Jenike and Johanson’s Jie Guo, Aleef Rahman, and Corin Holmes provide an overview of gravity reclaim fundamentals, and how to estimate the live capacity from gravity reclaim stockpiles.
Stockpiles provide an economical means of storing large volumes of bulk solids in all types of industries. Stockpiles vary in shape (conical or prismatic), and size, and can be covered or open to the environment, and they may be built by varying types of mobile equipment such as scrapers or front-end loaders, or by belt conveyors with various configurations for stacking. Once built, reclaiming from the stockpile is required and this can be by forced extraction, such as with scrapers, bucket wheels or front-end loaders, or by gravity, which employs different types of feeders or gates contained in tunnels beneath the stockpile.
A common method for gravity reclaim from large stockpiles is to use a series of hoppers and belt or apron feeders discharging onto a single belt conveyor. The primary hoppers/feeders can be arranged parallel or perpendicular to the belt conveyor. The number, size and location of the hoppers/feeders depend on key factors including the size of the pile, the reclaim rate required, and whether the material is free-flowing or cohesive. In some cases, with highly cohesive bulk solids, it may not be economically feasible to use a gravity reclaim system. This decision can be arrived at quite readily through the evaluation of representative flow characteristics of the stockpiled material.
General flow patterns in a silo
There are two primary flow patterns that can develop in a silo during discharge: funnel flow and mass flow. It is important to understand them before conducting the analysis. Both patterns are shown in Figure 1.
In funnel flow, an active flow channel forms above the hopper outlet, with stagnant material at the periphery. As the level of material in the hopper decreases, material from stagnant regions may or may not slide into the flowing channel, depending on the bulk solid’s cohesive strength. When the bulk solid has sufficient cohesive strength, the stagnant material does not slide into the flow channel, which results in the formation of a stable rathole. In addition to flow stoppages that occur as a consequence of ratholing, funnel flow can cause material degradation, results in a first-in-last-out flow sequence, and increases the extent to which sifting segregation impacts the uniformity of the discharging material.
In mass flow, all of the material is in motion whenever any is withdrawn from the hopper. Material from the centre as well as the periphery moves toward the outlet. Mass flow hoppers provide a first-in-first-out flow sequence, eliminate stagnant material, reduce sifting segregation, and provide a steady discharge with a consistent bulk density and a flow that is uniform and well controlled. Requirements for achieving mass flow include sizing the outlet large enough to prevent arching and ensuring the hopper walls have sufficiently low wall (material/surface boundary) friction and are steep enough to achieve flow at the walls.
A third type of flow pattern, called expanded flow, can develop when a mass flow hopper (or hoppers) is placed beneath a funnel flow hopper, as shown in Figure 2. The mass flow hopper is designed to activate a flow channel in the funnel flow hopper, which is sized to prevent the formation of a stable rathole. Particularly for large diameter silos, the major advantage of an expanded flow discharge pattern is the savings in headroom, as compared to an all mass flow design. This approach not only reduces the capital cost, but also facilitates retrofitting existing silos by minimising the additional headroom requirement. The mass flow hopper beneath the funnel flow hopper still has the benefit of discharging material reliably with a consistent bulk density. Note that segregation and material degradation problems are not necessarily minimised with an expanded flow pattern.
Flow pattern in stockpiles
For cohesive materials, as shown in Figure 3, they flow within a gravity reclaim stockpile (if designed properly) by following the same expanded flow pattern as they will in an expanded flow silo. In the case of the stockpile, the flow channel is established above the base of the pile. The combine effect from the reclaim hoppers and feeders results in the funnel flow component of the expanded flow design. Similarly, the discharge hoppers below the base of the pile should act as the mass flow portion of the expanded flow design; the active area resulting from the hoppers and feeders is ideally sized to prevent the formation of a stable rathole, although this is rarely achieved with cohesive materials.
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Even though stagnant material will remain within the pile, eliminating or minimising the formation of a stable rathole will allow for a greater percentage of the pile volume to be reclaimed by gravity alone. This design approach ensures an even feed rate and a low feeder load, and therefore low feeder power requirements. A non-mass flow discharge hopper design, regardless of the occurrence of ratholing above, will result in high feeder / power loads.
H = stockpile height
Hd =
critical height at which rathole becomes stable and enlarged crater forms above
Df = flow channel diameter
D = drawdown angle
ӨR= angle of repose
X =
offset of pile center to center of reclaim hopper
Free flowing materials
If free flow materials, such as dry sand, are stored in a pile, the flow pattern is simple as shown below in Figure 4. The drawn angle, D, and angle of repose, ӨR, are very similar.
Estimating live capacity
The methodology to determine the stockpile live capacity can be defined as follows. When material is withdrawn through the mass flow hoppers at the base of the stockpile, a flow channel forms within the stationary mass, and the material flows within that channel toward the openings. The flow channel above an individual hopper will relatively quickly expand to a round area, above which it will tend to be a steep sided circular cone, with a bottom diameter close to the largest dimension of the hopper inlet. The level of material in the channel falls as discharge proceeds, and the top surface of this cone sloughs off and slides into the channel at a drawdown angle, D (see Figure 3), which is governed by the internal friction of the material. For free-flowing materials, this angle is approximately equal to the angle of repose, ӨR, which describes the outer surface of the pile (and hence, its total capacity).
For cohesive materials, the angle is steeper than the angle of repose, and can be attributed more to the internal friction angle of the material.
Discharge within the gravity reclaim pile continues until the height, Hd, is reached where the stress in the rathole, of diameter Df, equals the strength of the material. A plot to demonstrate where the rathole collapses is shown in Figure 5.
Below this point, the flow channel angle will be very steep (generally on the order of 3-5° from vertical, again based on internal friction of the material), and the surrounding material will remain stagnant once the material above has emptied to the drawdown angle.
An example of the stockpile live capacity analysis is shown in Figure 6. As flow channels from adjacent feeders intersect (assuming there are multiple), then their combined effect will govern the potential for stable ratholes to remain, or if a larger reclaim area (described by the drawdown angle) will form above.
Flow property testing
As discussed above, the live capacity of the stockpile highly depends on the flow property of the material. A good understanding of the material properties is essential for estimating the live capacity of the stockpile under gravity reclaim. The typical flow property tests required are listed below.
Particle size distribution
Full-size bulk density test, which assists in estimating the bulk density on the surface of the stockpile.
Compressibility test, which provides the bulk density change with the increase of the consolidation pressure within the stockpile.
Cohesive strength test, which informs the internal friction of the bulk material and critical outlet dimensions to avoid arching and ratholing.
Wall friction test, which assists in assessing or designing mass flow reclaim hoppers underneath the stockpiles
Angle of repose test, which is useful for estimating the angle of the stockpile around its circumference.
Estimating the pressure within the stockpile
As illustrated in Figure 5, the pressure within the stockpile governs the critical rathole dimension Df required to collapse the rathole, i.e. where the draw-down occurs. It is vital to determine the pressure within the stockpile correctly.
One of the methods of calculating the pressure within the stockpile is to assume the pressure is hydrostatic and apply a relaxing factor, 0.7 for conical stockpiles and 0.8 for prismatic stockpiles, for the hydrostatic pressure.
In the mining industry, it is common to build two stockpiles adjacent to each other as shown in Figure 7. The pressure distribution within a stockpile can be influenced by the adjacent pile depending on the distance between the two piles.
For engineering design purposes, the following are recommended as a rule of thumb.
L > 1.5*H, the influence from each other between the two stockpiles can be neglected.
0.5*H < L < 1.5*H, the two stockpiles can be considered as one prismatic pile with a flat top, joining the two peaks.
L <0.5*H, the two piles can be deemed as one single stockpile with the peak on the center line of the two piles and the height being the same as the two piles, as shown by the light blue pile in Figure 7.
Some simulations were performed to demonstrate the pressures at the base of two adjacent stockpiles with varying distances, as shown in Figure 8. The dimensions of the stockpiles are shown in the figure, and the material was calibrated to have the same angle of repose for all three simulations. Note that they are much smaller than the stockpiles in the mining industry. Only the pressures above 36 kPa were displayed (orange represents pressures above 36 kPa, and red represents pressures above 45 kPa). As Figure 8 shows, high pressures are observed between the peaks of two stockpiles, which suggests the overlapping zone of the two piles is experiencing the same high pressures as the two peaks. Hence, the two piles should be considered as one prismatic pile with a flat top, as suggested above.
Conclusion
There are various facets to consider when designing or reviewing a gravity reclaim stockpile, such as:
Sizing the outlet of the mass flow hopper(s) large enough to prevent mechanical / cohesive arching, and so that the desired flow rate will be achieved.
Selecting the slope of the mass flow hopper(s) such that the material will slide along the walls.
Sizing the inlet of the mass flow hopper(s) such that a sufficient percent volume of material will be reclaimed from the total volume of the stockpile (i.e., “live capacity”).
Selecting the number and size (and distance X, from the stockpile symmetry axis shown in Figure 3) of the reclaim hoppers, if multiple hoppers are used, to again ensure that a sufficient live capacity will result.
The most cohesive material tested will provide the limiting design criteria for the pile being considered, both in terms of arching/ratholing potential and in designing the mass flow hoppers. Values of cohesive strength at lower consolidation pressures will have a greater influence on reclaim hopper outlet sizing to prevent arching, while cohesive strength at higher consolidation pressures will have a greater influence on ratholing and the resulting live capacity of the pile. Higher wall friction will, by design, require steeper hopper angles to ensure mass flow. Hence, a suitable liner or surface of construction is required not only from a flow perspective but must also be selected based on minimising abrasive wear.