5.3 Multi-Fraction Testing, Weighted Averages, Reporting & Precision for Coarse Aggregate
Key Takeaways
- ASTM C127 Section 7.3 requires the material larger than 37.5 mm to be tested in separate size fractions whenever more than 15% of the sample is retained on the 37.5-mm (1-1/2 in.) sieve.
- The minimum mass for each size fraction is the difference between the Table 1 masses prescribed for the maximum and minimum sizes of that fraction.
- Average absorption is a simple mass-weighted average of the fraction absorptions, but combined relative density must be computed as a weighted harmonic mean because volumes add, not densities.
- Mass percentages used to weight the fractions exclude material finer than the 4.75-mm (or substituted 2.36-mm) sieve.
- ASTM C127 reports density to the nearest 10 kg/m3 or 0.5 lb/ft3, relative density to the nearest 0.01 with the basis stated, and absorption to the nearest 0.1%; the single-operator acceptable range of two results is 0.020 to 0.025 in relative density.
Why One Number Is Not Enough for a Graded Aggregate
Everything in Section 5.2 assumed a single test on a single specimen. Real coarse aggregate is graded, and ASTM C127 anticipates that the technician will sometimes have to test it in pieces and then reassemble the answer. Section 7.3 states the trigger plainly: testing the coarse aggregate in several size fractions is permitted, and it becomes compulsory when the sample contains more than 15 % retained on the 37.5-mm (1-1/2 in.) sieve, in which case test the material larger than 37.5 mm in one or more size fractions separately from the smaller size fractions.
Two practical rules follow from that decision.
Specimen size for each fraction. When an aggregate is tested in separate size fractions, the minimum mass of test sample for each fraction is the difference between the masses prescribed for the maximum and minimum sizes of the fraction. For a fraction running from 19.0 mm up to 37.5 mm, that is the 37.5-mm requirement of 5 kg minus the 19.0-mm requirement of 3 kg, giving a 2 kg minimum for that fraction — not 5 kg, and not 3 kg.
Grading of the parent sample. Section 7.4 requires that when the sample is tested in two or more size fractions, the grading of the sample must be determined in accordance with Test Method C136, including the sieves used for separating the size fractions. And in calculating the percentage of material in each size fraction, ignore the quantity of material finer than the 4.75-mm (No. 4) sieve — or the 2.36-mm (No. 8) sieve, where that sieve was substituted under Section 7.2. The mass percentages that weight the average must therefore be renormalised over the coarse fractions only, not taken straight off the full gradation report.
Combining Absorption Across Fractions (ASTM C127 Section 9.5)
Absorption combines as a straightforward mass-weighted average:
where $A$ is the average absorption in percent, $A_1 \ldots A_n$ are the absorption percentages for each size fraction, and $P_1 \ldots P_n$ are the mass percentages of each size fraction present in the original sample (not including finer material, per Section 7.4).
Combining Relative Density Across Fractions
Relative density does not combine as a simple weighted average, and this is where candidates lose the item. A relative density is a mass divided by a volume; averaging densities directly averages the wrong quantity. The volumes are what add, so the combined value is a weighted harmonic mean:
Each term $P_i / (100,G_i)$ is the volume contributed by that fraction per unit mass of the whole; summing the volumes and inverting returns mass over total volume, which is what a relative density is.
Worked Example: A Two-Fraction Test
A 37.5-mm nominal maximum size crushed limestone is sieved under ASTM C136. Of the material retained on the 4.75-mm sieve, 22 % is retained on the 37.5-mm sieve — above the 15 % trigger — so Section 7.3 requires the coarse fraction to be tested separately.
| Size Fraction | Mass % of coarse material, $P_i$ | Bulk RD (SSD), $G_i$ | Absorption, $A_i$ |
|---|---|---|---|
| Plus 37.5 mm | 22.0 % | 2.712 | 0.9 % |
| 4.75 mm to 37.5 mm | 78.0 % | 2.655 | 1.6 % |
Step 1 — Confirm the weights renormalise to 100. $22.0 + 78.0 = 100.0$. The minus-4.75-mm material was excluded before these percentages were computed, exactly as Section 7.4 directs. Had the full gradation been used and the sand left in, both weights would be too small and every combined value would be biased.
Step 2 — Average absorption (Section 9.5).
Reported to the nearest 0.1 %: 1.4 %.
Step 3 — Combined bulk relative density (SSD).
Reported to the nearest 0.01: 2.67.
Step 4 — Compare with the wrong method. A simple arithmetic weighted average of the densities gives $0.22 \times 2.712 + 0.78 \times 2.655 = 0.59664 + 2.07090 = 2.6675$, which also rounds to 2.67. The two agree here because the two fractions differ by only 0.057 in relative density. That agreement is a trap. Spread the fractions apart — say a porous 2.35 fraction at 40 % against a dense 2.85 fraction at 60 % — and the harmonic mean gives $1 / (40/235 + 60/285) = 1 / (0.170213 + 0.210526) = 2.6266 \to 2.63$, while the arithmetic average gives $0.40 \times 2.35 + 0.60 \times 2.85 = 2.65$. A 0.02 error in relative density moves the absolute volume of a cubic yard of concrete by enough to matter to yield. Use the harmonic form every time; it costs nothing when the fractions are close and it is the only correct form when they are not.
Reporting Requirements (ASTM C127 Section 10)
ASTM C127 fixes three separate reporting obligations, and the third is the one most often skipped:
| What is reported | Required precision or content |
|---|---|
| Density (kg/m3 or lb/ft3) | Nearest 10 kg/m3, or 0.5 lb/ft3 |
| Relative density (specific gravity) | Nearest 0.01, and indicate the basis — oven-dry (OD), saturated-surface-dry (SSD), or apparent |
| Absorption | Nearest 0.1 % |
| Undried determinations | If the density, relative density, and absorption values were determined without first drying the aggregate as permitted in Section 8.2, note that fact in the report |
"Indicate the basis" is a content requirement, not a formatting nicety. A bare "specific gravity = 2.65" is ambiguous across three different quantities that a mix designer will use for three different purposes, and a laboratory report that omits the basis cannot be acted on.
The same three rules appear verbatim in ASTM C128 Section 11 for fine aggregate, so one memorised pattern covers both standards.
Precision: What Counts as a Real Difference
ASTM C127 Table 1 publishes precision estimates derived from AASHTO Materials Reference Laboratory proficiency sample data, and they tell a technician when two results genuinely disagree and when they are simply testing noise:
| Relative density basis | Single-operator 1s | Single-operator d2s | Multilaboratory 1s | Multilaboratory d2s |
|---|---|---|---|---|
| Relative density (OD) | 0.009 | 0.025 | 0.013 | 0.038 |
| Relative density (SSD) | 0.007 | 0.020 | 0.011 | 0.032 |
| Apparent relative density | 0.007 | 0.020 | 0.011 | 0.032 |
Read the d2s column as the practical decision rule: two properly conducted tests on the same material by the same operator should not differ by more than about 0.02 to 0.025 in relative density, and results from two different laboratories should not differ by more than about 0.03 to 0.04. If your retest lands 0.015 from the first, you have not found an error — you have found the method's normal scatter, and chasing it wastes a day. If it lands 0.08 away, something real is wrong: entrapped air left in the basket, aggregate lost out through the basket mesh, an SSD condition missed on one of the two runs, or a soak that never reached saturation.
Where the ASTM and AASHTO soak periods diverge. Section 11.1 records a genuine difference between the two documents that is easy to miss and is exactly the kind of detail an open-book written exam rewards: Test Method C127 requires a saturation period of 24 ± 4 h, while AASHTO Method T 85 requires a saturation period of 15 h minimum. ASTM adds that this difference has been found to have an insignificant effect on the precision indices — the two soak regimes give statistically comparable results — but the required period itself still differs, so quote the one the question cites.
One further footnote is worth noting: testing for these precision estimates started with aggregates in the oven-dry condition, which is a second, independent confirmation that oven-drying before the soak is the standard's normal order of operations rather than an alternative to it.
A coarse aggregate is tested in two size fractions. The plus-37.5 mm fraction is 30.0% of the coarse material with a bulk relative density (SSD) of 2.40; the 4.75 mm to 37.5 mm fraction is 70.0% with a bulk relative density (SSD) of 2.80. What is the combined bulk relative density (SSD), reported to the required precision?
Under ASTM C127 Section 7.3, when is a laboratory required to test coarse aggregate in separate size fractions rather than as a single specimen?
Two properly conducted single-operator ASTM C127 tests on the same coarse aggregate return bulk relative densities (SSD) of 2.64 and 2.66. What does the standard's precision statement indicate about this pair of results?