A bulk material is composed of many individual particles which, for bulk material characterization, must be considered as a continuum. Many influencing factors exist, such as moisture, temperature, particle size, particle shape, surface structure or even mechanical properties such as elastic, viscoelastic, plastic or brittle behavior. The chemical composition, gravitational force, interparticle and electrostatic Van-Der-Waals forces also influence the physical behavior of the bulk material.
The angle of repose corresponds to the hillside angle or the slope angele of an embankment. The angle of repose is calculated from the resulting height to the diameter of the bulk cone. It is needed to determine the volume or space requirement for heap storage or in the top of a silo. The angle of repose is often used as an indicator for the flowability of unconsolidated powder. Larger angle of repose indicate a poorer flow behavior. However, the angle of repose is not suitable for physical calculations of the flow behavior. Only in the case of cohesionless bulk solids, the angle of repose is equal to the internal and the effective friction angle of the shear test.
| Flow property | Angle of reqose |
|---|---|
| Excellent | 25 - 30 |
| Good | 31 - 35 |
| Fair (aid not needed) | 36 - 40 |
| Passable (may hang up) | 41 - 45 |
| Poor (must agitate, vibrate) | 46 - 55 |
| Very poor | 56 - 65 |
| Extremely poor | > 66 |
The shear test will simulate the circumstances in which the powder typically behaves within handling equipment. Qualitative physical properties are obtained, which are used for further calculations. For the design of wowder storage and conveying equipments the data optained by shear test are required. The standard measurement of the yield locus is taken from classic soil mechanics. Shear cell testing involves applying force to a powder sample at shearing. This data can be used directly in design methods for hoppers and bins. The flowability of powders depends on the consolidation stress. In the shear test the yield loci are determined for various normal stresses consolidated with the same pre-shear load. That means that each yield locus represents the shear resistance for the same consolidation conditions.
The powder changes packaging density depending on load and movement and therefore has a yield point dependent on the tension condition. The tension condition describes the yield point where the powder starts to move on the gliding area under influence of the shear stress (Τ). This is when it starts to flow.
By transferring the tensions into a normal loads(σ) – shear stress(τ) – diagram, a geometrical representation of the steady-state conditions in an arbitrary cutting planes in Mohr’s tension circle will be generated. Each (σ,τ) combination on the resulting line leads to the flowing of the powder. Tension conditions below the lines are stable, but above are physically not possible.
Mohr’s circle describes all stresses at a point in the powder mass. The minor an major principal stress are on the σ-axes. The midpoint of Mohr’s circle represents the average stress between major and minor principal stress. The stresses can only grow until the shear stress reaches the value where plastic deformation occurs. Stresses above this value are not possible.
The major principal stress causes consolidation to the corresponding density. Therefore, it is also the base parameter for other functions.
If another Mohr’s circle with the smallest principal stress of zero is constructed, which will touch the yield locus, then the compressive strength (σd) of the bulk material will result at the major principal stress. The ratio of compressive strength to the largest principal stress is used to classify the flowability of a bulk material. Compressive strength is also important for determining bridging in a silo.
These measurements and evaluation of the same provide a basic physical parameter that can be used to calculate other parameters, such as:
| file name | YL-250-a.yl |  |
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| date | 05 May 2016 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| material | validation powder | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| client | SHEAR-TEST.com | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| operator | MB | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| humidity | 12.47 % Moisture | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| note | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| device | ST200AUTO | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| shear cell | RSL ST30.cel | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Δσ | + 0 Pa | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ΔΤ | + 0 Pa | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| use prorating | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ρb0 = | 0.479 | g/cm³ | bulk density |
| ρbr = | 0.7382 | g/cm³ | density σr |
| YIELD LOCUS EVALUATION RESULTS | |||
| φe = | 33.5 | deg | effective angle of friction ≙ Φi at EN1991-4 ⇒ K |
| φi = | 29.9 | deg | angle of internal friction ≙ Φc at EN1991-4 [DEM := static friction] |
| Τc = | 1174 | Pa | cohesion [DEM := cohesion] |
| σ1 = | 49962 | Pa | major principal stress |
| σ2 = | 14452 | Pa | minor principal stress |
| σc = | 4665 | Pa | unconfined compressive strength |
| σt = | -1182 | Pa | tensile strength |
| ... | |||
| FL = | 10.71 | flowability factor = ffc = σ1 / σc | |
| R = | 0.999 | coefficient of correlation | |
| ... | |||
It is important that the location of the flow site is dependent of the packing density of the sample. For each initial density, there is a corresponding flow location. Because the exact load in the application is not known, several loci with different reference stresses(σr) are measured in order to interpolate the results. The effective friction angle(φe) is a function which is tangent to the large Mohr’s circles. Using the function of the effective friction angle, the horizontal load ratio (λ) can be calculated for any stress state between the measured flow locations.
Three yield loci (blue) of the same material at different reference stresses (σr)
showing the effective flow function (red)
Principal stresses from the effective angle of friction σ1(φe), σ2(φe)
Unconfined compressive strength from the flow function σd(σ1)
