Current societal requirements necessitate the effective delivery of complex projects that can do more while using less. Yet, recent large-scale project failures suggest that our ability to successfully deliver them is still at its infancy. Such failures can be seen to arise through various failure mechanisms; this work focuses on one such mechanism. Specifically, it examines the likelihood of a project sustaining a large-scale catastrophe, as triggered by single task failure and delivered via a cascading process. To do so, an analytical model was developed and tested on an empirical dataset by the means of numerical simulation. This paper makes three main contributions. First, it provides a methodology to identify the tasks most capable of impacting a project. In doing so, it is noted that a significant number of tasks induce no cascades, while a handful are capable of triggering surprisingly large ones. Secondly, it illustrates that crude task characteristics cannot aid in identifying them, highlighting the complexity of the underlying process and the utility of this approach. Thirdly, it draws parallels with systems encountered within the natural sciences by noting the emergence of self-organised criticality, commonly found within natural systems. These findings strengthen the need to account for structural intricacies of a project's underlying task precedence structure as they can provide the conditions upon which large-scale catastrophes materialise.