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The communication network is now one of the critical infrastructures in our society. However, the current communication networks are facing more and more large-scale region failure threats, such as natural disasters (e.g. earthquake, tornado) and physical attacks (e.g. dragging anchors or EMP attack). Therefore, a deep understanding of network behaviors under region failure is essential for the design and maintenance of future highly survivable networks. In this paper, we focus on the network vulnerability assessment under the geographically correlated region failure(s) caused by a random “line-segment” cut, an important region failure model that can efficiently capture the behaviors of some region failures like earthquake, tornado and anchor cutting. To facilitate such vulnerability assessment, we apply the geometrical probability theory to design a grid partition-based estimation scheme for Disrupted Link Capacity, Pairwise Traffic Reduction and Pairwise Disconnection Probability, three commonly used metrics for statistical vulnerability assessment. A theoretical framework is also established to determine a suitable grid partition such that a specified estimation error requirement is satisfied.