I'm going to take a more exploratory approach to bound certain aspects of the problem, rather than be assertive with disputable figures. The computations use unit masses for each story, therefore all energy values on graph axes are scaled down by the appropriate order of magnitude. The first case examines a classic WTC1 split at the 96th floor, rigid block above. No support fail energy is supplied in the first two cases, they are momentum-only to show how much energy is dissipated solely through the action of inelastic collision. The first case matches Greening's momentum-only y(t),v(t) result for WTC1.
By assuming inelastic collision between slabs (a very defensible assumption), the model requires
a certain amount of KE to be dissipated at each collision according to conservation of momentum. Dissipated does not mean disappeared. This energy is precisely what goes into deformation and pulverization of material. Since the components presenting the vast majority of collision surface area are the floors and office contents, it is not only reasonable but mandatory that the majority of energy dissipated through inelastic accretion be in those items.
Empirically it can be seen that the bulk of the perimeter and a substantial amount of core did not participate in the interior collapse and only a small percentage of columns were significantly buckled. This corroborates the prior observation that the bulk of energy dissipated in collision went into crushing the interior, because it had to go somewhere and it didn't
go into deformation of columns and couldn't go into descent speed. There are other independent sinks like gas expulsion, of course, but let's look at what's mandated by the assumption of inelastic collision, mindful that other incidental sinks will reduce the figures somewhat. (these can be revisited later)Kinetic energy dissipation at each impact story due to inelastic collision only
12 story block
Because a 12 story rigid block is not a realistic scenario, this is a single story upper block (no stories 98 - 110) plotted alongside the prior:
12 and 1 story block
The one story upper block case has a lower potential energy change over collapse because it has 11 fewer stories mass up top, so a direct comparison of dissipated kinetic energy will naturally be lower for the structure with smaller mass. Neither, incidentally, do those floors need to be crushed since they don't exist!
Both examples show how the energy dissipated in inelastic collision rises linearly with position
after a short time. Position, though, is proportional to a power of time (approximately squared). This is an increasingly brutal pounding on essentially similar floors going all the way down.
In a physics engine simulation which allows crush up and down, a rigid top versus crushing top with all else equal shows the two cases have nearly identical kinetic energies over time, now showing the nearly parabolic increase of KE as a function of time:
This indicates the overall energy distribution over time differs little with respect to rigidity of the upper block. The physics engine simulation has been specifically validated against the test case shown above. The prior examples then should serve as a reasonably good indicators of the energy distribution over time regardless of rigidity, and have already shown similar energy dissipation in collision with a miniscule upper block of one story. Notice the immediate loss of much kinetic energy at the moment of final compaction. It's dissipated quickly by slamming into the ground - the seismic signal - and it is tremendous.
How does this dissipated energy compare to other energies involved?
From the physics engine, a comparison of dissipated energies for multiples of support fail energy show dominant loss is to inelastic collision:
Except for the arresting case, the vertical upswings at the end are the counterpart to the KE curve vertical downswings when at full compaction. Conservation of energy requires this accumulation to go into the partitions of bouncing, dispersal, pulverization, heat, sound.
Finally, while there is ample reasoning to show pulverization in air is plausible, I'd like to point out that the assumption that it occurred in large quanities early on is just that - an assumption. Dust clouds are observed immediately but the actual concrete contribution in air is not known. Wallboard was present in abundance, it pulverizes easily. Large amounts of smoke was expelled quickly at the same time. The final distribution of dust is the result of the totality of collapse. It's apparent from the mechanics of this model that KE can become very large. It is most reasonable to believe that a significant amount of pulverization and dispersal resulted from the end of collapse.