For the reader's reference the Bazant papers on the WTC towers written from 2007 to the present are listed and linked:
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. Bažant 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
The third 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
The most recent Bazant paper on the WTC collapses is called:
Why the Observed Motion History of World Trade Center Towers Is Smooth (2011),
linked here.
>>>>>>>>>>>
I will first focus on the paper 'Closure to 'Mechanics of Progressive Collapse' by Bazant and Le. Jia-Liang Le was a graduate student at Northwestern University when this paper was written, so the comments within this paper are basically those of Bazant, a professor at Northwestern University at that time.
I will formulate 44 separate and highly specific questions on this paper. The specific questions are carefully formulated to help any impartial and honest reader to see the stupidity which most every JREF/ISF regular participating poster has demonstrated within this thread and throughout this forum on the topic of Bazant from 2010 to 2015.
I'll begin by reviewing the outline of this paper. The paper is written as an answer to 2 critical responses to the collapse mechanics as written in the original paper by Bazant and Verdure. The critical inquiries to which Bazant and graduate student Le are responding were presented by people commonly known as 'truthers'. The inquiries are presented by James Gourley and Gregory Szuladzinski. All quotes are directly from the paper.
Gregory Szuladzinski begins:
The paper presents a very interesting 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 sequence 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.
Question 1: Do you agree or disagree that Greg Szuladzinski is referring specifically to the WTC towers within this quote?
James R. Gourley's opening words are similar:
This discussion describes flaws in the modeling and analysis of the World Trade Center collapses by Bažant and Verdure in their paper entitled “Mechanics of Progressive Collapse: Learning
from World Trade Center and Building Demolitions.” 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 analyzing 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 Bažant and Verdure in their paper entitled “Mechanics of Progressive Collapse: Learning from World Trade Center and Building Demolitions."
Question 2: Do you agree or disagree that James Gourley is referring specifically to the case of the WTC towers in this quote?
Zdeněk P. Bažant 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
Question 3: Do you agree or disagree that Bazant, when answering James Gourley on each of these 8 points clearly labeled in the paper, is referring specifically to the case of the WTC towers?
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 the clearly marked section. Each of the 12 clearly marked objections and rebuttals make specific reference to the case of the WTC towers.
Question 4: Do you agree that Bazant, when answering G. Szuladzinski on each of these 4 points clearly labeled in the paper, is referring specifically to the case of the WTC towers?
This is the Bazant reply to J. Gourley's third point:
"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."
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."
This is the argument Bazant uses to explain to James Gourley that both blocks A (the 'lower block') and block C (the 'upper block') can be treated as 'rigid'.
Question 5: Is Bazant referring to the WTC towers specifically when making this argument about treating 'block A' and 'block C' as rigid?
Question 6: Is he claiming that 'block A' and 'block C' can be treated as rigid because only 'harmless elastic waves' can penetrate them, and that 'no wave attaining the material strength (of the 'blocks') can penetrate beyond the WTC crush fronts'?
Bazant continues to answer the points made by James Gourley...
"4. Can Crush-Up Proceed Simultaneously with Crush Down?It can, but only briefly at the beginning of collapse, as mentioned in the paper."
Question 7: Is Bazant claiming that in the case of the WTC collapses, 'crush up' cannot proceed 'crush down' except only briefly at the beginning of the collapse?
Bazant continues to explain point 4...
"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)."
Question 8: Is Bazant claiming that the 'upper floors (i.e., the floors comprising Part C)' would not be more likely than the 'lower floors' to 'deform and yield' during the collapse of the WTC towers?
Question 9: Is Bazant, when addressing J. Gourley, a known 'truther', about Gourley's specific reference to the WTC towers, talking about the 'lower' and 'upper' floors of the WTC towers, or is he talking about some other building?
Question 10: Why is Bazant writing about the thicker, more massive columns supporting the lower floors of the WTC towers if he was aware of the ROOSD propagation mechanism?
Question 11: Why is Bazant talking about the 'upper floors' of the WTC towers only deforming 'a little, i.e., elastically' if he was aware of the ROOSD propagation mechanism?
Bazant continues on the same point:
"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."
Question 12: Is Bazant referring specifically to the WTC towers when making this statement?
Question 13: Is Bazant claiming that 'crush up' is impossible in the case of the WTC towers?
Question 14: Does Bazant seem aware of the ROOSD propagation mechanism when making claims such as 'crush-up is impossible' when referring to the WTC towers?
Bazant continues to explain:
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 collapse 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 algebraic equations
Question 15: When Bazant refers to the 'two crushing fronts' and the 'tower top', is he referring to the specific cases of the WTC towers?
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 crush-front velocity v0 = 8.5 m / s for the North Tower and 8.97 m / s for the South Tower. The 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:
Question 16: When Bazant refers to the 'crush down' and 'crush up' fronts in this quote, is he referring to the specific cases of the WTC towers?
"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."
Question 17: Is Bazant writing about the specific cases of the WTC towers when making these claims?
Question 18: Is Bazant claiming that these calculations show that the 'crush up' phase of the WTC collapses does not start until the 'crush down' phase is finished?
Question 19: When Bazant refers to the 'solution presented in the paper', does he mean the 2007 paper by Bazant and Verdure?
Question 20: Is Bazant claiming that these more detailed equations show that the original equations in BV were valid when applied to the WTC collapses?
Bazant continues to explain:
"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%."
Question 21: When making this specific statement is he referring to the WTC towers?
"This finding further means that the replacement of the load-deflection curve in Fig. 3 of the paper by the energetically equivalent Maxwell line that corresponds to a uniform resisting force F? cannot be sufficiently accurate to study the beginning of two-way crush.)"
Therefore, a solution more accurate 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)."
Question 22: Is Bazant claiming that the crush up process of WTC1 stops when the first overlying story is 'squashed' by a distance of only about 1.0% of its original height?
"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)."
Question 23: Is Bazant referring to the specific cases of the WTC towers when making this statement?
Question 24: Why is Bazant referring to the strength of columns if the ROOSD propagation mechanism is independent of column strength?
"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 velocity evolutions in Fig. 1."
This is figure 1 from the Bazant and Le paper reproduced. The figure shows Dr Bazant'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."
Question 25: Is Bazant referring to the WTC towers when making this statement?
Question 26: When Bazant refers to the 'original paper', is he referring to the paper by Bazant and Verdure (2007)?
"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."
Question 27: Is Bazant referring to the WTC towers when making this statement?
Question 28: Is Bazant claiming that the crush up process for WTC1 advanced only 37 mm upward before coming to a stop, at which time only crush-down occurred until the collapse front made contact with the earth?
Question 29: Is Bazant claiming that the crush up process for WTC2 advanced only 26mm upward before coming to a stop, at which time only crush-down occurred until the collapse front made contact with the 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."
Question 30: Is Bazant referring to the WTC towers when making this statement?
Question 31: Is Bazant claiming that the 'crush up' phase of the WTC towers terminates 'when the axial displacement of columns is only about 10 times larger than their maximum elastic deformation'?
Question 32: Is Bazant claiming that it is 'correct and accurate' to ignore the phenomenon of 'crush up' and consider the WTC towers as being only 'crushed down' until the collapse front makes contact wth the earth?
"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 is one of the only intelligent comments made by either 'truther' representative throughout the whole paper. Any logical human being should question why the 'possibility of the ocurance of crush up would diminish as the WTC collapses progressed' But Bazant then proceeds once again to explain why 'crush up' is physically impossible...
"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."
This is figure 2 from the Bazant and Le paper reproduced. This is how Bazant defines variables for the equations he uses.
Question 33: Is Bazant referring to the specific cases of the WTC towers when making this argument on how 'crush up' cannot occur?
"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
"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 (deformation 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."
"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."
Question 34: Is Bazant referring to the WTC towers when making this statement?
Question 35: Is Bazant claiming that his work has confirmed that the 'crush-up cannot restart until the compacted layer hits the ground'?
Question 36: Is Bazant writing about the "crush up' of the collase front of the WTC towers, and how it cannot happen until the collapse front hits the earth?
"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."
Question 37: Why does Bazant consider variation of mass and column size when referring to the collapse propagation of the WTC towers if ROOSD propagation is independent of column strength?
Question 38: Does Bazant seem aware of the concept of a ROOSD propagation mechanism when making this statement?
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."
Question 39: Is Bazant referring to the WTC collapses specifically within this closing comment?
Question 40: Within every comment quoted above, when addressing two known 'truthers', was Bazant referring specifically to the WTC collapses?
Question 41: At any time within the quotes given, did Bazant seem aware of the ROOSD mechanism of propagation?
Question 42: Within the multiple references to the 'lower block', the 'upper block', a 'crush down phase', and a 'crush up phase', is Bazant referring specifically to the WTC towers?
Gourley, in his opening statement makes the following claim:
...a two-phase collapse analysis is not representative of reality, because it disregards well-accepted laws of physics and therefore is not instructive.
Question 43: Does Bazant, at any time within the paper, give any indication that he does not consider his own 'two-phase collapse analysis' to not be represenative of 'reality' as applied to the WTC towers?
Question 44: At any time throughout the paper does Bazant deny that BV equations 12 (the 'crush down' equation) and 17 (the 'crush up' equation) can be applied to the specific cases of the WTC towers?
These 44 highly specific questions are formulated in such a way that they can be answered by anyone interested in this subject. They are offered so that any interested person does not need to feel that asking and answering these questions is a task outside of their level of education or ability. I strongly encourage any interested reader to not blindly rely on any arguments made by those in positions of technical authority. Papers like the one being currently examined demonstrate that these authors cannot be trusted to represent the WTC collapses accurately to the public. They do not serve the interest of their profession or of the general public as they claim.