On the formation of collapse dolines: A modelling perspective

Collapse dolines are among the most striking surface features in karst areas. Although they can be the result of different formation mechanisms, evidence suggests that large collapse dolines form due to chemical and mechanical removal of material at and below the level of groundwater. We have applied a genetic model of a two-dimensional fracture network to calculate the rate of dissolutional bedrock removal in the heavily fractured (crushed) zone intersecting a karst conduit in the phreatic zone. To account for infilling and breakdown processes in the crushed zone two simple rules were added to the basic model: 1) continuous infilling of dissolutionally created voids prevents fractures from growing beyond some limited aperture, although the dissolution proceeds, 2) discontinuous collapsing causes sudden closure of a fracture once some critical aperture has been reached. Both rules limit the transmissivity of the network and the related flow rates. Therefore, the constant head difference between the input and the output points is sustained and the flow remains distributed over the entire crushed zone. Provided that restrictions posed by the two rules permit turbulent flow, dissolution rates also remain high in the entire region. High surface area of water-rock contact and high dissolution rates result in high overall removal rates of rock from the crushed zone, one of the necessary conditions for the formation of large closed depressions. Despite the fact that the model neglects some processes and dynamics that would increase the removal rate, the results suggest that large closed depressions could form in the order of 1 million years.