Question 3 of 5: Curing, Alternative Concretes and Strength-Test Statistics

Question 3: Curing, Alternative Concretes and Strength-Test Statistics (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (a) — Curing, and alternatives to conventional concrete (10 marks)

Curing defined (2 marks). Curing is the deliberate maintenance of satisfactory moisture content and temperature in freshly placed concrete for a period long enough for the cement to hydrate to the degree the design assumes. It is a process, not a material: it begins as soon as the concrete is finished and it consists of preventing the loss of the mixing water (by ponding, fogging, wet burlap, plastic sheeting or a membrane-forming compound), and of holding the concrete within a workable temperature range (by insulating blankets, hoardings and heat in Canadian winter concreting, and by shading, evaporation retarders and cool aggregate in hot weather). CSA A23.1 defines three curing regimes — basic, additional and extended — and requires the more onerous ones for elements exposed to freeze–thaw and de-icing chemicals.

Why it matters (2 marks). Hydration is a chemical reaction that consumes water, and it stops in any part of the concrete where the relative humidity in the capillary pores falls below about 80 per cent. Concrete that is allowed to dry does not simply cure more slowly; the hydration in the dried zone stops permanently and the capillary pore system stays coarse and interconnected. The consequences are all at the surface, which is exactly where durability is decided: the 28-day strength of a poorly cured member can be a third lower than that of a continuously moist-cured one, and the permeability of the cover concrete — which governs chloride ingress, carbonation, freeze–thaw scaling and therefore the corrosion of the reinforcement — can be several times higher. Early drying also produces plastic and drying shrinkage cracking, which gives chlorides a direct path to the steel. Curing is thus the cheapest durability measure available on any site, and the one most often shortened when the schedule slips.

What is meant by alternatives to conventional concrete (2 marks). Conventional concrete means the ordinary structural mixture of Portland cement, water, natural fine and coarse aggregate and, usually, an air-entraining or water-reducing admixture, proportioned for a strength around 25 to 40 MPa and placed and compacted by vibration. An alternative concrete is any material that keeps the essential idea — an aggregate skeleton bound by a hydraulic or chemical binder — but changes one of those ingredients or the way the mixture behaves, in order to obtain a property that conventional concrete cannot deliver, or to reduce its environmental cost. The drivers are usually one of four: a performance requirement (very high strength, very low permeability, tensile ductility), a constructability requirement (congested reinforcement, no access for vibration, rapid opening), a durability requirement in an aggressive exposure, or the reduction of the roughly 0.9 tonnes of carbon dioxide released per tonne of Portland cement clinker.

Four alternative concretes, with application and advantages (6 marks).

1. Self-consolidating concrete (SCC). A highly flowable, non-segregating concrete made with a high powder content, a low coarse-aggregate fraction and a polycarboxylate high-range water reducer together with a viscosity-modifying admixture, so that it spreads and fills the form under its own weight. Application: heavily reinforced sections such as bridge pier caps, shear walls and anchorage zones; architectural concrete where a blemish-free finish is required; repair and underpinning where a vibrator cannot reach. Advantages: complete filling of congested forms with no vibration, so no honeycombing and a much better cover; faster placing with less labour; a far quieter and safer site, since hand-arm vibration exposure is eliminated.

2. High-performance / high-strength concrete incorporating silica fume. A low water–binder-ratio concrete (typically 0.25 to 0.35) with silica fume and usually fly ash or slag, reaching 60 to 100 MPa or more with a very low chloride permeability. Application: columns in tall buildings, long-span and precast prestressed girders, marine and parking structures, bridge deck overlays. Advantages: smaller columns and thinner decks for the same load, hence more rentable floor area and less dead load; the pozzolanic reaction converts calcium hydroxide to additional binder and refines the pore structure, so chloride diffusion and therefore reinforcement corrosion are dramatically reduced — the reason it is the standard material for Canadian bridge decks exposed to de-icing salt.

3. Fibre-reinforced concrete, including ultra-high-performance and engineered cementitious composites. Concrete containing dispersed steel, glass or synthetic fibres; in the ultra-high-performance form the aggregate is fine and graded for maximum packing, the water–binder ratio is below 0.2, and steel fibres give strain-hardening tensile behaviour. Application: slabs on grade and industrial floors (replacing shrinkage mesh), shotcrete linings for tunnels and slopes, precast segments, thin architectural panels, and — for UHPC — field-cast joints between precast deck panels and the strengthening of existing structures. Advantages: the fibres bridge cracks and convert a brittle failure into a ductile one, giving post-cracking toughness and impact and fatigue resistance; crack widths stay small so permeability stays low; in slabs it removes a whole trade from the critical path.

4. Concrete with high-volume supplementary cementing materials, and recycled-aggregate concrete. The first replaces 40 to 60 per cent of the Portland cement with fly ash or ground granulated blast-furnace slag; the second replaces some or all of the virgin coarse aggregate with crushed returned or demolished concrete. Application: mass concrete such as raft foundations and dams, where heat is the governing problem; pavements, sidewalks, backfill and lean concrete for the recycled variety; both are routinely specified for their contribution to green-building credits. Advantages: a large reduction in embodied carbon and cost; a much lower rate of heat evolution, so thermal cracking in thick sections is controlled; better long-term strength, lower permeability and improved resistance to sulfate attack and alkali–aggregate reaction. The trade-offs, which should be stated, are slower early strength gain (so formwork stays longer and cold-weather protection is more important) and, for recycled aggregate, higher absorption and greater variability that must be allowed for in the mix design.

Part (b) — Statistical analysis of the 28-day strength data (10 marks)

Given. Twenty-five 28-day compressive strength results from one ready-mix plant, in psi: 4875, 4800, 5250, 4125, 5110, 4316, 4940, 4950, 4730, 4205, 4570, 4324, 4235, 5675, 4315, 5175, 4770, 4874, 5134, 3692, 4510, 3875, 4100, 3780, 3925. The minimum target value for compressive strength is 4000 psi.

Find. The mean, sample standard deviation, 95 per cent confidence interval and coefficient of variation of the data; whether the plant production meets the 4000 psi requirement, with reasons if it does not; and an assessment of the quality (the degree of control) the data represent.

Approach. Compute the sample mean and standard deviation, form the coefficient of variation and the Student-t confidence interval on the mean, then test the production against the specification on three separate footings — the required average strength that ACI 318 demands of a plant with this standard deviation, the two ACI 318 acceptance rules applied to the individual results, and the proportion of results falling below the target — and finally classify the standard deviation and coefficient of variation against the ACI 214R standards of control.

1. Compute the mean strength. With $n=25$ results totalling 114 255 psi, $$\bar{x}=\frac{1}{n}\sum x_i=\frac{114\,255}{25}$$ $$\boxed{\,\bar{x}=4\,570\ \text{psi}\,}$$
2. Compute the sample standard deviation. Using the $n-1$ divisor, which is the correct one for a sample rather than a population and the one ACI 214R specifies, $$s=\sqrt{\frac{\sum (x_i-\bar{x})^{2}}{n-1}}=\sqrt{\frac{6\,398\,552}{24}}$$ $$\boxed{\,s=516\ \text{psi}\,}$$ Because the sample contains fewer than 30 results, ACI 214R would apply a correction factor (1.03 at 25 tests) if this value were to be used to set a required average strength for future production; that refinement is noted here and not pursued, since the question asks for the standard deviation of the data as given.
3. Form the coefficient of variation. The coefficient of variation expresses the scatter as a fraction of the mean, which is what makes results from plants working at different strength levels comparable: $$V=\frac{s}{\bar{x}}\times 100=\frac{516.3}{4\,570.2}\times 100$$ $$\boxed{\,V=11.3\ \text{per cent}\,}$$
4. Compute the 95 per cent confidence interval on the mean. With the population standard deviation unknown and $n-1=24$ degrees of freedom, the two-sided 95 per cent Student-t multiplier is $t_{0.025,24}=2.064$, and $$\text{CI}=\bar{x}\pm t\,\frac{s}{\sqrt{n}}=4\,570.2\pm 2.064\times\frac{516.3}{\sqrt{25}}=4\,570.2\pm 213.1 .$$ $$\boxed{\ 4\,357\ \text{psi}\le \mu \le 4\,783\ \text{psi}\ \ (95\ \text{per cent})\ }$$ The whole interval lies above 4000 psi, so on the evidence of these 25 tests the average strength of the plant's production is above the target with 95 per cent confidence. That is a necessary condition for compliance, but it is far from sufficient, as the next two steps show.
5. Test the mean against the required average strength. A specified strength is not a target for the mean; the plant must aim high enough that individual results still comply. For $f_c'=4000$ psi with the standard deviation known, ACI 318 requires the larger of $$f_{cr}'=f_c'+1.34s=4000+1.34(516.3)=4\,692\ \text{psi}$$ $$f_{cr}'=f_c'+2.33s-500=4000+2.33(516.3)-500=4\,703\ \text{psi}$$ so that $$\boxed{\ f_{cr}'=4\,703\ \text{psi}\ \ \text{required, against}\ \ \bar{x}=4\,570\ \text{psi}\ \text{achieved}\ }$$ The plant is 133 psi short of the average strength its own scatter demands. This is the central finding of the question: the mix is not over-designed enough for the variability of the operation.
6. Apply the two ACI 318 acceptance rules to the individual results. The first rule requires every average of three consecutive strength tests to equal or exceed $f_c'$. Scanning the sequence, the averages centred on samples 22 and 23 fail: $$\frac{3875+4100+3780}{3}=3\,918\ \text{psi},\qquad \frac{4100+3780+3925}{3}=3\,935\ \text{psi},$$ both below 4000 psi. The second rule requires no individual test to fall below $f_c'$ by more than 500 psi; the lowest single result is 3692 psi, which is 308 psi below the target and therefore acceptable. $$\boxed{\ \text{Rule 1 (three-test average)}:\ \text{FAILS twice};\qquad \text{Rule 2 (individual test)}:\ \text{passes}\ }$$ As a further measure of exposure, the proportion of results expected below the target follows from the standard normal deviate $$z=\frac{f_c'-\bar{x}}{s}=\frac{4000-4570.2}{516.3}=-1.10\quad\Rightarrow\quad 13.5\ \text{per cent below }4000\ \text{psi},$$ against 4 of the 25 results (16.0 per cent) actually below it — close agreement, which confirms that the data are approximately normal and that the shortfall is systematic rather than the result of one rogue cylinder.
7. Answer the specification question and give the reasons. Taken together the three tests give one answer: the plant is not meeting the specification. The average is above 4000 psi and the confidence interval on the mean clears it comfortably, but the average falls 133 psi short of the required average strength for a plant with a 516 psi standard deviation, roughly one result in seven lies below the target, and the running three-test average dips below it twice near the end of the record. The causes to be investigated are the two the numbers point at. The first is that the mix is under-designed for the observed scatter — the remedy is to raise the target strength by lowering the water–cementing-materials ratio or increasing the cementing content until the mean reaches at least 4703 psi. The second is the scatter itself, and the record suggests it is not random: samples 20 to 25 contain five of the six lowest results in the whole set, which is the signature of a drift rather than of noise — a change of aggregate source or grading, wet aggregate raising the batch water, a mis-calibrated water meter or moisture probe, retempering with water on site, or a lapse in the curing of the cylinders. Poor sampling, capping or testing technique in that period would produce the same pattern and must be excluded before the mix itself is blamed.
8. Comment on the quality of the data. ACI 214R rates the standard of control from the standard deviation when the specified strength is at or below 5000 psi, and from the coefficient of variation above it; with $f_c'=4000$ psi the standard deviation governs here. For general construction testing the bands are: excellent below 400 psi, very good 400 to 500, good 500 to 600, fair 600 to 700, and poor above 700 psi. At $s=516$ psi this plant sits near the bottom of the good band — acceptable, but a long way from the 300 to 400 psi a well-run plant achieves. The coefficient of variation of 11.3 per cent is quoted alongside it as an auxiliary measure and is consistent with that rating. $$\boxed{\ s=516\ \text{psi}\ \Rightarrow\ \text{ACI 214R standard of control: good (500 to 600 psi band)}\ }$$ The data are internally consistent and approximately normally distributed, so they are trustworthy as a record; what they record is an operation whose control is merely adequate and whose target strength has not been set to match it. Improving the control is worth more than adding cement, because the required average strength is itself proportional to $s$: bringing the standard deviation down to 400 psi — the top of the “excellent” band, and entirely achievable for a ready-mix plant — would reduce the required average to $$f_{cr}'=\max\{4000+1.34(400),\ 4000+2.33(400)-500\}=\max\{4536,\ 4432\}=4\,536\ \text{psi},$$ which is 34 psi below the mean the plant already achieves. Tightening the process would therefore bring the operation into compliance with no change to the mix at all, and would remove the two failing three-test averages at the same time, since those came from a run of low results rather than from a low average.