During tunnelling through aquifers, waterproofing is a main task to ensure the safety and stability of the construction. Waterproofing is also required to ensure a workable platform for excavation. With the rapid development, the construction of tunnels is becoming more and more difficult and the geological hazards are becoming severer. Li et al. (2015) reported a construction failure due to the water problem, where had an extremely complicated geological environment in karst areas. And significant symptoms of water inrush were fairly difficult to discover. Similar failures were also reported by Yang and Zhang (2018) and Liang et al. (2016). In traditional design, the mean value of permeability coefficient is often used for design; however, the permeability coefficient usually has one to two orders of variation. Seepage paths are likely to exist at some soil zones with high permeability coefficients, although the portion of these zones may be small. The exist of such seepage paths can undermine the integrity of waterproofing effect and elevate the risk in tunnelling construction. In this study, the spatial variability of the permeability coefficient is taken into account by the concept of random field, which is further incorporated into the finite element program. In doing so, the existence of any seepage paths in soil zones with high permeability coefficients can be investigated and visualized. The corresponding risk can be assessed and some useful mitigation measures are proposed.