[论文解读] The Late Jolt -- Re-Examining the World Trade Center Catastrophe

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

Disaster Management and Resilience参考文献 6被引用 3

一句话总结

本文利用初始4.6秒之后的扩展视频分析，重新评估了世界贸易中心北塔重力驱动坍塌模型。研究发现，在4.6至7.7秒期间，每层的能量耗散飙升至2,500 MJ，相当于撞击区域耗散2,000 MJ，之后回落至基线水平，挑战了坍塌的必然性，表明坍塌机制在坍塌过程中发生了变化。

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.

研究动机与目标

• 利用初始4.6秒之后的扩展实证视频数据，重新表述北塔重力驱动坍塌模型。
• 利用测量的视频画面，量化不同坍塌阶段每层的能量耗散。
• 评估观察到的能量耗散模式是否与重力驱动坍塌模型一致。
• 评估若能量耗散持续保持高水平更长时间，坍塌是否可能中止。
• 在观察到的结构动力学和能量约束条件下，检验重力驱动坍塌模型的有效性。

提出的方法

• 将Ba´zant和Verdure的重力驱动坍塌模型应用于北塔坍塌，将分析扩展至初始4.6秒之后。
• 利用多个来源（History Channel、CBS、Etienne Sauret）的视频记录，测量塔楼屋顶随时间的向下位移。
• 采用改进的“压下方程”模型，引入随时间变化的能量耗散项，以模拟结构阻力。
• 引入可调节的能量耗散参数（W_extra），以模拟不同坍塌阶段的阻力水平变化。
• 使用Maxima中的龙格-库塔法进行数值积分，求解描述坍塌动力学的微分方程组。
• 通过摄像机位置和时间校准技术，同步并对比视频数据与模型预测结果。

实验结果

研究问题

• RQ1 坍塌期间每层的能量耗散是否与重力驱动坍塌模型的预测一致？
• RQ2 在坍塌启动后4.6至7.7秒之间，能量耗散行为是否发生了显著变化？
• RQ3 若能量耗散持续保持高水平更长时间，坍塌是否可能中止？
• RQ4 观察到的能量耗散模式是否与坍塌完全由重力驱动的假设相矛盾？
• RQ5 是否存在直接证据表明坍塌机制在事件过程中发生了改变，从而使统一的重力驱动模型失效？

主要发现

• 坍塌启动后最初4.6秒内，每层的能量耗散为250 MJ。
• 在4.6至7.7秒期间，能量耗散增加至每层2,500 MJ，表明结构阻力显著增强。
• 每层峰值能量耗散2,500 MJ，对应撞击区域耗散2,000 MJ，这是由于底部柱体强度随高度增加而增强。
• 7.7秒后，能量耗散回落至初始水平250 MJ/层。
• 观察到的能量耗散模式表明，坍塌机制在整个过程中并未遵循统一的重力驱动过程。
• 研究结果表明，若能量耗散仅维持高水平更短时间，坍塌本可中止，这挑战了重力驱动模型下该事件的必然性。