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

Question 3: Curing, Alternative Concretes and Strength 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 four alternatives to conventional concrete (10 marks). Curing is the deliberate maintenance of satisfactory moisture content and temperature in freshly placed concrete for a period long enough for the hydration of the cement to develop the properties the mix was designed for. It is not the same thing as setting or hardening, which happen anyway; curing is the act of supplying the conditions those reactions need. In practice it means ponding, fogging, wet burlap, plastic sheeting, a membrane-forming curing compound, leaving forms in place, or steam and insulated blankets when the ambient temperature is low. CSA A23.1 specifies curing by class, the basic requirement being three days at not less than 10 °C, with extended seven-day curing for exposed and abrasion-resistant surfaces.

Curing matters because hydration is a chemical reaction that consumes water and stops when the relative humidity inside the capillary pores falls below about 80 %. Concrete that dries out at one day may reach only half the 28-day strength of the same mix cured continuously, and the loss is concentrated where it hurts most — in the surface zone, which is precisely the material that must resist chloride ingress, freeze–thaw scaling and abrasion. Poor curing also produces plastic and drying-shrinkage cracking, because a surface that dries while the interior is still saturated shrinks against a restraint. In a Canadian climate the temperature half of the definition is equally important: hydration effectively stops near freezing, and concrete that freezes before it reaches about 3.5 MPa is permanently damaged by ice expansion in the capillary pores.

By alternatives to conventional concrete we mean mixes that depart deliberately from the ordinary Portland-cement, natural-aggregate, water-and-admixture recipe — by changing the binder, the aggregate, the reinforcement or the placing method — in order to buy a property that conventional concrete cannot economically deliver. Four are described below.

High-performance and high-strength concrete uses a very low water-to-binder ratio (often 0.25 to 0.35), a high-range water-reducing admixture and silica fume or other supplementary cementing materials to reach compressive strengths of 60 to 120 MPa with very low permeability. It is applied to the lower columns of tall buildings, to long-span and precast bridge girders and to marine and parking structures. The advantages are smaller sections and therefore more rentable floor area and less foundation load, longer spans, and a dense pore structure that greatly slows chloride diffusion and so extends service life in a de-icing-salt environment.

Self-consolidating (self-compacting) concrete is proportioned with a high powder content, a viscosity-modifying admixture and a strong superplasticiser so that it flows into place and de-airs under its own weight, with a slump flow of 550 to 750 mm and no vibration. It is used for heavily congested reinforcement, architectural and complex-geometry formwork, precast production and repairs in confined spaces. Its advantages are a uniform, void-free, high-quality surface finish, faster placing with a smaller crew, elimination of vibration noise and hand-arm vibration exposure, and reliable encasement of bars where a poker could never reach.

Fibre-reinforced concrete disperses steel, glass, synthetic or cellulose fibres through the matrix. Steel-fibre mixes are used for industrial floor slabs, shotcrete tunnel linings and precast segments; synthetic micro-fibres are used in slabs on grade to control plastic shrinkage cracking. The fibres bridge cracks after the matrix has cracked, so the advantages are post-crack toughness and energy absorption rather than higher first-crack strength — improved impact and fatigue resistance, tighter crack widths and hence better durability, and in slabs the ability to replace or reduce conventional mesh, which speeds construction.

Lightweight concrete replaces normal-density aggregate with expanded shale, clay or slate (structural lightweight, 1,600 to 1,900 kg/m³) or introduces a stable foam or no-fines structure (insulating lightweight). It is applied to composite floor slabs on steel deck, long-span bridge decks and topping slabs, and to roof insulation and fill. The advantages are a 20 to 30 % reduction in dead load, which reduces member sizes, foundation loads and seismic mass; better thermal insulation and fire resistance; and, where the aggregate is pre-wetted, internal curing that reduces autogenous shrinkage in low water-to-binder mixes. Other legitimate answers include roller-compacted concrete, pervious concrete, geopolymer or alkali-activated concrete, shotcrete, polymer concrete and recycled-aggregate concrete.

Part (b) — statistical evaluation of the cylinder results (10 marks).

Given. Twenty-five compressive-strength test results from a ready-mix plant, in psi, with a specified minimum (lower specification limit) of 4,250 psi:

Find. The mean, standard deviation, coefficient of variation and 95 % confidence interval on the mean; whether the plant is meeting the 4,250 psi requirement; and a comment on the quality (variability) of the data.

Approach. Compute the sample mean and the sample standard deviation with $n-1$ degrees of freedom, form the coefficient of variation and the Student-$t$ confidence interval on the mean, then test compliance in the way a concrete specification actually does — by comparing the mean with the required average strength that the measured variability demands, and by counting the individual results that fall below the limit.

1. Compute the sample mean. The mean of the 25 results is $$\bar{x} = \frac{1}{n}\sum x_i = \frac{114255}{25} = \boxed{4570\ \text{psi}}.$$ The results run from a minimum of 3692 psi to a maximum of 5675 psi, a range of 1983 psi, which is already a warning that the scatter is large relative to the 320 psi margin the mean holds over the specified minimum.
2. Compute the sample standard deviation and the coefficient of variation. Using the unbiased ($n-1$) estimator, $$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} = \sqrt{\frac{6.396e+06}{24}} = \boxed{516\ \text{psi}},$$ and the coefficient of variation, which expresses that scatter as a fraction of the mean, is $$V = \frac{s}{\bar{x}} \times 100 = \frac{516.3}{4570.2} \times 100 = \boxed{11.3\ \%}.$$ The divisor $n-1$ rather than $n$ is used because the mean has been estimated from the same sample.
3. Form the 95 % confidence interval on the mean. With $n = 25$ the standard error of the mean is $s/\sqrt{n} = 516.3/5 = 103.3\ \text{psi}$, and the two-sided 95 % Student-$t$ multiplier for 24 degrees of freedom is $t_{0.025,24} = 2.0639$. The interval is $$CI_{95} = \bar{x} \pm t\,\frac{s}{\sqrt{n}} = 4570 \pm 2.0639(103.3) = 4570 \pm 213,$$ that is $\boxed{4357\ \text{psi} \le \mu \le 4783\ \text{psi}}$ with 95 % confidence. Note carefully what this does and does not say: it brackets the true average strength of the production, not the strength of an individual cylinder.
4. Test compliance against the specified minimum. A specification limit applies to individual results, so the plant cannot simply aim its mean at 4,250 psi; it must overshoot by enough to absorb its own variability. ACI 318 and CSA A23.1 require an average strength $$f'_{cr} = \max\left[f'_c + 1.34s,\ f'_c + 2.33s - 500\right]$$ (in psi, for $f'_c \le 5000\ \text{psi}$). Substituting $s = 516$ psi, $4250 + 1.34(516) = 4942$ psi and $4250 + 2.33(516) - 500 = 4953$ psi, so $\boxed{f'_{cr} = 4953\ \text{psi}}$. The plant is averaging only 4570 psi, which is 383 psi below the required average, so the production does not meet the specification.
5. Confirm from the results themselves. Counting directly, 8 of the 25 cylinders (32 %) fell below the 4,250 psi target. Treating the results as normally distributed gives the same picture: the standardised distance from the mean to the limit is $$z = \frac{f'_c - \bar{x}}{s} = \frac{4250 - 4570}{516} = -0.620,$$ so an expected $\Phi(-0.620) = 26.8\ \%$ of production falls short — against the 10 % that the ACI/CSA required-average expressions are calibrated to allow. The Canadian acceptance rule in CSA A23.1 is also breached: no individual test may fall more than 500 psi (3.5 MPa) below the specified strength, and sample 20 at 3,692 psi is 58 psi low.
6. Comment on the quality of the data and the likely causes. ACI 214R classifies the overall variation of field-tested general construction concrete by the standard deviation: below 400 psi is excellent, 400 to 500 psi very good, 500 to 600 psi good, 600 to 700 psi fair and above 700 psi poor. At $s = 516$ psi with $V = 11.3\ \%$ this plant sits in the “good” band, so the variability is ordinary rather than pathological — $\boxed{\text{the failure is one of target strength, not of control}}$. The remedy is to raise the mean by about 383 psi, most directly by lowering the water-to-cement ratio. The scatter that does exist is attributable to the usual suspects: fluctuating aggregate moisture, so that the batch water and hence the water-to-cement ratio drifts; variation in cement and supplementary-cementing-material properties between deliveries; batching and mixing-time variation and inadequate mixer maintenance; retempering with water on site and long haul times; and testing variation itself — poor rodding, non-standard curing of the cylinders, capping defects and out-of-tolerance loading rates, which ACI 214R notes can account for a quarter of the measured variance.

Final results.