Due to the unexpected context of disaster management (with heterogeneous and non-dedicated potential data sources), the classical Big-Data approaches within this business domain (schematically focused on data storage and pattern recognition) appear to be limited, especially when trying to get a situational level of such crises from data gathered from the field. That is why this article aims at discussing a specific vision of Big-Data for data management, in two steps: (i) analyzing this business domain to identify relevant characteristics, impacted or concerned by Big-Data, and describe the new key challenges that need to be tackled, and (ii) designing an innovative Big-Data framework dedicated to this particular business domain. After having highlighted the importance to push abstraction levels and especially data interpretation as a way to perform vertical intelligence in data analysis (instead of horizontal intelligence with usual approaches), the proposed Big-Data framework brings a layered approach according to three dimensions: gathering (data level), interpretation (information level), exploitation (knowledge level).