Granular Material Characterisation

It is important to know the properties of a granular material in order to be able com- pare the results for one substance against another. For example, all other things being equal, a material with a higher particulate density would presumably produce different results to one with a lower density.

Key variables that need to be measured include particulate density, bulk (or "tapped" [Abdullah and Geldart, 1999]) density, angle of repose [Chou et al., 2010], particulate size distribution, and the material’s internal angle of friction.

Angle of Repose

There are two angles of repose that need to be considered when working with granular material; the static and the dynamic. The static angle is the maximum angle to the horizontal a stable pile of the material in question will attain before an avalanche takes place. The dynamic angle is the angle the slope settles at once an avalanche has taken

3.4. EXPERIMENTAL METHODOLOGY 55 place; the dynamic angle is generally shallower than the static [Chou et al., 2014]. For this study, the static angle of repose was measured using a simple system of creating piles of the substance to be tested, and then measuring the height and two diameters, taken at right angles, of the pile. Simple trigonometry using the average of the two diameters and the pile’s height gives the static angle of repose. Five piles were created for each material, and an average angle taken. Results are presented in Table 3.2.

Note that the angle of repose is a measurement of an unstressed granular material. While it is useful for cross-material comparison, it is less robust than the internal angle of friction, which is discussed later in Chapter 4, along with the flow function. These two measurements are not included here due to the greater amount of analysis that is required to obtain their values.

Table 3.2:The angle of repose for the various materials used in this study, found by measuring piles of the material in question and simple trigonometry.

Material Angle of repose±0.3°

Taranaki Ash 32.1

Beach Sand 29.3

Pumice 33.4

Millet 26.6

Particle Size Distribution

In a rotating drum, a size distribution of the particulates in the granular material can affect the flow [Abdullah and Geldart, 1999; Alexander et al., 2002; Liao et al., 2013] and segregation of the material (i.e., the percolation effect [Chou et al., 2010]).

Size distribution of the materials used in this study was undertaken using standard geological sieves. These sieves are graded on an exponential scale known as theφscale. Negative numbers on the φ scale relate to the coarsest materials, while the positive numbers denote finer materials (Fig. 3.4.1). For example, -8φparticulates are 256 mm or greater in diameter and would be classified as boulders, while 8φmaterials are <8 and≥4μm across and are referred to as silt [Wentworth, 1922]. Each increment in

theφscale in the negative to positive direction represents a halving of the size of the particulates that will pass through the associated mesh; the conversion between the

φscale and millimetres (d) is given in Equation 3.4.1. The sieves used to measure the size distribution of a material are able to be stacked, with the material that passes from one falling into the one below. By arranging the sieves so that the largest meshes are at the top, a material can be separated out into its constituent sizes. If the weight of the sample is measured before being passed through the sieves and the contents of each sieve weighed afterwards, the size distribution of the material in question can be ascertained.

Figure 3.4.1:A table that converts between mm, the Wentworth grade, and theφ scale. Image originally presented in Hedrick et al. [2013].

d=2−φ (3.4.1)

Figure 3.4.2 shows the size distributions of the materials used in this study.

Particulate Density

Particulate density is an important characteristic for granular materials [Chou et al., 2010]. The particulate density can be measured at a precision of up to four decimal places using a gas pycnometer. The more accurate the weight measurement supplied

3.4. EXPERIMENTAL METHODOLOGY 57

Figure 3.4.2:The size distributions of the materials used in this study. Thexaxis is the mesh size of the geological sieves in millimetres. Theyaxis is the mass percentage of the sample with diametersgreaterthan the respective millimetre measurement and

lessthan the sieve size above. Blue is the beach sand, red the ash, yellow the pumice, and green the millet. As can be seen from the figure, the beach sand is skewed towards the finer particulate sizes, with a mode between 0.5 and 1 mm (0.707 mm). The ash is relatively normally distributed with a peak between 1 and 2 mm (1.414 mm). The pumice has a wide distribution, skewed towards the fine. Finally, the millet is essentially unimodal at 1.414 mm.

to a pycnometer will obviously aid in the accuracy of the densities obtained. Note that the results from the machine are sensitive to moisture in the air; to allow direct com- parison between samples, they must be put through the process on the same day to minimise variation in moisture exposure; it is beneficial to avoid days where it is rain- ing. The size (i.e., volume) of the sample container used when measuring the particu- late density must be known accurately, or the pycnometer will give erroneous results.

The pycnometer can be set to analyse the same sample multiple times in order to ob- tain an average particulate density value. For the machine used in this study, this can be up to 100 times, but accurate results were obtained with 10 repetitions.

The standard deviation required can also be set on this study’s pycnometer. As may be expected, the higher the accuracy required, the longer the machine will take to analyse

the sample, and the more prone the final value will be to error. As for the purposes of this work the material density is only used for comparison of materials after other experiments which will be subject to wider error margins than the pycnometer, the standard deviation was set to 0.01%.

The equipment used here was a Quantachrome12Ultrapycnometer 1000 nitrogen py- cnometer. The particulate densities of the materials are presented in Table 3.3. Note that the density of the pumice was calculated from data provided by Eric Breard, and the millet density was supplied by Dr. Luke Fullard. Size distributions and angles of repose for these materials were found by the author.

Table 3.3:The particulate densities for the various materials used in this study,±0.01 g cm−3. These were found using a gas pycnometer or supplied with the material by other workers, as covered in the main text.

Material Density(g cm−3)

Taranaki Ash 3.03

Beach Sand 2.69

Pumice 1.60

Millet 1.31

Bulk or "Tapped" Density

The methodology for finding the bulk density of a granular material for this study is very simple. The material was poured into a measuring cylinder of a known weight. After this, the combined cylinder and sample was weighed. Finally, to take into account the possible variation in particulate packing, the cylinder is tapped 100 times, causing the material to settle. The final fill level on the cylinder is noted, and this allows for the density of the material to be found. The bulk densities found for the materials used in this study are presented in Table 3.4.

3.4. EXPERIMENTAL METHODOLOGY 59

Table 3.4:The bulk densities, in kg m−3to four significant figures, of the materials used in this study.

Material Density(kg m−3)

Ash 1402

Beach 1606

Pumice 897.9

Millet 747.0