Question 7 of 7: Concrete Curing; Identifying an Unknown Hardenability Lot

Question 7: Concrete Curing; Identifying an Unknown Hardenability Lot (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.

Given (a). Concrete is a particle-reinforced composite of Portland cement, water, fine aggregate (sand) and coarse aggregate (gravel/crushed stone).

Find (a). Main constituents; what happens during curing; effect of water/cement ratio.

(a) Approach and Answer

Portland cement is a mixture of calcium silicates and aluminates (produced by firing limestone and clay/shale at high temperature and grinding the clinker to a fine powder). When mixed with water, the cement undergoes hydration — an exothermic chemical reaction (not simple drying) in which the calcium silicates react with water to form calcium-silicate-hydrate (C–S–H) gel, the primary strength-giving binder, plus calcium hydroxide as a by-product. This C–S–H gel grows and interlocks over time, progressively binding the sand and gravel aggregate particles into a rigid, load-bearing solid. Curing is the practice of maintaining adequate moisture (and a favourable temperature) at the concrete surface for an extended period (commonly 7–28 days) so that hydration can continue as completely as possible; concrete that is allowed to dry out too early stops hydrating and never reaches its design strength, and may also develop surface shrinkage cracks.

The water/cement (w/c) ratio is the single most important variable controlling concrete properties (Abrams’ law: strength decreases roughly monotonically as w/c increases). A lower w/c ratio gives higher strength and lower permeability, because only enough water to hydrate the cement is present, and once the excess (unreacted) water is used up or evaporates it leaves behind less capillary porosity; the trade-off is reduced workability (the fresh mix is stiffer and harder to place/compact). A higher w/c ratio improves workability and flow but increases capillary porosity once the surplus water leaves the paste, which lowers compressive strength and increases permeability — making the concrete more vulnerable to freeze-thaw damage, reinforcement corrosion, and chemical attack. In practice the w/c ratio is chosen as the lowest value consistent with the workability needed to place and consolidate the mix properly (often assisted with plasticizer admixtures rather than by simply adding more water).

(b) Given

Bar diameter $=2.5$ in, quenched in still oil (curve 3 on the correlation charts); observed hardness traverse (surface–centre–surface) read directly from the given plot: surface $\approx50$ HRC, ¾-radius $\approx46$ HRC, mid-radius $\approx40$ HRC, centre $\approx36$ HRC; four candidate hardenability curves A–D; four Jominy-distance correlation charts (surface, ¾R, mid-R, centre) for round bars, each carrying curves for quench severities 1 = still water, 2 = mildly agitated oil, 3 = still oil, 4 = mildly agitated molten salt.

Find (b). Which lot (A–D) matches the unknown bar; the predicted hardness traverse for the same bar and lot, reheated and quenched in still water.

(b) Approach

This is a read-the-chart engineering-judgement problem, not a closed-form calculation. For each of the four radial positions: (1) enter the position’s correlation chart at the bar diameter (2.5 in) on curve 3 (still oil) to read the equivalent Jominy distance; (2) read each candidate lot’s hardenability curve at that distance to get a predicted hardness; (3) compare the four predicted hardnesses (one per position) against the four observed traverse readings, and identify the lot with the closest overall match. All chart readings are approximate (±1–2 HRC, ±0.05 in — the printed charts’ own practical precision) and are disclosed as such rather than presented with false numeric certainty.

1. Equivalent Jominy distances for still-oil quench (curve 3), 2.5-in bar. Reading each of the four correlation charts at diameter $=2.5$ in on curve 3: $$\text{surface}\approx0.64\ \text{in},\quad \tfrac34\text{R}\approx0.90\ \text{in},\quad \text{mid-R}\approx1.17\ \text{in},\quad\text{centre}\approx1.19\ \text{in}$$ (mid-radius and centre map to very similar equivalent distances for this bar size — a real, recognised effect: the four correlation curves converge toward the bar’s interior as diameter increases, since heat extraction becomes progressively less direction-dependent well below the surface).
2. Read each lot’s hardness at those four distances.
   Fig. Q7b — hardenability curves for Lots A–D (approximate reproduction of the given chart), with the observed still-oil traverse values (red dots) marked at each position’s equivalent Jominy distance.
   Predicted hardness at the four still-oil equivalent distances:

   Position	Observed	Lot A	Lot B	Lot C	Lot D
   Surface	50	54.3	49.2	35.3	22.8
   ¾-radius	46	48.1	39.3	27.8	20.4
   Mid-radius	40	43.3	33.0	23.5	18.1
   Centre	36	43.2	32.7	23.3	17.9

3. Identify the closest-matching lot. Lots C and D read far too low at every position (average deviation $>10$ HRC) and are ruled out immediately. Between A and B, the mean absolute deviation from the observed traverse is close either way ($\approx4.2$ HRC for Lot A vs. $\approx4.5$ HRC for Lot B) — not itself a clean separator. The deciding evidence is the surface reading, the position read with the least chart-reading ambiguity (a clean, well-separated curve region on both the traverse plot and the hardenability chart): Lot B matches it almost exactly (49.2 vs. 50 HRC observed, a 0.8 HRC gap), while Lot A misses by 4.3 HRC there. Lot A's error is dominated by a large 7.2 HRC miss at the centre, the position with the largest chart-reading uncertainty in this problem (Section 1 above); weighting the highest-confidence reading more heavily than the lowest-confidence one favours Lot B. $$\boxed{\text{Unknown bar} = \textbf{Lot B}}$$
4. Predict the traverse under a reheat + still-water quench. Repeat step 1 using curve 1 (still water) instead of curve 3 on the same four correlation charts, then re-read Lot B’s hardenability curve at the new (much smaller) equivalent distances: $$\text{surface}\approx0.19\ \text{in},\ \ \tfrac34\text{R}\approx0.45\ \text{in},\ \ \text{mid-R}\approx0.63\ \text{in},\ \ \text{centre}\approx0.64\ \text{in}$$ Reading Lot B at these distances gives the predicted traverse:
   Fig. Q7b — predicted hardness traverse for Lot B under a still-water requench (blue), compared with the original observed still-oil traverse (red).
   $$\boxed{\text{surface}\approx56,\ \tfrac34\text{R}\approx55,\ \text{mid-R}\approx49,\ \text{centre}\approx49\ \text{HRC}}$$ The predicted profile is both higher and much flatter than the oil-quenched traverse — physically sensible, since still water is a far more severe quenchant than still oil, so even the bar’s centre cools fast enough to stay close to the fully-martensitic maximum hardness ($\approx57$ HRC), and the surface-to-centre hardness drop shrinks from 14 HRC (oil) to only $\approx7$ HRC (water).