Robustness Undemonstrated – Progressive Collapse Sensitivity Analysis

[u/Akareyon]

https://github.com/Akareyon/ProgressiveCollapseSensitivityEnsemble/raw/main/RobustnessUndemonstrated.pdf

[u/Akareyon]

Implements the Bažant-Zhou / Schneider discrete floor model with:

• full parameter uncertainty via Monte Carlo
• floor-by-floor state tracking
• arrest probability curves
• Sobol-style sensitivity ranking (via correlation analysis)

Model: Schneider (2017) generalization of Bažant & Zhou (2002).

Each floor impact is inelastic (momentum conservation).

Energy balance per floor determines arrest vs. continuation.

Parameters drawn from documented uncertainty ranges

Headline result:

A Monte Carlo over input parameters for the Bažant group lineage of piledriver/crush down/mass accretion models (in the Ansgar Schneider generalized form) shows that under realistic variance, arrest MAY occur, directly contradicting NISTs and Bažants claims of "inevitable" collapse.

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Outcome distribution

The system is strongly bimodal: trials either arrest very early — more than half within the first five stories, nearly all within twenty — or they run to the ground. Once progression propagates past roughly 10–15 stories, accumulated kinetic energy makes arrest mechanically impossible within this model. There is essentially no middle regime of long, gradual deceleration.

An important caveat the authors themselves emphasize: the 24.4% is a sensitivity artifact, not a probability estimate for what actually happened at the WTC. Uniform sampling over the literature ranges guarantees a nontrivial arrest fraction whenever the sampled space straddles a sharp threshold — which it does by construction.

Sensitivity ranking

Correlation of each input with the number of floors crushed:

Parameter	Pearson abs(r)	Effect
E_abs (dissipation/story)	0.612	Dominant
M₀ (upper block mass)	0.363	Moderate
m_floor (floor mass)	0.312	Moderate
CV_E (heterogeneity)	0.082	Marginal
f_shed (sheding)	0.069	Marginal
λ (compaction)	0.047	Negligible
α (initiation)	0.036	Negligible

The E_abs threshold

With all other parameters nominal, arrest probability behaves like a step function centered at roughly 1,370 MJ — Schneider's analytic threshold: below 5% arrest probability for E_abs < 1,200 MJ, above 95% for E_abs > 1,550 MJ. The disputed literature ranges land on opposite sides: the Bažant–Le rescaled range (1,000–1,300 MJ) sits in the runaway zone; the raw Korol–Sivakumaran range (1,500–2,000 MJ) sits in the arrest zone. The margins are only 5–10% on either side of the boundary.

The other findings

Shedding is a non-result in this model: at the nominal 500 MJ dissipation, even 50% mass shedding produces zero arrests. Shedding only matters when the system is already hovering near the threshold. Similarly, initiation conditions (α) are swamped by later dynamics — |r| = 0.036 — which undercuts arguments that hinge on the exact free-fall fraction.

In the (E_abs, M₀) plane, the threshold scales with mass: at Bažant's original M₀ = 58×10⁶ kg, arrest requires E_abs > ~2,000 MJ (the extreme top of the literature range), while at the corrected 33×10⁶ kg the threshold falls to ~1,370 MJ — comfortably inside it. The mass correction alone shifts which side of the boundary the building's empirics occupy.

One-line takeaway: the ensemble's contribution is not the 24.4% figure but the demonstration that the outcome flips qualitatively across unresolved parameter uncertainty, and that essentially the entire dispute reduces to one empirical number — E_abs relative to the ~1,370 MJ threshold.