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Public infrastructure systems provide many of the services that are critical to the health, functioning, and security of society. Many of these infrastructures, however, lack continuous physical sensor monitoring to be able to detect failure events or damage that has occurred to these systems. We propose the use of social sensor big data to detect these events. We focus on two main infrastructure systems, transportation and energy, and use data from Twitter streams to detect damage to bridges, highways, gas lines, and power infrastructure. Through a three-step filtering approach and assignment to geographical cells, we are able to filter out noise in this data to produce relevant geolocated tweets identifying failure events. Applying the strategy to real-world data, we demonstrate the ability of our approach to utilize social sensor big data to detect damage and failure events in these critical public infrastructures.