Basic processes and mechanisms governing the evolution of karst

Models of karstification based on the physics of fluid flow in fractures of soluble rock, and the physical chemistry of dissolution of limestone by CO2 containing water have been presented during the last two decades. This paper gives a review of the basic principles of such models, their most important results, and future perspectives. The basic element of evolving karst systems is a single isolated fracture, where a constant hydraulic head drives calcite aggressive water from the input to the output. Non linear dissolution kinetics with order n = 4 induce a positive feedback by which dissolutional widening at the exit enhances flow rates thus increasing widening and so on until flow rates increase dramatically in a breakthrough event. After this the hydraulic head breaks down and widening of the fracture proceeds fast but even along its entire length under conditions of constant recharge. The significance of modelling such a single fracture results from the fact that an equation for the breakthrough time specifies the parameters determining the processes of early karstification. In a next step the boundary conditions for isolated fractures are varied by including different lithologies of the rock, expressed by different dissolution kinetics. This can enhance or retard karstification. Subterranean sources of CO2 can also be simulated by changing the equilibrium concentration of the solution at the point where CO2 is injected. This leads to accelerated karstification. At the confluence of solutions from two isolated tubes into a third one, mixing corrosion can release free carbon dioxide. Its effect to solutional widening in such a system of three conduits is discussed. Although these simple models give interesting insights into karst processes more realistic models are required. Combining single fractures into two-dimensional networks models of karst in its dimensions of length and breadth under constant head conditions are presented. In first steps the Ford-Ewers' high-dip and low-dip models are simulated. Their results agree to what one expects from field observations. Including varying lithologies produces a variety of new features. Finally we show that mixing corrosion has a strong impact on cave evolution. By this effect micro climatic conditions in the catchment area of the cave exert significant influence. A common feature in the evolution of such two-dimensional models is the competition of various possible pathways to achieve breakthrough first. Varying conditions in lithologies, carbon dioxide injection or changing hydrological boundary conditions change the chances for the competing conduits. Karst systems developing at steep cliffs in the dimensions of length and depth are characterized by unconfined aquifers with constant recharge to the water table. Modelling of such systems shows that dissolution of limestone occurs close to the water table. The widening of the fractures there causes lowering of the water table until it becomes stable when base level is reached, and a water table cave grows headwards into the aquifer. When prominent deep fractures with large aperture widths are present deep phreatic loops originate below the water table. A river or a lake on a karst plateau imposes constant head conditions at this location in addition to the constant recharge from meteoric precipitation. In this case a breakthrough cave system evolves along the water table kept stable by the constant head input. But simultaneously deep phreatic loops arise below it. In conclusion we find that all cave theories such as those of Swinnerton (1932), Rhoades and Sinacori (1941), and the Four-statemodel of Ford are reconciled. They are not contradictory but they result from the same physics and chemistry under different boundary conditions.