Discrete element analysis of granular materials

Discrete Element Analysis of Granular Materials
During oil and gas production, several years after drilling a borehole, sand
particles and small sandstone particles start to break away from the borehole
surface. These particles can damage the transport pipes and other equipment in a
short period of time. By simulating this borehole behaviour with the thick-walled
cylinder test, four phenomena were found which cannot be explained by
conventional continuum mechanics:
1. Despite the compressive stress, failure occurs on the micro level due to
tension cracks.
2. These cracks are not diagonal to, but parallel to, the borehole surface.
3. These cracks cause two diametrically opposite breakouts.
4. The functional failure of the borehole starts at a higher radial pressure than
predicted.
In 1979, Cundall developed a computer model, based on the basic elements of
granular materials, i.e. the grains themselves and their interactions, to describe
the behaviour of these materials. Lindhout tried, in 1992, to use this model to
describe the cylinder test. Due to compaction problems, stability problems and
the large computational time, this could not be achieved. Therefore a new model
was developed by the author, which does not use the equations of motion, but the
equations of equilibrium, to calculate the new grain positions. This model can be
used both for non-cohesive grains (sand) and for cohesive grains (sandstone).
The results can generally be described by an advanced Mohr-Coulomb model.
However, there are a few exceptions.
Firstly, during loading of a granular structure, many contacts between the grains
will collapse, not due to shear deformation as Coulomb suggests, but due to
tension failure. Secondly, these micro cracks always occur in the direction of the
major principal stress, which might be another direction than the observed failure
surface. In this way, the axial micro cracks form a diagonal failure surface during
a biaxial test, but the axial micro cracks in a cylinder test may form a failure
surface parallel to the borehole surface.
During the formation of natural sandstone, the difference between the horizontal
and vertical stress causes anisotropy in the strength behaviour of this material.
This or other anisotropies may explain the diametrically opposite breakouts.
The conclusion that a borehole fails at a higher radial pressure than predicted,
originates from the definition difference between local failure and functional
failure and the large rest capacity of a thick-walled cylinder.