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Survivability of telecommunication networks has emerged as a fundamental concern for network design and operation. The network physical infrastructures are vulnerable to correlated failures arising from disastrous events. Particularly, some disasters such as natural disasters and malicious attacks may propagate across geographical areas in a short period of time. Due to such disaster propagation, network failures may occur in more than one locations. This paper investigates network survivability in the presence of disaster propagation. Specifically, it develops a model to characterize the network performance during the transient period that starts after the disaster occurrence, in the subsequent disaster propagation, and until the network fully recovers. Based on the model, network survivability analysis is exemplified for three repair strategies. The results not only are helpful in estimating quantitatively the survivability of a network (design) but also provide insights on choosing among different repair strategies.