Page 275 - The Combined Finite-Discrete Element Method

258 FLUID COUPLING

The models for gas pressure evaluation vary from a fixed, user-supplied pressure-time
diagram for the pressure of detonation gas, which is then applied to the user-defined
surfaces of the solid (for instance, the borehole walls) to the full scale gas flow models
through the fracturing solid. It is noted that these models are not concerned with the
detonation process as such. They concentrate on the expansion of the detonation gas and
its penetration into cracks.
The problem with user predefined gas pressure is that the resulting fracture and frag-
mentation process (although modelled by a computer using complex algorithms and large
CPU times) is in essence supplied by the user, in a sense that the extent of fracture and
fragmentation depends upon the magnitude and duration of the gas pressure applied to
the borehole walls.
Full scale gas flow models can be classified as follows:
• Models based on tracing gas flow through individual cracks. This is the most real-
istic approach. However, it requires robust crack detection algorithms, which also
incorporate procedures for the detection of connectivity between individual cracks and
voids. These procedures have proven much more difficult than the detection of con-
tacts between solid particles. This is because the geometry of solid particles is readily
available, while the geometry of voids is only implicitly defined and has to be deduced
from the geometry of solid particles.
• Models based on porous media-based idealisation of fractured solid. The fracturing
solid is approximated by a porous medium requiring estimation of the porosity. The
errors arising from this process and the extent to which the final results are influenced
by transient geometry of the fracturing solid are not easy to estimate. Full scale gas
flow models are also coupled with considerable algorithmic complexities and extensive
CPU requirements.
In real problems, the detonation gas pressure drops rapidly due to a relatively small
change in volume, and most of the work done by the gas is done while the pressure is
high. Only a small portion of energy remains at lower pressures of detonation gas. Thus,
although it is an experimental fact that the detonation gas penetrates cracks and voids,
the extent of gas flow through the larger section of the solid domain remains an open
question. For instance, in some blasting operations, small explosive charges in closely
spaced boreholes are used to induce only partial breaking of the rock without significant
fracture and fragmentation. In these, the gas flow effects are clearly small. On the other
hand, in operations of explosive induced loosening of soil, a significant gas flow may
be present.
In short, successful modelling of detonation gas induced fracture and fragmentation may
not always require a complex, full scale gas flow model. However, proper evaluation of
gas pressure with gas expansion should include the preservation of energy balance. This is
recognised in a set of models that take into account the equation of state of the detonation
gas and spatial distribution of gas pressure due to gas flow without considering a full
scale model of gas flow. In these models, detonation gas penetration into the cracks and
the spatial gradient of detonation gas pressure are taken into account through a set of
problem parameters such as gas penetration depth. In this chapter, such a detonation gas
expansion model, together with a model for spatial pressure distribution in the context of
the combined finite-discrete element modelling of detonation gas induced fragmentation,
is described in detail.