The article presents an access control model called Criticality Aware Access Control (CAAC) for criticality (emergency) management in smart infrastructures. Criticalities are consequences of events which take a system (in our case, a smart infrastructure) into an unstable state. They require the execution of specific response actions in order to bring them under control. The principal aim of CAAC is to grant the right set of access privileges (to facilitate response action execution), at the right time, to the right set of subjects, for the right duration, in order to control the criticalities within the system. In this regard, the CAAC model uses a stochastic model called the Action Generation Model to determine the required response actions for the combination of criticalities present within the system. It then facilitates response actions by adaptively altering the privileges to specific subjects, in a proactive manner, without the need for any explicit access requests. In this article, we formalize the CAAC model and validate it based on two design goals -proactivity and adaptiveness. Finally, we present a case study demonstrating CAAC's operation on an oil-rig platform in order to aid in the response to health-and fire-related criticalities.