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Silo Loads
by David Stuart Dick

There are unique relationships between the flow pattern of a product in a silo, the stresses in the flowing product and the loads the product applies to the silo walls. The contents of a silo, like any bulk granular material with internal friction, have ‘active’ and ‘passive’ states of stress. These active and passive states develop in the bulk solid as it flows in a flow channel.

Pressure Fields

When flowing in a parallel-sided channel with no convergence the solid generally moves as a plug. It behaves elastically and there is little if any relative movement between the particles. The pressure on the solid increases with depth below the surface. The major principal stress in the solid is vertical and the minor principal stress horizontal. This is called an active pressure field.

In a converging hopper section where the cross section of the flow channel is reducing the solid must deform. It is forced to contract horizontally and expand vertically. The major principal stress aligns horizontally and the minor principal stress aligns vertically. This is called a passive pressure field.

The vertical stresses are highest at the bottom of the parallel walled section. At the top of the hopper section the high stresses are transferred to the walls since the solid starts contracting horizontally and the major principal stress is horizontal. Further down in the hopper the vertical stresses are low since most of the weight of the solid is supported in the upper part of the hopper. In fact, the pressure distribution in the lower part of the hopper is independent of head of solid in the silo. This has major implications on how the silo operates.

In a mass flow silo all the product in the silo is in motion whenever any is withdrawn. Product slides on the hopper wall and the convergence is defined. In funnel flow the product forms its own flow channel within stagnant material and there is often no convergence. Therefore, while the pressures at the outlet of a mass flow hopper are low and independent of head, the pressure at the outlet of a funnel flow silo are not independent of head and may be high.

Cohesive solids can develop strength and the strength is a function of compacting pressure. In a mass flow hopper the outlet size can be designed based on known, low outlet pressures. The loads on mass flow feeders, density of discharged product, particle attrition, wear on feeder parts etc. are all low and constant.

Stresses

There is a fixed relationship (K) between the major and minor principal stresses in a flowing solid. Equilibrium of the mass allows us to calculate the pressures applied to the walls of a silo. In general the relationship K is taken as a constant - somewhat dependent on the properties of the product but strongly dependent on the flow conditions. For example, during initial fill conditions K is usually taken as 1 for design purposes. For flow conditions K is between 0.2 and 0.6 in the parallel-sided cylindrical section of a silo. In the converging hopper section K may be as low as 1.5 or as high as 10. High values apply for relatively incompressible solids in steep hoppers. In a diverging section K is usually taken as 0.2.

Many codes of practice for silo design were formulated before flow patterns were well understood. Consequently, the methods given in codes are usually based on the elementary theory of Janssen with factors applied to account for different conditions. A common approach of modern designers is to calculate loads as accurately as possible but check that the design is adequate for all the major codes of practice. An accurate calculation will often predict higher loads than the codes.

Dynamic, Fluidized and Eccentric Loads

Other loads that must be considered are dynamic loads, loads due to fluidized product and loads due to eccentric flow. Under normal conditions dynamic loads will not occur in mass flow silos. Dynamic loads in funnel flow may be due to collapsing ratholes, stuck product releasing from one side of the silo or collapsing bridges. Each of these phenomena has caused numerous silo failures.

Fluidization can only occur when handling a fine product (particle sizes generally less than 200 micron). However, at least one silo has failed due to fluidization with larger particles. This happened when a very moist compressible product was squeezed under the weight of product until all the void spaces were filled with moisture. The product lost its angle of internal friction and became a liquid with suspended solids. The loads were higher than the hopper could support and it let go spilling the contents of the silo onto the ground.

Normally a fine powder will adopt the properties of a fluid when it is handled at too high a rate. The powder does not have enough time to de-aerate and when it reaches the outlet, if the pressure is high enough it will fluidize. Sometimes aerating nozzles, designed to encourage flow will provide enough gas to push a marginal situation into a fluidized condition. Apart from the high loading condition fluidization will often cause flooding of downstream equipment. It is a condition that should be avoided.

An eccentric load due to eccentric flow channels is also a condition that will not normally be found in mass flow silos. The relatively thin skin of a silo is very efficient in resisting the tensile loads imposed by uniform product loading. When non-uniform, due to an eccentric flow channel, an additional horizontal bending moment is introduced. If the silo skin is not designed to resist horizontal bending, it wrinkles or cracks. Some concrete silos are designed with walls thick enough to resist bending but very few steel silos would be designed this way.

Thanks to David for his contribution. He can be reached in the UK at:

Powder Engineering Systems

Carrington Business Park

Manchester, M31 4YR

United Kingdom

Phone: +44 161 667 4523

Fax: +44 161 667 4524

http://www.powderengineering.com

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