  We derive a mathematical model of progressive collapse and examine role of
compaction. Contrary to a previous result by Ba\v{z}ant and Verdure, J. Engr.
Mech. ASCE 133 (2006) 308, we find that compaction slows down the avalanche by
effectively increasing the resistive force. We compare currently available
estimates of the resistive force, that of Ba\v{z}ant and Verdure (2006)
corrected for compaction for World Trade Center (WTC) 2, and of Beck,
www.arxiv.org:physics/0609105, for WTC 1 and 2. We concentrate on a damage wave
propagating through the building before the avalanche that figures in both
models: an implicit heat wave that reduces the resistive force of the building
by 60% in Ba\v{z}ant and Verdure (2006), or a wave of massive destruction that
reduces the resistive force by 75% in Beck (2006). We show that the avalanche
cannot supply the energy to the heat wave as this increases the resistive force
by two orders of magnitude. We thus reaffirm the conclusion of Beck (2006) that
the avalanche is initiated in the wake of the damage wave.
