# Testing of industrial products - Aggregates for construction

## Details of the cross-testing experiment on the Shape Index test

### Laboratories

22 laboratories from 11 European countries took part in this cross-test. In the tables where results are reported, they appear under codes.

### 4.2 Materials

The materials for this cross-test were chosen and sampled by Partner 4 in UK. Information about the sampling and sample reduction can be found in the report on the cross-test with the Flakiness Index, for which the same materials were used. The three aggregates chosen as levels for the cross-test had different particle shape:

• Level 1. Limestone with good particle shape
• Level 2. Chloritic schist with poor particle shape
• Level 3. Crushed flint gravel with extremely poor particle shape

It might be worth noting that the finest fraction (4/8 mm) is over-represented in the materials chosen for the cross-test, if compared to the average of the aggregates usually tested by this method.

Table 1. Grading of the materials obtained with the main sieve series as average of three laboratory samples.
Size fraction Level 1 (rounded % by mass) Level 2 (rounded % by mass) Level 3 (rounded % by mass)
4/8 mm14894
8/16 mm69526
16/32 mm30
Sum100100100
Approximate sieved mass80 kg20 kg20 kg

### Results

Each participating laboratory was supposed to carry out two tests on each level.

### Statistical analysis

The statistical treatment of the results of this cross-test resembles the one given to other test procedures in the course of this project and was carried out by Partner 4. It starts with the elimination of statistical outliers. Usually Cochran's test is applied to the ranges of the two results from each laboratory and then Grubbs' test to the averages.

Statistician's notes on the treatment of outliers:

The data for Laboratories G and O were excluded from the calculation of the precision values at all levels, because their data gave rise to outliers at two levels.

The data for Laboratories H and I were excluded from the calculation of the precision values for Level 3, because they gave rise to an outlier or a straggler in the laboratory averages for this level.

The data for Laboratory N gave high laboratory averages and ranges at all three levels, and an outlier in the ranges for Level 2. It would be reasonable to exclude all their data from the calculation of the precision values, but their data were not excluded because it was considered that this would mean excluding too much data.

The data for Level 2 for Laboratory P gave rise to an outlier in the ranges. It would be reasonable to exclude these data from the calculation of the precision values, but the data were not excluded because it was considered that this would give a very truncated distribution of ranges at Level 2 in comparison with the distributions obtained at the other two levels.

After the exclusion of outliers, the precision data are calculated and possible functional relations between average results of the levels and precision values are considered.

Finally the statistical evaluation deals with the performance of the single participating laboratories.

### Practical considerations

Anybody concerned with the practical side of the testing of aggregates might - after a look at the data obtained in this experiment - ask whether statistician's labour was not lost on Levels 2 and 3, when calculating precision data on the basis of such results. If after elimination of statistical outliers, the results still range from 20 to 55 per cent (Level 2) or from 30 to 75 per cent (Level 3), the question arises whether it is necessary to carry out any further calculations on such poor results. Possible reasons for these ranges in the results are discussed below.

### Size fractions and test portion mass

The participants in this cross-test were faced with a series of uncertainties, which they solved in different ways. The difficulties will be pointed out in the following, taking as example Level 1. How the participating laboratories interpreted the instructions is shown on Table 2.

The first question was: follow the testing instructions or the test procedure prEN 933-4? If the testing instructions were followed, as some laboratories did, 1,7 kg of the material of Level 1 were tested and no further questions arose, except whether this kind of procedure might lead to precision data for prEN 933-4. If the test procedure prEN 933-4 was followed, as other participants did, the first difficulty was that the material might exceed a size range, where D <= 2d. According to the test procedure, this kind of material must be separated into particle size fractions d/D, where D <= 2d. The separation must be done using "appropriate sieves".

The first action therefore, should be a grading test. The main purpose of this test is to establish the maximum particle size and to decide whether the sample must be tested in size fractions or can be tested as a whole. The material for Level 1 is in UK called a 20 mm aggregate, which probably means that most particles will pass a test sieve with openings of 20 mm. The grading as established by using the preferred test sieve series of prEN 932-2 is shown on Table 1, according to which the upper size is 32 mm, so that the resulting test portion mass is 6 kg. As a consequence of this large test portion mass, some laboratories reduced the mass of the main size fractions by sample reduction.

Table 2. Way of proceeding of the different laboratories (Level 1).
d/D in mmTest portion mass (kg) Laboratory number
Laboratories that followed testing instructions
-- without sieving1.76
1.6260
1.6309
-- stating upper and lower sieve
4/25 1.753
8/251.769
4/22.51.6128
4/321.7216
4/321.7224
4/200.4234
4/251.7236
10/201.6248
10/201.6249
-- followed prEN 933-4 and separated 4/321.7 54
into fractions with D <= 2d 4/251.7 70
4/321.6167
4/221.6204
pr EN 933-4 for test portion mass 4/325.4197
4/324.8205

As "appropriate sieves" is not exactly defined, other solutions are possible. A grading test using the sieves with the openings of 25, 20, 16, 12,5 10 and 8 mm gave the results in Table 3. In this case the upper limiting sieve would be 20 mm. According to Table 1 of prEN 933-4 the test portion mass would be about 2,3 kg. The exact answers of 3 laboratories are not known, but even without them there seems to be enough diversity of interpretation.

Table 3. Grading of the aggregate used in Level 1.
size fraction (mm)20/2516/20 12,5/1610/12,58/105/8
% by mass123 541741

### Over- and undersize

The next question which faced the participating laboratories was whether the over- and undersize should be included in the test portion. This question arises because the test procedure mentions the expression "principal size fraction", but does not regulate expressly the treatment of over- and undersize. It is assumed that most participants tested the main size fraction and the over- and undersize bigger than 4 mm. Some laboratories indicated, however, that over- and undersize was not included in the test. Similar questions arose for Levels 2 and 3 where the materials were called 14 mm and 10 mm respectively.

### Other factors influencing the results

In order to see whether there were still additional factors influencing the result, a short extension of the experiment was carried out. Laboratory 224 kindly volunteered to repeat the test on what was left of its samples. This time the following instructions were given. First, the grading of the material was to be determined on what was left of the laboratory sample, using the preferred sieve series. After having separated thus the sample into the size fractions 4/8, 8/16 and 16/32 mm, the mass of 300 particles of each fraction was to be noted, the shape of these particles determined, and the mass of the non-cubical particles noted. Finally the weighted Shape Index calculated as prescribed by the test procedure. The average results were as shown in Table 4. From these data it can be deduced that there must be other factors as well.

Table 4. Results of re-tests in Laboratory 224.
Level 1Level 2Level 3
Shape Index237380

### Comments from the participating laboratories.

• treatment of over- and undersize; and
• whether there should be a limiting minimum percentage of a size fraction in the sample, in order to test this size fraction.

### Testing both size and shape in practice.

It would be convenient in practice if the determination of the Shape Index of an aggregate could be carried out on size fractions produced during a determination of the particle size distribution of the aggregate. For this to be permissible, the CEN standards that describe the two methods would have to allow the Shape Index test to be carried out starting with a test portion of the same mass as that used for the determination of the particle size distribution. However, there is a statistical question that needs to be considered if this is to be done. Whereas the precision of the sieve test depends very much on the grading of the material, but not very much on the shape, the opposite is true of the shape test - its precision depends very much on the shape of the material, but not very much on the grading. Hence the test portion mass that gives a satisfactory precision in the sieve test may not be adequate for the shape test, or vice versa.

However, theoretical formulae for the relation between repeatability and test portion size can be given for both the sieve test and the shape test (see "functional relationships"). Hence these formulae could be used to derive a procedure that uses a common test portion and gives (in theory) a chosen, satisfactory, level of repeatability in both tests. Such a procedure would then have to be tried out in practice to make sure that the performance predicted by the theory is actually achieved. Other "sorting" tests (e.g. Flakiness Index, percentage of crushed particles, and the percentage of lightweight contaminants) could be treated similarly.

When doing a Shape Index test, one can obtain a size fraction that contains a much larger number of particles than one needs to examine to achieve a satisfactory degree of precision. DIN 52114 provides for this situation by giving the rule that at least 300 particles should be examined from each size fraction. (The results of the sieve test are then needed as weights to calculate the weighted Shape Index for the whole test portion.) Another possibility that must be considered in the Shape Index test is that a size fraction can contain only a small number of particles: the method for the Shape Index test should say what should be done in this case too.

The method for quantitative petrographic examination given in BS 812 Part 104 covers both possibilities. It gives a Table (and a formula) to use to calculate the test portion mass, and then allows the mass examined (mi) in a size fraction to be calculated from the mass found (Mi) in the size fraction as:

mi = Mi × (Di ÷ D)3

where Di is the upper size of the size fraction, and D is the aperture size of the sieve through which 100 % of the test portion passes. According to the theory behind this method, it minimises the total number of particles from a test portion that must be examined to give a chosen level of repeatability. The method is applicable only when a measurement is needed of the composition of the test portion as a whole (it is not applicable when the composition of each size fraction is needed). It should be noted that the formula given in BS 812 Part 104 for the test portion mass may require modification before it can be applied to the Shape Index test because it was derived by using a value for a "shape factor" that may not be valid for poorly-shaped aggregates that give an SI as high as 50 %.