Activity network analysis is a widely used tool for managing project risk. Traditionally, this type of analysis is used to evaluate task criticality by assuming linear cause-and-effect phenomena, where the size of a local failure (e.g., task delay) dictates its possible global impact (e.g., project delay). Motivated by the question of whether activity networks are subject to nonlinear cause-and-effect phenomena, a computational framework is developed and applied to real-world project data to evaluate project systemic risk. Specifically, project systemic risk is viewed as the result of a cascading process which unravels across an activity network, where the failure of a single task can consequently affect its immediate, down-stream task(s). As a result, we demonstrate that local failures are capable of triggering failure cascades of intermittent sizes. In turn, a modest local disruption can fuel exceedingly large, systemic failures. In addition, the probability for this to happen is much higher than anticipated. A systematic examination of why this is the case is subsequently performed with results attributing the emergence of large-scale failures to topological and temporal features of activity networks. Finally, local mitigation is assessed in terms of containing these failures cascades–results illustrate that this form of mitigation is both ineffective and insufficient. Given the ubiquity of our findings, our work has the potential of deepening our current theoretical understanding on the causal mechanisms responsible for large-scale project failures.