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Why Fact-check? Why preserve a visual record?

The Website Written as a Book
Introduction
1: Science and Subjective Viewpoints
2: Toward Accurate Collapse Histories
....2.1: Progressive Floor Collapses in the WTC Towers
....2.2: General Global Characteristics of Collapses
....2.3: Mathematical Basis of ROOSD Propagation
....2.4: WTC1 Accurate Collapse History
....2.5: WTC2 Accurate Collapse History
....2.6: WTC7 Accurate Collapse History
3: WTC Collapse Misrepresentations
....3.1: Purpose of the NIST Reports
....3.2: NIST WTC1 Misrepresentations
....3.3: NIST WTC7 Misrepresentations
....3.4: NIST WTC2 Misrepresentations
....3.5: Reviewing the Purpose of NIST and FEMA Reports
....3.6: Bazant Misrepresentation of Collapse Progressions
....3.7: Block Misrepresentations of Collapse Progressions
....3.8: AE911T Misrepresentations of the Collapses
4: Scientific Institutions Can Be Unaware of Contradiction
5: Reassessing the Question of Demolition
....5.1: The Case of WTC1
....5.2: The Case of WTC2
....5.3: The Case of WTC7
6: WTC Collapse Records Studied as Meme Replication
....6.1: Meme Replication in Technical Literature
....6.2: Meme Replication in Mass Media
....6.3: Meme Replication in Popular Culture
....6.4: John Q Public and the WTC Collapse Records
Conclusions

WTC Twin Towers Collapse Dynamics

Official, Legal Attempts to Explain Collapses

Academic Attempts to Explain Collapses Reviewed

On the Limits of Science and Technology

WTC Video Record

WTC Photographic Record
WTC1 Attack to Collapse
WTC2 Attack to Collapse
WTC 7
.
-----PHOTO RECORD OF FIRE PROGRESSION-----
Fire Progression, WTC1 North Face
Fire Progression, WTC1 South Face
Fire Progression, WTC1 East Face
Fire Progression, WTC1 West Face
Fire Progression, WTC2 North Face
Fire Progression, WTC2 South Face
Fire Progression, WTC2 East Face
Fire Progression, WTC2 West Face
.
----DEBRIS LAYOUT AND CONDITION, BY REGION-----
Debris: WTC1 Around Footprint
Debris: WTC2 Around Footprint
Debris: From WTC1 Westward
Debris: From WTC1 Northward
Debris: From WTC2 Eastward
Debris: From WTC2 Southward
Debris: Plaza Area, Northeast Complex
Debris: Hilton Hotel, Southwest Complex
Debris: General, Unidentified Locations
Damage to Surrounding Buildings
Perimeter Column Photo Record
Perimeter Columns: Types of Damage
Core Box Columns: Types of Damage
Complete Photo Archive
Other Major 9-11 Photo Archives
The 911Dataset Project

WTC Structural Information

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Online Misrepresentations of the WTC Collapses

Forum, Blog Representations of the WTC Collapses

The Book Tested Through Experiments

Miscellaneous Notes, Resources
FAQ for Miscellaneous Notes
History Commons 9/11 Timeline
The 911Dataset Project
Skyscraper Safety Campaign
First and Largest 9/11 Conspiracy Theory
Key Words in Book and Website
Trapped Within a Narrowed False Choice
Vulnerability and Requestioning
On Memes and Memetics
Obedience, Conformity and Mental Structure
Denial, Avoidance (Taboo) and Mental Structure
Taboos Against Reviewing the Collapse Events
Extreme Situations and Mental Structure
Suggestibility, Hypnosis and Mental Structure
Awareness and Behavior
Magical, Religious, Scientific Cause-Effect Relations
The Extreme Limits of Mental Dysfunction
Orwell's "Crimestop", "Doublethink", "Blackwhite"
William James, Max Born: Science as Philosophy
Plato on Self Reflection and Mental Structure
Rewriting History, part 1
Rewriting History, part 2
On Smart Idiots

New Ideas in Education

Bazant's 4 Papers Reviewed

Bazant's 4 Papers Reviewed




THE WTC COLLAPSE ARGUMENTS OF ZDENEK BAZANT


The vague nature of the NIST reports when describing the collapse progression mechanisms of the Twin Towers has led to a long series of misrepresentations of the WTC collapses in ASCE publications and elsewhere that continues to this day. An excellent example of what lies at the heart of these misrepresentations is a series of papers appearing in the Journal of engineering mechanics by Zdenek Bazant.

Dr Bazant wrote 5 papers on the WTC collapses which appear in ASCE journals. The first paper, published in 2002, is based on a simple argument that can be stated in a single sentence. In his own words: "The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load carrying capacity, the whole tower was doomed."

He wrote 3 more papers in succession in 2007-8 in which he develops a general one dimensional mechanical model of the motion of the progressive collapse of a building and applies the model to the Twin Towers. The model was already examined in part 2.3: Mathematical Basis of ROOSD Propagation in step 4.

It is quite fascinating to observe how this model, based on the mechanics of interacting blocks and gross assumptions, had gone from being a simple 1-D formulation to something that has been taken quite literally. The block mechanics first derived in these papers is now often portrayed as the most realistic description of the collapse progressions of the Twin Towers to date. This has occurred even though it is easy to show that block mechanics grossly contradicts what is observable and verifiable within the visual record of the events themselves. Block mechanics is taken to represent the history of the towers so completely that overwhelming visual evidence that the real collapse modes were quite different goes virtually unmentioned in pretty much all professional and government literature. Even stranger, many groups and individuals that argue contrary to Bazant have adopted the same block mechanics formulation to express their own understanding of the collapse progression modes of the Twin Towers, as will be demonstrated in sections 3.6 and 3.7.


For those readers who find this section to be too technically complex, I have prepared a simpler way to spot the mistakes within these papers using direct quotes from the papers followed by simple, straightforward questions linked here.



CRUSH DOWN, THEN CRUSH UP BLOCK MECHANICS

Bazant's original crush down, then crush up conception of collapse progression was published in 2 parts in 2007. The first part, called "The Mechanics of Progressive Collapse", describes the general model. In his own words, in the paper:

" a dynamic one-dimensional continuum model of
progressive collapse is developed. The collapse, in which two phases'"crush-down followed by crush-up'"must be distinguished, is described in each phase by a nonlinear second-order differential equation for the propagation of the crushing front of a compacted block of accreting mass."


In the second part of the paper, called "Closure To The Mechanics of Progressive Collapse", he describes the Twin Towers collapses in terms of crush down, then crush up

His final paper on the subject of the WTC collapses is called "What did and did not cause the collapse of the WTC towers in New York", published in 2008. In it Dr Bazant claims the crush down, crush up model applies to the Twin WTC Towers and describes how it specifically applies to the collapse of each tower. He then claims to prove that allegations of controlled demolition have no merit by applying the block model to the WTC towers.



INFLUENCE OF THE BAZANT PAPERS

The papers, though absurdly incorrect in their assertion that block formulations can be applied to the WTC towers, have had a major influence in describing the collapse progression mode of the twin towers. The crush down, then crush up mechanics proposed is now taken quite literally as the actual collapse progression mode for both towers.

Block mechanics is now an integral part of the technical historic record of the collapses. As a result there is no accurate portrayal of the true collapse progression mode within any academic or government literature. A literal interpretation of the blocks described by Bazant serves as the current description of how the buildings collapsed within recorded technical history.




COUNTER-ARGUMENTS TO THE COLLAPSE PROPAGATION MODEL ALSO RELY ON BLOCK MECHANICS


Block mechanics has resulted in a number of claims and counter-claims also based on block mechanics. For example, the underlying description of collapse progression by AE911T described in section 3.7 is also based on block mechanics.

The irony of such counter claims is that by phrasing collapse mechanics in terms of blocks just as Bazant had, counter-arguments reinforce the false historic description of the collapse modes of the Twin Towers in terms of crushing blocks. Therefore, while they appear to counter the Bazant formulation of collapse mechanics at a superficial glance, they actually reinforce it and support it by embracing the same block approach. Common arguments both for and against CD rely on the mistaken need to destroy the whole lower and upper portions with demolition devices. Some argue that the upper block cannot crush the lower portion and will somehow come to rest before striking earth while others argue it can crush the block below before crushing itself when striking the earth. But both approaches express collapse progression in terms of interacting blocks.

Block mechanics is a key component within common arguments for demolition. It is an integral part of each polarized position within the false dichotomy by which the history of the collapses is currently represented.




THE 4 PAPERS RE-EXAMINED

How did block mechanics come to be taken so literally? How did people come to believe that the WTC towers had "crushed down" before "crushing up"? The first literal interpretations of the collapse modes of the Twin Towers in terms of block comes from Dr Bazant himself within his 2007-2008 papers on the subject. All 4 papers are examined and reviewed in order to show how such a misunderstanding originally came about.






Review of: Why Did the World Trade Center Collapse?-Simple Analysis

Zdenek P. Bazant and Yong Zhou (BZ), published in 2002 available here


The basic argument is written in the abstract as: "The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load carrying capacity, the whole tower was doomed."

He rephrases the basic argument slightly in a paper written in 2008 (BLGB, introduction) as:

"First, let us review the basic argument (Bazant 2001; Bazant and Zhou 2002). After a drop through at least the height h of one story heated by fire, the mass of the upper part of each tower has lost enormous gravitational energy, equal to mgh. Because the energy dissipation by buckling of the hot columns must have been negligible by comparison, most of this energy must have been converted into kinetic energy K = m0v2/2 of the upper part of tower, moving at velocity v. Calculation of energy Wc dissipated by the crushing of all columns of the underlying (cold and intact) story showed that, approximately, the kinetic energy of impact K > 8.4 Wc (Eq. 3 of Bazant and Zhou 2002)."




The BZ argument is a simple IF-THEN statement: If A Then B, where

A= Separation of building into 2 portions, allowing top portion to fall freely for 12 ft before striking lower portion.

B= Cascading destruction is assured, even if all upper columns strike the lower with an impossibly exact precision.

BZ does not show how condition "A", the initiation of collapse, comes about. It only argues that once "A" (collapse initiation) happens, "B" must follow.

Because BZ provides no proof of how condition "A" comes to be, it offers no provable explanation for the collapse initiation mechanism of WTC 1 or 2 (the "how" of condition "A") for WTC1 or anything concerning the collapse of WTC 7.


On Bouncing Buildings

In the simplest terms, BZ asks and answers the question: "Can buildings bounce?" "If a top portion is dropped 12 ft for whatever reason, even if the upper columns land with the perfection of a ballerina on the columns below, will a building bounce?"

The original argument was first formulated by Bazant only 3 days after 9/11/01. The first formulation is sometimes referred to as a "back of the envelope calculation", which seems an appropriate description as the basic argument is very simple and can, quite literally, be formulated on the back of an envelope. The question "Can buildings bounce?" could have easily been answered before 9-11-01 had anyone a desire to do so, as the analysis and logic is quite simple.

After all, why would anyone expect any building to be built to survive a 12 ft freefall? Is there any reason why buildings would be intentionally designed to handle such a collision? The factor of safety (FOS) of the supporting columns required for such a building would need to be ridiculously high, resulting in column cross-sections much larger than what is actually necessary to hold a building up safely. Even before BZ was written it would have been safe to say that there is no tall office building in any city on earth that is built with an FOS which allows a building to "catch itself" after a 12 ft drop.



Bazant's 5 stages of collapse and the 5 visual reconstructions


In the 2002 paper Dr Bazant describes a simplified description of the Twin Towers collapses as occurring in 5 stages. He describes the collapses in the same general way in the 2007-2008 papers. In his own words:

"Introduction and Failure Scenario

The 110-story towers of the World Trade Center were designed to withstand as a whole the forces caused by a horizontal impact of a large commercial aircraft (Appendix I). So why did a total collapse occur? The cause was the dynamic consequence of the prolonged heating of the steel columns to very high temperature. The heating lowered the yield strength and caused viscoplastic (creep) buckling of the columns of the framed tube along the perimeter of the tower and of the columns in the building core.

The likely scenario of failure is approximately as follows. In stage 1 (Fig. 1), the conflagration, caused by the aircraft fuel spilled into the structure, causes the steel of the columns to be exposed to sustained temperatures apparently exceeding 800°C. The heating is probably accelerated by a loss of the protective thermal insulation of steel during the initial blast. At such temperatures, structural steel suffers a decrease of yield strength and exhibits significant viscoplastic deformation (i.e., creep'"an increase of deformation under sustained load). This leads to creep buckling of columns (Bazant and Cedolin 1991, Sec. 9), which consequently lose their load carrying capacity (stage 2). Once more than half of the columns in the critical floor that is heated most suffer buckling (stage 3), the weight of the upper part of the structure above this floor can no longer be supported, and so the upper part starts falling down onto the lower part below the critical floor, gathering speed until it impacts the lower part. At that moment, the upper part has acquired an enormous kinetic energy and a significant downward velocity. The vertical impact of the mass of the upper part onto the lower part (stage 4) applies enormous vertical dynamic load on the underlying structure, far exceeding its load capacity, even though it is not heated. This causes failure of an underlying multifloor segment of the tower (stage 4), in which the failure of the connections of the floor-carrying trusses to the columns is either accompanied or quickly followed by buckling of the core columns and overall buckling of the framed tube, with the buckles probably spanning the height of many floors (stage 5, at right), and the upper part possibly getting wedged inside an emptied lower part of the framed tube (stage 5, at left). The buckling is initially plastic but quickly leads to fracture in the plastic hinges. The part of building lying beneath is then impacted again by an even larger mass falling with a greater velocity, and the series of impacts and failures then proceeds all the way down (stage 5)."





Fig 2.61, which is figure 1 from the paper reproduced. Stages of collapse of the building (floor height exaggerated) The figure shows Dr Bazant's conception of the 5 stages of collapse described in the paper.





According to his own description, the 5 stages are:

stage 1) Airplane damage, fire and fuel
stage 2) Creep buckling
stage 3) Majority of columns lose strength, building starts to move downwards
stage 4) First significant collision
stage 5) Collapse propagation


The collapse initiation sequence is contained within stages 2, 3 and 4. The bolded comments are only his opinion of what he thinks may have happened during the collapse initiation sequence. They do not constitute proof of anything.

After the NIST reports and papers by Bazant were published, independent researchers were able to reconstruct collapse events directly from the visual record in order to fact-check all government and non-government claims of what happened. Researchers were able to reconstruct aircraft impacts, resulting fires, deformations seen on each building, and key elements of the collapses and resulting rubble layout. In total, the reconstructions can be categorized in a way that roughly corresponds to Bazant's description of 5 stages of collapse.

The 5 visual re-constructions are:

The aircraft impacts and resulting fires
Early deformation
Collapse initiation sequence
Collapse progression
The debris layout and condition


Using these visual reconstructions, researchers are able to check the accuracy of specific claims made by Bazant, the NIST, and other groups and individuals.

The 4 Bazant papers deal primarily with stages 4 and 5, or collapse progression. The papers skip over the initial buckling sequence (stages 2 and 3), only giving the most general narration of what he believes may have happened during this time. For analysis of stages 2 and 3, Dr Bazant relies on the NIST reports.



THE PROGRESSIVE COLLAPSE MECHANICS OF ZDENEK BAZANT





Dr Bazant's next paper was published in 2 parts in 2007, 2008, both of which are listed below.


Part 1: Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions

Zdenek P. Bazant and Mathieu Verdure (BV), published in 2007, the paper linked here


Part 2: Closure to 'Mechanics of Progressive Collapse: Learning from World Trade
Center and Building Demolitions' by Zdenek P. Bazant and Mathieu Verdure


Zdenek P. Bazant and Jia-Liang Le (BL), published in 2007,

March 2007, Vol. 133, No. 3, pp. 308"319.
DOI: 10.1061/(ASCE)0733-9399(2007)133:3(308)
The paper is linked here


It is quite interesting to see how the crush down, then crush up is described in increasingly literal terms within his final 3 papers written in 2007-2008. The concept is introduced in BV, but within the closure of BV the model is described as a literal process that actually happened to the WTC buildings.

In the first of the 2 papers on the mechanics of progressive collapse, in his own words,

"a dynamic one-dimensional continuum model of progressive collapse is developed. The collapse, in which two phases -crush-down followed by crush-up - must be distinguished, is described in each phase by a nonlinear second-order differential equation for the propagation of the crushing front of a compacted block of accreting mass."


The propagation model starts with the collapse front moving downward with an initial velocity (after a 12 ft freefall) and is modeled as 2 large blocks colliding with destruction occurring only along their contact surfaces. Just as in his first paper in 2002, a possible collapse initiation and initial column buckling sequence are addressed only as a narration.


The basic mechanics in his own words:

"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 as demonstrated in section 2.1 of this book.



The 4 simplifying assumptions in Bazant's collapse progression mechanics based on colliding blocks, in his own words:

"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."



These 4 simplifying hypotheses do not apply to WTC1 or WTC2. The physical observations presented in secion 2.1 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 the WTC towers because the collapse front seemed to go around the core. Column buckling has nothing to do with the real frictional force since the perimeters and large visible portions of the core were stripped of flooring and left unsupported in an unbuckled condition.


CRUSH DOWN, THEN CRUSH UP BLOCK MECHANICS FIRST DESCRIBED

This is where Bazant first explains why the lower block must be completely crushed before significant crush up begins. He gives more detailed arguments the next 2 papers. In total, Bazant offers 3 separate arguments as to why the lower block must be completely crushed before significant crushing of the upper portion of the building can begin.

It is quite fascinating to read these proofs while having rather overwhelming visual evidence that the events described never happened. Throughout the 3 papers written in 2007-2008, Bazant describes the WTC collapses quite literally in terms of crush down, then crush up. This literal interpretation continues today within the historic representations of the collapse progressions of the Twin Towers.

The ingrained belief in a crush down, followed by a crush up process occurring in the Twin Towers is is fascinating to observe since Bazant seems very certain within the 3 papers that it is a real event.

This conviction in a provably false mechanism demonstrates how deceived and mis-led people can be. Within each explanation of why crush down must occur before crush up, one can witness a verifiably false certainty within the "proofs".



BAZANT'S FIRST PROOF THAT CRUSH DOWN MUST PROCEED CRUSH UP

The first explanation by Bazant of why crush down must be complete before crush up begins is reproduced below:


"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



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, for example, can 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 be applied to WTC1, and they do not seem to apply to the majority of Verinage style demolitions. Yet note how Bazant appears increasingly convinced throughout the papers published in 2007-2008 that the mechanics describe the behavior of the Twin Towers.


"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 Bazant 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 variable z(t) is of the crush front relative to the roofline motion. The early crush up that Bazant claims cannot occur most certainly did occur. The roofline ceased to exist as an intact structure early into the collapse progression. Therefore use of the variable z(t) incorrectly suggests the roofline remained intact. The physical observations in the OOS propagation study show that eqs 12 and 17 cannot be applied to WTC1. Floor by floor ejections moving down the NW corner, west face and SW corner of WTC1 are observable and measurable. They certainly appear to be the actual collapse fronts. 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.


"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 described by Bazant is clearly not consistent with the physical observations in the OOS propagation study.




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, no consistent examples of buildings that behave that way can be found. So why do some people, including Dr Bazant, believe in "crush down, then crush up"? The concept 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.




As written in part 2.3, I strongly recommend approaching analysis of the BV, BL, and BLGB papers through the following 6 perspectives:



1) Direct comparison between Bazant and Seffen methods and their key equations of motion (Seffen eq 12 compared to Bazant eqs 12 and 17).

2) A basic study of 1-dimensional stacked system collision interactions with a variety of parameters altered linked here. This gives one a simple, practical sense of 1-dimensional multiple body interactions, like the type described in BV eqs 12 and 17, and the possible varieties of mechanical movements that can result from them.

3) Direct comparison of claims within BV to the actual collapse propagation rates which were recorded after the 2007-2008 Bazant papers were written.

4) Statements by Bazant in BL (the closure to BV) and BLGB demonstrating how he understood the relationship between BV eqs 12, 17 and the actual collapses of WTC1, 2.

5) Quotes by David Benson demonstrating how he understood the relationship between BV eqs 12, 17 and the actual collapses of WTC1, 2 linked here

6) Comparison of statements about WTC1 and 2 made within BV, BL, and BLGB directly with the visual record of events through the lens of the most accurate mappings of the WTC1, 2 collapse behavior (available in parts 2.1, 2.2, 2.3, and 2.4 of my book).



With the tools now available each of these separate lenses can help shed light on the accuracy and meaning of BV eqs 12 and 17. The first 3 listed perspectives were already examined in part 2.3: Mathematical Basis of ROOSD Propagation, in step 4. It was found that the model suffered from the following limitations and mistakes:

  • Inability to verify predictions
  • Limited understanding of WTC collapse features
  • Inability to identify a specific WTC collapse mode
  • Misrepresentation of the actual crushing process along the collapse front contact interface


The last 3 listed perspectives are examined next.









The second part of the paper is examined:

Review of Closure to "Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions”


Within the closure to progressive collapse, Dr Bazant begins to compare his crush down, then crush up model to the Twin Towers collapses in quite literal ways. Within BV, the first paper of the pair, Dr Bazant suggested only twice that his model based on colliding blocks and based on 4 assumptions is applicable to the WTC towers. In the closure, in contrast, Bazant assumes his model of collapse progression is applicable to the Twin towers throughout the paper and he begins to speak of the towers themselves in terms of colliding blocks subject to the 4 simplifying assumptions.

It is within the closure paper and his last paper, titled "What did and did not cause the WTC collapses in New York", that Bazant applies his model of crush down, then crush up to the WTC collapses quite literally. He concludes his last paper by explicitly stating that his progression model matches all observables of the twin towers collapses (a provably false statement).

The paper is written as a response to 2 critical responses to the collapse mechanics as written in BV.




Gregory Szuladzinski begins:

The paper presents a very nteresting concept of an accidental demolition, whereby heavy damage sustained by an intermediate
story of a building leads to the upper part of the structure crushing the lower one in a equence of story collapse steps. The focus of
the paper is on the treatment of equations of motion and very few numbers are quoted; that is, numbers that relate to the physical properties of the structure discussed, namely the World Trade
Center (WTC) towers. The following comments are intended to fill that gap as well as to ascertain the likelihood of the applicability of this concept.





Gregory is clearly referring to application of BV equations 12 and 17 to the specific case of the WTC towers. There can be no mistake that he is discussing the specific cases of WTC1 and 2 throughout the discussion.









James R. Gourley's opening words are similar:

This discussion describes flaws in the modeling and analysis of the World Trade Center collapses by Baant and Verdure in their paper entitled "Mechanics of Progressive Collapse: Learning
from World Trade Center and Building emolitions." First, the paper's two-phased approach to the collapse analysis will be considered. The writers will demonstrate that a two-phase collapse analysis is not representative of reality, because it disregards well-accepted laws of physics and therefore is not instructive. Second, the original paper's summary of the findings of the NIST report will be analyzed.




James is also clearly addressing the application of equations 12 and 17 in BV to the specific cases of WTC1 and 2. He explicitly identifies BV as a modeling and analysis of the World Trade Center collapses when he states:

This discussion describes flaws in the modeling and analysis of the World Trade Center collapses by Baant and Verdure in their paper entitled "Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions."









Zdeněk P. Baant and Jia-Liang Le opens to Gourley:



Discussion by James R. Gourley

The interdisciplinary interests of Gourley, a chemical engineer with a doctorate in jurisprudence, are appreciated. Although none
of the discusser's criticisms is scientifically correct, his discussion provides a welcome opportunity to dispel doubts recently voiced
by some in the community outside structural mechanics and engineering. It also provides an opportunity to rebut a previous similar discussion widely circulated on the Internet, co-authored by S. E. Jones, Associate Professor of Physics at Brigham Young University and a cold fusion specialist. For the sake of clarity, this
closure is organized into the points listed subsequently and rebutted one by one.


He then argues the 8 points in order, each point being clearly labelled:

1. Newton's Third Law

2. Are the Internal Forces in Upper and Lower Parts of
Tower Equal?

3. Localization of Energy Dissipation into Crushing Front

4. Can Crush-Up Proceed Simultaneously with Crush Down?

5. Why Can Crush-Up Not Begin Later?

6. Variation or Mass and Column Size along Tower Height

7. Were the Columns in the Stories above Aircraft Impact
Hot Enough to Fail?

8. Steel Temperature and NIST Report






Likewise he opens his replies to the G. Szuladzinski discussion:


Discussion by G. Szuladzinski

The interest of Szuladzinski, a specialist in homeland security, is appreciated. After close scrutiny, however, his calculations are found to be incorrect, for reasons explained in the following.



and clearly lists each reply in order:


1. Load-Displacement Curve of Columns and Energy Absorption Capacity

2. Does Excess of over Gravity Load Imply Arrest of Collapse?

3. Is the Equation of Motion for Calculating the Duration of Fall Correct?

4. Could Stress Waves Ahead of Crushing Front Destroy the Tower?




Each discussion by Gourley and Szuladzinski, and each rebuttal by Bazant, can be easily reviewed simply by going to clearly marked section. Each of the 12 clearly marked objections and rebuttals make specific reference to the case of the WTC towers.


"Discussion by James R. Gourley
3. Localization of Energy Dissipation into Crushing Front:
In the discusser's opinion: the hypothesis that "the energy is dissipated at the crushing front 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." This is a fundamental misunderstanding. Of course, blocks C and A are not rigid and elastic waves do propagate into them."


Block C basically disintegrates early into the collapse, shortly after collapse initiation. Dr Bazant doesn't seem to be aware of this throughout his 2007-2008 papers. He argues that even though we cannot see what happens within the clouds of dust, the upper portion, called block C, must have survived intact until hitting the earth because of the calculations in this paper. He continues...

But the wave velocity, given by v = ?Et / ? where Et = tangential e modulus of steel in the loaded columns and ? = mass density, tends to zero as soon as the plastic or racturing response is triggered, because in that case, Et ? 0. Therefore, as explained in courses on stress waves, no wave attaining the material strength can penetrate beyond the crushing (or plastic) front. Only harmless elastic waves can. Propagation of the crushing front is not a wave-propagation phenomenon. Destruction of many stories at the rate corresponding to the elastic wave speed, which would appear as simultaneous, is impossible. This is why the collapse is called progressive. Blocks C and A can, of course, deform. Yet, contrary to the discusser's claim, they may be treated in calculations as rigid because their elastic deformations are about 1,000 times smaller than the deformations at the crushing front."



Block C disintegrates shortly after collapse initiation, so, in retrospect, this reasoning seems absurd. He makes the claim that the elastic deformations of "upper block C" are about 1,000 times smaller than the deformations at the crushing front when visual evidence discovered later shows the upper block fell apart early, with 5 to 10 story high pieces of perimeter walls breaking away from it and falling to earth.

Perhaps these claims seemed plausible in 2008, but they seem outdated and absurd when compared to current knowledge of the photographic record.



"4. Can Crush-Up Proceed Simultaneously with Crush Down?I

t can, but only briefly at the beginning of collapse, as mentioned in the paper."


He explicitly states that he considered crush down, then crush up to be what happened to the Twin Towers.

"Statements such as "the columns supporting the lower floors . . . were thicker, sturdier, and more massive,"
although true, do not support the conclusion
that "the upper floors (i.e., the floors comprising Part C) would be more likely than the lower floors to deform and yield during collapse" (deform they could, of course, but
only a little, i.e., elastically)."


They deformed more than a little. They dis-integrated.

"More-detailed calculations than those included in their paper were made by Bažant and Verdure to address this question. On the basis of a simple estimate of energy corresponding to the area between the load-deflection curve of columns and the gravity force for crush down or crush up, it was concluded at the onset that the latter area is much larger, making crush-up impossible."


Impossible? Visual evidence discovered since Dr Bazant wrote these words conclusively shows that the upper portion must have disintegrated early into the collapse. Dr Bazant is obviously wrong in his conviction that crush-up was impossible, yet he maintains this conviction throughout this paper and his next paper on the subject, BLGB. When Bazant's descriptions are compared to the visual reconstructions of the collapse progressions currently available, it is clear that he is taking his 1 dimensional analytical model of crush down, then crush up as a real description of the collapse modes of the Twin Towers. He continues...



BAZANT'S SECOND PROOF THAT CRUSH-DOWN MUST PRECEDE CRUSH-UP

He proceeds to show "rigorous proof" in the form of 2 differential equations with only 2 degrees of freedom why early significant "crush up" cannot exist during the WTC1 collapse even though we now know the "upper block C" was destroyed early in the collapse.

We have now carried out accurate calculations, which rigorously justify this conclusion and may be summarized as follows.

Consider that there are two crushing fronts, one propagating upward into the falling block, and the other down-ward. Denote v1 , v2 = current velocities of the downward and upward crushing fronts (positive if downward); x(t) , z(t)
= coordinates of the mass points at these fronts before the collapse began (Lagrangian oordinates); and q(t) = current coordinate of the tower top. All the coordinates are measured from the initial tower top downward. After the ollapse of the first critical story, the falling upper Part C with the compacted Part B impacts the stationary lower Part A. During that impact, the total momentum and the total energy must both be conserved. These conditions yield two lgebraic equations


No compacted layer B ever existed to protect "block C" from "block A". They are only analytical abstractions mistaken to be real qualities of the Twin Towers. Bazant clearly maintains an increasingly false certainty that the mechanism he describes applies to the Twin Towers.

With the gift of hindsight, it is easily verifiable that his repeated insistence on no significant early crush up is misguided. He seems convinced, yet he is provably wrong.



During impact, ? = 0.2 for the North Tower and 0.205 for the South Tower. For the North or South Tower: m0 = 54.18· 106 or 112.80· 106 kg, m1 = 2.60· 106 or 2.68· 106 kg,
m2 = 3.87· 106 or 3.98· 106 kg, and ms = .627· 106 kg for both. For a fall through the height of the critical story, by solving Eq. (2) of Bazant et al. 2007, one obtains the rush-front velocity v0 = 8.5 m / s for the North Tower and 8.97 m / s for the South Tower. he solution of Eqs. (1) and (2) yields the following velocities after impact: v1 = 6.43 or 6.80 m / s, v2 = 4.70 or 4.94 m / s, and vcu = 2.23 or 2.25 m / s for the North or South Tower. These data represent the initial values for the differential equations of motion of the upper Part C and of the compacted layer B. If Lagrangian coordinates x(t) and z(t) of the crush-down and crush-up fronts are used, these equations can easily be shown to have the following forms:



He is applying a 1 dimensional "buckle-up, buckle-down" set of equations with 2 degrees of freedom to describe the complexity of WTC1 motion. In reality there is no such thing as a compacted layer of "zone B" rubble protecting "block C" from "block A". There is no such thing as normal forces Fc and Fj acting through a "zone B" on "blocks". There is no such thing as a surviving "block C", no such thing as crush-down, then crush-up, very little proof of buckled columns, core or perimeter, within the rubble. Yet Bazant writes as if he is certain these features represent the real movement. Untroubled by such contradictions within the visual record, Dr Bazant continues...


"These two simultaneous differential equations have been converted to four first-order differential equations and solved
numerically by the Runge-Kutta method. The solution has been found to be almost identical to the solution presented in the paper, which was obtained under the simplifying assumption that the crush-up does not start until after the crush down is finished."


He claims to rigorously prove that crush down must run to completion before significant crush-up can occur based on his calculations. We now know that none of this actually happened. He continues...

"The reason for the difference being negligible is that the condition of simultaneous crush-up, x ? 0, is violated
very early, at a moment at which the height of the first overlying story is reduced by about 1%."


And what is the condition for simultaneous crush-up, according to Dr Bazant? One percent of a 12 foot floor height is about 1 to 2 inches. Dr Bazant believes that the crush-up process in WTC1 will be arrested after penetrating about 1 inch upwards. Watch how he mathematically justifies this claim during the earliest moments of collapse...


"This finding further means that the replacement of the load-deflection curve in Fig. 3 of the paper by the energetically quivalent Maxwell line that corresponds to a uniform resisting force F? cannot be sufficiently accurate to study the beginning of two-way crush.)"


So for the first floor of crushing, he recalculates (and reaches the same absurd conclusion)....

Therefore, a solution more ac-
curate than that in the paper has been obtained on the basis of Eqs. (3) and (4). In that solution, the variation of the crushing force F? within the story was taken into account, as shown by the actual calculated resistance force labeled F(u) in Fig. 3 of the paper, by the force labeled F(z) on top of Fig. 4 of the paper, and by the resistance curves for the crushing of subsequent stories shown in Fig. 5 of the paper. The precise curve F(u) was calculated from Eq. 8 of Bazant and Zhou (2002). Very small time steps, necessary to resolve the changes of velocity and acceleration during the collapse of one story, have been used in this calculation. Fig. 1 shows the calculated evolution of displacement and velocity during the collapse of the first overlying story in two-way crush. The result is that the crush-up stops (i.e., (x) )_ drops to zero? when the first overlying story is squashed by the distance of only about 1.0% of its original height for the North Tower, and only by about 0.7% for the South Tower (these values are about 11 or 8 times greater than the elastic limit of column deformation)."


Crush-up stops after an upward crush of only an inch or two. How does it stop? If the above passage is read carefully, one can observe the mechanism described depends on the strength of the upper columns riding on a zone B. According to Dr Bazant, since the "upward force" on the "upper block" is insufficient to buckle the "upper block" columns upwards, he concludes an "upper block C" will survive until it collides with the earth. This is explained in more detail over the next few passages:

"Why is the distance smaller
for the South Tower even though the falling upper part is much more massive? That is because the initial crush-up velocity is similar for both towers, whereas the columns are much stronger (in proportion to the weight carried)."


Dr Bazant believes it will be the upper columns pushing against a rubble zone B that will preserve the upper block.


"The load-displacement diagram of the overlying story is qualitatively similar to the curve with unloading rebound sketched in Fig. (4c) of the paper and accurately plotted without rebound in Fig. 3 of the paper. The results of accurate computations are shown by the displacement and velocty evolutions in Fig. 1."




Fig 2.62, which is figure 1 from the Bazant and Le paper reproduced. The figure shows Dr azant's conception of how the "crush up" process compares to the "crush down" process for both WTC1 (north tower) and WTC2 (south tower). According to Bazant, the process of "crush up" in WTC1 will be arrested after it proceeds a mere 1 inch upward. At this point, the "upper block" will be "cushioned" by a region of accumulated rubble which he calls "zone B". The "upper block" of WTC1 and 2 then "survives" until its lower edge makes firm contact with the earth through the completely compacted lower portion of the building. Lastly, the "upper block" is crushed upward and is destroyed.



"So it must be concluded that the simplifying hypothesis of one-way crushing (i.e., of absence of simultaneous crush-up),
made in the original paper, was perfectly justified and caused only an imperceptible difference in the results."


Except for the fact that the upper block actually dis-integrated.

"The crush-up simultaneous with the crush down is found to have advanced into the overlying story by only 37 mm for the North Tower
and 26 mm for the South Tower."


Dr Bazant claims there could have been only 37 mm of upwards penetration before the "upper block" restabilizes on a rubble zone B and rides it down to earth.

"This means that the initial crush-up phase terminates when the axial displacement of columns is only about 10 times larger than their maximum elastic deformation. Hence, simplifying the analysis by neglecting the initial two-way crushing phase was correct and
accurate."


Once again he states that the survival of the upper block is due to column strength within the upper portion. This column strength pushes against a homogeneous zone B. According to Bazant, the resulting upward force is insufficient to buckle the upper columns. This is what he considers to be the mechanism that preserves the upper block. According to Dr Bazant, the impossibility of significant crush-up has been "proven". In reality the upper block basically disintegrated .



"5. Why Can Crush-Up Not Begin Later? The discusser further states that "it is difficult to imagine, again from a basic physical standpoint, how the possibility of the occurrence of crush-up would diminish as the collapse progressed."


This was about the only thing James Gourley said correctly in the paper. It is pretty difficult to imagine why crush up cannot occur with a real building, and especially with the Twin Towers. Dr Bazant explains:

"Yet the discusser could have imagined it easily, even without calculations, if he considered the free-body equilibrium diagram
of compacted layer B, as in Fig. 2(f) of the paper."


In figure 2f, shown below, Dr Bazant simplifies the complex process of crushing, column spearing, the outward splitting of whole perimeter walls and the bypassing of core columns like opposing spears as two "big blocks" with the following block scenario:



Fig 2.63, which is figure 2 from the Bazant and Le paper reproduced. This is how Bazant defines variables for the equations he uses.



For a reader that wants to understand why Dr Bazant mistakes the upper block C to be virtually indestructible, it is important to understand this diagram and to understand how Bazant concluded no significant early crush up is possible. He continues...


"After including the inertia force, it immediately follows from this diagram that the normal force in the supposed crush up front acting upward onto Part C is


For Bazant, it is the force through the base of the upper columns pushing against zone B compared to their buckling strength that determines if crush up occurs. If the upward force is insufficient to buckle the upper columns, the upper portion is considered to remain intact. Sufficient upward buckling force is only attained when the base of the upper columns strike the earth through zone B.

Currently, researchers have the ability to compare these claims with a reconstructed visual record of the actualy collapse progressions of the Twin Towers. It is clear that Bazant is taking an extremely simplified analytical model quite literally. Throughout his final 2 papers on the subject in 2007-2008, he increasingly takes the simplified 1 dimensional model for real building behavior.



"The discussers' statement that "the yield and deformation strength of . . . Part C would be very similar to the yield and
deformation strength of . . . the lower structure" shows a misunderstanding of the mechanics of failure. Aside from the fact that "deformation strength" is a meaningless term (de-
formation depends on the load but has nothing to do with strength), this statement is irrelevant to what the discussers try to assert. It is the normal force in the upper Part C that is much smaller, not necessarily the strength (or load capacity) of Part C per se."


No intact upper block C exists. No such single normal force exists. They are analytical abstractions mistakenly taken for real behavior.

"Force F? acting on Part C upward can easily be calculated from the dynamic equilibrium of Part C (see Fig. 2g), and it is found that F? never exceeds the column crushing force of the overlying story. This confirms again
that the crush-up cannot restart until the compacted layer hits the ground."


Yet again, he states his reasoning why he believes the upper portion will experience no significant crush up until striking earth. He believes that the "upward force" on the "upper block" never exceeds the column crushing force of the story above. To him, it is the strength of the upper columns, their inability to buckle upwards, that preserves the upper block from damage.

It is natural to wonder: Why don't the upper and lower column stubs just spear through rubble zone B, allowing upper and lower portions to penetrate each other and mutually destroy one another? In Bazant's view, the rubble zone B provides a cushion of debris on which the bottom column stubs of the upper portion can remain supported, thus shielding the upper block C from damage. I know that makes no sense, but that is what Dr Bazant's crush-up, crush-down mechanics is based on, just as he has described in this section.





"6. Variation or Mass and Column Size along Tower Height:

This variation was accurately taken into account by Bazant et al. (2007). Those who do not attempt to calculate might be surprised that the effects of this variation on the history of motion and on the collapse duration are rather small. Intuitively, the main reason is that, as good design requires, the cross-section areas of columns increase (in multistory steps, of course) roughly in proportion to the mass of the overlying
structure. For this reason, the effect of column size approximately compensates for the effect of the columns’ mass."


Varying column strength means nothing since the columns were bypassed by the falling debris as the reconstructed visual record of the collapse progressions show. Dr Bazant did not know that the entire east-west width of the WTC1 core temporarily survived the collapse. He also did not know the true conditions of the large, large majority of core and perimeter column sections within the rubble. In truth, varying column strength has nothing to do with the rates of descent.

He concludes his rebuttal to James Gourley with this comment:



Closing Comments Although everyone is certainly entitled to express his or her opinion on any issue of concern, interested critics should realize that,
to help discern the truth about an engineering problem such as the WTC collapse, it is necessary to become acquainted with the relevant material from an appropriate textbook on structural mechanics. Otherwise critics run the risk of misleading and wrongly influencing the public with incorrect information."


This paper by Dr Bazant served to mislead and wrongly influence the public with a literal interepretation of block mechanics asserted with false certainty since 2007 to the present.



Discussion by G. Szuladzinski

The following graphic shows Dr Bazant's free-body diagram in which upward and downward forces Fc and Fj act though "blocks". If the upper portion disintegrates, the diagram has no meaning.



Fig 2.64, which is figure 3 from the Bazant and Le paper reproduced. As Dr Bazant illustrates, he believes these forces act through the upper and lower columns, separated from one another through a "zone B". Zone B effectively buffers the "upper block" from the "lower block", protecting the "upper block" from all but "harmless elastic waves" .



"3. Is the Equation of Motion for Calculating the Duration of Fall Correct? It is not. Under the heading “Duration of Fall,” the discusser writes the equation of motion (Newton's law) as d(mv) / dt = m0g (in the discusser's notation, m is M, and m0 is M 0). He states that “M 0 is the mass of the upper part of the building,” and argues that "the net effect of gravity applies now only to M 0.” This statement is incorrect. The accreted mass, which he denotes as ?z, does not disappear and thus is also subjected to gravity. Therefore, the discusser's equation of motion for the falling mass must be revised as d?m?t?v? / dt = m?t?g, and the solution is totally different from the last equation of the discusser. This is, of course, only the most simplified form of the equation of motion, originally applied to WTC collapse by E. Kausel of MIT (Kausel 2001). A realistic form of the equation of motion must take into account the energy dissipation Fc per unit height, the debris compaction ratio, and the mass shedding ratio, as shown in Eq. (12) of the paper."


A realistic form of the equations of motion must take into account that no postulated upper block C exists, the upper portion of WTC1 effectively fell apart shortly after collapse initiation.


"For the resistance to motion near the end of collapse, it is also necessary to include the energy per unit height required
for the comminution of concrete floor slabs and walls and for expelling air at high speed, which is found to be close to the speed of sound (Bažant et al. 2007). The discrepancy between the observed collapse duration and the collapse duration of 23.8 s calculated by the discusser does not support his conclusion that "the postulated failure mode is not a proper explanation of the WTC Towers collapse."


No, but there are numerous observed features during the collapses of WTC1 and 2 which show the failure mode postulated by Dr Bazant grossly contradicts observables.

"Rather, what this discrepancy means is that the discusser's calculations are erroneous. The collapse duration alculated in the paper for the most realistic choice of input
values is in agreement with the observations."


In agreement with the observations? A 1 dimensional 2 variable block model based on crush down, then crush-up agrees with observations? The visual reconstructions of the collapse processes show these statements to be untrue.

"Moreover, a more accurate analysis by Bazant et al. (2007) is found to be
in nearly perfect agreement with the video ecords of motion, available for the first few seconds of collapse, as well as with the available seismic records for both towers."


Near perfect agreement? The mechanism is an analytical abstraction.

Since BL was written, researchers that use the complete photographic record (and not just bits and pieces) mapped propagation rates using much more than the first few seconds of motion and the seismic records. The behavior of both cores has been mapped. The behavior of all perimeter walls has been mapped. Bazant's postulated failure mode is not a proper explanation of the WTC Towers collapse. The literal interpretation of crush down, then crush up mechanics is verifiably incorrect.



"Could Stress Waves Ahead of Crushing Front Destroy the Tower? They could not. The discusser is, of course, right in pointing out that the “stress wave . . . will partially reflect from all the discontinuities" ?though not only 'reflect' but also 'diffract'). But while alluding to shock fronts, he is not right in stating that a "shock loading . . . will greatly magnify the effect of all discontinuities."
Since the stress-strain diagram of the steel used, as reported by FEMA (Figs. B-2 and B-3 in McAlister 2002), exhibits a long yield plateau, rather than hardening of gradu lly decreasing slope, the shock front coincides with the crushing front, which is not a wave phenomenon. The only waves than can penetrate ahead of this front are elastic. When these waves hit discontinuities such as joints, local energy-absorbing plastic strains and fractures will be created, and what will be reflected and iffracted will be weakened elastic waves.
Thus it is not true that "during such eflections, enhancements take place." Rather, the energy of these waves ahead of the crushing front will quickly dissipate during repeated reflections and diffractions, and only noncatastrophic localized damage will happen to the structure until the crushing front arrives. To sum up, the existence of stress waves ahead
of the crushing front does not cast any doubt on the analysis in the paper."


The visual evidence of the upper block dis-integrating and the incorrect belief in it's survival does that.

After all the verifiably incorrect statements in this paper, Dr Bazant concludes thus:




"Conclusion Although closing comments similar to those in the preceding discussion could be repeated, let it suffice to say that the discusser's conclusion that "the motion will be arrested during the damaged story collapse and the building will stand" is incorrect. Thus, the recent allegations of controlled demolition are baseless."


The paper basically presents poor arguments by both Gregory Szuladzinski and James Gourley, counters these poor arguments using an incorrect, outdated 1 dimensional model based on a surviving "upper block" that grossly contradicts the visual record, and thus concludes "allegations of controlled demolition are baseless".









Dr Bazant's final paper on the WTC collapses was written in 2008.

The paper: 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
(BGLB) is linked here


In his final paper on the WTC collapses, Dr Bazant applies his crush down, then crush up progressive collapse model to the Twin Towers quite literally and liberally throughout the paper. He concludes the paper byclaiming his model matches all observables. In his own words, from the conclusion:

"One and the same mathematical model, with one and the same set of parameters, is shown capable of matching all of the observations, including: (1) the video records of the first few seconds of motion of both towers, (2) the seismic records for both towers, (3) the mass and size distributions of the comminuted particles of concrete, (4) the energy requirement for the comminution that occurred, (5) the wide spread of the fine dust around the tower, (6) the loud booms heard during collapse, (7) the fast expansion of dust clouds during collapse, and (8) the dust content of cloud implied by its size."


Careful reconstruction of the collapse progression from the visual record done since this paper was written (appearing as section 2.1 of this book) allows a superior re-evaluation of this claim by Bazant. Mapping of the perimeter walls, building core, visible collapse fronts and resulting rubble condition and distribution allow anyone to verify that crush down, then crush up block mechanics doesn't match all observations as he claims in the conclusion. In fact, it does not match a single observation of the many cited in the WTC progressive floor collapse model in the OOS regions presented earlier.



The abstract of the paper reproduced in its entirety:

"Abstract: Previous analysis of progressive collapse showed that gravity alone suffices to explain the overall collapse of the World Trade Center (WTC) towers. However, it remains to be checked whether the recent allegations of controlled demolition have any scientific merit. The present analysis proves that they do not. The video record available for the first few seconds of collapse is shown to agree with the motion history calculated from the differential equation of progressive collapse but, despite uncertain values of some parameters, it is totally out of range of the free fall hypothesis, on which these allegations rest. It is shown that the observed size range (0.01 mm"0.1 mm) of the dust particles of pulverized concrete is consistent with the theory of comminution caused by impact, and that less than 10% of the total gravitational energy, converted to kinetic energy, sufficed to produce this dust (whereas more than 150 tons of TNT per tower would have to be installed, into many small holes drilled into concrete, to produce the same pulverization). The air ejected from the building by gravitational collapse must have attained, near the ground, the speed of almost 500 mph (or 223 m/s, or 803 km/h) on the average, and fluctuations must have reached the speed of sound. This explains the loud booms and wide spreading of pulverized concrete and other fragments, and shows that the lower margin of the dust cloud could not have coincided with the crushing front. The
resisting upward forces due to pulverization and to ejection of air, dust and solid fragments, neglected in previous studies, are found to be indeed negligible during the first few seconds of collapse but not insignificant near the end of crush-down. The calculated crush-down duration is found to match a logical interpretation of seismic record, while the free fall duration grossly disagrees with this record."




Review of the abstract:

"Previous analysis of progressive collapse showed that gravity alone suffices to explain the overall collapse of the World Trade Center (WTC) towers. However, it remains to be checked whether the recent allegations of controlled demolition have any scientific merit. The present analysis proves that they do not."


This is not true. Collapse initiation (meaning early deformation into the initial lateral progression of column buckling) is the key place to look to distinguish between a natural collapse and demolition. Most of the arguments in BLGB concern collapse progression, studying features that would be indistinguishable whether the demolition occurred or not.

"The video record available for the first few seconds of collapse is shown to
agree with the motion history calculated from the differential equation of progressive collapse but, despite uncertain values of some parameters, it is totally out of range of the free fall hypothesis, on which these allegations rest."


A demolition which utilizes weaker seams within the building's structure would undergo just about the same collapse progression as one that started by natural failures. The difference is in how the collapse initiated, not how it progressed.

"It is shown that the observed size range (0.01 mm"0.1 mm) of the
dust particles of pulverized concrete is consistent with the theory of comminution caused by impact, and that less than 10% of the total gravitational energy, converted to kinetic energy, sufficed to produce this dust (whereas more than 150 tons of TNT per tower would have to be installed, into
many small holes drilled into concrete, to produce the same pulverization)."


Why the absurd comparison with "more than 150 tons of TNT per tower would have to be installed, into many small holes drilled into concrete"??? A demolition which utilizes weaker seams within the building's structure would undergo just about the same collapse progression as one that started by natural failures. The difference is in how the collapse initiated, not how it progressed. Expected concrete comminution would be about the same in both cases.

"The air ejected from the building by gravitational collapse must have attained, near the ground, the speed of almost 500 mph (or 223 m/s, or 803 km/h) on the average, and fluctuations must have reached the speed of sound. This explains the loud booms and wide spreading of pulverized concrete and other fragments, and shows that the lower margin of the dust cloud could not have coincided with the crushing front."


Collapse progression would be about the same for both cases.

"The resisting upward forces due to pulverization and to ejection of air, dust and solid fragments, neglected in previous studies, are found to be indeed negligible during the first few seconds of collapse but not insignificant near the end of crush-down. The calculated crush-down duration is found to match a logical interpretation of seismic record, while the free fall duration grossly disagrees with this record."


Once again, anyone who cares to measure can see that the collapse front of WTC1 does not propagate along a free fall trajectory. A demolition exploiting weaker natural seams within the structure would be expected to fall just as a collapse initiated naturally, neither case being at freefall. The difference is in what caused initiation. Propagation features will be mostly identical in both cases.


Bazant introduces the same analytical model of crush down, then crush up, applying it literally to the Twin Towers:


"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 differential 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."



Fig 2.65, which is figure 2 in the Bazant, Le, Greening, Benson paper reproduced. This illustrated Dr Bazant's conception of the WTC twin towers collapse scenario in 2008. Once again, he conceives than of experiencing a "crush down" phase which, when completed, is followed by a "crush up" phase. He conceives of energy dissipation as having an element due to column buckling. He also assigns variables describing notion in terms of this conception.



The physical observations within part 2.1 of this book show that these claims are wrong. The differential equations of motion derived in BV cannot be applied to WTC1. In reality there is no such thing as "crush down, then crush up" for WTC1. The claim in bold letters, made in 2008, seems absurd when tested against the new video imagery now available.

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

"Variation of Mass and Buckling Resistance along the Height

Based on the area under the buckling curve in Fig. 3 of Bazant and Verdure (2007), the energy dissipation due to column buckling at the impact zone of the North Tower (96th story) is Fb(1 - )h = 0.51 GJ (or approximately 0.5 GJ, as estimated by Bazant and Zhou 2002). For other stories, this quantity is scaled according to the approximate cross section area of columns."


The physical observations in part 2.1 show that columns buckling did not contribute to the frictional forces resisting collapse propagation. As in the 2007 papers, Dr Bazant seems to believe they are a significant factor.


In figure 3 shown below, in a section titled "Velocity of Air Ejected from Tower", Dr Bazant illustrates his conception of the transition of crush-down to crush-up.



"It is nevertheless interesting to check the amount of explosives that would be required to produce all of the pulverized concrete dust found on the ground. Explosives are notoriously inefficient as a comminution tool. At most 10% of their explosive energy gets converted into the fracture energy of comminution, and only if the explosive charges are installed in small holes drilled into the solid to be comminuted. Noting that 1 kg of TNT releases chemically about 4 MJ of energy, the total mass of TNT required to pulverize 14.6 — 107 kg concrete material into dust of the sizes found on the ground would be 316 tons. So, in order to achieve solely by explosives the documented degree of concrete pulverization, about 1.36 tons of TNT per story would have to be installed into small holes drilled into the concrete slab of each story, and then wired to explode in a precise time sequence to simulate free fall."


If demolition by exploiting natural weaker seams in the structure is possible, the resulting pulveration would be about the same as a collapse that is initiated naturally. Why would a demolition plan include such an absurd placement of an absurd amount of TNT if it doesn't have to?

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

"Note in Fig. 7 that the motion identified from the videos is generally seen to pass well inside the predicted band of uncertainty of the motion calculated from Eq. (2). This fact supports the present analysis. The main point to note is that the curve identified from the video record grossly disagrees with the free fall curve, for each tower. The belief that the towers collapsed at the rate of free fall has been a main argument of the critics claiming controlled demolition.
The video record alone suffices to prove this argument false."




The claim of free-fall collapse propagation for WTC1 is provably false. Dr Bazant incorrectly claims that "The belief that the towers collapsed
at the rate of free fall has been a main argument of the critics claiming controlled demolition". There are many critics and some of them can measure accurately.



He continues,


"These conclusions show the allegations of controlled demolition to be absurd and leave no doubt that the towers failed due to gravity-driven progressive collapse triggered by the effects of fire."


as long as the question is posed as an artificially narowed false choice between two extremes.

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

"These durations match reasonably well the durations of the crush-down phase calculated from Eq. (2), which are 12.81 s and 10.47 s for the North and South towers, under the assumption that the reduction factor applied to Fb is 2/3. If the full uncertainty range, 2 [0.5, 0.8], is considered, the calculated mean durations are 12.82 s and 10.49 s, respectively. This uncertainty is shown by error bars in Fig. 8. Now note that these durations are, on the average, 65.5% and 47.3% longer than those of a free fall of the upper part of each tower, which are 7.74 s for the North Tower and 7.11 s for the South Tower. So, the seismic record, too, appears to contradict the hypothesis of progressive demolition by timed explosives."





Eq 2 was derived in BV. It is incorrect to apply it to WTC1 since the 4 physical observations in the OOS collapse propagation study show the simplifying assumptions used to derive the equation cannot be applied to WTC1.
Dr Bazant once again presents a hypothesis of progressive demolition by timed explosives as being dependent on "freefall" collapse. In a demolition which exploits known vulnerable seams within the building's structure, the collapse propagation is the same as that of a natural collapse.

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


"Since the initial crush-up phase terminates at very small axial deformation, it must be concluded that the simplifying hypothesis of one-way crushing is perfectly justified and causes only an imperceptible difference in results."


The is once again justifying his hypothesis that one way crushing applies to WTC1 is absurd. Just as in BL reviewed earlier, he is continuing to portray an anaytical abstraction as representative of reaal building behavior. One way downward crushing doesn't match the visual record as presented in the OOS collapse propagation study.

"If random fluctuation of column strength is taken into account, the crush-up resisting force F0c in the first overlying story may be lower or higher than indicated by the foregoing deterministic analysis. If it is lower, the crush-up will penetrate deeper. But even for the maximum imaginable standard deviation of the average column strength in a story, the crush-up will get arrested before it penetrates the full story height."


The visual evidence shows that the crush-up obviously did not "get
arrested before it penetrated the full story height". It is hard to believe comments like these were allowed to stand unchallenged for so long.


"In comparison with all these calculations, the claim that the observed fineness, extent and spread of pulverized dust could be explained only by planted
explosives has been found to be absurd. Only gravity driven impact could have produced the concrete dust as found on the ground."


Once again, a demolition initiated with planted explosives will have the same concrete pulverization characteristics as one initiated naturally. Dr Bazant seems incapable of recognizing this distinction.

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

"Some lay critics claim that out should be about 95%, in the (mistaken) belief that this would give a faster collapse and thus vindicate their allegation of free fall."


Free fall? Dr Bazant seems to persist in the mistaken belief that allegations of free fall are central to the argument for demolition. The claim that WTC1 fell at free fall is provably false. Collapse propagations considerably less than free fall in OOS regions through a progressive floor collapse mechanism can be expected whether the buildings were demolished or not.


"Previously Refuted Hypotheses of Critics

Some other hypotheses have already been refuted in the discussions at the U.S. National Congress of Theoretical and Applied Mechanics in Boulder, June 2006. This includes the hypothesis that the structural frame was somehow brought to the brink of strain-softening damage and then destroyed by a peculiar phenomenon called the ”fracture wave”, causing the collapse to occur at the rate of free fall."


A demolition which exploits natural weaker seams within the building's structure would have the same collapse propagation rates as a natural collapse. He yet again associates the accusation of demolition as meaning a free fall collapse would be expected.

"There are three serious problems with this hypothesis: 1) It treats strain-softening as a local, rather than nonlocal, phenomenon (Bazant and Verdure 2007); 2) it considers the structural frame to have somehow been brought to a uniform state on the brink of strain softening, which is impossible because
such a state is unstable and localizes as soon as the strain softening threshold at any place (Bazant and Cedolin 2003, Sec 13.2); 3) the ‘fracture wave’ is supposed to cause comminution of concrete but the energy required for comminution cannot be delivered by this wave."

"Another previously refuted hypothesis of the lay critics is that, without explosives, the towers would have had to topple like a tree, pivoting about the base (Bazant and Zhou 2002) (Fig. 6b or c)."


Topple like a tree?

"This hypothesis was allegedly supported by the observed tilt of the upper part
of tower at the beginning of collapse (Fig. 6a). However, rotation about a point at the base of the upper part (Fig. 6c) would cause a horizontal reaction approximately 10.3— greater than the horizontal shear capacity of the story, and the shear capacity must have been exceeded already at the tilt of only 2.8 (Bazant and Zhou 2002). Thereafter, the top part must have been rotating essentially about its centroid, which must have been falling almost vertically.
The rotation rate must have decreased during the collapse as further stationary mass accreted to the moving block. So, it is no surprise at all that the towers collapsed essentially on their footprint. Gravity alone must have caused just that (Bazant and Zhou 2002)."



When this was written it was believed that WTC1 had tilted at least 8 degrees to the south during the initial column failure sequence. This is the claim made by the NIST multiple times within their reports on the collapse. Careful review of the visual record has shown that all columns initially failed over a tilt of less than 1 degree.


"In the structural engineering community, one early speculation was that, because of a supposedly insufficient strength of the connections between the floor trusses and the columns, the floors ‘pancaked’ first, leaving an empty framed tube, which lost stability only later. This hypothesis, however, was invalidated at NIST by careful examination of the photographic record, which shows some perimeter columns to be deflected by up to 1.4 m inward. This cannot be explained by a difference in thermal expansion of the opposite flanges of column. NIST explains this deflection by a horizontal pull from catenary action of sagging floor trusses, the cause of which has already been discussed. This pull would have been impossible if the floor trusses disconnected from the perimeter columns."


Careful review of the visual record demonstrates that the NIST characterization of building movement over the initial column failure sequence was effectively a fabrication.



BLGB conclusions reviewed in parts:

"Several of the parameters of the present mathematical model have a large range of uncertainty. However, the solution exhibits small sensitivity to some of them, and the values of others can be fixed on the basis of observations or physical analysis. One and the same mathematical model, with one and the same set of parameters, is shown capable of matching all of the observations, including: (1) the video records of the first few seconds of motion of both towers, (2) the seismic records for both towers, (3) the mass and size distributions of the comminuted particles of concrete, (4) the energy requirement for the comminution that occurred, (5) the wide spread of the fine dust around the tower, (6) the loud booms heard during collapse, (7) the fast expansion of dust clouds during collapse, and (8) the dust content of cloud implied by its size."


As pointed out repeatedly, please notice how none of the 8 points listed address how each tower originally failed in the first place. The crush down, then crush up mechanism proposed by Bazant doesn't match a single observable of the many collapse progression features documented in the OOS progressive collapse model.


"At the same time, the alternative allegations of some kind of controlled demolition are shown to be totally out of range of the present mathematical model, even if the full range of parameter uncertainties is considered."


This is not true since a demolition which exploits weaker natural seams within the building's design would exhibit similar collapse propagation characteristics.


"These conclusions show the allegations of controlled demolition to be absurd and leave no doubt that the towers failed due to gravity-driven progressive collapse triggered by the effects of fire."


By mischaracterizing the most central arguments for demolition as extreme cases like the verifiably false belief in free-fall, or the need for (150) tons of TNT to pulverize concrete, or the belief the towers should "topple like trees", Dr Bazant can paint all those who are not blind to extreme contradictions between the official version of events and witnessed events as believing absurd claims.


Concerning the key differentiator between CD and natural collapse, early deformation and collapse initiation, BLGB offers little of use.







David Benson, a co-author of BLGB, discusses WTC collapse mechanics with this author


The following quotes are from David Benson, one of the co-authors of BLGB. I had the pleasure of communicating with David Benson at the time BLGB was first published in 2008 and these quotes are from our correspondence.

The quotes demonstrate how without a good knowledge of the recorded events, analytical ability can lead to unrealistic claims. When these statements are compared with what is currently known about initial and progressive motion of the collapses, it becomes clear why careful observation and measurement are the fundamental constraints within a physical theory. Analytical ability divorced from careful observation can lead to wildly incorrect assertions and false certainty as the quotes demonstrate.


David Benson in recorded dialog with the author:

"On another matter, we ordinarily start with the simplest hypothesis and stik with it until some evidence shows the hypothesis must be modified. In the case of the top portion, the simplest is that it stayed on top most of the way down; say with the roof at around floor 25. Until someone develops some actual evidence to the contrary, I'll stick with that rather than unending speculation and new simulations of the resulting hypothesis."

from this post

He believed that some top portion stayed on with the roof until around floor 25. This was the simplest hypothesis?


"Better to call the section cushed, rather than compressed, as it is inelastic. It did contain, for the most part, the core columns; only a few were bypassed."

from this post

It was later discovered that the entire east-west width of the core survived the initial collapse.



"Albert Einstein once said something to the effect that a model should be as simple as possible, but no simplier. The B&V crush-down equation meets that criterion as long as one only considers measurements taken on the antenna mast. With your careful observations of perimeter wall sections breaking off at and above floor 98 and OneWhiteeEye's observation earlier on this thread to the effect that this led to a inhomogeneity in the structure, I then, as reported earlier on this thread, in effect moved zone C up to start at floor 102. That fits the antenna tower measurements and also (approximately) the additional observation that OneWhiteEye posted earlier on this thread, regarding the SW corner of WTC 1."



"So, the simplest possible model for WTC 1 collapse works very well even though I now conclude that some 4+ floors of early crush-up occurred due to the inhomogeneity introduced by missing perimeter wall sections. But not more early crushup than that. Once those were crushed, the homogeneity is re-introduced so that Bazant & Le then applies. I think. It's a point that needs checking."



He quotes one form of Einsteins razor, and then completely misapplies it.



"More complex equations simply are not required. Parsimony suggests the B&V crush-down equation with vertical avalanche resisting force together with starting the crushing front around floor 102, being good enough for the data in hand, is indeed good enough."

from this post

Good enough?


"Assuming homogeneity, Bazaant & Le show thaqt zone C is almost industrucible. That's mechincs for you. The sturcture obviiously was not homogeneous and you have, in other threads, shown some distruction along the west and north walls. In of itself that mass loss is not important, but it does mean the floor trusses in those areas have been weakened. So an average of about 4--6 stories above floor 98 do not come close to satisfying the homogeneity condition. Fine. consider then that zone C is from floor, say, 102 up. To keep the equation simple, assume crush-down begins from there. As I mentiioned in this thread yesterday, this works well enough to match the additional observations by OneWhiteEye.
"

from this post

That's mechanics for you.



"Zone C simply disappears into the obscuring dusts. Not sufficient reason to assume it is being crushed first. If sufficiently close to homogeneous, then from Bazant & Le it is not being crushed at all."

from this post

If sufficiently close to homogeneous?



"OneWhiteEye --- I've been thorugh all this before. Homogenization is fine when the tilt is taken into account; crushing proceeded on 3+ floors simultaneaously which is surely better represented by homogenization that by stepwise floor-by-floor model. However, both give essentially ythe same results; shagster actually went to the effort of running his own version of Greening's ideas using minifloors to demonstrate this; although, after some study, this is analytically obvious.


"The issue of early crush-up never seems to die, does it? The problem is that it would have to proceed against the force of gravity, not with it. Instead what you seem to have noticed in frame 1007 is a lack of one dimensionality, with zone C west perimeter wall going outside the lower portion, yes? That actually does not trouble me, yet.
"

from this post

No, it did eventually die, except for the cult following and the fact that BLGB is still considered the most up-to-date model of the collapse progressions of WTC1 and WTC2 in academic literature.

"No sign of zone C falling aprat as long as it can be seen. Unlike the case of WTC 2."

from this post

In 2009 he determines there is no visual evidence for an "upper block" falling apart within the visual record. He had access to the same visual record the author used to assemble the first visual recontruction of the collapse progression processes in later in the same year.

"Major_Tom ---
Do you doubt Newton's Laws?
Do you doubt http://en.wikipedia.org/wiki/D'Alembert's_principle?
Do you doubt the applicability of the four simplifying assumptions in B&V?
If not, the conclusion of little early crush-up of zone C follows.
Further, the timing studies in BLGB show that most of zone C mass must have stayed on top most of the way down."

from this post

It is just that simple. How could I have doubted those assumptions?



"As for the core punching through the roof, I conjecture this occurred when the upper mechanical floors and up to the roof encountered the greater resistance offered around floors 75--79, about 30 stories (about 110 meters) down. No air escaping through such a puncture will be separately observable in any of the photos, IMO."

from this post

He is describing how his idea of crush down, then crush up is consistent with surviving core columns as tall as 77 floors. He concludes that the core must have "punctured" the surviving roof.



MT: "Can you please explain how such tall surviving sections of the core can exist with horizontal bracing still attached without the need the debris to go around it, not through it (hence a gaping hole up the middle of the debris distribution)?

David Benson:

"The west and north walls peeled away sufficiently rapidly that deebris tended to move west and north near the spire. Similarly, but to a lesser extent, to south and east. There actually wasn't a gaping hole, just less density and in particular no structural steel to break connections."



A huge homogeneous piston.


"OneWhiteEye --- B&L show little inital crush-up, not none at all. Since it is so small, the argument is that the crush-down only in B&V is a valid approximation."

from this post


"Major_Tom --- B&V have four simplifying assumptions which lead to the crush-down ODE. These assumptions are reasonable for WTC 1 but not, by video timing, for WTC 2 after a few seconds. In the case of WTC 2 it is clear from the ABC video of the collpase proceeding down to the Mariott rooftop level that the collapse was proceeding much too slowly; the inference is that the top section broke apart and fell off rather early on.

But as BLGB indicates, this could not have happened to WTC 1 or the timing would be off."

from this post


"OneWhiteEye --- I'm not the one with any doubts about the matter: there can be no significant early crush-up."

from this post



"Read Bazant & Le to understand why zone C can be consired to be essentially rigid during crush-down.
I offered to start a thread about how to build a table-top demonstrator that will allow one to see that,
indeed, zone C remains intact during crush-down. I didn't bother when I realized that nobody here would bother to actually build it, test it, and in the process dicover that the application of Newton's laws and
d'Alembert's principle in Bazant & Verdure agrees with reality."

from this post


"See Bazant & Le for a further exposition of why early crush-up is very small. It is, I admit, a difficult
point. But it is similar to a house riding down a landslide for which many examples have occurred in southern California."

from this post

A general summary of the 4 Bazant papers:


1) The first paper published in 2002 states a simple truism, that tall buildings are certainly not designed to catch themselves once an upper portion begins to fall. This was argued by considering the most extreme case which could not possibly be considered to represent a real event.


2) In the 3 papers published in 2007-2008, Bazant presents a progressive collapse model based on blocks colliding with one another and formulated mathematically as a 1 dimensional "crush down, then crush up" mechanics. He increasingly applies the model to the case of the Twin Towers quite literally throughout the 3 papers. His final conclusion is that his model matches all observables.


3) Anyone can verify that the current historic representation of the collapse modes is provably incorrect by carefully examining the visual record of the collapses. Even so, the block mechanics is taken quite literally and currently represents the historical explanation for the mechanics of the actual collapses. (Wikipedia description of the collapses as an example)


4) In the final 2 papers Bazant claims to prove that allegations of demolition are baseless. To do this...

5) Using the logic of BZ, anyone can see that the collapse initiation sequences were the most important time intervals to examine the towers for either a failure mechanism or for signs of controlled demolition.

Instead, demolition is described within the argument in its most extreme terms, as an artificially narrowed false choice. The argument was always phrased as total gravity driven vs total decimation of the lower portion, with no middle ground. An actual demolition would probably incorporate gravitational destruction within the demolition plan.

Therefore, 2 extreme sides of collapse mechanics are pitted against each other within the paper as if there is no middle ground between total gravity-driven progression and total dismemberment of the lower portion.


6) Without a realistic concept of global mass flow within the towers during the collapses, it is impossible to approach the question of demolition in a remotely realistic way. In retrospect, after reconstructing the photographic record of the collapse progression processes and comparing them with claims made within these papers, there is no doubt that Dr Bazant does not have a practical sense of global mass flow or a good grasp of the visual record.

Likewise, those who counter Bazant with block models of their own show a similar ignorance of the photographic record and global mass flow as will be demonstrated in the next, in sections 2.7 and 2.8.

Therefore, the papers cannot effectively argue a mathematical model for collapse or realistically address claims of demolition without a realistic concept of global mass flow directly from the visual record. In retrospect, he clearly had little understanding of the collective visual record.





The central element of block mechanics: The homogeneous crush front.

Looking at the crushing blocks compared with the observations that are now documented, it is stunning that this passed for a model on building mechanics at one time (in 2008) and that is passed the peer review process:



Actually, according the the most up-to-date government, academic and professional literature on the subject of the Twin Towers collapse progression processes, this still is the model for Twin Towers collapse mechanics


The ability to believe in models of physical systems that do not have to match observables in the system being studied creates theories that are treated as largely divorced from the actual system being modeled, so no amount of contradiction with the visual record seems to contradict belief in the model.









Continue to part 2.7: Block Mechanics Misrepresentations of Collapses






Created on 11/10/2011 07:45 PM by admin
Updated on 03/29/2016 09:22 PM by admin
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