Over at the911forum,
I revived an older thread, which started out with someone's misbegotten hypothesis on something, which in turn caused OneWhiteEye to revisit some other thread where he (?) had derived from theoretical considerations of conversation of momentum (and, implicitly, energy) what the collapse acceleration will be if all collisions are inelastic, and asuming that no energy is dissipated beyond the work done in those inelastic collisions.
The result is, analytically, that acceleration will in the long run converge on 1/3 of g. It will start out faster if the initial mass ("top block") is larger, and then take somewhat longer to get near 1/3 g, but the difference is not large. It turns out that it doesn't matter how high the floors are or what their individual mass is.
I get approximately the same result through discrete iteration with a spreadsheet in which I compute each individual collision of "top block" with next floor below from the 95th (or 80th) down to the ground: Acceleration starts somewhat below 1g and above 2/3 g, and drops to not much above 1/3 g towards the end.
Acceleration of 1/3 of g means directly that only 1/3 of the potential energy is turned and sustained as kinetic energy, and the rest is dissipated in the inelastic collisions, mostly as deformation and fracture, and to a small extent as heat.
We are currently thinking hard about whether these close to 2/3 of available energy that gets converted into "destruction" already takes care of / includes all, most, some or none of the destruction of the structural supports that necessarily must be destroyed for collapse to continue
*). My
intuition says that
most of the energy required to break structural connections is already accounted for in the loss of kinetic energy due to inelastic collision, OWE seems to think otherwise, but I don't know how to model this, and he isn't there yet.
Any energy expended on top of (or temporally after) the inelastic collision to break connections would decrease the collapse acceleration. Again, my hunch is that this is not very significant.
The same is true for all energy (and momentum) that's transferred down the columns and into the ground and thus lost to planet earth. Here, too, my hunch is that this is not very significant.
Now this model that we are talking about seems too simple and unrealistic, but I think it does get us pretty close to true values. The reason is that I think that in the chaos of the collapse front, even though everything is not going smoot and uniform and all collisions have elastic components, it eventually all adds up to being insignificantly different from a total inelastic scenario: As some have said, the perimeter mesh helps to keep most of the material confined to the footprint so there isn't a lot of mass shedding; components that get kicked down elastically undergo further collisions with other floors to give them more chances to dissipate energy and get caught up with the bulk of the collapse front.
Anyway, expect any top-down collapse starting with a sufficient top mass to start above 2/3 g, drop quickly (after a few floors) below 1/2 g and soon converge near 1/3 g.
*) We don't show it in that thread, but we both know (from Bazant's limiting cases) that this amount of energy easily suffices to break enough connections (say: all long truss to column connections). Iirc, Bazant has shown that if the top 15 floors reach a velocity that is equivalent to a free-fall drop of 0.5 meters, then their kinetic energy will overwhelm the next floor worth of connections, and from then on the structure is doomed. (Notice that this scenario does not need to assume any actual free fall at collapse initiation!)
BUT the "initiation" was a progressing cascade. Where does that process produce a drop?? However if I press that line I will get dumped on from both sides - Bazantophiles and Bazantophobes. 
"They" are allowed to mix factors from two different scenarios. You and I are not allowed. So deal with them separately. 
