Fracture Networks from a deterministic physical model as 'forerunners' of Maze Caves

'Fractures are the chief forerunners of caves because they transmit water much more rapidly than intergranular pores.[1] Thus, the cave networks can follow the fracture networks from which the Karst caves formed by a variety of processes. Traditional models of continental Karst define water flow through subsurface geologic formations, slowly dissolving the rock along the pathways (e.g. water saturated with respect to carbon dioxide flowing through fractured carbonate formations). We have developed a deterministic, physical model of fracturing in a model geologic layer of a given thickness, when that layer is strained in one direction and subsequently in a perpendicular direction. It was observed that the connected fracture networks from our model visually resemble maps of maze caves. Since these detailed cave maps offer critical tools in modeling cave development patterns and conduit flow in Karst systems, we were able to test the qualitative resemblance by using statistical analyses to compare our model networks in geologic layers of four different thicknesses with the corresponding statistical analyses of four different maze caves, formed in a variety of geologic settings. The statistical studies performed are: i) standard box-counting to determine if either the caves or the model networks are fractal. We found that both are fractal with a fractal dimension Df ≈ 1.75 . ii) for each section inside a closed path, we determined the area and perimeter-length, enabling a study of the tortuosity of the networks. From the dependence of the section's area upon its perimeter-length, we have found a power-law behavior (for sufficiently large sections) characterized by a 'tortuosity' exponent. These exponents have similar values for both the model networks and the maze caves. The best agreement is between our thickest model layer and the maze-like part of Wind Cave in South Dakota where the data from the model and the cave overlie each other. For the present networks from the physical model, we assumed that the geologic layer was of uniform thickness and that the strain in both directions were the same. The latter may not be the case for the Brazilian, Toca de Boa Cave. These assumptions can be easily modified in our computer code to reflect different geologic histories. Even so the quantitative agreement suggests that our model networks are statistically realistic both for the 'forerunners' of caves and for general fracture networks in geologic layers, which should assist the study of underground fluid flow in many applications for which fracture patterns and fluid flow are difficult to determine (e.g., hydrology, watershed management, oil recovery, carbon dioxide sequestration, etc.). Keywords - Fracture Networks, Karst, Caves, Structurally Variable Pathways, hydrogeological modeling 1 Arthur N. Palmer, CAVE GEOLOGY, pub. Cave Books, Dayton OH, (2007).