Slow evolution punctuated by burst like events localized onto interfaces or interface zones control the evolution of a wide variety of geological systems, such as glaciers, earthquakes, rock falls, and landslides. In Earth subsurface and cryosphere, the build-up of energy drives rocks and ice towards critical points at which a small perturbation can trigger a rapid release of energy. We propose a physics-based modelling approach to the development of a better theoretical understanding of the friction and fracture processes that control burst-like dynamics leading to these geohazards, and the construction of numerical models with potential predictive capability that utilize this advance in understanding.