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 alternative concretes (10 marks)

Definition of curing (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 not drying and it is not simply the passage of time: it is the act of keeping water in the concrete, or supplying more, while the temperature is held in a range where hydration proceeds at a useful rate. CSA A23.1 sets out three regimes — basic curing of three days at or above 10 °C, additional curing of seven days, and extended curing to reach 70 % of the specified strength — and the methods available are ponding and immersion, wet coverings such as burlap, plastic sheeting, membrane-forming compounds, leaving the formwork in place, and for precast work accelerated steam or radiant heat.

Importance of curing (2 marks). Hydration only proceeds while the relative humidity in the capillary pores stays above roughly 80 %, so concrete that is allowed to dry stops gaining strength permanently — rewetting later never fully recovers what was lost. Poor curing typically costs a third or more of the potential 28-day strength, and the surface zone, which is exactly the zone that resists carbonation, chloride ingress, abrasion and freeze-thaw scaling, suffers most because it dries first. Curing also controls early plastic and drying shrinkage cracking, which otherwise creates the pathways along which those same aggressive agents travel. In Canadian practice, protection against early-age freezing is part of the same duty of care: concrete that freezes before it reaches about 3.5 MPa is permanently damaged.

What is meant by alternatives to conventional concrete (part of the 6 marks). Conventional concrete means the ordinary normal-density, normal-strength mixture of Portland cement, water, fine and coarse aggregate, placed by vibration and reaching perhaps 25 to 40 MPa. An alternative concrete is any material in which one of those ingredients, one of those proportions or the placing method itself is deliberately changed to obtain a property the conventional mixture cannot deliver — higher strength, lower density, self-levelling flow, post-cracking tensile capacity, permeability by design, or a smaller carbon footprint. Four examples follow.

1. High-performance and high-strength concrete. A very low water-cementing-materials ratio, typically below 0.35, with a high-range water reducer and silica fume, giving compressive strengths from 60 to well over 100 MPa and a very low permeability. Application: columns in tall buildings, long-span and marine bridge girders, and any structure where chloride-induced corrosion governs the service life. Advantages: smaller sections and therefore more rentable floor area and less self-weight; greatly extended service life through low diffusivity; reduced creep and shrinkage in prestressed members.

2. Self-consolidating (self-compacting) concrete. A highly flowable mixture, with a slump flow of 550 to 750 mm, stabilised by a large volume of fines and a viscosity-modifying admixture so that it spreads and de-airs under its own weight. Application: heavily reinforced sections such as bridge diaphragms and shear walls, architectural concrete where the finished surface is the finished product, and precast production. Advantages: no vibration, so faster placing, less labour, quieter and safer sites, no honeycombing behind congested bars, and a superior as-struck finish.

3. Fibre-reinforced concrete. Steel, glass, synthetic or cellulose fibres dispersed through the matrix at typically 0.5 to 2 % by volume, bridging cracks once they form. Application: industrial and airport floor slabs, shotcrete tunnel and slope linings, precast segments, and blast- or impact-resistant elements. Advantages: substantial post-cracking toughness and energy absorption, control of plastic shrinkage cracking, reduced or eliminated crack-control mesh, and much better resistance to spalling under impact and fire.

4. Lightweight concrete. Expanded shale, clay or slate aggregate, or a deliberately introduced air or foam phase, bringing the density down from about 2400 to between 1400 and 1900 kg/m³ for the structural grades. Application: composite floor decks in tall buildings, bridge deck replacements where the existing substructure has no spare capacity, and precast panels that must be handled by lighter cranes. Advantages: a quarter to a third less dead load and therefore smaller foundations, columns and seismic mass; better thermal insulation and fire resistance; internal curing from the pre-wetted porous aggregate, which reduces autogenous shrinkage.

Roller-compacted concrete for dams and haul roads, pervious concrete for stormwater management, and high-volume fly ash or slag concrete for carbon reduction would be equally acceptable answers.

Part (b) — Statistical analysis of the cylinder results (10 marks)

Given. Twenty-five compressive strength tests from a ready-mix plant, in psi, against a minimum target of 4000 psi:

Find. The sample mean, sample standard deviation, 95 % confidence interval on the mean and coefficient of variation; a verdict on whether the plant is meeting the 4000 psi requirement, with reasons if it is not; and a comment on the quality of the data.

Approach. Compute the four statistics from the 25 results, test the production against the two ACI 318 acceptance criteria and against the required average strength that the measured scatter demands, then judge the quality of the data from the coefficient of variation using the ACI 214R standards-of-control bands.

1. Part (b), step 1 — mean strength. For $n=25$ results, $$\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}=\frac{118\,000}{25}$$ $$\boxed{\bar{x}=4720\ \text{psi}}$$ The mean already sits only 18 % above the 4000 psi target, which is the first sign of trouble: with real production scatter a mean this close to the specification cannot keep the individual results above it.
2. Part (b), step 2 — sample standard deviation. Using the $n-1$ divisor, as required for a sample rather than a population, $$s=\sqrt{\frac{\sum(x_{i}-\bar{x})^{2}}{n-1}} =\sqrt{\frac{1.2122\times10^{7}}{24}}$$ $$\boxed{s=711\ \text{psi}}$$
3. Part (b), step 3 — 95 % confidence interval on the mean. The population standard deviation is unknown, so the interval uses Student's $t$ with $n-1=24$ degrees of freedom, for which $t_{0.025,24}=2.064$: $$\bar{x}\pm t_{0.025,\,n-1}\frac{s}{\sqrt{n}} =4720\pm2.064\times\frac{711}{\sqrt{25}}=4720\pm293$$ $$\boxed{4427\ \text{psi}\le\mu\le5013\ \text{psi}\ \ (95\ \%)}$$ The interval is an interval on the mean of the process, not on an individual cylinder; note that its lower bound is still above 4000 psi, which is why the confidence interval alone must not be used to declare the concrete acceptable.
4. Part (b), step 4 — coefficient of variation. $$V=\frac{s}{\bar{x}}\times100=\frac{711}{4720}\times100$$ $$\boxed{V=15.1\ \%}$$
5. Part (b), step 5 — is the plant meeting the requirement? Two independent checks both say no. First, the ACI 318 acceptance rules require that every average of three consecutive tests equals or exceeds the specified strength and that no single test falls more than 500 psi below it. Scanning the 25 results, the lowest three-test average is $$\tfrac{1}{3}(3680+4100+3680)=3820\ \text{psi}\lt4000\ \text{psi}$$ so the first criterion fails, even though the lowest single cylinder, 3680 psi, clears the 3500 psi floor set by the second. Second, the mixture was never proportioned strongly enough for its own scatter: the required average strength is $$f'_{cr}=\max\bigl(f'_{c}+1.34s,\ f'_{c}+2.33s-500\bigr) =\max(4952,\ 5156)=5156\ \text{psi}$$ against an actual mean of 4720 psi. $$\boxed{\text{Production does NOT meet the 4000 psi requirement}}$$ Four of the 25 cylinders, 16 % of the production, fell below the target, which is consistent with the normal-distribution estimate: $z=(4000-4720)/711=-1.01$ gives a 16 % expected failure rate.
6. Part (b), step 6 — possible reasons, and the quality of the data. The failure is one of variability at least as much as of average strength, so the causes to look for are the ones that move results about: uncontrolled batch water, from unmeasured aggregate moisture or water added at the truck to restore slump; inconsistent aggregate grading or moisture between stockpiles; weigh-scale drift or admixture dispenser error; variable mixing time or truck discharge time; and, on the testing side, poor sampling, careless capping, cylinders left uncured or cured at the wrong temperature, and loading-rate errors in the press. The coefficient of variation is the measure of that scatter, and on the ACI 214R scale for general construction — excellent below 7 %, very good 7 to 9 %, good 9 to 11 %, fair 11 to 14 %, poor above 14 % — $$\boxed{V=15.1\ \%\ \Rightarrow\ \text{POOR standard of control}}$$ The data quality is therefore the finding, not an aside: until the coefficient of variation is brought down towards 10 %, the plant must over-design the mix to about 5160 psi to deliver 4000 psi reliably, which is an expensive way to buy back lost control.

The run chart adds one finding the summary statistics conceal: the four failing cylinders are clustered in the last third of the record, and the general level after sample 19 is visibly lower than before it. That is the signature of a step change — a new aggregate stockpile, a cement change, a colder spell, or a slipping scale — rather than of random scatter, and it is where the investigation should start.