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A bulk solid transmit small tensile strengths, transmits compressive and shear stresses and flows under the influence of shear stresses if they are large enough. In fluidized state a bulk material may behave like a liquid, and in the other limiting case as a solid. Therefore, stress ratios between horizontal pressure (σh) and vertical pressure (σv) of 0 <λ <1 are possible.

Stress ratio (λ) = horizontal pressure(σh) / vertical pressure(σv)




Groups of characteristics of bulk materials:

Charakteristika von Schüttgütern

plastic bulk materials(1) φi=0 ΤC>0
cohesive bulk materials (2) φi>0ΤC>0
cohesion less bulk materials (3) φi>0 ΤC=0
fluidized bulk materials (4) φi=0 ΤC=0




Ideal plastic bulk materials (1)

Ideal plastische SchüttgüterC>0, φi=0) Ideal plastic powders are mostly saturated and have very high cohesion. It is difficult for the individual particles to change their position. Because of the saturation of the powder ther is no influence of the compression load and the packing density. Consequently, because of incompressibility, the  change of pressure can not lead to change of number of contacts and the shear stresses are only dependent of the cohesion. 

About the almost high cohesion of such materials there are difficult to handle. Some samples also show only at higher normal stresses a plastic behavior. Measurements at different loads can demonstrate this.

Cohesive powders (2)

Kohäsive SchüttgüterC>0, φi>0) By cohesive powders the inter-particular forces are frictional forces and cohesive forces.

The rearrangement of particles is more or less limited by the cohesion, so that a previous compression from the normal and shear stresses have an influence on the behavior afterwards. Also, the slope angle depending on the previous history and can take different angles. To get qualified physical properties, measurements must be performed in shear testers always where the flow behavior is measured under load.
This bulk material can be described by the equation: Τ = σ * tan(φi) + ΤC.
Cohesive powder have a stationary value which is independent of the previous normal stress. The line through the stationary points is the same for all measured points of all different yield loci for different consolidation stress. The powder is in flowing condition nearly cohesionless. Even time consolidations can thereby be undone.

In practice, this group of bulk materials probably the most common. Depending on the flow properties, these materials are more or less difficult to handle. However, the physical properties under operating conditions are essential and must always be measured. The compressive strength can occur bridging, if the hopper angle or outlet are not adequate. Time consolidation should be considered as well.


Cohesionless solids (3)

Kohäsionslose SchüttgüterC=0, φi>0) For free flowing materials only frictional forces between particles can exist. The number of contacts can be changed by changing the pressure. Because of no cohesion, a complete rearrangement of the particles is possible. The free flowing bulk materials can be described by the linear equation τ=σ*tan(φi). The yield locus of such material passes through the origin of the σ-τ diagram and the internal friction angle (φi) corresponds to the angle of repose of the bulk material.  

These bulk materials are usually easy to handle. Due the missing of compressive strength, bridging does not occur and preloads are even reversible. The bulk density at normal stress and the stress ratio should be determined.


Fluidized powders (4)

C=0, φi=0) Fluidized powders are cohesionless and internal friction become zero by their high particle distances. In the fluidized state, the bulk solids behave more like a liquid.

This can happen by filling of silos or by collapsing of a bridge or rate hole. In such cases it coarse many problems like flooding out of a silo.




Flowability factor (FL bzw. ffc)

By measuring a yield locus, several physical properties describe the behavior of the bulk material. For the classification of powders, and to express the flowability in a single parameter, the flowability factor (FL = ffc = σ1 / σc) was developed. This factor is Dimensionless and enable the classification of bulk materials into different classes:

FL > 25 cohesionless
25 > FL > 15 slightly cohesive
15 > FL > 5 cohesive
5 > FL > 2 very cohesive
2 > FL > 1 plastic
1 > FL solid

Especially for materials which very different density, an extended calculation basis for the flow factor were developed:

Relative flow factor: FLR = ( σ1 - σ2 ) / σc

absolute flow factor: FLA = FLR * ρb0

Each measured yield locus are based on their own consolidation stress or by the major principal stress (σ1). It is only possible to compare materials with each other by the same reference stress.
By measuring several yield loci at different consolidation stresses we obtain the flow function which describes the flow factor over a range.



Flow functions with associated flowability factors for three different materials. 
Automatically generated analysis of the flow function(s) according to the measurements.




The flow function describes the dependence of the unconfined compressive strength (σc) to the principal stress (σ1). This is needed to calculate the critical outlet diameter in a silo.  In simplified terms, the load on the bulk material bridge must be greater than the unconfined compressive strength so that the material can flow.


Excerpt from the automatic solo calculation:



Berechnung des kritischen Auslaufdurchmesser am Silotrichter

flow function σc(σ) = FL(σ) = 5.1 deg * σ + 401 Pa
bmin = 0.15 m  
hmin = 1.61 m  
outlet > critical bridge = TRUE


Measurements and evaluations of physical properties of powders and bulk solids yield locus flow function effective angele of friction bridging in a silo