2.8 Summary
3.2.2 Annular Shear Cell
A brief note on nomenclature is required before discussing use of the annular shear cell. In the literature, the name Jenike shear cell is often used interchangeably for both linear shear cells and annular shear cells. Some authors use Schulze ring shear tester in lieu of annular shear cell [Louati et al., 2015; Scieszka and Adamecki, 2013]; others use Portishead ring shear cell [Walker, 1967] or Couette cells [Abrahamsson et al., 2014; Höhner et al., 2013; Mansard and Colin, 2012; Reddy et al., 2011]. Note that in this thesis, linear cells will be referred to as Jenike shear cells (after their inventor - see Jenike [1964b]), while their toroidal cousins will be given the designation annular shear cell (ASC).
Figure 3.2.1:The lighting rig constructed for this research. There are four 500W halogen lamps mounted on a custom frame, constructed from spare office shelf mounts. The two lamps mounted to the reverse of the rig were not used. On the left of the image, just visible is the computer used to control the drum motor, and the stack of airtight boxes used to store samples. Photograph taken by the author.
3.2. EQUIPMENT 43
Usage of the Annular Shear Cell
The usage of the annular shear cell in this project was informed by Section 4 of the ASTM International methodology standard D6773 [ASTM, 2008].
A description of the methodology of using an ASC is summarised as follows. A material is loaded into a circular trough (Fig. 3.2.2), which itself is attached to a motor enabling the trough to turn at very slow but steady rotational velocities. The material is sub- ject to a range of shear forces and normal stresses (analogous to pressures), with the trough being rotated both with and against the shear forces, which are supplied by a series of weights attached to an arm that pulls on the trough in a lateral direction due to a pulley. A sensor mounted to the trough measures the amount of force that is ap- plied in a direction congruent with the shear forces. As the direction on the trough is switched between the two possibilities, the measured force will vary between two av- erage values; comparison of these average values and the applied normal stress allows the investigator to find a value for the shear strength of the material.
The maximum normal stress that a material is subjected to is determined by the ASTM standard D6773 [ASTM, 2008] , and is shown in Table 3.1. This stress is also called the consolidation stress.
Table 3.1:This table shows the consolidation stress that a material should be
subjected to in an annular shear cell, based on the material’s bulk density. (Found in the ASTM Standard D6773.)
ρ(kg m−3) σ(kPa) < 300 ˜ 1.5 300 - 799 ˜ 2.0 800 - 1599 ˜ 2.5 1600 - 2400 ˜ 3.0 > 2400 ˜ 4.0
Having the correct consolidation stress is important to avoid a material that is over- or under-consolidated. An under-consolidated material is one in which the material has a greater void space fraction than the critical case, while in an over-consolidated system, the particulates themselves have begun to break down [Campbell, 2006] - both
scenarios will produce behaviour from the granular material that will introduce errors into the shear strength measurements by the ASC. The concept of critical consolidation in a material is demonstrated by Figure 3.2.3.
The average of the two peak force values, i.e., the resultant shear stress, is plotted against the applied normal stress (the weights on top of the trough, combined with those hung from the pulley attached to the arm). By making use of Mohr-Coulomb circles analysis (see Section 4.4), it is possible to find the unconfined yield stress (UYS) and major consolidation stress (MCS) (also known as the minor and major principle stresses, respectively) of a particular combination of applied shear stresses and a spe- cific normal stress.
There are limitations to the usage of an ASC. The investigator must make sure that the material is not under- or over-filled in the trough. An under-filled trough will not have enough particles for the system to truly reflect the shear strength of the material. An over-filled system will overflow during use and result in the properties of the system changing with time, rendering the results unusable. An optimal fill level was found by trial and error and marked on the trough for reproducibility between runs. The same fill level was used for both the sand and the ash, as they were similar enough to each other in this regard.
The individual particulates must also not be so wide as to introduce serious edge ef- fects into the system. Each different ASC will have its own tolerances on both of these factors4. It is also important to consider the air moisture in the laboratory [Gómez- Arriaran et al., 2015]; if the material itself gains moisture, this can have a significant effect on its flowability5. In addition, while the ASC is an improvement over the Jenike shear cells that came before it, the ASC is still subject to operator induced errors; the accuracy of the data obtained from an ASC can vary significantly if care is not taken
4The particles in the experiments presented in this thesis were all sieved to sizes (0.25 to 4 mm) well below the tolerances for the ASC used in this project [ASTM, 2008].
5Moisture content as a concern was mitigated by several means, including drying the samples in an oven, storing them in airtight containers, and running the experiments in an air-conditioned laboratory.
3.2. EQUIPMENT 45
Figure 3.2.2:The parts of an annular shear cell, specifically the one used in this study. A is the counter-weight used to bring the normal stress below that which would be provided by an unladen lid. B is the controls for the unit, and also houses the motor that drives the rotation of the trough, which is seen in C. The data, in the form of a voltage, is recoded by the laptop, D. The weights on E provide the shear stress to the system. Photograph taken by the author.
to follow a strict sequence of steps [ASTM, 2008] - it is for this reason than the ASTM standard was created.
Figure 3.2.3:An illustration of the concept of critical consolidation,νc. An under- or
over-consolidated material will produce strange total shear strength results. Care must also be taken not to apply too much load to a sample, or the critical
consolidation will be change. An edited version of a figure originally presented by Campbell [2006].
The ASC used in this study was constructed as an exact copy of the instrument de- scribed by Carr and Walker [1967] at the University of Canterbury, New Zealand.