[Paper Review] The Late Jolt -- Re-Examining the World Trade Center Catastrophe

Ansgar Schneider|arXiv (Cornell University)|Dec 17, 2017

Disaster Management and Resilience6 references3 citations

TL;DR

This paper re-evaluates the gravity-driven collapse model of the World Trade Center's North Tower using extended video analysis beyond the initial 4.6 seconds. It finds energy dissipation per storey surged to 2,500 MJ between 4.6–7.7 seconds—equivalent to 2,000 MJ in the impact zone—before dropping back to baseline, challenging the inevitability of the collapse and suggesting the mechanism changed mid-collapse.

ABSTRACT

A model of a gravity-driven collapse of a tall building has been proposed by Bažant et al. We apply this model to the collapse of the North Tower of the World Trade Center to determine the energy dissipation per storey during the collapse. Our findings are (at most) 250\,MJ during the first 4.6 sec. In the time interval between 4.6 and 7.7 sec after collapse initiation we find an additional energy dissipation per storey of 2500\,MJ. Because the steel columns increase in strength towards the ground this value corresponds to a value of 2000\,MJ for the storeys in the aircraft impact zone. After 7.7 sec the value reduces again. These results have two possible interpretations: (1) If due to the building design (column strength, shape etc.) the energy dissipation per storey cannot reach the high values which we observed, then the collapse cannot be described by the gravity-driven collapse model. (2) If the collapse is described correctly by the gravity-driven collapse model, then then we fond direct evidence that the collapse mechanism did not follow the same pattern during the whole of the collapse. The possible amount of energy dissipation was reduced by an order of magnitude during two long time time intervals. In both cases there is no a priori reason to justify the sometimes expressed belief that the collapse was inevitable even after the falling top section had gained a significant amount of momentum. In fact, if the amount of energy dissipation had stayed only little longer on the high level, then a gravity-driven collapse would have arrested. Note that (1) implies that if in principle the gravity-driven collapse model describes gravity-driven collapses of tall buildings, then the collapse was not gravity-driven.

Motivation & Objective

• To re-express the gravity-driven collapse model of the North Tower using extended empirical video data beyond the first 4.6 seconds.
• To quantify energy dissipation per storey during different collapse phases using measured video footage.
• To assess whether the observed energy dissipation patterns are consistent with the gravity-driven collapse model.
• To evaluate whether the collapse could have arrested if energy dissipation had remained high longer.
• To test the validity of the gravity-driven collapse model under observed structural dynamics and energy constraints.

Proposed method

• Applies the Ba´zant and Verdure gravity-driven collapse model to the North Tower's collapse, extending analysis beyond the initial 4.6 seconds.
• Uses video recordings from multiple sources (History Channel, CBS, Etienne Sauret) to measure the downward displacement of the tower's roof over time.
• Employs a modified version of the Crush-Down Equation with time-dependent energy dissipation terms to model structural resistance.
• Introduces adjustable energy dissipation parameters (W_extra) to simulate varying resistance levels during collapse phases.
• Uses numerical integration via the Runge-Kutta method in Maxima to solve the system of differential equations governing collapse dynamics.
• Synchronizes and compares video data with model predictions using camera position and time calibration techniques.

Experimental results

Research questions

• RQ1 Was the energy dissipation per storey during the collapse consistent with the predictions of the gravity-driven collapse model?
• RQ2 Did the collapse exhibit a significant change in energy dissipation behavior between 4.6 and 7.7 seconds after initiation?
• RQ3 Could the collapse have arrested if energy dissipation had remained at high levels for a longer duration?
• RQ4 Does the observed energy dissipation pattern contradict the assumption that the collapse was purely gravity-driven?
• RQ5 Is there direct evidence that the collapse mechanism changed during the event, invalidating the uniform gravity-driven model?

Key findings

• Energy dissipation per storey reached 250 MJ during the first 4.6 seconds after collapse initiation.
• Between 4.6 and 7.7 seconds, energy dissipation increased to 2,500 MJ per storey, indicating a significant rise in structural resistance.
• The peak energy dissipation of 2,500 MJ per storey corresponds to 2,000 MJ in the impact zone due to increasing column strength toward the base.
• After 7.7 seconds, energy dissipation dropped back to the initial level of 250 MJ per storey.
• The observed energy dissipation pattern suggests the collapse mechanism did not follow a uniform gravity-driven process throughout.
• The findings imply that if energy dissipation had remained high for even a short time longer, the collapse could have arrested, challenging the inevitability of the event under the gravity-driven model.