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. Specific gravity and absorption (ASTM C127 for coarse, C128 for fine aggregate). The test reports the bulk, bulk saturated-surface-dry and apparent specific gravities together with the absorption, i.e. the mass of water the pores take up expressed as a percentage of the oven-dry mass. Its significance is that every mix proportioning calculation is a volume calculation dressed up as a mass calculation: the bulk specific gravity converts the batch masses into the absolute volumes that must add to a cubic metre, and it is the same quantity that appears as G_sb in the VMA formula for asphalt mixtures. Its use in practice is threefold — batching concrete and asphalt by volume, correcting the mixing water for aggregate that is drier or wetter than saturated-surface-dry, and screening aggregates, since an unusually low specific gravity together with a high absorption points to a porous, frost-susceptible particle.

II. Soundness (ASTM C88, sodium or magnesium sulphate). A graded sample is cycled five times through immersion in a saturated sulphate solution and oven drying; salt crystallising in the pores generates internal pressures comparable with those from freezing water, and the loss is reported as the weighted percentage of material that breaks down. Its significance is that it is an accelerated durability index — it predicts whether an aggregate will disintegrate under weathering rather than whether it is strong today. Its use is in acceptance of aggregate for exposed concrete, for pavement surfacings and for any Canadian application subject to freeze-thaw and de-icing salt, where typical limits are of the order of 12 % loss with sodium sulphate and 18 % with magnesium sulphate.

III. Sieve analysis (ASTM C136). A dried, weighed sample is shaken through a nest of standard sieves and the mass retained on each is converted to percent passing, from which the gradation curve, the fineness modulus and the nominal maximum size follow. Its significance is that gradation controls the packing of the aggregate skeleton, and packing in turn controls void content, and void content controls how much paste or binder the mixture needs. A well-graded aggregate needs less cement or asphalt for the same workability, so it is cheaper, shrinks less and is more durable. Its use is in compliance testing against a specification envelope such as ASTM C33, in proportioning concrete and asphalt mixtures, in blending two or three stockpiles to hit a target curve, and in routine production control, where a shift in the curve is the first warning that a crusher setting or a stockpile has changed.

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

Given. A single dry aggregate sample was sieved and the mass retained on each sieve recorded, with the material passing the finest sieve collected in the pan.

Find. The percent retained, cumulative percent retained and percent passing for every sieve; the fineness modulus of the sample; and a gradation curve of percent passing against sieve size with a comment on the shape of that curve.

Approach. Sum the retained masses to recover the total dry mass, convert each retained mass to a percentage of that total, accumulate down the nest to get cumulative percent retained and hence percent passing, add the cumulative percentages to obtain the fineness modulus, then plot percent passing against sieve size on a logarithmic size axis and read the shape.

1. Part (b), step 1 — recover the total dry mass. The total is the sum of everything retained plus the pan: $$M_{\text{total}}=\sum M_{i}+M_{\text{pan}} =(0+35.2+299.6+149.7+125.8+60.4)+7.3$$ $$\boxed{M_{\text{total}}=678.0\ \text{g}}$$ Recovering the total this way rather than from the mass weighed out before sieving is deliberate: ASTM C136 requires the two to agree within 0.3 %, and any larger discrepancy means material was lost and the test must be repeated.
2. Part (b), step 2 — percent retained on each sieve. Each retained mass becomes a percentage of the total, $$R_{i}=\frac{M_{i}}{M_{\text{total}}}\times100$$ so the 4.75 mm sieve, for instance, gives $R=299.6/678.0\times100=44.19\ \%$. Working down the nest produces 0.00, 5.19, 44.19, 22.08, 18.55 and 8.91 %, with 1.08 % in the pan; these sum to 100 % as they must.
3. Part (b), step 3 — cumulative percent retained and percent passing. Accumulating from the coarsest sieve downwards and subtracting from 100 gives the two columns the specification is written against: $$C_{i}=\sum_{j\le i}R_{j},\qquad P_{i}=100-C_{i}$$ The results are tabulated below. The sample is 100 % finer than 25 mm, 50.6 % passes the 4.75 mm sieve and only 1.1 % is finer than 0.075 mm, so this is a well-cleaned mixed coarse-and-fine aggregate rather than either a concrete sand or a clean coarse stone.
4. Part (b), step 4 — fineness modulus. The fineness modulus is the sum of the cumulative percentages retained on the sieves of the standard series, divided by 100: $$FM=\frac{\sum C_{i}}{100} =\frac{0.00+5.19+49.38+71.46+90.01+98.92}{100}$$ $$\boxed{FM=3.15}$$ Physically the fineness modulus is the average sieve size of the sample expressed on a doubling scale, so a larger value means a coarser aggregate; 3.15 sits just above the 2.3 to 3.1 band that ASTM C33 allows for concrete sand, which is consistent with a sample that still holds nearly half its mass above the 4.75 mm sieve.
5. Part (b), step 5 — plot and characterise the gradation. Percent passing is plotted against sieve size on a logarithmic size axis, which is what turns a well-graded aggregate into a smooth, gentle S-curve. Reading the plotted curve at the three standard percentages gives $D_{10}=0.426\ \text{mm}$, $D_{30}=2.12\ \text{mm}$ and $D_{60}=5.50\ \text{mm}$, so $$C_{u}=\frac{D_{60}}{D_{10}}=\frac{5.50}{0.426}=12.9,\qquad C_{c}=\frac{D_{30}^{2}}{D_{10}D_{60}}=\frac{2.12^{2}}{0.426\times5.50}=1.92$$ $$\boxed{C_{u}=12.9\ (\gt 4)\ \text{and}\ C_{c}=1.92\ (\text{between 1 and 3}) \Rightarrow\ \text{well graded}}$$

Comment on the gradation. The curve is a continuous, smoothly rising S-shape with no flat step and no vertical segment, and it spans the whole range from 25 mm down to 0.075 mm. That shape, confirmed by a uniformity coefficient of 12.9 and a curvature coefficient of 1.92, is the definition of a well-graded (dense-graded) aggregate: every particle size is represented in the proportions needed for the smaller particles to fill the voids between the larger ones. Practically this means a low void content, so the mixture will need comparatively little cement paste or asphalt binder, will be economical, will compact readily and will develop good aggregate interlock and stability. Two contrasting shapes are worth naming for comparison: a curve that is steep over a narrow band and flat elsewhere is uniformly graded (single-sized, high voids), and a curve with a horizontal plateau where one or more intermediate sizes are missing is gap graded, which is prone to segregation. The only caution here is the small deficiency of the very finest sizes, with barely 10 % passing 0.425 mm, which would need checking against ASTM C33 if the material were intended as a combined aggregate for structural concrete.