Page 46 - The Combined Finite-Discrete Element Method

THE COMBINED FINITE-DISCRETE ELEMENT METHOD 29

potential energy of a building is transformed into kinetic energy, which in turn is trans-
formed into strain energy at impact. Strain energy results in the material limits of structural
elements being exceeded, and therefore the material is broken, bent or crushed, resulting
in progressive collapse, which eventually transforms the building into a pile of rubble.
Similar situations have in the past occurred with a derailed train impacting against
the bridge above the rail, resulting in the failure and collapse of the bridge (accident at
Eschede in Germany, June 1998). Again, at the impact, the kinetic energy of the train
together with the potential energy of the bridge is transferred into strain energy, resulting
in the failure of the structural elements of the bridge and leading to the final collapse
of the bridge. Yet another case of structural collapse can be seen in a situation where a
house has collapsed due to the failure of ground under it (Walsall, West Midlands, May
1999). Again, what was a continuous structure has been transformed into a pile of separate
particles. In this process kinetic energy, inertia forces and interaction between individual
structural elements or falling and failing fragments has played an important role.
In the past, a common cause of structural collapse has been gas explosion. In mod-
ern days, blast loads are also becoming a frequent hazard due to wars, civil unrest
and terrorism.
The common feature of all the above listed problems is a transition from continua to
discontinua, i.e. failure, fracture, fragmentation and collapse. In the process, a transition
from a static system to a dynamic system occurs. Subsequent contact-impact and energy
dissipation mechanisms lead to the final state of rest, which often is just a pile of rubble.
With predictive modelling capacity enabling simulations of various collapse scenarios,
perhaps better design, structural, protective or procedural measures could be taken to at
least reduce the risk to human life. The practical importance of knowing how a structure
is going to collapse in the demolition process, or how a structure is going to behave under
hazardous loads (for instance, will the evacuation routes be blocked), or what will be the
size distribution of blasted or crushed material, cannot be overestimated.

1.6 THE COMBINED FINITE-DISCRETE ELEMENT METHOD

The only numerical tool currently available to a scientist or engineer that can properly
take systems comprising millions of deformable discrete elements that simultaneously
fracture and fragment is the combined finite-discrete element method. The combined
finite-discrete element method merges finite element tools and techniques with discrete
element algorithms. Finite element-based analysis of continua is merged with discrete
element-based transient dynamics, contact detection and contact interaction solutions.
Thus, transient dynamic analysis of systems comprising a large number (from a few
thousands to more than a million) of deformable bodies which interact with each other
and in this process can break, fracture or fragment, becomes possible.
A typical combined finite-discrete element simulation is shown in Figure 1.44. The
right-hand support of a simply supported beam is suddenly released. Thus, the beam rotates
about the left-hand support and breaks due to inertia forces, as shown in Figure 1.45.
Inertia forces play an important role in the failure of the beam. The beam breaks at the
point of maximum bending moment due to the combined self-weight and inertia forces.
The left-hand part of the beam subsequently breaks away from the right-hand support,
resulting in a free fall of both parts of the beam as shown in Figure 1.45.