Bazant's crush-down/crush-up model

[pgimeno]

I'm trying to understand Bazant's crush-down/crush-up model, which I know is widely accepted. I am not questioning it, I merely want to understand it, and hopefully the explanation will be useful for someone else too.

In order to explain where my doubts arise, I propose the following thought experiment.

Consider a "WTC top" composed of the top 12 WTC1 floors, just floating freely in space. No gravity there.

Consider also a "WTC bottom" made of the bottom 98 floors of WTC1, attached to a rigid, indestructible platform which has some rockets mounted. These rockets are assumed to be able to put a thrust to the "WTC bottom + platform" mount and are regulated so that once started, in the platform an accelerometer always measures 9.81 m/s². The "WTC bottom" is aligned with the "WTC top" just like the real building was, and is separated from it just the distance of two floors, which IIRC was Bazant's assumption.

Here's a simple diagram of the setup:

At a given point of time, the rockets are started. From within a camera in the platform, the crushing should look just like the collapse predicted by Bazant (this thought experiment is assumed to be set up exactly like in Bazant's model, including the column-to-column collisions).

What I'm doing with this setup is merely to change the reference frame with respect to Bazant's description, defining the "WTC top" as having zero velocity. If it has a theoretical pitfall which causes it not to be equivalent to Bazant's model, I'd like to know.

But if it is, can someone please explain why the "WTC top" is not significantly crushed by the impact and successive force exerted on it until it reaches the platform, just as the "WTC bottom" is? That's the part that I'm not getting, and I believe it's the part that most people have trouble with.

Obviously, in this experiment the "WTC top" will accelerate at the first impact, reaching about 1/3 of g as it crushes the "WTC bottom", since the top's downward acceleration was about 2/3 of g.

The only explanation I can find for the top not being crushed is that the crush front will "lag" with respect to the accelerating platform's reference frame, thus its global acceleration will be less than g, possibly allowing for the "WTC top" to resist the force, because it's less force given that the acceleration of the crush front is reduced due to that "lag". Is that the cause? If so, why doesn't the same happen to the "WTC bottom"?

 

[R.Mackey]

Interesting way to frame the problem. There is a slight difference between your schematic and the real problem, however -- it's only equivalent if you assume the rockets are firing for a long time, and there's no remaining dynamic response in the intact tower, before you yank away the supports between the lower and upper portions leaving the upper portion to be at constant velocity while the rest continues to accelerate. But it's a minor detail.

There is a second important detail: Your rockets will have to throttle down as the collapse continues. They're providing a constant acceleration only on the intact portion of the lower block, i.e. a lower force as the mass of that block decreases with time. You have it drawn correctly, specifying a constant acceleration rather than a constant force, but it's a bit counter-intuitive for rocket engines.

Ideally you will get the same kind of "crush down / crush up" behavior. What happens is that at impact, the accelerating lower block hits the nonaccelerating (and thus slower) upper block, damage occurs to both. But the remainder of the upper block has been accelerated, being pushed by the mass below, at a rate lower than 1 g. And -- this is the key point -- the rubble interface layer between is at the same velocity as the upper block, and is not accelerating at 1 g.

As the lower structure continues to accelerate through the rubble layer and upper block, it suffers increasingly more damage at the top of the lower block. It has the same force pushing up, but it hits an increasingly larger mass and thus is opposed by more and more inertia.

The upper block, on the other hand, never feels any worse acceleration than it did at initial contact. At least, that is, until it hits the rocket platform itself, which we have declared to be ideal and indestructible, at which point the upper block begins to be destroyed in the "crush down" phase.

So, one more time: As the collapse progresses, the rocket-accelerated lower block is being driven at constant acceleration into a growing, larger and larger mass. Correspondingly, the resisting force goes up, and the lower block continues to suffer damage. The upper block, however, becomes a smaller and smaller fraction of the total impacted mass, and the force upon it actually decreases -- it suffers its worst damage at first contact, and afterwards will tend to survive.

Have you read Dr. Bazant's papers? In particular, have you read where he clarified this issue to Frank Gourley?

 

[femr2]

Even with the ideal and simplified Bazantian abstracted model, this portion stands out at this point...

[WTC Top] suffers its worst damage at first contact, and afterwards will tend to survive

To me this clearly implies simultaneous crush-up and crush-down at all times, even if you accept one side crushing more than t'other.

Of course these simplified abstractions don't directly apply to real world behaviour and are, as is made clear, a limiting case. Real world behaviour of, say, WTC 1 was clearly quite different.

ETA...

at which point the upper block begins to be destroyed in the "crush down" phase.

Did you mean "Crush up" ?

 

[ergo]

Consider a "WTC top" composed of the top 12 WTC1 floors, just floating freely in space. No gravity there...

What I'm doing with this setup is merely to change the reference frame with respect to Bazant's description, defining the "WTC top" as having zero velocity. If it has a theoretical pitfall which causes it not to be equivalent to Bazant's model, I'd like to know.

Well, if it's floating in space then it will ride with the acceleration upward of the lower rocket block indefinitely. If it's hitting against some immutable resistance or force then yes, it will be crushed between the lower rocket block and the force. So your intuition about it is correct, and you are not to be blamed for having "trouble" with it or "not getting" it.

 

[pgimeno]

Thanks for your answer. "Putting the E in the JREF", as I've seen some say

Interesting way to frame the problem. There is a slight difference between your schematic and the real problem, however -- it's only equivalent if you assume the rockets are firing for a long time, and there's no remaining dynamic response in the intact tower, before you yank away the supports between the lower and upper portions leaving the upper portion to be at constant velocity while the rest continues to accelerate. But it's a minor detail.

There is a second important detail: Your rockets will have to throttle down as the collapse continues. They're providing a constant acceleration only on the intact portion of the lower block, i.e. a lower force as the mass of that block decreases with time. You have it drawn correctly, specifying a constant acceleration rather than a constant force, but it's a bit counter-intuitive for rocket engines.

Sorry for any real-world inaccuracies. The experiment was designed for the intuition to make it easier to shift the reference frame. The pretended effect was that the situation was the same exact one, just as an aid in understanding. Seems I got it "right enough".

Ideally you will get the same kind of "crush down / crush up" behavior. What happens is that at impact, the accelerating lower block hits the nonaccelerating (and thus slower) upper block, damage occurs to both. But the remainder of the upper block has been accelerated, being pushed by the mass below, at a rate lower than 1 g. And -- this is the key point -- the rubble interface layer between is at the same velocity as the upper block, and is not accelerating at 1 g.

Indeed; however the rubble part is accelerated as well and pushes the upper block, which in itself also opposes an inertia which results in a force in the interface between itself and the rubble layer. If (emphasis on the if) the force is enough to crush it, then as it is crushed there will be less mass of it that opposes the movement and its crush-up will eventually be arrested, because of lack of mass, until the platform comes (unless the platform comes before that happens). That's how I see it.

So the problem is, in my view: is there something that ensures that the force between the rubble and the top will always be less than needed for crushing it?

Or is the no-crush-up just a specific case studied for the situation with the towers (and maybe applicable to some other buildings), but not valid in general? I'm starting to think that this is the explanation.

As the lower structure continues to accelerate through the rubble layer and upper block, it suffers increasingly more damage at the top of the lower block. It has the same force pushing up, but it hits an increasingly larger mass and thus is opposed by more and more inertia.

This part is perfectly clear. That's the obvious reason for the crushing to be produced at all.

Have you read Dr. Bazant's papers? In particular, have you read where he clarified this issue to Frank Gourley?

Seems that that will be my next reading

I have only read the first article (BZ) and have been waiting for an excuse to read the rest. Major Tom almost got me to read more of them, pity he didn't focus on one of them.

 

[pgimeno]

To me this clearly implies simultaneous crush-up and crush-down at all times, even if you accept one side crushing more than t'other.

Pending R.Mackey's reply and a reading of the explanation to Gourley on my side, will you at least concede my point that even if it is crushed, it would be eventually arrested as the top loses mass?

 

[R.Mackey]

Sorry for any real-world inaccuracies. The experiment was designed for the intuition to make it easier to shift the reference frame. The pretended effect was that the situation was the same exact one, just as an aid in understanding. Seems I got it "right enough".

Like I said, it's an interesting approach, and one that might help shed light on the issue. I just wanted to be thorough because it's a little bit more complex than it appears.

Indeed; however the rubble part is accelerated as well and pushes the upper block, which in itself also opposes an inertia which results in a force in the interface between itself and the rubble layer.

Ah, but no.

Think about your model. The rocket engines are accelerating the "ground." That means the only parts that accelerate with the rocket engine are those for which there is a stable load path going back to the ground. Everything else is not accelerating, and being hit by this structure.

The rubble does not have a stable load path to ground. They are free objects. They are not reliably carried by the lower structure's columns, but are instead impacting all over the place -- columns, floors, eccentrically, and so on. Thus, the rubble counts as part of the detached mass, which includes the upper block.

So the problem is, in my view: is there something that ensures that the force between the rubble and the top will always be less than needed for crushing it?

Yes, there is. Think of it like this -- F = m a, right? The forces on the upper block, once there is a significant rubble layer, are inertial forces. If you measure the aggregate deceleration of the upper block, you know the stress in that block.

As the upper block + rubble layer increases, m increases. F, on the other hand, is decreasing in your reframe of the problem -- the rockets have to throttle down. As a result, a decreases. That means the stress in the surviving upper block decreases as the collapse continues.

The peak stress in the upper block is the failure stress of the floor at the collision interface. It simply cannot transmit any higher stress than that. So we expect to see some damage to the upper block at the initial contact, followed by very little damage to the upper block afterward, until it again hits the "immovable" rocket platform at which point it will fail floor-by-floor in the crush up phase.

Or is the no-crush-up just a specific case studied for the situation with the towers (and maybe applicable to some other buildings), but not valid in general? I'm starting to think that this is the explanation.

It is valid in general. But there are some special cases. In the case of verinage, for instance, we also see a "crush down -- crush up" sequence, although the degree of near symmetric crushing at impact tends to be higher. This has more to do with the real details of the problem, where Bazant's hypothesis is an ideal case. Reality has to account for the actual failure modes of materials and connections.

In the real WTC situation, we don't have a true "crush down / crush up" anyway. What actually happens is the core and perimeter structure of the lower block funnels falling material onto the floors. The truss floors preferentially fail downward, whereas the beam-framed floors in the core preferentially fail upward. I wrote a cartoon describing this in the supporting presentation for my debate with Tony Szamboti, which you can read here: http://www.911myths.com/index.php/Ryanmackey (pages 20-25 of the presentation, downloadable as PPT or PDF).

I have only read the first article (BZ) and have been waiting for an excuse to read the rest. Major Tom almost got me to read more of them, pity he didn't focus on one of them.

Well, consider this an excuse. No reason not to read it for your own education.

What the Truthers do wrong is neglect the rubble layer. If the rubble layer didn't exist, somehow swept away as soon as it was produced, then the impact of upper and lower block would result in relatively symmetric damage. However, after the upper block has shrunk by only four or six floors, the rubble layer outmasses the surviving upper block, and you absolutely cannot neglect its behavior. Your reformulation of the problem is useful because it clarifies that the rubble layer must be treated as a free object, and thus is more accurately lumped with the upper block than the lower block. Once you get this point straight, the correct result should be intuitive.

 

[femr2]

will you at least concede my point that even if it is crushed, it would be eventually arrested as the top loses mass?

I don't understand what you are asking. If what is crushed ? What would be arrested ?

If you are suggesting that in a purely mathematical sense, not directly applicable to the real world, that the relative amount of crush-up as opposed to crush-down would be equal to zero, then, as Ryan has said it could tend towards zero.

But of course, that's just maths. Bazant never intended on modelling the real-world behaviour.

Even the terms crush-down and crush-up can only be loosely associated with the towers destruction when describing the real world behaviour.

 

[ergo]

What the Truthers do wrong is neglect the rubble layer.

How thick is this rubble layer? Where do we see evidence of it? I might believe in it if I could see it. Anywhere.

If the rubble layer didn't exist, somehow swept away as soon as it was produced, then the impact of upper and lower block would result in relatively symmetric damage. However, after the upper block has shrunk by only four or six floors, the rubble layer outmasses the surviving upper block, and you absolutely cannot neglect its behavior.

You mean this behaviour? :

The rubble ... are free objects. They are not reliably carried by the lower structure's columns, but are instead impacting all over the place -- columns, floors, eccentrically, and so on. Thus, the rubble counts as part of the detached mass, which includes the upper block.

The rubble's eccentricity means it must therefore be coupled with the upper block? Why? And why in both cases?

 

[R.Mackey]

Let me make a slight correction to the "throttling down" comment --

The rocket thrust would throttle down, but the actual thrust profile would have to match the timing of the overall collapse. My observation above that the thrust should be equal to 1 g times the mass of the surviving lower block is not quite right; there is an additional thrust component opposing the "downward" force exerted by the impacted pieces, which will be some fraction of their mass and difficult to predict.

The idea is simply to move with the reference frame of the interface, whatever thrust profile that may be. That interface will not accelerate at 1 g, but rather will have a varying acceleration over time. This is what I mean by "throttling down."

 

[Loss Leader]

But if it is, can someone please explain why the "WTC top" is not significantly crushed by the impact and successive force exerted on it until it reaches the platform, just as the "WTC bottom" is? That's the part that I'm not getting, and I believe it's the part that most people have trouble with.

As a lay person with no engineering background or knowledge of the mechanics of the tower collapses:

I think the top will be crushed. It will be completely ruined. You won't be able to hold meetings there or, really, get any work done. However, that doesn't look like it matters. The mass of the top won't change whether it is crushed or not. It will weigh the same. So the damage that it's going to do to your thought experiment rocket will stay the same (adding to it the mass of each new crushed section) so long as the rocket's acceleration into the top is 32 ft/sec2 or whatever gravity is these days.


ETA: Having now read Mackey's response, I realize that I have absolutely no idea what I am talking about and should, in all probability, just be ignored.

 

[pgimeno]

I don't understand what you are asking. If what is crushed ? What would be arrested ?

Sorry, let me rephrase:

Will you at least concede my point that even if the top is crushed-up as the collapse progresses, its crushing would be eventually arrested(*) as the top loses mass (because it's converted in rubble), since the total force would be decreasing and thus the columns will eventually be able to support the force?

(*) "Stopped" might be a better word? Sorry, English is not my first language.

(note that this question was previous to Mackey's clarification, which I am still in the process to digest)

 

[Loss Leader]

Sorry, let me rephrase:

Will you at least concede my point that even if the top is crushed-up as the collapse progresses, its crushing would be eventually arrested(*) as the top loses mass (because it's converted in rubble), since the total force would be decreasing and thus the columns will eventually be able to support the force?

See, this one I think I know. It wouldn't be arrested because the top is not losing mass. So long as you're still accelerating a static body into it, you're going to get the full force. Force=MA is not Force=M(that's still all in one piece)A. The M never changes. In fact, as Mackey has said, the M grows as lower floors are crushed because they stop being part of the static mass and become part of the thing it's hitting.

 

[R.Mackey]

See, this one I think I know. It wouldn't be arrested because the top is not losing mass. So long as you're still accelerating a static body into it, you're going to get the full force. Force=MA is not Force=M(that's still all in one piece)A. The M never changes. In fact, as Mackey has said, the M grows as lower floors are crushed because they stop being part of the static mass and become part of the thing it's hitting.

Yup.

Think about it this way, if it helps: What about the very top floor? When does it fail?

The force on the top floor is only equal to its own mass times its deceleration. That deceleration will be some fraction of 1 g, thus it never collapses -- its load is actually less than it was when it was free-standing and static -- until it suddenly hits an immovable object, and has to dissipate all of its built-up momentum in a hurry.

As a result it's easy to see that the very top of the upper block will outlast the entire lower block, no matter what, in the ideal case. The situation for the floor just below the very top is similar, except it's also loaded with the inertial force of the floor above. And so on. In short, the load on the upper block stays bounded, regardless of how much the debris layer in between grows. The same cannot be said for the lower block.

 

[femr2]

It wouldn't be arrested because the top is not losing mass.

pgimeno is not referring to *collapse arrest*, but rather to *crush-up arrest*.

 

[Sam.I.Am]

as the top loses mass (because it's converted in rubble)

The mass is still there, just in a different form. 1 pound weighs 1 pound regardless of the form it's in.

The old adage "The straw that broke the Camels back" comes to mind. That one straw weighing a single gram was "The final straw".

Truthers seem to forget this basic principal when discussing the falling rubble. It's not the individual pieces that count, it's all of the individual pieces almost simultaneously piling onto the lower floors one or two floors at a time in one chaotic event that counts. Even if those pieces could be carefully placed, one after the other over a week or more per floor the end result would be the same. The floor will fail and it will take out all of the floors below it in sequence.

 

[Loss Leader]

Yup.

I'm so proud. I printed out your post and showed it to my wife.

pgimeno is not referring to *collapse arrest*, but rather to *crush-up arrest*.

Maybe. But, then, why does his question include this phrase:

and thus the columns will eventually be able to support the force?

That sounds like he means that the crush-down should eventually be arrested when the top floor of the top section is finally destroyed.

 

[pgimeno]

The mass is still there, just in a different form. 1 pound weighs 1 pound regardless of the form it's in.

Under the "rubble is able to crush the top" assumption, the mass of the top is converted into rubble as the crushing progresses, thus the top loses mass which now forms part of the rubble layer. As the top has less and less mass, it has less inertia too, which is what causes the force between the rubble and the top in this assumption. Eventually, the force will be less than the structure can resist and the crush-up will be arrested. That's what I meant. You are right and my assertion that the top loses mass was correct. I neglected to specify that that mass is converted to rubble, which apparently has caused confusion.

---

However it's important to ensure there is clear understanding that the Bazant model does not, and is not intended to, reflect the real world WTC behaviour.

I don't lose track of it at any moment. But it proved that the gravity collapse was unstoppable once started, something that many people still contend.

---

Sorry, I badly need some sleep, almost 4am here, not in a good condition for this kind of brain frying

Hopefully I will get it tomorrow with a fresher mind.

 

[Sam.I.Am]

I neglected to specify that that mass is converted to rubble, which apparently has caused confusion.

Ok, that makes much more sense. After rereading what you wrote I admit that I misunderstood what you were getting at.

 

[Major_Tom]

Can the Bazant concept of crush down, then crush up be applied to WTC1?

In this thread people tend to agree that it cannot.

But Bazant applies it to WTC1 in BLGB. From the paper(BLGB)What Did and Did not Cause Collapse of WTC Twin Towers in New York

Zdenek P. Bazant, Jia-Liang Le, Frank R. Greening and David B. Benson

http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/476 WTC collapse.pdf






"Generalization of Differential Equation of Progressive Collapse

The gravity-driven progressive collapse of a tower consists of two phases—the crush-down, followed by crush-up (Fig. 2 bottom), each of which is governed by a different differential equation (Ba?zant and Verdure 2007, pp. 312-313). During the crush-down, the falling upper part of tower (C in Fig. 2 bottom), having a compacted layer of debris at its bottom (zone B), is crushing the lower part (zone A) with negligible damage to itself. During the crush-up, the moving upper part C of tower is being crushed at bottom by the compacted debris B resting on the ground. The fact that the crush-up of entire stories cannot occur simultaneously with the crush-down is demonstrated by the condition of dynamic equilibrium of compacted layer B, along with an estimate of the inertia force of this layer due to vertical deceleration or acceleration; see Eq. 10 and Fig. 2(f) of Bazant and Verdure (2007). This previous demonstration, however, was only approximate since it did not take into account the variation of crushing forces Fc and F0c during the collapse of a story. An accurate analysis of simultaneous (deterministic) crush-up and crush-down is reported in Ba?zant and Le (2008) and is reviewed in the Appendix, where the differetial equations and the initial conditions for a two-way crush are formulated. It is found that, immediately after the first critical story collapses, crush fronts will propagate both downwards and upwards. However, the crush-up front will advance into the overlying story only by about 1% of its original height h and then stop. Consequently, the effect of the initial two-way crush is imperceptible and the hypothesis that the crush-down and crush-up cannot occur simultaneously is almost exact."


Does Bazant seem to believe that the concept of crush down, then crush up can be applied to WTC1? From the above quote, clearly he does.

We see him applying crush down, then crush up to WTC1 in a paper entitled "What Did and Did not Cause Collapse of WTC Twin Towers in New York" yet the posters here tend to agree that we cannot apply this concept to WTC1.

Well, you should let Dr Bazant know.