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)

Definition of curing (2 marks). Curing is the deliberate maintenance of a satisfactory moisture content and temperature in freshly placed concrete for a specified period, so that the cement can continue to hydrate and the concrete can develop the strength, impermeability and volume stability the design assumed. It begins as soon as the surface is finished, or in hot, windy weather even before finishing, and it is achieved by ponding, continuous sprinkling, wet burlap, plastic sheeting, curing compounds, insulating blankets or steam. CSA A23.1 defines three regimes — basic curing, additional curing and extended curing — and prescribes which applies to which exposure class.

Importance of curing (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. The outer 30 to 50 mm dries first and is precisely the layer that must protect the reinforcement, resist abrasion and keep chlorides out, so inadequate curing damages the concrete exactly where it matters most. Properly cured concrete gains its design strength, develops a discontinuous capillary system and therefore low permeability, resists freeze–thaw and de-icer scaling, and suffers less plastic-shrinkage and drying-shrinkage cracking. Poorly cured concrete may reach only half to two thirds of the strength of a companion cylinder cured in the laboratory, dusts and crazes at the surface, and carbonates rapidly.

What is meant by alternatives to conventional concrete (2 marks). Conventional concrete is the familiar mixture of Portland cement, normal-density aggregate, water and possibly an air-entraining admixture, proportioned for a slump of 50 to 150 mm, consolidated by internal vibration and designed principally for compressive strength. An alternative concrete is any material that departs deliberately from that recipe or that method — by changing the binder (supplementary cementing materials, geopolymers), the aggregate (lightweight, heavyweight, recycled), the rheology (self-consolidating, no-slump), the reinforcement (fibres, textile) or the placing method (shotcrete, roller compaction) — in order to obtain a property that conventional concrete cannot provide economically. The point is not novelty for its own sake but the purchase of a specific performance: lower density, higher toughness, faster placement, better durability or a smaller carbon footprint.

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

1. Self-consolidating concrete (SCC). A highly flowable, non-segregating concrete that spreads under its own weight and fills the formwork completely without any vibration, achieved with a high-range water reducer, a viscosity-modifying admixture and a high fines content. It is used in precast plants, in heavily reinforced sections such as bridge diaphragms and shear walls, in architectural formwork where a blemish-free finish is required, and in repairs where a vibrator cannot reach. The advantages are faster placement with less labour, elimination of vibration noise and hand–arm vibration exposure, a uniform, honeycomb-free surface, and reliable consolidation around congested bars.

2. Roller-compacted concrete (RCC). A zero-slump mixture of aggregate, cement and just enough water to permit compaction, hauled by dump truck, spread by paver or grader and compacted with vibratory rollers exactly like an earth fill. It is used for gravity dams and their spillways, for heavy-duty industrial and intermodal yards, log-sorting yards and haul roads, and for pavement widening. The advantages are extremely rapid placement of large volumes, a low cement content and therefore low cost and low heat of hydration, no formwork or reinforcement, and a load-carrying capacity far beyond that of an asphalt pavement of the same thickness.

3. Fibre-reinforced concrete (FRC). Concrete in which short, randomly oriented steel, synthetic or glass fibres are dispersed throughout the matrix, typically at 0.1 to 2 per cent by volume. It is used in slabs on grade and industrial floors, in shotcrete linings for tunnels and slope stabilisation, in precast panels and pipes, and in overlays. The advantages are post-cracking toughness and residual tensile capacity in place of a brittle failure, tighter and better distributed cracks, improved impact and fatigue resistance, and in many slab applications the elimination of conventional shrinkage and temperature reinforcement, which removes a labour-intensive step from the placement.

4. Lightweight-aggregate concrete. Structural concrete made with expanded shale, clay or slate aggregate, reaching densities of 1400 to 1900 kg/m³ against about 2400 kg/m³ for normal-density concrete while still developing 20 to 40 MPa. It is used for long-span bridge decks, for composite floor slabs on steel deck in tall buildings, for topping slabs on existing structures, and for floating and offshore structures. The advantages are a 20 to 30 per cent reduction in dead load, which reduces member sizes, foundation loads and seismic inertia forces; better thermal insulation and fire resistance; and, because the porous aggregate is pre-wetted, an internal-curing reservoir that continues to hydrate the paste and reduces autogenous shrinkage in low water-to-cement mixtures.

Part (b) — Statistical evaluation of the ready-mix production (10 marks)

Given. Twenty-five cylinder compressive strengths taken periodically from one ready-mix plant, and a lower specification limit (the minimum target value) of 4350 psi.

Find. The mean, standard deviation, 95 per cent confidence interval on the mean and coefficient of variation of the 25 results; a decision on whether production satisfies the 4350 psi requirement, with reasons if it does not; and an assessment of the quality of the testing and production control the data reveal.

Approach. Compute the sample mean and the sample standard deviation with the n − 1 divisor, form the coefficient of variation and the Student-t confidence interval on the mean, then test compliance against the required average strength that ACI 318 and CSA A23.1 derive from the specified strength and the measured standard deviation, and finally classify the control using the ACI 214R bands.

1. Compute the sample mean. The arithmetic mean of the 25 results is $$\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i=\frac{118\,000}{25}$$ $$\boxed{\bar{x}=4720\ \text{psi}}$$ The mean already sits 370 psi above the 4350 psi lower limit, but a mean above a lower limit proves nothing on its own — the scatter decides whether individual batches comply.
2. Compute the sample standard deviation. Using the unbiased estimator, $$s=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^{2}}{n-1}}=\sqrt{\frac{12\,120\,600}{24}}$$ $$\boxed{s=711\ \text{psi}}$$ The n − 1 divisor is used because the mean has been estimated from the same 25 results; with n = 25 the difference from the n divisor is about 2 per cent, which is not negligible when the answer is compared with a specification band.
3. Form the coefficient of variation. The coefficient of variation expresses the scatter as a fraction of the mean, which allows plants working at different strength levels to be compared: $$V=\frac{s}{\bar{x}}\times 100=\frac{711}{4720}\times 100$$ $$\boxed{V=15.1\ \text{per cent}}$$
4. Compute the 95 per cent confidence interval on the mean. With the population standard deviation unknown and estimated from the sample, the interval uses the Student-t statistic with n − 1 = 24 degrees of freedom, for which t_0.025,24 = 2.064: $$\bar{x}\pm t_{0.025,\,n-1}\frac{s}{\sqrt{n}}=4720\pm 2.064\left(\frac{711}{\sqrt{25}}\right)=4720\pm 2.064(142.1)$$ $$\boxed{\text{95 per cent CI on the mean}=4720\pm 293=\left[4427,\ 5013\right]\ \text{psi}}$$ The interval is a statement about the average strength of the concrete the plant is producing, not about individual cylinders; it says the true production mean is very unlikely to be below 4427 psi.
5. Test compliance against the specification. A specification limit is met not by having the mean above it but by having so few results below it that the risk is acceptable. Standardising the lower limit, $$z=\frac{f'_{c}-\bar{x}}{s}=\frac{4350-4720}{711}=-0.52$$ so on a normal model about 30 per cent of all batches fall below 4350 psi. The sample bears this out directly: ten of the twenty-five results (numbers 4, 6, 10, 13, 15, 20, 22, 23, 24 and 25) are below 4350 psi, which is 40 per cent of the record. ACI 318 and CSA A23.1 require the plant to target an average strength high enough that this cannot happen; for a specified strength at or below 5000 psi that required average is $$f'_{cr}=\max\left(f'_{c}+1.34s,\ f'_{c}+2.33s-500\right)=\max\left(4350+953,\ 4350+1657-500\right)$$ $$\boxed{f'_{cr}=5506\ \text{psi}>\bar{x}=4720\ \text{psi}\ \Rightarrow\ \text{production does NOT meet the requirement}}$$
6. Identify the likely reasons for the shortfall. The problem is not primarily the strength level — it is the scatter. A standard deviation of 711 psi at this strength forces the target mean 1156 psi above the specified value, and the plant is running only 370 psi above it. Causes of that scatter fall into three groups. In the materials: variation in aggregate moisture content that is not compensated at the batch plant, so the effective water-to-cement ratio swings from load to load; variable aggregate grading or fineness modulus between stockpiles; cement or supplementary cementing material from more than one source; and inconsistent admixture dosing. In batching and delivery: scale calibration drift, unmeasured water added at the jobsite to restore slump, and variable mixing or haul times. In testing: poor sampling from the truck, inadequate rodding or vibration of the cylinders, cylinders left in the sun or the frost before transport to the laboratory, capping that is not plane, and an untrained or unaccredited technician. Because roughly one third of the total variance in a plant of this quality is usually testing variance, the first corrective step is to audit the field and laboratory procedures against CSA A23.2-3C and A23.2-9C before touching the mix design; the second is moisture-compensated batching; and the third is to raise the target mean while the variability is being brought under control.
7. Comment on the quality of the data. ACI 214R classifies concrete production control by the standard deviation for general construction testing, with values under 400 psi excellent, 400 to 500 psi very good, 500 to 600 psi good, 600 to 700 psi fair and above 700 psi poor; on the coefficient of variation the corresponding bands are under 7 per cent excellent through to above 14 per cent poor. With s = 711 psi and V = 15.1 per cent this plant falls in the poor class on both measures. The record spans 3680 to 6110 psi, a range of 2430 psi or 3.4 standard deviations, which is about what a normal population of 25 would produce, so there is no evidence of a single wild outlier; the scatter is systemic rather than accidental. There is also no visible trend from result 1 to result 25 — the low values are scattered through the record rather than clustered at the end — so the problem is random batch-to-batch variability, not a drift such as a progressively wetter aggregate stockpile. Twenty-five consecutive results is, however, the minimum sample ACI 214R accepts for establishing a standard deviation, so the value of 711 psi is itself uncertain to roughly ±15 per cent and should be reviewed as more data accumulate.