Computational Modelling

Granular Flow - Application

Influence of shape on the extraction of a post

Contact personnel:  P.W. Cleary

In this example, a series of two-dimensional DEM simulations are presented of the motion of the ground surrounding a post during extraction. The influence of the shape of the ground particles and of the post is examined. The post, 750 mm high and 200 mm thick and buried to a depth of 650 mm, is withdrawn vertically from the ground at 0.25 m/s. The earth surrounding the post is modelled by DEM particles of diameter 5 to 20 mm. A friction coefficient of 0.75 and a coefficient of restitution 0.3 was used for these simulations.

In the following series, the influence of both particle shape and the smoothness of the post surface are demonstrated.

Circular particles surrounding a smooth post

The first animation below demonstrates that the microstructure of circular particles (even with a reasonable size distribution) has little strength, and allows particles to flow freely into the void formed by the retreating post. A thin layer of particles on either side of the post moves upwards with the post. This is clearly shown by the deformation of the colour strata.

Circular particles surrounding a rough post

Particles are able slide along a smooth post relatively easily, inhibited only by tangential friction. The second animation shows the effect of adding a slight roughness - in the form of small 5 mm diameter semi-circular protrusions - to the surface of the post. It can be observed that many particles are trapped by the protrusions, further inhibiting the relative motion of particles in contact with the post. The locked microstructure of material above and to the sides of these trapped particles must fracture, resulting in a wider layer of particles on each side of the post moving upward as the post is withdrawn. This behaviour is seen to enhance the inter-mixing of the colour strata.

Non-circular particles surrounding a smooth post

The influence of non-circularity of the particles has been examined by replacing the circular particles by particles of super-quadrics form:

For the present calculations, a range of values was considered for the particle aspect ratio (0.7 < b/a < 1.0) and "blockiness" (3 < n,m < 8).

The third animation shows that non-circular ground particles have a greater tendancy to resist shearing by forming aggregates. This results in a wider layer of particles on each side of the post moving upward compared with circular particles. The inter-mixing of the colour strata is therefore observed to be greater than for circular particles surrounding a smooth post.

Non-circular particles surrounding a rough post

Finally, the fourth animation shows the effect of adding both a slight roughness to the post surface, and non-circular particles. It can be observed that these effects are additive, resulting in a very large layer of particles on each side of the post moving upward as the post is withdrawn. The inter-mixing of the colour strata is observed to be greatest for this case.

Predicted force required for extraction

For each of the above-described cases, the force required to extract the post at a speed of 0.25 m/s has been calculated from the DEM simulations. The temporal variation of the force (exponentially smoothed) calculated for each of the four cases is plotted below:

circular particles / smooth post	circular particles / rough post
non-circular particles / smooth post	non-circular particles / rough post

Initially, the resistance on extraction of the post is very high as it attempts to lift all the surrounding particles. As the particle microstructure fails, there is a strong decrease in resistance. This occurs on a very fast timescale for a smooth post, and is therefore not visible on the above plots. For a rough post, the phenomena is much slower, and results in the sharp decrease in force observed in the corresponding above plots. On a longer timescale, the resistance decreases linearly with the amount of material being lifted, which in turn is linearly proportional to the depth of the post in the ground. This dependence is modified by the efficiency of force transmission from the post through the particle microstructure. Since non-circular particles are very efficient at transmitting force, little modification of the underlying linear dependence is observed. Circular particle microstructures, however, fail by rolling; this strongly inhibits their ability to transmit force to their neighbours, and results in the noticeable alteration of the linear dependence observed in the above plots.

The average force per unit time required to extract the post is shown in the following plot:

The calculated forces indicate that while both the non-circularity of the particles and the roughness of the post cause an increase in the required extraction force, the latter appears to have the greater influence.

It is interesting to note that while circular particles surrounding a rough post are observed to be slightly more disturbed further from the post than non-circular particles surrounding a smooth post, they provide less resistance to extraction. This reflects the small amount of force required to cause the circular particle microstructure to fail.

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last updated July 18, 2007 05:23 PM

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