Bazant's crush-down/crush-up is hilarious.
In an idealized collision, as described in Bazant Zhou, not only is it a non-physical assumption, you can use
tested theory to
quantitatively show how preposterous such an assumption is.
I had hoped to do so, myself, by now, but haven't even begun. You can search JREF and physorg for my posts, re the work of Ari-Gur, et. al., and some others. If you or somebody you know can do numerical work on a computer, you should be able to do this. Also, at one point, anyway, you could get code (or perhaps it was pseudo-code) from a university in Israel (Technion something or other, I think), associated with Ari-Gur. In other words, you may not even have to code anything, just provide proper inputs and interpret the output. (Hopefully, with pretty graphs.
)
Well, actually, I think the right way to do this must involve modification of the algorithms such that horizontal movement is constrained every floor height. (Refinements would attempt further constraining, to reflect spandrels.) You should also confer with the experts to see what sorts of scaling corrections should be applied. To get a sense of this, see the Calladine and English paper, which I've also posted on.
At the end of the day, though, once a collapse gets going, nobody believes perfect, axial collisions of column segments will occur, so the more interesting problems of 1) whether a collapse can begin with enough 'oomph' to become unstoppable*, remains and 2) what a global collapse would actually look like, including computation of what pulverized building content plumes would look like.
The main benefit of
quantitatively debunking Bazant Zhou is to attract serious interest in individuals capable of doing serious work on progressive collapse, to focus on the WTC cases. Even should this come to pass, though, this is not an easy problem, and I doubt there's really convincing evidence for any theory, at least in the initial stages of collapse, applied to a real-life skyscraper - even if it were only 20 stories.
You couldn't practically test your theory, that's for sure! You'd have to test on computer, and I don't think software and hardware limitations permit convincing tests.
There was a recent structures conference which has some presentations on progressive collapse, that I posted on. It's a fair guess that contacting them will be far more informative than posting here. Why don't you contact them, and get their input? Be sure to ask them how they test their theories. (I'm not a fan of theories that you can't test.)
If you do talk to any experts, please ask them what sort of a 'relaxation time' is a good estimate. A column which is too far off plumb will support 0 weight, so we can presume that impacts have, as an upper bound, on average approximately h * (1 - cos(15 degrees))/ h ~ 3.4% of the collapse height to load the base. The rest of the time, the base can unload.
What happens when unloading? I really don't know. Some of the strain energy not associated with the remaining static load will simply go into vertical oscillations. I expect that this will limit how much additional dynamic load can be absorbed by the base during the next storey's impact. What % gets lost through the ground, what % gets lost in internal states of excitation of the various floors, and what % gets lost as heat within the columns? I don't know, but that's something that an earthquake engineers should be able to help you estimate.
The more strain energy that can be dissipated from the columns, between storey impacts, the slower the collapse should be. A sufficiently precise analysis might thus be useful for discriminating between an assisted collapse (CD) and an unassisted collapse, without having to model fluid flows and pulverization. I'm thinking mostly of the early stages of collapse. In later stage, I expect you would need less collapse 'assistance' (assuming that's your goal) in the first place, and secondly approximations by Bazant, et.al., (in subsequent papers) such as "energy dissipated in the crushing front" are probably good approximations.
* IMO, this has to be the case once all column lines get disconnected at the same general height. The columns cross-sectional area in WTC scenarios in only ~ 2%, so columns will hit floors (not columns), floors lose that contest (ouch), etc.... A column with punctured floor elements will not topple just because it's 'traumatized' (I make fun of this notion by saying that I don't believe in 'boo' collapses), neither will the floors provide enough resistance to prevent being punctured and the collapse from accelerating.
