Evolution of karst conduit networks in transition from pressurized flow to free-surface flow

Abstract

Most of the existing models of speleogenesis are limited to situations where flow in all conduits is pressurized. The feedback between the distribution of hydraulic head and growth of new solution conduits determines the geometry of the resulting conduit network. We present a novel modeling approach that allows a transition from pressurized (pipe) flow to a free-surface (open-channel) flow in evolving discrete conduit networks. It calculates flow, solute transport and dissolution enlargement within each time step and steps through time until a stable flow pattern is established. The flow in each time step is calculated by calling the US Environmental Protection Agency Storm Water Management Model (US Environmental Protection Agency, 2014), which efficiently solves the 1-D Saint-Venant equations in a network of conduits. Two basic scenarios are modeled, a low-dip scenario and a high-dip scenario. In the low-dip scenario a slightly inclined plane is populated with a rectangular grid of solution conduits. The recharge is distributed to randomly selected junctions. The results for the pressurized flow regime resemble those of the existing models. When the network becomes vadose, a stable flow pathway develops along a system of conduits that occupy the lowest positions at their inlet junctions. This depends on the initial diameter and inlet position of a conduit, its total incision in a pressurized regime and its alignment relative to the dip of the plane, which plays important role during the vadose entrenchment. In the high-dip scenario a sub-vertical network with recharge on the top and outflow on the side is modeled. It is used to demonstrate the vertical development of karst due to drawdown of the water table, development of invasion vadose caves during vadose flow diversion and to demonstrate the potential importance of deeply penetrating conductive structures.