Question 2 of 5: Aggregate Testing and Sieve Analysis

Question 2: Aggregate Testing and Sieve Analysis (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) — Significance and use of the three tests (6 marks)

I. Sieve analysis (CSA A23.2-2A, ASTM C136). A weighed, oven-dried sample is shaken through a nest of standard sieves and the mass retained on each is recorded, from which the percentage passing each size is computed. Its significance is that particle size distribution controls the void content of the aggregate skeleton and therefore the paste or binder demand, the workability, the segregation tendency and the finishability of the mixture. It is used to check a supply against the grading limits of CSA A23.1 or ASTM C33, to compute the fineness modulus for mix proportioning, to design blends of two or more stockpiles so the combined curve falls inside the specification band, and as a routine production-control test that detects segregation in a stockpile or breakdown in a crusher long before it shows up in strength results.

II. Durability, or soundness, test (CSA A23.2-9A, ASTM C88; also unconfined freeze–thaw CSA A23.2-24A and Micro-Deval ASTM D6928). A graded sample is subjected to five cycles of immersion in a saturated magnesium or sodium sulfate solution followed by oven drying, and the mass loss is measured; the growth of salt crystals in the pores reproduces the disruptive pressure that ice generates in service. Its significance is that it measures the resistance of the aggregate to weathering — disintegration under repeated freezing and thawing or wetting and drying. It is used to accept or reject aggregate for exposed concrete and pavement in a freeze–thaw climate, typically with a limiting loss of 12 per cent for fine and 12 to 18 per cent for coarse aggregate, and it is the front line of defence against popouts and D-cracking, which no amount of air entrainment in the paste can prevent if the stone itself is unsound.

III. Abrasion test (Los Angeles abrasion, ASTM C131 for the coarse fraction and C535 for the large-size fraction). A graded charge of aggregate is tumbled in a rotating steel drum with a charge of steel spheres for a fixed number of revolutions, and the percentage passing the 1.70 mm sieve afterwards is reported. Its significance is that it measures the combined resistance of the aggregate to impact, attrition and crushing — the degradation mechanisms of handling, stockpiling, mixing, compaction and traffic. It is used to accept aggregate for concrete and asphalt pavement surfaces, for granular base and for railway ballast, with limits commonly between 35 and 50 per cent loss depending on the application; a high LA loss warns that the grading measured in the laboratory will not be the grading present in the finished pavement, because the material will have broken down under the roller.

Part (b) — Sieve analysis, fineness modulus and gradation (14 marks)

Given. The masses retained on each sieve of a single dry aggregate sample, as printed on page 3 of the examination.

Find. The complete sieve analysis (percentage retained, cumulative percentage retained and percentage passing on every sieve), the fineness modulus of the sample, and a comment on the gradation drawn from the shape of the percent-passing curve plotted against sieve size on a semi-logarithmic scale.

Approach. Sum the retained masses to obtain the total sample mass, convert each retained mass to a percentage of that total, accumulate downwards to obtain cumulative percentage retained and hence percentage passing, sum the cumulative retentions to obtain the fineness modulus, then plot the passing values against the logarithm of the sieve opening and compare the shape with the maximum-density (Fuller) curve for the same nominal maximum size.

1. Establish the total mass of the sample. The total is the sum of everything retained on the sieves plus the material caught in the pan: $$M_{tot}=6.5+40.2+293.6+151.2+120.8+65.4+12.3$$ $$\boxed{M_{tot}=690.0\ \text{g}}$$ The masses add exactly to a round figure, which indicates that no material was lost in the shaking and that the analysis can be carried through without a correction for loss.
2. Convert each retained mass to a percentage retained. Each individual retention is $$R_i=\frac{m_i}{M_{tot}}\times 100$$ so the 25 mm sieve retains (6.5/690.0)(100) = 0.94 per cent, the 9.5 mm sieve 5.83 per cent, the 4.75 mm sieve 42.55 per cent, the 2.00 mm sieve 21.91 per cent, the 0.425 mm sieve 17.51 per cent, the 0.075 mm sieve 9.48 per cent, and the pan holds the remaining 1.78 per cent. The single largest retention, 42.55 per cent between the 9.5 mm and 4.75 mm sieves, is already a strong hint about the shape of the curve.
3. Accumulate downwards to obtain cumulative percentage retained and percentage passing. Working from the coarsest sieve down, $$C_i=\sum_{j\le i}R_j,\qquad P_i=100-C_i$$ which produces the full analysis tabulated below.

   Completed sieve analysis of the 690.0 g sample

   Sieve, mm	Retained, g	Retained, %	Cumulative retained, %	Passing, %
   25	6.5	0.94	0.94	99.06
   9.5	40.2	5.83	6.77	93.23
   4.75	293.6	42.55	49.32	50.68
   2.00	151.2	21.91	71.23	28.77
   0.425	120.8	17.51	88.74	11.26
   0.075	65.4	9.48	98.22	1.78
   Pan	12.3	1.78	100.00	—

   The passing column closes at 100 per cent on the coarsest sieve and at 1.78 per cent on the 0.075 mm sieve, so the analysis is internally consistent.
4. Compute the fineness modulus. The fineness modulus is defined as the sum of the cumulative percentages retained on the specified sieves, divided by 100: $$FM=\frac{\sum C_i}{100}=\frac{0.94+6.77+49.32+71.23+88.74+98.22}{100}$$ $$\boxed{FM=\frac{315.22}{100}=3.15}$$ The result is an index, not a physical quantity: it is roughly the average sieve number, counting downwards, on which the material rests, so a larger value means a coarser sample. A change of 0.2 in fineness modulus between deliveries is the usual trigger for re-proportioning a concrete mix.
5. Plot percent passing against sieve size on a semi-logarithmic grid. The sieve openings span from 25 mm down to 0.075 mm, a range of more than two and a half orders of magnitude, so a linear size axis would compress the whole fine end into a few millimetres of paper. Plotting against the logarithm of the opening spreads the sizes evenly and turns the ideal maximum-density blend into a gentle, nearly straight line, which is why the semi-logarithmic sheet is issued with the paper.
   Figure 2.1 — The sample gradation plotted on a semi-logarithmic grid, with the Fuller maximum-density curve for a 25 mm nominal maximum size shown for comparison. The measured curve is flat at both ends and very steep between 9.5 mm and 4.75 mm.
6. Comment on the gradation from the shape of the curve. A well-graded, dense blend plots as a smooth curve that stays close to the maximum-density line $$P(d)=100\left(\frac{d}{D}\right)^{0.45}$$ which for a nominal maximum size D = 25 mm passes through 64.7 per cent at 9.5 mm, 47.4 per cent at 4.75 mm, 32.1 per cent at 2.00 mm, 16.0 per cent at 0.425 mm and 7.3 per cent at 0.075 mm. The measured curve departs from that reference in a very specific way. Between 25 mm and 9.5 mm it is almost horizontal, only 6.8 per cent of the sample lying in that band; it then plunges, 42.6 per cent of the whole sample falling between 9.5 mm and 4.75 mm; and it flattens again at the fine end, delivering only 1.8 per cent finer than 0.075 mm against the 7.3 per cent the maximum-density line calls for. $$\boxed{\text{Poorly graded: a single dominant size fraction near 4.75 to 9.5 mm, with deficiencies at both the coarse and the fine ends}}$$
7. Draw the practical consequences of that shape. A curve that is flat, steep, flat is the signature of a one-size (uniformly graded) material rather than a continuously graded one, and it carries three consequences. The void content of the compacted skeleton is high, so more paste or binder is needed to fill it, which raises cost and shrinkage in concrete and raises the binder demand in asphalt. The shortage of material finer than 0.425 mm (only 11.3 per cent passes) means poor cohesion, a harsh, unworkable concrete mix that bleeds and finishes badly. And with half the sample coarser than 4.75 mm the material is neither a fine aggregate nor a clean coarse aggregate; measured against ASTM C33 the fineness modulus of 3.15 is just outside the 2.3 to 3.1 band for fine aggregate, confirming that it is an all-in or pit-run material. The correct remedy is to blend it with a well-graded natural sand, which would lift the fine end of the curve towards the maximum-density line and bring the fineness modulus down into the usable range.