A model of the early evolution of karst aquifers in limestone in the dimensions of length and depth

A new model of the early evolution of limestone karst aquifers in the dimensions of length and depth is presented. In its initial state the aquifer consists of a rock massive with evenly spaced fractures of about 50 µm aperture widths with an hydraulic conductivity of 10-7 ms-1, In addition to this a coarser network of prominent fractures with aperture widths of several 100 µm is also present. Boundary conditions of constant recharge 450 mm/year, or constant head from the input of allogenic streams are imposed. First the position of the water table in the aquifer is calculated, then dissolutional widening during a time step in all the fractures below the water table is found by use of the well-known nonlinear dissolution kinetics of limestone. This is iterated and the position of the water table as well as the fracture widths are found as a function of time. In the case of constant recharge to a karst plateau, the water table in any case drops to base level and conduits there propagate from the spring headwards. If constant head conditions are valid the position of the water table remains almost stable and conduits propagate along the water table from the input towards the spring. There is competition between conduit evolution along prominent fractures and along tight fissures close to the water table. In any case under constant head conditions one of these pathways wins, and early karst evolution is terminated by a breakthrough event with an explosive increase of the flow through the aquifer until constant head conditions break down. Depending on the boundary conditions of constant head or constant recharge or a combination of both it is possible to describe models of cave genesis, which have been derived from field evidence, such as the water table models of Swinnerton (Geol. Soc. Am. Bull., 34 (1932) 662) and Rhoades and Sinacori (J. Geol., 49 (1941) 785) as well as the four-state model by Ford and Ewers (Can. J. Earth Sci., 15 (1978) 1783).