Analytical solution for modeling discharge into a tunnel drilled in a heterogeneous unconfined aquifer

Predicting transient inflow rates into a tunnel is an important issue faced by hydrogeologists. Most existing analytical solutions overestimate the initial discharge due to the assumption that drilling was instantaneous over the entire tunnel length. In addition, they assume a homogeneous system. An alternative model was recently developed for tunnels intersecting heterogeneous formations, but its application was reduced to the case of confined flow to deep tunnels in weakly diffusive aquifers. In this paper, we adapt existing analytical solutions for drainage systems to the specific case of a tunnel progressively drilled in a highly diffusive heterogeneous unconfined aquifer. The case of a tunnel overlying an impervious layer is analytically solved by applying the superposition principle, while the case of a tunnel constructed some distance above an impervious layer is solved by discretizing the tunnel length into subsectors. Both models can simulate transient discharge into a tunnel drilled at various speeds through a heterogeneous unconfined aquifer, and allow the prediction of discharge rates in shallow tunnels located in highly diffusive aquifers. We successfully applied this approach to a tunnel in heterogeneous volcanic rock.