The aim of this paper is to provide a framework to improve urban resilience independently of the nature of the disturbances. Recent disasters had a significant impact on critical infrastructures providing essential urban services such as energy, transportation, telecommunication, water and food supply or health care. Indeed, several natural and human-made hazards may lead to disruptions, and most critical infrastructures are networked and highly interdependent. Henceforth, resilience building remain focused on specific hazards or on improving the resilience, separately, of single infrastructures. In order to enhance urban resilience, this paper is based on learnings from three case studies that are the 2001 WTC terrorist attack, hurricanes Irma and Maria in 2017 and the 2016 Seine river flood in Paris. These events highlight disruptions to urban services, but also some resilience options. In light of both the literature and our case studies, a framework of unspecific resilience is provided for improving some resilience principles, namely omnivory, redundancy, buffering, high flux, homeostasis and flatness within electric energy, water and food supply and transportation networks. Rebuilding resilience within this framework is further discussed with respect to all kinds of disruptive events.