Question 2 of 5: Aggregate Laboratory Tests and Sieve Analysis

Question 2: Aggregate Laboratory Tests 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 aggregate tests (6 marks)

I. Specific gravity and absorption (CSA A23.2-6A/-12A; ASTM C127 for coarse, C128 for fine aggregate). The test soaks the aggregate for 24 hours, brings it to the saturated surface-dry condition and weighs it in air and in water, yielding the bulk, bulk SSD and apparent relative densities and the absorption as a percentage of the oven-dry mass. Its significance is that aggregate is batched by mass but occupies volume, so no mix design can be converted from proportions to a batch ticket without the bulk relative density: it is the quantity that converts the mass of stone into the volume of the aggregate skeleton in the absolute-volume method, and the same number reappears in every asphalt volumetric calculation as $G_{sb}$ (see Q.4). The absorption has two uses. It is the moisture correction applied to the batch water every time the stockpile condition changes, without which the effective water–cement ratio and therefore the strength drift from batch to batch. It is also a durability indicator in its own right: a high absorption signals a porous aggregate that will hold freezable water, will demand extra binder in an asphalt mix, and will usually perform poorly in the soundness test.

II. Soundness (CSA A23.2-9A; ASTM C88, sodium or magnesium sulfate). Sized fractions of the aggregate are subjected to five cycles of immersion in a saturated sulfate solution and oven drying; salt crystallising in the pores generates internal pressure analogous to the pressure of freezing water, and the loss in mass after the cycles is reported. Its significance is that it is the standard accelerated screen for the resistance of an aggregate to weathering — in the Canadian climate specifically to freeze–thaw. An unsound aggregate produces popouts and D-cracking at the surface of a pavement or a deck, and the damage is entirely a property of the stone, not of the paste, so no amount of air entrainment or extra cement will cure it. Its use is as an acceptance criterion: CSA A23.1 and ASTM C33 set maximum losses (commonly of the order of 12 per cent with sodium sulfate or 18 per cent with magnesium sulfate) below which the aggregate may be used without further evidence, and above which a record of satisfactory field performance or a direct freeze–thaw test (CSA A23.2-24A) is required.

III. Sieve analysis (CSA A23.2-2A; ASTM C136). A dried, weighed sample is shaken through a nest of standard sieves and the mass retained on each is recorded, from which the percentage retained, the cumulative percentage retained and the cumulative percentage passing are computed, along with the maximum size, the nominal maximum size and the fineness modulus. Its significance is that particle size distribution controls the void content of the aggregate skeleton, and the void content controls how much paste or binder is needed to fill it. A well-graded aggregate has a low void content, so it needs less paste, less water and less cement for the same workability, which means less shrinkage, less heat and lower cost; a gap-graded or uniformly graded aggregate needs more. Its uses are as an acceptance test against the grading limits of CSA A23.1 or ASTM C33, as the input to the proportioning of both concrete and asphalt mixes, and as a production-control test that detects segregation in the stockpile or degradation in the crusher long before the strength tests would.

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

Given. A single dry sample sieved on the nest below.

Find. The percentage retained, cumulative percentage retained and cumulative percentage passing on each sieve; the fineness modulus of the sample; the gradation curve plotted on three-cycle semi-logarithmic paper; and a reasoned comment on the gradation from the shape of that curve.

Approach. Total the retained masses to get the sample mass, convert each retained mass to a percentage, accumulate downward to get cumulative percentage retained and subtract from 100 to get cumulative percentage passing; form the fineness modulus as one hundredth of the sum of the cumulative percentages retained; then plot passing against sieve size on a logarithmic size axis and read the shape against the maximum-density line and the standard uniformity descriptors.

1. Establish the total sample mass. The sample mass is the sum of everything recovered from the nest, including the pan: $$W=\sum W_i = 0+35.2+299.6+149.7+125.8+60.4+7.3$$ $$\boxed{\,W=678.0\ \text{g}\,}$$ This total, not the mass weighed out before sieving, is the denominator for every percentage; using the pre-test mass would leave the columns failing to close if any material were lost in handling.
2. Convert each retained mass to a percentage retained. For each sieve, $$R_i=\frac{W_i}{W}\times 100 .$$ Taking the 4.75 mm sieve as the worked instance, $R=299.6/678.0\times 100=44.19$, and repeating for the remainder gives the second column of the table below. The seven values sum to 100.00, which is the first arithmetic check.
3. Accumulate downward to get cumulative percentage retained and cumulative percentage passing. The cumulative percentage retained on a sieve is the sum of the percentages retained on it and on every coarser sieve, and the cumulative percentage passing is its complement: $$C_i=\sum_{j\le i} R_j,\qquad P_i=100-C_i .$$ On the 4.75 mm sieve, $C=0+5.19+44.19=49.38$ and $P=50.62$. The full set is:

   Sieve (mm)	Mass retained (g)	Percent retained	Cumulative percent retained	Cumulative percent passing
   25	0	0.00	0.00	100.00
   9.5	35.2	5.19	5.19	94.81
   4.75	299.6	44.19	49.38	50.62
   2.00	149.7	22.08	71.46	28.54
   0.425	125.8	18.55	90.01	9.99
   0.075	60.4	8.91	98.92	1.08
   Pan	7.3	1.08	100.00	0.00

   Reading off the first two columns, the maximum size is 25 mm (the smallest sieve through which the whole sample passes) and the nominal maximum size is 9.5 mm (the sieve above the first one to retain more than 10 per cent of the sample).
4. Form the fineness modulus. The fineness modulus is one hundredth of the sum of the cumulative percentages retained on the specified sieves, the pan excluded: $$FM=\frac{\sum C_i}{100}=\frac{0.00+5.19+49.38+71.46+90.01+98.92}{100}=\frac{314.97}{100}$$ $$\boxed{\,FM=3.15\,}$$ A fineness modulus of 3.15 sits just above the 2.3 to 3.1 band that ASTM C33 allows for concrete fine aggregate, so on fineness alone this material is at the coarse edge of a sand — consistent with the fact that a little under half of it is retained on the 4.75 mm sieve and it is therefore really a sandy fine gravel rather than a sand.
5. Plot the gradation curve and read its shape. Cumulative percentage passing is plotted against sieve size on a logarithmic size axis, which is what the three-cycle semi-logarithmic paper issued with the examination provides. Two quantitative descriptors follow from the plotted curve. The first pair are the uniformity and curvature coefficients, obtained by logarithmic interpolation for the sizes at 10, 30 and 60 per cent passing: $$D_{10}=0.426\ \text{mm},\qquad D_{30}=2.12\ \text{mm},\qquad D_{60}=5.50\ \text{mm},$$ $$C_u=\frac{D_{60}}{D_{10}}=\frac{5.50}{0.426}=12.9,\qquad C_c=\frac{D_{30}^{2}}{D_{10}D_{60}}=\frac{2.12^{2}}{0.426\times 5.50}=1.92 .$$ $$\boxed{\ C_u=12.9\ (>6),\qquad C_c=1.92\ (\text{between }1\text{ and }3)\ \Rightarrow\ \text{well graded}\ }$$ The second is the comparison with the Fuller maximum-density line for the sample's own maximum size, $P=100\,(d/D)^{n}$ with $D=25$ mm and $n=0.45$, which gives 64.7, 47.4, 32.1, 16.0 and 7.3 per cent passing the 9.5, 4.75, 2.00, 0.425 and 0.075 mm sieves respectively.

Comment on the gradation. The plotted curve is smooth and continuous over the whole range with no horizontal plateau, and the coefficients confirm what the eye sees: with $C_u=12.9$ and $C_c=1.92$ the material satisfies both of the usual well-graded criteria, so this is a well-graded (dense-graded), not a gap-graded or uniformly graded, aggregate. Two qualifications should be made, and both are read straight off the shape of the graph. First, the curve is noticeably steeper between 9.5 and 4.75 mm than anywhere else — 44 per cent of the whole sample sits in that one band — and it crosses the maximum-density line at about the 40 per cent level, lying above the line on the coarse side and below it on the fine side. The blend is therefore coarser than the maximum-density grading and would pack a little less densely than an ideal Fuller curve of the same maximum size. Second, only 1.1 per cent of the sample passes the 0.075 mm sieve against the 7.3 per cent the Fuller line calls for, so the material is markedly short of filler. For a concrete this is the more workable of the two errors and is easily corrected by blending; for an asphalt mix it would leave the mastic thin and the dust-to-binder ratio well below the usual 0.6 to 1.2 window, and a mineral filler would have to be added.