EVOLUTION OF CONDUITS IN CARBONATE AQUIFERS AFTER BREAKTHROUGH

Numerical modeling has become a widely-used tool to investigate the early stages of karstification. Modeling typically shows that the process of fracture enlargement from apertures of less than 0.1 mm up to the onset of turbulent flow takes some 10⁴ years. This point is known as breakthrough and occurs when fracture aperture is about 1 cm. Almost all numerical models have been terminated at this point, and the course of conduit evolution after breakthrough has not been studied in detail.

A series of numerical simulations were performed for a single pipe-full conduit, commencing at breakthrough. Both numerical modeling and field measurements have shown that conduit enlargement (i.e. wall retreat) rates may be as great as 1 mm/year, and a range 0.01 - 1 mm/year was used in the modeling. Simulations also varied Darcy-Weisbach friction factors (0.03 - 3), the catchment areas for the conduit (0.1 - 1000 km²) and the mode of groundwater recharge (allogenic or autogenic).

Simulations demonstrate three distinct phases for conduit development after breakthrough. During the initial phase there are rapid increases in conduit diameter, discharge, velocity, and Reynolds number. This phase ends in the allogenic case when all surface stream flow is captured by the conduit. The second phase is characterized by constant discharge, a continued increase in conduit diameter, but a steady decrease in velocity, Reynolds number, and hydraulic gradient. The second phase ends where mean conduit velocity diminishes to about 0.02 m/s and sediment transport competence is lost, resulting in the commencement of sedimentation in the conduit. An equilibrium is established in the third phase between conduit diameter and velocity, with excess sediments being intermittently removed to the spring by high-discharge events. In the autogenic case, the decrease in hydraulic gradient in phase 2 promotes convergent groundwater flow to the low-head conduit and results in the formation of a conduit network.

This model accounts for the widespread occurrence of clastic sediments in karst conduits as well as the observed distribution of measured tracer velocities, where many karst conduits have maximum observed velocities of about 0.1 m/s.