The beginnings of shear cells tests for determining the behaviour of bulk solids lie in the ground breaking work of Andrew W. Jenike of the University of Utah, in the late 1950s and early 1960s. His Bulletin 108 paper in 1961 titled “Gravity Flow of Bulk Solids” can perhaps be taken as the starting point for a whole industry concerned with the design of storage facilities for bulk solids.
We should perhaps begin by defining bulk solids and who better to provide this definition than Jenike himself. His motivation for developing the shear cell tests that have become the norm in the industry are provided by the following excerpt from his Bulletin 108.
We can see from this except that Jenike was concerned with inadequacies of the existing tests and so decided to develop a test method of his own. This test method and subsequent developments have become the standard in the industry.
However, he provides some cautions about the limitations of the theory that he describes in his elegant mathematical analysis. The one that is most significant to transfer chutes is this one:
We can clearly see from this comment that his analysis was never intended to apply to conveyor transfer chutes where the dynamic component of the flow was significant. This, in effect, rules out the vast majority of conveyor transfer chutes. This applies to both the bulk flow of solids and the wall friction effects. Jenike’s other much cited work, Bulletin 123, published 3 years later is entirely concerned with hopper design and certain types of feeders, all of which operate in the quasi-static flow regime. There is no mention at all of high speed inertial flows. He clearly understood these limitations.
It can also be seen that he recognised the issues concerned with gas interactions an issue which I will deal with separately.
Despite the above, a vast industry has built up, particularly in Australia, where the results of shear cell tests have been used as the basis for transfer chute design. This situation has arisen particularly from the work in two key Universities, both of which have centred their research on the coal industry. Paper after paper from a wide range of sources have been written quoting Jenike’s work as essential to the determination of material properties. I do wonder if many of these authors have actual read Jenike’s work.
It has become standard practice, and in fact due diligence to order shear cell tests on samples of ore from any prospective mine. I have been asked on numerous occasions to interpret the relevance of these tests to chute design and my response has always been the same; they are irrelevant and even misleading. Courses promoting these tests for transfer chute design have been conducted across the country for decades, despite their conflict with Jenike’s clear statement of limitations.
As well as shear cell tests, ‘wall friction’ tests have been conducted which involve pressing a sample of the ore in question, reduced to less than 6mm in size, against a variety of test surfaces. The irrelevance of these tests should not need explanation in the light of Jenike’s initial statement of limitations, but perhaps an example might assist to reveal just how far this can be taken without any questioning the reality of the numbers.
The table of recommended chute wall angles below was produced for an iron ore material, without reference to the design of the transfer chute concerned. The material concerned contains lumps over 250 mm in diameter which like most materials these days are being carried on belts that are travelling at 5 m/s or better. The numbers have been slightly altered by no more than a few percent to disguise their origin, but the essence of their message remains. It goes without saying that a ‘chute’ with a wall angle of 90 degrees is not a chute!
These tests entirely ignore the effects of ore velocity. Once again, an attempt is made to apply quasi-static results from hopper design to the dynamic flow in transfer chutes. The inertia of the ore is entirely overlooked. Perhaps this is best illustrated with an analogy. Consider a car on a hill. It would be very steep hill that would allow the car to move forward with the brakes applied. Perhaps 70 degrees. Now consider the same car travelling at 100 km/hr on a level road. Suddenly apply the brakes and what happens? The car keeps moving. Why? Because it has inertia. It is no different with ore in a chute. In the case of transfer chutes, it is only when the ratio of the frictional forces become significant in relation to the inertial forces that wall friction is of any significance.
The wall friction tests usually show that, amongst the feasible lining materials, ceramics give the lowest friction angle for iron ore. The tests also recommend wall angles that are beyond the range of reasonable chute design. That is to say, greater than about 70 degrees. The example above of a 90 degree wall angle is an extreme but not isolated example. I have seen chutes designed with wall angles of 78 degrees! Because of this, a whole generation of chutes have been applied in the iron ore industry with extremely expensive ceramic linings, set at extremely high wall angles. The result of this is that there is no deceleration of the ore within the chute and the entire burden of deceleration of the ore is borne by the skirt liners. Unless these skirt liners are crowded, thus increasing the wear intensity, the surcharge angle on the receiving belt will be low or even negative. An example of this is shown in the image below.
The drawback of using these wall angles is when the chute design calls for a wear ledges to be installed. These immediately invalidate any ore-against -material tests.
In practical chute design, the wall angles must be as low as possible while accommodating the flow of the material concerned. Extensive testing at Bulk Solids Modelling has shown that these angles can be determined for a given design with high confidence, particularly in the case of cohesive ores. This modelling technology has been successfully applied since 1997 to a variety of ores.
The reality is that in transfer chutes the inertial component cannot be ignored. For this reason alone, shear cell tests are not applicable. Even according to the father of this entire field of endeavour. Whereas in quasi-static flows the shear generally happens in the fines and the coarse fraction can be ignored to a large extent (according to Jenike at least), the opposite is true in dense granular (inertial) flows. The presence of large particles within the flow has a massive effect on the overall flow, these particles having extremely low Bond Numbers. This fact will be apparent to anyone who has observed granular flows of bulk solids in the field.