The strength it had on the day

Every concrete strength quoted on this site is a twenty-eight-day value. It is the number in the specification, the number on the cube report, and the number the design calculation used.

It is also a number that did not exist on any of the days the structure was most heavily worked. Formwork is struck at three days. The next storey is cast at seven. A prestressing force is transferred at two. A precast unit is lifted out of its mould before it has been cured for a day. On every one of those occasions the concrete carried a load, and the strength it had was not the strength on the certificate.

Two curves, and one of them is much flatter #

Strength against age is described well by a single expression:

$$\frac{f(t)}{f_{28}} = \exp\!\left[s\left(1 - \sqrt{28/t}\right)\right],$$

with $s$ a coefficient of the cement type — 0.25 for an ordinary Portland cement, lower for a rapid-hardening one and higher for a blend with fly ash.

The modulus follows it, and not proportionally:

$$\frac{E(t)}{E_{28}} = \left(\frac{f(t)}{f_{28}}\right)^{0.3}.$$

That exponent is the finding. A power of 0.3 flattens everything: a strength ratio of 0.60 becomes a stiffness ratio of 0.86, and a strength ratio of 0.78 becomes 0.93.

At three days the concrete has three fifths of its strength and six sevenths of its stiffness. A structure loaded early is close to its final shape and a long way from its final capacity, and the two questions that get asked about young concrete therefore have opposite answers.

Why that is the right way round, and the wrong way round #

The concrete in a floor slab at three days is carrying its own weight and the formwork of the storey above. That is a service condition, and what it produces is a deflection.

For that question the flat modulus curve is good news. A slab propped and struck at three days deflects only about fifteen per cent more than it eventually would, and the long-term creep deflection will dwarf the difference anyway. The elastic part of a young slab’s deflection is very nearly the elastic part of an old one’s.

The bad news is on the other axis. If something goes wrong — a load dropped, a prop kicked out, a stack of blocks placed where nobody expected — the question is a strength one, and the strength really is only three fifths of the design value. The margin against an accident at three days is 60 per cent of the margin the design provided, and the deflection check that everyone looks at gives no indication of it.

That asymmetry is the reason striking criteria are written in terms of strength rather than of deflection, and it is why they are written as a strength rather than as an age.

It also explains a pattern in what goes wrong on sites. Early-age incidents are almost never deflection failures and almost always strength ones: a prop punched through a slab, a corner broken off a precast unit, a crack under a stacked load. The deflection everybody watches is the quantity least affected by youth, and the capacity nobody can see is the one most affected.

Temperature is an age, not a modifier #

The second half of the subject is that time is the wrong variable. Hydration is a chemical reaction, its rate follows Arrhenius, and what governs the strength gained is not elapsed time but maturity: the integral of the rate over the history.

Written as an equivalent age at a reference temperature,

$$t_e = \sum \Delta t \exp\!\left[\frac{E_a}{R}\left(\frac{1}{T_{ref}} - \frac{1}{T}\right)\right],$$

which for structural concrete gives a rate of 1.95 at 35 °C and 0.48 at 5 °C relative to 20. One day of a hot pour is nearly two days of a normal one, and two days of a cold one is not quite one.

The consequence for a programme is direct. The 20 N/mm² a striking calculation asks for arrives at 2.2 days at 20 °C, at 1.7 days at 35 °C, and at 4.6 days at 5 °C. A winter pour takes more than twice as long to reach the same criterion, and the criterion is the same criterion; nothing about the concrete has changed.

What the exponent is doing #

The 0.3 is worth an explanation rather than a citation, because it is the number the whole first half of this page turns on.

Strength and stiffness are set by different features of the same microstructure. Strength is a failure property: it is decided by the weakest link in the paste — the largest pore, the worst-bonded interface, the biggest unhydrated region — so it responds sharply to anything that changes the extremes of the distribution.

Stiffness is an average property: the modulus of a composite is a volume-weighted combination of the phases present, so it responds to how much hydrated paste exists rather than to how badly the worst part of it is put together. Hydration fills pores from the start, so most of the stiffness arrives with the first half of the reaction.

That difference in kind is what produces a difference in exponent. A rule of thumb that the modulus goes as the cube root of the strength appears in every code and in several materials, and it is not empirical accident: a property decided by an average and a property decided by an extreme cannot scale together.

The same split appears elsewhere in the collection with the same consequence: the modulus is the one number a stronger steel does not change, for exactly the same reason in reverse.

The crossover, which is the part that costs money #

Maturity alone would say that hot curing is free acceleration. It is not, and the mechanism has a name.

Concrete that hydrates quickly forms its products where they are made, near the cement grains, rather than diffusing out into the pore space. The result is a denser shell around each grain, which slows later hydration, and a coarser pore structure in between. The concrete arrives at its early strength sooner and at its ultimate strength lower — permanently lower, because the microstructure is set.

For the mix drawn, curing at 35 °C gives 43 per cent more strength at twelve hours and 9.5 per cent less at twenty-eight days. The two curves cross somewhere around a week.

That is a genuinely awkward result for anybody who takes acceleration seriously. Steam curing, heated formwork and hot-weather placing all buy programme and all cost final strength, and the cost is invisible until the twenty-eight-day cubes come back — by which time the structure is several storeys further up.

Which free body produced the number #

There is no free body here in the usual sense, because the quantity being computed is a material property rather than a force. What replaces it is a statement about which specimen the number belongs to, and getting that wrong is the commonest error in the subject.

A cube tested at twenty-eight days has been cured in a tank at 20 °C. The structure has not. A thick element self-heats — the hydration is exothermic and the heat cannot escape — so the middle of a two-metre raft may reach 60 °C while a 200 mm slab in a cold wind stays at ambient. The structure and its cube are two different materials with the same mix design, and the difference is entirely temperature history.

That is what a maturity meter is for: a thermocouple cast into the element, integrating the real history to produce an equivalent age, and a calibration curve relating that age to strength for the actual mix. It is the only method that answers the question the striking decision asks — what is the strength of this element now — rather than the question a cube answers, which is what the mix is capable of under laboratory curing.

Where it decides the structure rather than the programme #

Three situations turn maturity from a scheduling matter into a design one.

Transfer of prestress. A pretensioned beam is stressed against its abutments and the force is released into the concrete at two or three days. At that moment the concrete carries the full prestress with none of the applied load to balance it — the worst case for the top fibre — and it does so at a strength around 60 per cent of the design value. Transfer strength is specified separately for exactly this reason, and it frequently governs the section rather than the service condition.

Early-age thermal cracking. A thick pour heats, expands, and is restrained by whatever it was cast against; on cooling it contracts and cracks. The steel decides how many cracks and not how much movement, and the calculation needs the tensile strength at the age the cooling happens — three or four days, where it is a little over half the mature value.

Backpropping. A slab struck early is propped from the floors below, and how much load it carries depends on the relative stiffnesses of a series of slabs of different ages. The flat modulus curve is what makes that tractable: slabs at three and twenty-eight days have stiffnesses within fifteen per cent, so the load shares out nearly equally between the propped floors rather than concentrating on the oldest.

The strength keeps going up, and nobody counts it #

The other end of the curve is worth a paragraph, because it is the only place in this collection where a structure gets stronger with time.

The same expression that gives 78 per cent at seven days gives 112 per cent at ninety days and 120 per cent at a year, and for a blended cement the late gain is larger still. A structure assessed at thirty years has concrete substantially stronger than its specification, and a core taken from it will say so.

That matters for assessment rather than for design. An existing structure being checked against a heavier load has a real reserve that its drawings do not record, and coring is the way to find it. It is not, however, a reserve anybody may design for: the twenty-eight-day value is a contractual and statistical construct, and the late gain is not guaranteed, not uniform, and not testable in advance.

So the same curve is a liability at three days and an asset at thirty years, and only one of the two ends appears in the design.

The programme is the load case #

The most useful way to read all of this is that a construction programme is a set of load cases with dates on them, and the dates are structural inputs.

A design office produces a structure for the completed condition and a contractor produces a sequence in which it is built. Between the two sits a set of questions of the form what carried what, when, and with what strength — and each of those has three inputs, of which the design office controls one, the contractor controls one, and the weather controls the third.

That is an unusual distribution of authority for a structural quantity. The mix decides the shape of the strength curve. The programme decides which point on it is being asked about. The temperature decides what age the concrete thinks it is. Nobody is in charge of all three, and the calculation that combines them is usually done by the temporary works engineer with the least information.

The failure mode that follows is quiet: a structure that was fine, propped as designed, until a warm week let the programme run ahead and a cold week let a pour fall behind, and a slab was struck at an equivalent age of two days rather than four. Nothing about that appears in a drawing, a specification, or a cube result, and the only instrument that would have seen it is a thermocouple.

What a striking criterion actually says #

A striking criterion is usually written as a strength — “props may be removed when the concrete reaches 15 N/mm²” — and it is worth unpacking what that strength is doing, because it is not one requirement but three.

It has to carry the flexural load of the slab’s own weight over the propping arrangement, which is a strength requirement and usually the easy one.

It has to have enough stiffness that the deflection on striking, plus the creep that follows it, stays inside the limit — which is where the flat modulus curve helps and where the age at striking matters much less than intuition suggests.

And it has to be able to take the bearing and punching of the props themselves and any construction load placed immediately, which is a local strength check on a young material.

The three are collapsed into a single number, and the collapsing is done by whoever wrote the criterion rather than by the person applying it. A criterion in newtons per square millimetre is an answer with its question removed, which is fine until the arrangement changes.

The check that could refuse it #

The maturity claim is the strongest one on this page and it is falsifiable with a pair of cubes, which is worth stating because it is done rarely and settles the argument when it is.

Cast two sets from one batch. Cure one at 20 °C and one at 35, and test both at ages chosen so their equivalent ages match — three days at 20 against 1.54 days at 35, say. If maturity governs, the two should give the same strength.

They do, to within the scatter, over the range where the concrete is still gaining quickly. That is the evidence for the whole equivalent-age construction, and it is a genuine prediction: nothing about the two specimens is the same except a computed integral.

Then test both at twenty-eight days of real time. Now they should differ, and by the crossover amount, with the hot one lower. If the two agreed there, the crossover effect would be refuted and hot curing would be free.

Two tests, one confirming the model and one confirming its limit, from a single batch of concrete. The reason it is not routine is that a site wants to know the strength today rather than to characterise its mix, and the two purposes want different specimens.

Where the model stops #

The expression is calibrated for ages above about three days. Below that it over-predicts: it gives 34 per cent at one day where a real mix gives twenty-five or less, because the setting process is not the same as the hardening one.

Maturity assumes one activation energy. The rate constant changes with the degree of hydration and with the cement chemistry, and a single Arrhenius term is a good approximation over a limited range rather than a law.

The crossover penalty is a fitted allowance. Its existence is well established; its size depends on the mix, the peak temperature and how long the concrete spends there, none of which appears in the arithmetic used here.

Shrinkage and creep are on their own clocks. Both are age-dependent and neither follows the strength curve; a structure loaded at three days creeps far more over its life than one loaded at twenty-eight, and that is a separate calculation with its own age function.

And nothing here is a durability statement. A concrete cured hot is weaker and also more permeable, which matters more for its hundred-year life than the nine per cent of strength does.

Where the ladder goes #

Later rungs on this anchor: maturity meters and the calibration a site actually uses. Adiabatic temperature rise and thermal modelling of thick pours. The crossover effect and its microstructural explanation. Transfer strength in pretensioning, and why it governs sections. Backpropping and load sharing between slabs of different ages. Early-age tensile strength, which is what a cracking calculation needs and which is measured even less often than compressive. Accelerated curing regimes and what they cost. And the wider question: how many of a structure’s most severe load cases occur before the material it is made of exists in the form the design assumed.