The present work aims to study the effect of random geometry on the long-term criticality safety. Preliminary considerations on uranium depositions in randomly fractured rocks have been obtained through an approximated analytical solution to calculate spherical fuel lumps with random locations. With stochastic and heterogeneous conditions applied, the present work examines the conservatives of the neutronic models for repository criticality safety assessment, and provides deeper understandings of the system. The major finding is that, when parameters are chosen to optimized the criticality, keff for systems with the random geometries can be well-bounded by the average case.