heating too early or too fast does damage of its own, and above roughly seventy degrees Celsius some mixes become vulnerable to delayed ettringite formation, an expansive reaction that shows up years later. None of that is in the equation, and the equation will happily hand you such a temperature.

And the same closing warning as its linear cousin, because it applies with equal force to both. Maturity predicts strength gain only against a previously established, mixture-specific strength-maturity curve. It does not measure strength. The number this page returns is a number of hours. Formwork stripping, shore removal and tendon stressing are specification and code decisions and belong to the person the specification names.