In this chapter, the snowpack compressed by the gravity of snow is modeled as a multilayer sandwich on a slope with several parallel planes of transverse slippage. The invariant integral of snowpack describes the critical state at the head of this structure when the avalanche starts on moving. This critical state is characterized in terms of physical and geometrical parameters of snow and slope. The solution of the avalanche motion equation was used to simulate the motion of the famous avalanche that happened on February 7, 2003, in Vallee de la Sionne in Switzerland. Also, the progressive failure of skyscrapers is studied and compared with the similar mechanics of avalanches. As applied to the WTC collapse on September 11, 2001, it is shown that its progressive failure would have taken more than 15 cek while, in fact, it took about 12 s which is characteristic for the free-fall demolition. This chapter is for those who are interested in the analysis of progressive failure leading to disasters and catastrophes.
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