Disasters and emergencies are featured by their unexpected consequences on the human being life. Crisis Management Systems (CMS) handling them require effective collaboration between their services, and need dynamic adaptation at runtime when an execution context change occurs. To manage disasters, several approaches are proposed in the literature where few of them have advocated context-awareness as a solution to reduce and avoid disasters' consequences. By using specific platforms, each approach have addressed a particular concern of the disaster, and did not cover all its life-cycle phases; this fact does decreases the large-scale use of their proposals. This paper presents a context-aware dynamic adaptation approach that deals with the impact of context changes onto running service-based applications of a CMS. This approach is specified on the Service Component Architecture (SCA) and implemented with the FraSCAti Platform. A CMS example is unrolled to demonstrate what context-aware adaptation can do for disaster management.