The 9/11 Forum

Introduction by Reviewer: Bazant and Verdure is one of the easiest Bazant papers to review because once the "crush down, then crush up" premise is no longer accepted, the resulting equations cease to have any real physical meaning.

It is a hard paper to read if you are not comfortable with formulations of equations of motion.

Structural engineers do not study the mechanics of falling buildings. This type of study would probably be more familiar to a person with a strong background in mathematics and physics. My own observations suggest that the many engineers involved in the CD debate tend to over-rate their abilities to understand complex falling and colliding bodies. Much of the confusion about a paper like Bazant and Verdure is that some engineers seem to imagine they can understand it and vocally voice their incorrect opinions about it.

This paper shows that a lot of bad information does pass a "peer review" process without the simplest reality checks.

(BV)Mechanics of Progressive Collapse: Learning from World
Trade Center and Building Demolitions

Zdenek P. Bažant and Mathieu Verdure

http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/466.pdf




The paper derives a simple 1-D collapse propagation model. The propagation model starts with the collapse front moving downward with an initial velocity (after a 12 ft freefall). Collapse initiation and the initial column buckling sequence are not addressed.

Dr Bazant gives his opinion of what happened during collapse initiation in this section:


"Review of Causes of WTC Collapse

Although the structural damage inflicted by aircraft was severe, it
was only local. Without stripping of a significant portion of the
steel insulation during impact, the subsequent fire would likely
not have led to overall collapse (Bažant and Zhou 2002a; NIST
2005). As generally accepted by the community of specialists in
structural mechanics and structural engineering (though not by a
few outsiders claiming a conspiracy with planted explosives), the
failure scenario was as follows:

1. About 60% of the 60 columns of the impacted face of framed
tube (and about 13% of the total of 287 columns) were severed,
and many more were significantly deflected. This
caused stress redistribution, which significantly increased the
load of some columns, attaining or nearing the load capacity
for some of them."

The damaged columns were on or near the north face but the building failed southward. in 1 dimension one need only consider simple opposing forces when finding equilibrium conditions. In a 3 dimensional world like ours static equilibrium requires

sum of all F =0, F is force, bold is vector quantity
sum of all T =0, T is torque

if we consider an east-west axis on the south face at about floor 98, we can see that the loss of north face columns would create loss of torque about the axis, which must be resupplied for the building not to rotate.

Load redistribution from airplane damage would not occur evenly among all surviving columns. A failure of north face columns would cause load redistribution among surviving columns on the north side of the building more than the south side.

This means the extra load must be transferred to surviving columns on the north side of the building significantly more than to south side columns to maintain equilibrium.

Notice that we see no sagging IB or any significant deformation on the north side as a result of this load redistribution. Inward bowing happened only on the opposite side of the impact damage. The building did not fail towards the airplane hole, but in the opposite direction.

He continues,

2. "Because a significant amount of steel insulation was stripped,
many structural steel members heated up to 600°C, as confirmed
by annealing studies of steel debris (NIST 2005) (the
structural steel used loses about 20% of its yield strength
already at 300°C, and about 85% at 600°C (NIST 2005);
and exhibits significant viscoplasticity, or creep, above
450°C (e.g., Cottrell 1964, p. 299), especially in the columns
overstressed due to load redistribution; the press reports right
after September 11, 2001 indicating temperature in excess of
800°C, turned out to be groundless, but Bažant and Zhou’s
analysis did not depend on that).

3. Differential thermal expansion, combined with heat-induced
viscoplastic deformation, caused the floor trusses to sag. The
catenary action of the sagging trusses pulled many perimeter
columns inward (by about 1 m, NIST 2005). The bowing of
these columns served as a huge imperfection inducing multistory
out-of-plane buckling of framed tube wall. The lateral
deflections of some columns due to aircraft impact, the differential
thermal expansion, and overstress due to load redistribution
also diminished buckling strength."

The bold letters highlight the claim by both the NIST and Dr Bazant that sagging long trusses destabilized the perimeter which caused collapse initiation.

4." The combination of seven effects—(1) Overstress of some
columns due to initial load redistribution; (2) overheating
due to loss of steel insulation; (3) drastic lowering of yield
limit and creep threshold by heat; (4) lateral deflections of
many columns due to thermal strains and sagging floor
trusses; (5) weakened lateral support due to reduced in-plane
stiffness of sagging floors; (6) multistory bowing of some
columns (for which the critical load is an order of magnitude
less than it is for one-story buckling); and (7) local plastic
buckling of heated column webs—finally led to buckling of
columns (Fig. 1(b)). As a result, the upper part of the tower
fell, with little resistance, through at least one floor height,
impacting the lower part of the tower. This triggered progressive
collapse because the kinetic energy of the falling upper
part exceeded (by an order of magnitude) the energy that
could be absorbed by limited plastic deformations and fracturing
in the lower part of the tower."




Bold lettering is mine. It represents Dr Bazant's unsubstantiated opinion of what he thinks happened during collapse initiation. It is presented as fact but it is just his opinion.

Appendix C of the OOS collapse propagation study provides a large body of detailed images of the as-is condition all regions of the rubble after 9-11-01 and during various stages of the clean-up. Almost no buckled core or perimeter columns can be found. The NIST claims to have recovered only 2 core columns from the collapse initiation regions from WTC1 and 2. No one has ever provided visual evidence of more than a few core columns that show signs of creep-buckling.


"In broad terms, this scenario was proposed by Bažant (2001),
and Bažant and Zhou (2002a,b) on the basis of simplified analysis
relying solely on energy considerations. Up to the moment of
collapse trigger, the foregoing scenario was identified by meticulous,
exhaustive, and very realistic computer simulations of
unprecedented detail, conducted by S. Shyam Sunder’s team at
NIST. The subsequent progressive collapse was not simulated at
NIST because its inevitability, once triggered by impact after column
buckling, had already been proven by Bažant and Zhou’s
(2002a) comparison of kinetic energy to energy absorption capability.
The elastically calculated stresses caused by impact of the
upper part of tower onto the lower part were found to be 31 times
greater than the design stresses"

In bold Dr Bazant claims that "meticulous, exhaustive, and very realistic computer simulations" done by the NIST have confirmed his initial opinion. This is untrue as there are serious contradictions with the NIST attributing inward bowing on the WTC1 south face to sagging floors. The floors would have to sag about 9 ft over a period of 15 minutes. The inward bowing occurred on the opposite face as the airplane strike. It appeared in a region where fire was not witnessed 10 minutes previously. The IB formed in an area where large unexplained fire ejections were witnessed minutes earlier, as WTC2 collapsed.
This is the official story in a nutshell: Dr Bazant guessed, "meticulous, exhaustive, and very realistic computer simulations" done by the NIST confirmed Bazant's guess and collapse initiation of WTC1 is considered solved. The official collapse initiation sequence requires 60 ft floor trusses to sag up to 9 ft in an area where fire was not seen coming from the windows 10-15 minutes earlier. There are many contradictions in a collapse initiation scenario that depends on substantial floor sagging and it seems absurd to call the NIST's work on collapse initiation "meticulous, exhaustive, and very realistic".

These "meticulous, exhaustive, and very realistic computer simulations" done by the NIST on the causes of early deformation, inward bowing and south wall destabilization is the strongest proof which Dr Bazant and the NIST offer that confirm his description of collapse initiation is correct.

"The kinetic energy of the top part of the tower impacting the
floor below was found to be about 8.4( larger than the plastic
energy absorption capability of the underlying story, and considerably
higher than that if fracturing were taken into account
(Bažant and Zhou 2002a)). This fact, along with the fact that
during the progressive collapse of underlying stories (Figs. 1(d)
and 2) the loss of gravitational potential per story is much greater
than the energy dissipated per story, was sufficient for Bažant and
Zhou (2002a) to conclude, purely on energy grounds, that the
tower was doomed once the top part of the tower dropped through
the height of one story (or even 0.5 m). It was also observed that
this conclusion made any calculations of the dynamics of progressive
collapse after the first single-story drop of upper part superfluous."

.............................................



"Therefore, no further analysis has been necessary to prove that
the WTC towers had to fall the way they did, due to gravity alone.
However, a theory describing the progressive collapse dynamics
beyond the initial trigger, with the WTC as a paradigm, could
nevertheless be very useful for other purposes, especially for
learning from demolitions. It could also help to clear up misunderstanding
(and thus to dispel the myth of planted explosives).
Its formulation is the main objective of what follows."

In the case of CD, planted explosives would be the cause of the "initial trigger". Collapse propagation may be similar for both CD and natural collapse. How can a collapse propagation model be used to "dispel the myth of planted explosives" if propagation is about the same in both cases?

The mass of columns is assumed to be lumped, half and half,
into the mass of the upper and lower floors. Let u denote the
vertical displacement of the top floor relative to the floor below
(Figs. 3 and 4), and F(u) the corresponding vertical load that all
the columns of the floor transmit. To analyze progressive collapse,
the complete load-displacement diagram F(u) must be
known (Figs. 3 and 4 top left). It begins by elastic shortening and,
after the peak load F0, curve F(u) steeply declines with u due to
plastic buckling, combined with fracturing (for columns heated
above approximately 450°C, the buckling is viscoplastic). For
single column buckling, the inelastic deformation localizes into
three plastic (or softening) hinges (Sec. 8.6 in Bažant and Cedolin
2003; see Figs. 2b,c and 5b in Bažant and Zhou 2002a). For
multistory buckling, the load-deflection diagram has a similar
shape but the ordinates can be reduced by an order of magnitude;
in that case, the framed tube wall is likely to buckle as a plate,
which requires four hinges to form on some columns lines and
three on others (see Fig. 2c of Bažant and Zhou). Such a buckling
mode is suggested by photographs of flying large fragments of the
framed-tube wall, which show rows of what looks like broken-off
plastic hinges.

For WTC1 collapse propagation is largely independent of column buckling. A column load displacement function has little to do with the actual frictional forces encountered during collapse propagation.

..........................

Some critics have been under the mistaken impression that
collapse cannot occur if (because of safety factors used in design)
the weight mg of the upper part is less than the load capacity F0
of the floor. This led them to postulate various strange ideas(such
as “fracture wave” and planted explosives). However, the criterion
in Eq. (5) makes it clear that this impression is erroneous. If
Eq. (5) is violated, there is (regardless of F0) no way to deny the
inevitability of progressive collapse driven only by gravity.

Equation 5 is violated whether or not collapse initiation was caused intentionally. It is violated for any tall office building because they are not designed to handle a good bounce. Collapse initiation is the key factor which distinguishes between CD and a natural collapse.

...............................

Thus it appears reasonable to make four simplifying hypotheses:

(1) The only displacements are
vertical and only the mean of vertical displacement over the
whole floor needs to be considered.

(2) Energy is dissipated only
at the crushing front (this implies that the blocks in Fig. 2 may be
treated as rigid, i.e., the deformations of the blocks away from the
crushing front may be neglected).

(3) The relation of resisting
normal force F (transmitted by all the columns of each floor) to
the relative displacement u between two adjacent floors obeys a
known load-displacement diagram (Fig.4), terminating with a
specified compaction ratio ( which must be adjusted to take into
account lateral shedding of a certain known fraction of rubble
outside the tower perimeter).

(4) The stories are so numerous, and
the collapse front traverses so many stories, that a continuum
smearing (i.e., homogenization) gives a sufficiently accurate overall
picture.


If it can be shown that these 4 simplifying hypotheses do not apply to WTC1, the resulting crush down (eq 12) and the crush up (eq 17) equations cannot be applied to WTC1.

The 4 physical observations in the OOS study clearly show that hypothesis 3 cannot be true because the collapse front must have bypassed core and perimeter columns. postulate 4 (homogeneity) cannot be applied to WTC1 because the collapse front seemed to go around the core. Column buckling has nothing to do with the real frictional force.

"First it needs to be decided whether crushed Zone B will
propagate down or up through the tower. The equation of motion
of Zone B requires that

F1 - F2 = s0g -
v·
10

where F1 and F2 are the normal forces (positive for compression)
acting on the top and bottom of the compacted Zone B (Fig. 2(c)).
This expression is positive if Zone B is falling slower than a free
fall, which is reasonable to expect and is confirmed by the solution
to be given. Therefore F2F1 always. So, neither upward,
nor two-sided simultaneous, propagation of crushing front is
possible."

This conclusion seems mathematically sound, but it cannot possibly be applied to WTC1 or any building literally. There is no such thing as "crush down, then crush up" for WTC1. Verinage style demolitions can also give Dr Bazant an excellent test of his "crush down, then crush up" hypothesis. Actual Verinage style demolitions exhibit a wide range of crush up, crush down ratios, relatively equal degrees of crush down, crush up not being uncommon.

"This is true, however, only for a deterministic theory. A front
propagating intermittently up and down would nevertheless
be found possible if Fc(z) were considered to be a random (autocorrelated
) field. In that case, short intervals (t may exist in
which the difference Fc1-Fc2 of random Fc values at the bottom
and top of crushed Block B would exceed the right-hand side
of Eq. (10). During those short intervals, crush-up would
occur instead of crush-down, more frequently for a larger coefficient
of variation. The greater the value of s0, the larger the
right-hand side of Eq. (10), and thus the smaller the chance of
crush-up. So, random crush-up intervals could be significant only
at the beginning of collapse, when s0 is still small enough. Stochastic
analysis, however, would make little difference overall
and is beyond the scope of this paper."

The OOS collapse propagation study shows the idea of limited crush up to be meaningless wrt WTC1. The "upper block" must have been completely rubblized early in the collapse or the entire core width couldn't have survived to at least the 60th floor.

.....................................


"The phase of downward propagation of the front will be called
the crush-down phase, or Phase I (Fig. 4(b)). After the lower
crushing front hits the ground, the upper crushing front of the
compacted zone can begin propagating into the falling upper part
of the tower (Fig. 4(d)). This will be called the crush-up phase, or
Phase II"

These phases cannot apply to WTC1, and they do not seem to apply to the majority of Verinage style demolitions.

.....................

"4. For the typical WTC characteristics, the collapse takes about
10.8 s (Fig. 6 top left), which is not much longer (precisely
only 17% longer) than the duration of free fall in vacuum
from the tower top to the ground, which is 9.21 s (the duration
of 10.8 s is within the range of Bažant and Zhou’s
(2002a) crude estimate). For all of the wide range of parameter
values considered in Fig. 6, the collapse takes less than
about double the free fall duration."

"Eqs. (12) and (17) show that Fc(z) can be evaluated from
precise monitoring of motion history z(t) and y(t), provided
that 
z and 
z are known. A millisecond accuracy for
z(t) or y(t) would be required. Such information can, in theory,
be extracted from a high-speed camera record of the collapse.
Approximate information could be extracted from a
regular video of collapse, but only for the first few seconds
of collapse because later all of the moving part of the WTC
towers became shrouded in a cloud of dust and smoke (the visible
lower edge of the cloud of dust and debris expelled from
the tower was surely not the collapse front but was moving
ahead of it, by some unknown distance)."

The 4 physical observations in the OOS propagation study show that eqs 12 and 17 cannot be applied to WTC1. We can see floor by floor ejections moving down the NW corner, west face and SW corner of WTC1. They certainly seem as if they are the collapse front. How can he know these ejection fronts are not the collapse front? The propagation velocities have already been measured down 2 different corners. This additional data must be considered by anyone proposing equations of motion describing WTC1 downward propagation of the collapse front.


"Although progressive collapse of
the modern massive piers and towers would be much harder to
initiate, a terrorist attack of sufficient magnitude might not be
inconceivable. Once a local damage causes a sufficient downward
displacement of the superior part of structure, collapse is unstoppable.
One question, for instance, is whether it might be within
the means of a terrorist to cause, e.g., the formation and slipping
of an inclined band of vertical splitting cracks typical of compression
fracture of concrete."

According to Dr Bazant's own logic, a massive tower can be subject to progressive collapse by a terrorist or a demolition team with the displacement of all core columns (at their connections) along only one floor of the tower. If a sufficient number core columns on only one floor are displaced at the connections and allowed to fall, the building is doomed.

................................

"3. Distinction must be made between crush-down and crush-up
phases, for which the crushing front of a moving block with
accreting mass propagates into the stationary stories below,
or into the moving stories above, respectively. This leads to a
second-order nonlinear differential equation for propagation
of the crushing front, which is different for the crush-down
phase and the subsequent crush-up phase.

4. The mode and duration of collapse of WTC towers are consistent
with the present model, but not much could be learned
because, after the first few seconds, the motion became obstructed
from view by a shroud of dust and smoke."

Collapse propagation data down the NW and SW corners is available. The mode of collapse is clearly not consistent with the 4 physical observations in the OOS propagation study.



Conclusions:

The crush down (eq 12) and crush up (eq 17) equations of motion for progressive collapse cannot be applied to WTC1. "Crush down, then crush up" has no application for WTC1 whatsoever. IT also cannot be observed in many Verinage style demolitions, where the top part of a building is intentionally dropped on the bottom part. While "crush up, then crush down" seems mathematically sound, we can find no consistent examples of buildings that behave that way. So why do some people, including Dr Bazant, believe in "crush down, then crush up"? The concept "crush down, then crush up" seems only the brain-child of a mathematical calculation in BV that the author and many of his readers began to take literally. Many people considered the process of "crush-down, then crush-up" to exist and be applicable to WTC1 without any supporting visual evidence. It is clearly not.

BV summary


1) Review of Causes of WTC Collapse

2) Motion of Crushing Columns of One Story
and Energy Dissipation

3) Deceleration and Acceleration during the Crushing
of One Story

4) Energy Criterion of Progressive Collapse Trigger

5) Options for Transition to Global Continuum Model

6) Energetically Equivalent Mean Crushing Force

7) One-Dimensional Continuum Model for Crushing
Front Propagation

8 ) Differential Equations of Progressive Collapse
or Demolition

9) Dimensionless Formulation

10) Numerical Solution and Parametric Study

11) What Can We Learn?—Proposal for Monitoring
Demolitions

12) Usefulness of Varying Demolition Mode

13) Complex Three-Dimensional Situations

14) Massive Structures

15) Alternative Formulations, Extensions, Ramifications

16) Implications and Conclusions

As far as I understand this theory...

1) the magnitude of the involved forces is much to high to arrest the upper part after a free fall of 12ft.

Can we agree? Yes. If the upper part fall 12ft straight down then BANG.

2) If there is a "pillow" of debris that is compressed between the upper part and the lower part then the force to the lower part is determined by the mass and velocity of the pillow + the mass and velocity of the upper part BUT the force to the upper part is determined by its own mass and the difference of the velocities of the pillow and the upper part

Can we agree? Let's say yes for the moment. It's some simplification.

3) For these conditions the force to the lower part always exceeds the force to the upper part. Therefore F1 > F2.

Can we agree? Yes.

4) According to 1) at least F1 is magnitudes higher than the elastic abilities of the lower part. Therefore the collapse must go on and on.

Can we agree? Yes.

Given that F2 will also exceed the elastic abilities of the upper part where do I find the remaining damage to the upper block in the equations?

If there was a remaining damage due to plastic deformation then the next impact has little work to do to rubble-ize the previously damaged floor of the upper block.

Would it be reasonable to say that...

damage to the upper block/damage to the lower block = F2/F1

...for a simplification?
(The stories are so numerous, and the collapse front traverses so many stories, that a continuum
smearing (i.e., homogenization) gives a sufficiently accurate overall picture.)

Given that some floors of the lower part are somehow stronger than the floors in the remaining upper part would it be reasonable to say that...

damage to the upper block/damage to the lower block =
(F2-strength of the upper floor)/(F1-strength of the lower floor)

Of course this is not a mathematical equation. It's just a way to describe a general correlation.
???????????????????????????????????????????????????????????????

Would it be possible that...
(F1-strength of the lower floor) <= (F2-strength of the upper floor)
...at least in some cases e.g. floor 75?

How many floors down would the upper block survive before it's totally rubble-ized? I bet the upper block is gone before reaching floor 75 WTC1.

Since the Bazant papers calculate the "most optimistic way" of a column on column impact...
Do they? What's about the pillow?
...the more realistic way is to calculate a displaced upper block. It's a pity but the necessary data for the horizontal core connections were never released.
And the much more realistic way is to forget about the compressed pillow since we know that the debris avalanches ran down inside the tube and most probably left nothing but pure steel behind.
???????????????????????????????????????????????????????????????

Imho Bazant essentially solve the problem rhetorically. He states, because F1>F2 it is allowed to set F2=0 at least for "phase 1". His conclusion...

Bazant wrote:Therefore F2<F1 always. So, neither upward, nor two-sided simultaneous, propagation of crushing front is possible.

By contrast to the crush-down phase, the compacted Zone B with accreting mass is not moving with Part C but is now stationary [Fig. 4(d)], and this makes a difference.

There are 2 ways to compress Zone B.
1) Zone B is compressed due to it's own mass and velocity impacting the lower stationary floor.
2) Zone B is compressed between Part A and Part C.

Let's say, Zone B and Part A are in free fall. To overcome the total energy necessary to crush the floor below Zone B must decelerate. The kinetic energy of Zone B must decrease for the same amount of energy that is needed to crush the floor below. The mass of Zone B grows to Zone B1. Now, the remaining kinetic energy can be used to accelerate the new mass while gravity is also acting on the entire mass of Zone B1. However, Part A is still in free fall.
The velocity change of Zone B (before it accelerates again) represents the amount of kinetic energy of the mass of Zone B (without the still stationary mass of one floor) necessary to crush one floor below. Now the grown mass has the same "delta v" in comparison to Part A and Part A must impact Zone B at about that difference of velocity (representing the necessary energy to crush one floor below). There is no way for the upper Part A to get through of it without damage.

In the end I would expect the mass of Zone B plus two additional floors start falling again at about the velocity of the upper part. Zone B2 has now to fall one floor down to crush the next floor while Part A needs to fall at least 2 floors.
The velocity grows with the time. v = gt
It is inevitable that Part A will impact Zone Bx again. When it happens then the velocity of Zone Bx always represents enough kinetic energy to crush at least one floor of Part A. In other words, in the reference frame of Zone B the upper block is now falling at that velocity onto Zone B.

The major difference in arguing this way is the way how to describe the impact. Usually (e.g. Dr. Greening) the masses of the floors are described as "floating masses" in the air. This way one can use the formulas for an inelastic collision to calculate a resulting velocity.

v = (m1v1 + m2v2)/(m1+m2)

That formula is right for one car crashing into another car. Hence, in the moment of impact and after a lot of deformation the combined mass moves at v. The friction to the ground will stop that combined wreck sometimes.
Imho that formula cannot be used for floors welded to the core. Why?
Let's say the stationary car is welded to the ground. I would say the resulting velocity of the combined wreck will be much different.
That means the falling mass FIRST has to crush all support of one floor and subsequently can accelerate the "floating" mass. In other words, v2 is always zero while v1 is the velocity of the upper mass AFTER the crushing of all supports and AFTER a significant loss of kinetic energy.
Right, that loss of KE represents the necessary amount of KE to crush all supports of one floor and the deformation during that crushing consumes more energy. The formula for inelastic collision gives an additional loss of KE (and therefore velocity) due to further deformation and heat until both floating masses move at the very same velocity.

That may explain why it looks like a building crushes approximately in a symmetrical manner up and down.

Am I wrong? Is anyone able to put that process into functions maybe based on Bazants formulas.

achimspok wrote:Am I wrong?

No.

Is anyone able to put that process into functions maybe based on Bazants formulas.

Bazant's result stems from assumptions and choice of parametric input. Even in his analysis, it's not that terribly far from concurrent crush-up.



The red shaded area is the energy deficit, substantial but not large compared to the energy of deformation up to the indicated result. Another impact, without enough 'cushion' from the emerging debris layer?

I've spent a good deal of time examining this very question. There is nothing wrong with what Bazant does, however it is a special case and one which is not necessarily most optimistic for survival of the structure as a whole (though it certainly leans absurdly far in that direction compared to actual) but definitely most optimistic for survival of the upper block!

Please indulge me with some time to reply, you raise some interesting points about the mechanics here and in a couple of other threads and I've been meaning to comment on them but time gets away so easily.

achimspok wrote:There are 2 ways to compress Zone B.
1) Zone B is compressed due to it's own mass and velocity impacting the lower stationary floor.
2) Zone B is compressed between Part A and Part C.

The first thing to bear in mind with this scenario is that Zone B forms as C is falling (yes, it's C on top in the jargon) so technically both will happen with magnitudes dependent on the configuration.

Let's say, Zone B and Part A are in free fall.

Possible in a discrete slab model but not exactly the case with snap-through as Bazant presents it, but let's run with it.

However, Part A is still in free fall.

Yes, and in a slab model with brittle connections this usually leads to concurrent crush up, which differs from Bazant's continuum model with homogenized mass distribution. I believe his results are fine for that case, as counter-intuitive as it may be.

There is no way for the upper Part A to get through of it without damage.

And so it is even in Bazant's scenario, just not enough to initiate crushup, but how much does the actual collapse correspond to this? In my scenarios, simultaneous crush-up is expected, but I don't think rigid, discrete slabs are a good analog.

It is inevitable that Part A will impact Zone Bx again. When it happens then the velocity of Zone Bx always represents enough kinetic energy to crush at least one floor of Part A. In other words, in the reference frame of Zone B the upper block is now falling at that velocity onto Zone B.

Yes, I've found that simultaneous crush-up is simply normal crush-up in a downwardly accelerated reference frame, which is energetically possible (favorable!). Under certain conditions, the two processes are decoupled for all practical purposes. The crush-down experiences a lower effective driving pressure, and there isn't great sensitivity to mass shedding for minor values, as we know.

The major difference in arguing this way is the way how to describe the impact.

I believe it makes all the difference as to the solution path from the potential bifurcation point.

Usually (e.g. Dr. Greening) the masses of the floors are described as "floating masses" in the air. This way one can use the formulas for an inelastic collision to calculate a resulting velocity.

v = (m1v1 + m2v2)/(m1+m2)

That formula is right for one car crashing into another car. Hence, in the moment of impact and after a lot of deformation the combined mass moves at v. The friction to the ground will stop that combined wreck sometimes.
Imho that formula cannot be used for floors welded to the core. Why?

It is OK, it must simply be supplemented by an applied external force due to the coupling with the lower structure and ultimately to the ground. The beauty of an inelastic collision is it doesn't matter if it's treated as instantaneous for the purposes transactional accounting. The same result occurs whether it crushes a lot and takes time or crushes only a little, quickly.

Let's say the stationary car is welded to the ground. I would say the resulting velocity of the combined wreck will be much different.

Even the friction of tires with the parking brake applied is a signficant sink, and it is just a matter of degrees. You've got the right idea, but there's no problem. The mechanics can be treated as the superposition of an inelastic collision plus support fail energy sink, either discrete or continuous.

...the more realistic way is to calculate a displaced upper block. It's a pity but the necessary data for the horizontal core connections were never released.
And the much more realistic way is to forget about the compressed pillow since we know that the debris avalanches ran down inside the tube and most probably left nothing but pure steel behind.

The best is to forget the block thing completely after about the 80th floor. No more block.

A displaced upper block is a nice way to see early destruction, from the 98th floor down to the 90th or 85th floor.

After that, good-bye blocks.