Fractal Modelling of Karst Conduits

Three kinds of porosity and permeability, rock matrix porosity, fracture porosity and conduit porosity, must be considered when creating spatially distributed mathematical models of karst systems. These components are responsible for the two kinds of karst flows that can be observed in nature and that must be reproduced by the mathematical models: the slow flow that takes place through the matrix of porous and small fractures and the fast flow through large fractures and conduits. Although the three components present fractal characteristics, the aim of this work is the fractal behaviour of the karst conduits. Two aspects of the karst conduits are considered: their geometry and their topology. The geometry is defined by the sections of the conduits and their tortuosity while the topology is given by the network characteristics of the conduits (connectivity, spatial density and three-dimensional distribution in space). This work deals with the calculation of the fractal dimensions of the different characteristics and how the fractal dimension can be used for morphometric characterization of karst networks, for simulating three-dimensional networks of karst conduits and for calculating the volume of conduits and thus the total conduit porosity of the karst system. The karst system of Sierra de las Nieves in Malaga province (Southern Spain), a high relief karst where the endokarst is very well developed and has given birth to super-caves, is used to illustrate the methodology.