Toward a better understanding of fissure growth in karst formations: Investigations from genesis to maturation and the influence of fracture-matrix interactions.

摘要

There has been interest in quantitative modeling of early karstification with the objectives of estimating time-scales of conduit growth and understanding the nature of cave patterns. In particular, the initiation phase has been studied in great detail because it is the slowest phase in the development of caverns. In this study aperture variability in a two-dimensional framework and fracture-matrix interaction are studied to better understand their role in time estimations of aperture growth.; The initial phase of karst development is studied from its nascent stage as a fissure into the early stages of turbulence. In uniform fissures in rapidly dissolving minerals, the concentration reaches the solubility limit within a short distance along the flow path. However, the variability in the aperture field inherently provides instabilities to the system and growth is propagated along these perturbations. Flow is focused into preferential channels which are enlarged at a faster rate than surrounding regions of slow flow. As a result, a positive feedback mechanism takes place and creates growth in a highly selective manner. Only in large domains (>25 correlation lengths), can the instabilities create competition for flow at the solution front as well and lead to significant branching. It is this branching which creates the non-monotonic behavior in breakthrough times (defined as the point in which turbulent flow is first encountered). It has been observed that the non-monotonic behavior is scale dependent. Smaller domains do not exhibit this behavior because there are only a few correlation lengths between the fingertip and the lateral domain boundaries. Aperture variability significantly impacts dissolution patterns in a two-dimensional framework.; While aperture variability speeds up growth, the inclusion of the porous bedrock can inhibit growth. The porous matrix serving as a large low-conductive reservoir can significantly influence the development of the fracture by slowing down dissolution growth through matrix diffusion. In a one-dimensional model, this issue is further explored.; Although the focus of the study is on modeling of early karstification, there are many common themes between this problem and other reactive transport problems that this model can be made suitable for exploring.