femr2 wrote:I've been having a think about this, and may consider setting up a 'grid' consisting of multiple instances of the spreadsheet model to try and express more defined regional behaviour.
Lots of work! It would be cool. Don't underestimate the value of running the existing sheet using only an adjustment to the top mass.
I assume you mean matching to slowest rate of descent.
Yes, there's a real min and max displacement value seen in the videos. It's racing way ahead on the south side and actually remains stationary for a while on the NW corner. A model of aggregate behavior, not just uniform in the horizontal dimension, but also requiring full participation of all mass at each level, cannot be compared directly to a heterogeneous front proceeding at different rates. The best to be hoped for is fairness in including the opposite extreme in some meaningful way.
One way is by fitting the slowest extreme, too, to see the difference.
As above, some 'resistance' would need to be included.
OK, so you can jack the energy up until it arrests then....
Treatment of collapse arrest has been in the model since day one. The method employed is that if the energetics calcs result in a deficit of energy, the resultant full post floor impact velocity is set to zero, the failure floor is recorded, and progression is allowed by allowing the cap mass (including any coalesced mass) to drop from rest...continues...
...just let it drop again at the appropriate time, all controlled by parametric settings, piece of pie. What physical correspondence does it have? None. There's nothing driven from a constitutive stance, because it's outside the scope of the model. The NW corner receives a substantial punch from above and survives. Nothing in this model is going to get it going again except the whim of the programmer. It has arrested. The model has 12 stories of building still on top of it! In reality, there's only air above, being undermined from below is what got it going, and it may have initially dropped at rates greater than freefall. How would that be addressed in the model? Arbitrarily reduce static capacity to zero AND temporarily increase gravity?
Why can't we just cheat similarly when trying to model the fastest advance?
Better but still questionable and loose, would be considering the extremes together, making a single weighted composite displacement which the model tries to match. There's the crush front we're discussing at one extreme, and the NW corner standing there while everything else falls around it at the other extreme. I doubt the discrete slab model would have any difficulty fitting that profile with some energy sinks and mass loss included. Looks like your first illustration incorporating stretch is at least a candidate for a match. It's questionable how much detail can be gleaned from such a fitting, but at least it's not arbitrary and it's arguably within the scope of the model.
If you take the spire tip as the slowest extreme, what sort of dissipative energies must be assigned, and are they remotely realistic? This is the only point I was trying to make in suggesting a fit to the slowest extreme. It's a no-go from the predictive modeling perspective, the behavior dictated by decree not by dynamics. If dissipated energy is increased until arrest, I guess you've found the amount required to stop the collapse, that's pretty interesting. That's what 1D models are for.
There is another approach to fitting arrest. Mass can be removed from above to give arrest immediately, that would be closer to the real situation in the NW corner than increasing energy dissipation. Re-initiation being completely outside the scope of this model.
Why resist going the other way and adding mass to simulate the other side, where the mass was last seen tipping towards, and coincidentally is the fastest visible progression? How much mass has to come off one side to arrest under energy sinks you feel comfortable with? Great, now add that amount to the other side, since that's where it went anyway, and run again. If you can't match the front at 5 seconds, starting from 92 and with a realistic stretch, then maybe the fast extreme is
also outside the scope of the model?
Incidentally, I do have a 1D physics-based slab simulation, with reasonable parameters including static strength, that can reinitiate crush-down from ongoing crush-up. There's nothing that says there only needs to be one generalized coordinate in 1D. But I still can't model the NW corner in this framework, even if (not necessarily unrealistic) vibrational energy accumulated in the lower structure could re-precipitate global failure, because there's still 12 floors of mass on top and the NW corner had none! The model I'm currently working with doesn't allow any mass bypass, and neither does yours. This is a double-edged sword.
If so, then some resistance/energy sink would be included.
While it's unrealistic to exclude energy sinks
per se, this model has other unrealistic aspects which
may tend to counter the omission, to what degree is infinitely debatable and some I've mentioned. Fully inelastic collisions make a lot of KE go away, because of a definition or constraint imposed intellectually. It may as well be magic because there are very few materials that display near-perfect inelastic behavior over a wide range of velocities. Remember Silly Putty? It would bounce if thrown at a hard surface, but was like modeling clay when working in the hands.
It is known for this model, implied in the collision, the mass below is swept up and accelerated to the upper block velocity. It's implicit in the dynamics that have been defined. Conversely, and also by definition, KE is forced to go into unrecoverable energy distribution: permanent deformation, fracture, lossy ejections, heat, sound, the works. And it does, obviously. The distribution over time and location of the PE is quite debatable, indeed it's part of the central mechanics debate. The simple model doesn't care whether all of those sinks are truly unrecoverable (like vibration), and to what extent energy can be mediated ahead of Zone B. I don't know how the energy distribution actually went, so there's little I can add to sorting this out. I'm quite confident it does goes beyond simple inelastic collision losses, so adding dissipative sinks would be appropriate for the purposes of comparison.
But comparison to what? Only an aggregate quantity, such as overall collapse time as defined by (say) 90% of the mass reaching rest at pile location. Comparison to the extreme leading front in a limited area? No, not a valid comparison, per above. An interesting one, for sure, and even educational, but not one from which one can determine that there was some sort of violation of physical laws governing a PE-driven collapse. It's reaching too far.
The divvying of energy is one thing, the motion of mass is another. The biggest drawback of this model is not inelastic collision, in fact that seems to be a virtue; the hitch is that mass elements must remain in their original sequence. Nothing can bypass, or race ahead, or lag behind - all mass is entrained at collision time. I can look right at any of the videos and see that's not how it went, therefore am thankful for whatever comes out of a model that has such assumptions.
Truth is, we're not that far off from a match under the apparent conditions of the slightest cheating. Given the model, I'd call that significant. And a piece of pie.
In this context, 92. In a wider sense, I'm leaning toward 95, with slightly earlier start point.
I tend to stick around 96-98, or higher, never used 92 before this discussion.
Looks pretty uniform except for the last 4, and that adding ~3 story-masses at the top would make a simple uniform model more accurate. Did I read it correctly?
We haven't begun to include anything other than conservation of momentum that will retard the descent in any way yet...
Except fully inelastic, head-on collisions that immediately entrain
all the mass at a given level...
The model can't be used to 'prove' anything as such, but I do think that it would be very useful, to me at least, to progress through discussion of inclusion of each of the available but currently omitted factors...mass loss, some crush...
No doubt very useful.
---------------------
Agreed, but could you outline the modes of failure ? (May be able to address them)
Some has been touched on already above, including elasticity, but these two words encapsulate a lot: deflection and ablation.
The first is any wedging effect. Axe, ship bow, upper block tilting in that direction before dropping. Material in front of the advancing front is no longer required to be swept up in totality. Look at WTC2's upper block shove the E perimeter out. It was like a paring knife. Much of the lower block on the N side directly below the failure point continued to stand well after the passage of the block. All of the mass from above went down, not all of the mass below was entrained, easily observed directly on video with my own eyes - slab model not generally applicable. QED
I think a similar thing happened with WTC1. Not only does tipping redistribute the mass you've so carefully assembled into a 1D world, it creates a geometry that allows a fairly strong portion of the upper block to do more damage than it receives. The structure is not homogeneous, so it isn't always like against like. The upper perimeter in WTC2 may have been badly damaged in its sliding contact with the lower while shearing it away, but it retained the majority of its shape a long time. Even if it was rubble-ized by explosives!
Why should WTC1 be radically different? One difference may be a greater percentage staying over the perimeter area longer. The antenna mast motion is consistent with gradual continued rotation of the upper block, with the hat truss area staying more or less cohesive through the first half of the fall. This is a dense and more rigid subset of building impinging on the structure below in an orientation favorable for cleaving and or shoving material aside instead of sweeping it up. It's also consistent with the lateral location of the leading front seen in the video.
What about the part of the upper block that's dragging over the core, some which remained standing after the wave passed? This is where ablation comes in. We're working with an exclusive accretion model for the dynamics of collision, so it's not a big deal that mass shedding is left out. In an local ablative model. KE can be
retained via the loss of mass, as opposed to continued application of resisting force. It may be more energetically favorable for the core impulses to shear the upper block than to absorb KE from it in a sustained fashion. The rubble falls more slowly, but it is detached.
Think road rash. I saw a guy go off the back of his motorcycle and slide across pavement like he was on ice. I'm not sure when he would have stopped if hadn't started tumbling like his bike. Getting a leg sucked underneath the rest of his body imparted angular momentum, stopped the ablation, which brought things to a more rapid conclusion. His arse certainly wasn't transmitting the drag force to the rest of his body, but it was leaving a ghastly stripe on the road.
For the specific purpose of speculative research, no probs.
)
