The 9/11 Forum

OWE asks:

I wonder why the case of continuous media, discussed in B&L, differs so dramatically? Can an upper block that has experienced 10x maximum elastic deformation of its lowest story stand on its own at one-third gravity? Seems reasonable. How about when it's going to get smacked one more time before the ride smoothes out?

Because we are talking about different types of collisions. An OODRD crush mode is very different from the column buckle/rebuckle mode upon which in B&V and B&L was formulated.

The column buckle/rebuckle/rebuckle mode of Bazant is pure fantasy. The argument in B&L that the upper block will remain largely preserved because columns cannot buckle upwards is meaningless. Basically he has a PhD and many people who couldn't understand the details in his argument beleived what he said without applying some simple reality checks, like studying the video evidence or looking at the resulting rubble.

OOSRD is the only known natural crush mode that matches all observables. If we size resistance to OOS floor to building connection strength rather than column strength, crush-up makes perfect sense.

Contradiction gone.

Yes. I think a limiting case model has been confused with a description of actual events for far too long. Time for a new model.

I've got plans for this thread, Major_Tom. Snail's pace. Thanks for the tip of the hat.

Major_Tom wrote:How can we manipulate this to use it as an OOSRD learning tool? The only thing we need to change is the connection strength. We want constant strength, not varying strength.

A lot can be done with constant strength. That's what I started with, even for the self-supporting structures. However, there is a limit to how far that can go as you scale up. The inevitable result for a structure of many stories is something that either can't stand or can't be crushed. Going to 3D will decouple structural strength from encountered resistance. The intermediate step of 2D (recall your resistance map) offers alternative paths of descent, but has more inherent stability than 3D.

We don't have this increased resistance for OOSRD, so you'd think that OOSRD dynamics collapses to earth easier than his examples.

Definitely.

Is that true for WTC1?

Not necessarily. It just wasn't as clean as 1D, not even at the very start. But the essence might come through.

How can we distinguish OOS crush-up, crush-down or mix on the basis of our super-cool Sauret measurements?

Perhaps by carrying the measurements just a little further, not an easy thing. An abrupt slowdown of the roofline would indicate a greater resistance encountered, something that would be expected if the engagement of the upper and lower portions were more full and complete; there will come a point where there's no path for the hat truss (in particular) to avoid collision.

The second point is very important for OOSRD. Would the order of crush-up before or after crush-down really matter to the ability to induce and sustain OOSRD conditions?

No, I think the phenomena can and did exist independently and simultaneously. I think the OOSRD unzipped the structure.

Major_Tom wrote:I have not seen any cases of terminal velocity in OWE's examples. Always accelerations and one phenomenon called "terminal acceleration". How can we explain terminal velocities witnessed moving down the southwest corner?

There's insignificant frictional forces involved in the simulations so far. Interestingly enough, I think re-collisions of a large number of pieces will give an effective resistance with velocity dependence.

Achimspok posted a nice little video recently on the OOSRD reaching what seems to be terminal velocity after reaching only the 85th floor.

It's a new release so maybe you haven't yet seen it at

I haven't, I'll check it out.

OWE may argue that if we consider resistive forces that are proportional to v or v^2 we can be expected to reach a terminal velocity. True, but after only 10 floors? This means that the resistive term with v^2 dominates?

Possibly. Good thought. Depends on the coefficient. The shape of the curve will dictate. Like I said, the roofline motion is or at least can be (or appears to be) decoupled from the interior progression. David B. Benson sees no v component, only v^2, but that is the roofline.

For OODRD we guess that a constant resistive force will dominate with smaller contributions from terms with v or v^2 (why not). How can the v^2 resistive term dominate so early?

It just depends on the dynamics. The relative magnitude of the coefficient determines the rapidity of onset. This would be an interesting avenue to explore computationally.

Are there other natural examples of such dynamic behavior?

Ever see the Prell shampoo commerical? The pearl is dropped in the bottle of shampoo, reaches constant velocity quickly. Give me a little time, I'd love to come up with real examples.

What would a -c*v^2 resistive force represent physically? (I know you'll say concrete pulverization, but does that really explain terminal velocity reached at floor 85?)

Yes, I would say pulverization, absolutely. Terminal velocity at 85 is rapid dynamic equilibrium. The difficult aspect to explain is the velocity itself being pretty high, since I'd have no trouble otherwise visualizing terminal velocity by way of little accretion, literally the same thing happening over and over again, very jerky when observed at fine granularity but with a net constant average velocity. It's easier to imagine when it's near-arrest at each collision but that's obviously too slow and there's little reason to expect the knife edge to occur there.

Excellent questions, and much more thought required to give good answers.

Found a couple of old videos scouring physorg. The first is kinda OK, but both are pretty glaring examples of bad construction and blatant disregard for the limits of the engine. Future models, trust me, will have a lot more thought behind them. This was almost two years ago, learned a lot since then.

http://www.megaupload.com/?d=BX5WB182


This is what happens when just throwing a structure together willy-nilly. I fired a high velocity cube at the building when I got tired of looking at it:

http://www.megaupload.com/?d=YW1FRL7O

Pays to scale up slowly and carefully, and not bribe the building inspectors!

More stills from previous experiments lost. As I look back on some of these, I'm appalled, but it was a learning experience. Four-piece floor slabs do not always work well with the fixed joints.



http://i36.tinypic.com/1zobyg4.jpg



http://i38.tinypic.com/20sg9jc.jpg



http://i37.tinypic.com/2zdss4x.jpg



http://i38.tinypic.com/zlb23p.jpg



http://i36.tinypic.com/2lt24py.jpg

Major_Tom wrote:Achimspok posted a nice little video recently on the OOSRD reaching what seems to be terminal velocity after reaching only the 85th floor.

I have to spend more time with this, but I have a problem with the 100 m/s figure. The progression has been crudely measured to be less than 30 m/s, hasn't it? As pointed out in the video, it takes 10 seconds of freefall to get to that speed, yet I see perimeter pieces outpacing it that may have started dropping after the internal material. Obviously, these pieces have not had 10 seconds of drop.

I think the problem stems from incorrect assumptions about starting location and time. It's hard enough to explain the rapid terminal velocity without inflating it by a factor of four. There are expulsions at initiation much lower than floor 98 (if that's what's used). I mean, it doesn't matter the cause, they are there.

On the matter of terminal velocity itself, there is no need for ongoing acceleration to maintain a progressive collapse. The current state of the art (my opinion) is vertical avalanche, and that predicts terminal velocity early.

In another thread, War Wheel says:

The cap masses differ by a factor of more than 2, yet the collapse rates are essentially the same.
(Mean) descent rate is not a function of cap mass.

In the end it really doesn't matter which estimate one uses, because the real point is that any sane person is going to have them much too close relative to the cap mass ratio.

Turns out it's not so odd, the average velocity of phase 1 crush-down from two different starting heights is pretty much the same, so long as you compare velocities using a generalized displacement coordinate normalized to the total crush distance in each case. Naturally, calculating average velocity over the entire crush-down interval satisfies this, as the generalized coordinate value is 1 for both cases.

It is a non-intuitive result only because the comparison of average velocities over the the entire interval is not the same as comparing average velocities at any specific point in time. Throughout the descent, a higher cap mass leads the lesser mass and has a higher instantaneous velocity. However, the smaller mass comes from higher up, has correspondingly further to fall, therefore continues to accelerate until reaching similar final instantaneous and average velocities.

This was a great issue to bring up because it could easily (and did) lead to incredulity about the mechanics of collapse over something that is expected, not anomalous. I had no ready answer for this but the toy simulations came to the rescue. The discussion in the other thread includes an example of how the velocity of crush down in two identical structures with different split points is the same over the entire descent when parameterized by fraction of total descent. Here, I want to extend on that by showing a couple of cases that are set up differently to allow different top masses yet have the same overall displacement, and compare the results from several cap masses.

This experiment is to determine the influence of cap mass, similar to ones done previously but with a pair of tests using different connection strength schemes to determine the influence there as well. The configuration is 100 stories, upper block consists only of topmost slab which drops onto the remaining structure and crushes to completion. Except for the top slab, slab masses are identical; the top slab mass is varied through 1x, 2x, 4x and 8x the normal slab masses as a varying parameter. The slabs are 0.2 x story height, AKA 0.2 stretch or 5x compaction.

These are also at least minimally self-supporting structures, they would continue to stand if not for the split introduced as an initial defect. This is necessary to conduct the experiment by definition, but it imposes certain constraints on the construction scheme. As the top mass is increased, the structural capacity in terms of joint strength must also be increased, so mass is not the only variable in the simulation, energy lost to joint breakage is also variable.

Many previous experiments used a simple scheme where the load at each level determines the joint breakage force to within a scaling constant. This results in the lowest connection of a 100-story structure of uniform slab mass being 100 times stronger (in terms of peak impulse, at least) than the top connection. That's not too realistic in the context of skyscrapers, but that does bring up an interesting point: when someone says (e.g.) DCR of 0.5, that can't apply throughout the vertical extent or you do get a situation where the ground story is 100x stronger than the top.

To illustrate the influence of connection strength gradient, a pair of trial sets are done with:

- a linear gradient of 100% capacity required at the bottom to 10% of that value at the top
- a constant connection strength all the way up, set to 100% capacity required at bottom

The latter has the necessary bottom connection strength all the way up the structure, but overall capacity was reduced to the minimum reasonable amount to ensure crush down could occur even at lowest slab mass, one-third the capacity of the first set. Thus the energy consumed by connection breakage, while not presumed to be identical, may be similar in both sets. It is the difference in capacity gradient that will be explored.

The linear gradient case for 1x/2x/4x/8x top slab mass.

Displacement:


Velocity:


====================================================

The flat (no gradient) case for 1x/2x/4x/8x top slab mass.

Displacement:


Velocity:

If you compare to the graphs posted in the referenced War Wheel thread, the immediate obvious difference is that this scheme does not result in the final velocities ending up the same in each case, the heavier ones are faster - all falling the same distance. Otherwise, there's not much discernable difference amongst any of the different schemes, shape-wise.

Because the data coming from the physics engine is not a measurement, rather the result of a calculation, it isn't subject to error or noise. The jitter in the velocity trace is the series of jolts from collision, with the snap-back characteristic of the many-jointed chain. This velocity data is perfectly good to use for the purpose of obtaining a good analytical interpolation and then differentiating to get an approximate acceleration curve.

I chose a 4th degree polynomial for the fit, for no special reasons other than I thought 3rd degree could provide a good fit to varying acceleration after differentiation. The constant (offset) coefficient was set to zero as a boundary condition. The latter end (not fixed) of the sets is not quite such a good fit as the front, so I would de-emphasize the particulars of the trailing end of the interpolations and especially derivatives. Sets have been trimmed to a common length of time.


I show this work for the linear gradient case:

V1: velocity for cap mass of 1x


V2: velocity for cap mass of 2x


V4: velocity for cap mass of 4x


V8: velocity for cap mass of 8x



and present the equations for both cases:

********************* FIT RESULTS **********************
Linear 100% - 10%
********************************************************

V1 = -5.8208*x + 0.83714*x^2 - 0.096904*x^3 + 0.0038063*x^4
V2 = -7.089*x + 1.1775*x^2 - 0.13343*x^3 + 0.0051659*x^4
V4 = -8.3721*x + 1.4503*x^2 - 0.15785*x^3 + 0.0059602*x^4
V8 = -9.5897*x + 1.6226*x^2 - 0.16626*x^3 + 0.0060285*x^4

********************* FIT RESULTS **********************
Flat 100%
********************************************************

V1 = -5.3313*x + 0.77229*x^2 - 0.095449*x^3 + 0.0038442*x^4
V2 = -6.6026*x + 1.0934*x^2 - 0.1292*x^3 + 0.0050967*x^4
V3 = -7.9173*x + 1.3791*x^2 - 0.15566*x^3 + 0.0059776*x^4
V4 = -9.2764*x + 1.5677*x^2 - 0.16408*x^3 + 0.0059893*x^4

The velocity fits for the linear gradient:


and the accelerations obtained by taking the derivative of the interpolation:



======================================

Velocity for flat:


Acceleration for flat:



======================================

Both overlaid, velocity:


Acceleration:

The actual collapse times differ, from lightest to heaviest, by about 2 seconds. That's not insubstantial, but perhaps not as much intuitively expected when scaling up the mass 8 times. The overwhelming factor is having to plow through a line of masses that add up to much more than the original mass, even at 8x top load.

Once again, the rough convergence on a single constant acceleration value is seen - terminal acceleration. The interpolations indicate a sort of oscillation rather than asymptotic approach - but, again, I wouldn't read too much into it past 5 or 6 seconds in. Not to say there isn't something of interest there, but it will need to be studied further. Same with the crossover point of the clusters towards the end.

The linear gradient, as expected, exhibited slightly higher initial accelerations than the flat counterpart because the flat is stronger higher up, but both join by about three seconds in. Less than 5 seconds into progression, all trials have about the same acceleration, around one-third g. By this time, there is a fair difference in the velocities seen with the different masses, but this difference will remain fairly constant and represent a lesser percentage discrepancy against the overall average velocity the longer the collapse continues.

The actual collapse times differ, from lightest to heaviest, by about 2 seconds. That's not insubstantial, but perhaps not as much intuitively expected when scaling up the mass 8 times.

Didn't you show (on the other thread) that even a 50/50 split demonstrated this effect?

The interpolations indicate a sort of oscillation rather than asymptotic approach

This is expected in a horrizontal (accretive) domino system, as is the insensitivity to initiating mass.

For clarity, we're talking about
__ __ / / /| | | | |
not __ __ /| | |

This might prove to be a useful in eliminating models that do not have this property from consideration.

War Wheel wrote:Didn't you show (on the other thread) that even a 50/50 split demonstrated this effect?

Yes, but the values didn't match as closely. There were some less-than-clean aspects of those runs, sort of quick and dirty (like a forgot about an 8x cap mass I had set). I'd like to do a more controlled series of test with a variety of splits to map that out, using the normalized position coordinate.

This is expected in a horrizontal (accretive) domino system, as is the insensitivity to initiating mass.

Fascinating! This I want to explore.