Probabilistic estimation of tunnel inflow from a karstic conduit network

•Safe tunnel planning relies on robust estimations of possible karstic water inflows.•A novel approach that combines stochastic karst generation and hydrological models.•Stochastic methods allow estimating the uncertainty linked to multiple parameters.•Complex karstic network geometries influence the long-term inflow distribution.•Pressure gradient and matrix permeability values are key parameters of the estimation. When planning infrastructures such as tunnels in karstified formations, a risk assessment of groundwater inflow must be conducted. The aim of this paper is to present a workflow for the probabilistic estimation of the water inflow from karst conduits using a Monte-Carlo approach. The procedure involves three main steps. First, realistic stochastic karstic conduit network geometries are generated based on fracture and stratigraphic information using the Stochastic Karstic Simulation approach (SKS). To represent the geological uncertainty, different scenarios are considered. Then, a discrete–continuum numerical modeling approach is employed, allowing the flow calculation to account for the exchange between the matrix and the conduits as well as the transition between turbulent and laminar flow in the conduits. Because it is not known if and where (at which depths) the tunnel may hit a karst conduit, and what will be the pressure gradient in the system, different hydrogeological scenarios are considered in the uncertainty analysis phase including a randomized location of the tunnel, a range of possible pressure gradients, and a range of possible matrix permeability values. The final step consists of the statistical analysis of the results. The proposed workflow allows estimating the range of plausible inflows and studying how the inflows are related to the network geometry properties and to the hydrodynamic parameters of the aquifer. This method is illustrated in a simple synthetic but realistic case of a rather deep and confined karstic formation. In that situation, the results show that even if the pressure difference in the system and the matrix permeability value are important factors controlling the long-term inflow, the karstic conduit network geometry and connectivity also play a critical role in the determination of the potential discharge. Overall, this study demonstrates the possibility and advantages of using stochastic analysis in the early phases of project planning to predict possible long-term water inflow in tunnel after its constr