A hybrid model to evaluate subsurface chemical weathering and fracture karstification in quartz sandstone

A hybrid numerical, finite differences and semi-analytical/empirical model has been developed to evaluate the spatial and time scale of chemical weathering along a fracture in quartz sandstones. The model is based on the diffusion transport occurring from the bedrock mass toward the fracture walls driven by the SiO2 concentration gradient between water in the bedrock pores (high silica content) and water flowing in the fracture (low silica content). Because of molecular diffusion, intergranular water becomes undersaturated with respect to silica. This promotes dissolution of quartz at grain boundaries and results in a porosity profile decreasing from the fracture walls toward the rock interior. Bedrock individual grains are released and gradually removed by the water flowing into the fracture when a critical value of porosity is reached (Grain Release Threshold, GRT): this process drastically increases the fracture enlargement rate. The model outcomes establish a minimum time of 90 ka to reach the GRT. This time is independent of length, aperture and dip of the fracture, but is controlled by parameters such as the initial fracture aperture, water temperature, quartz grain size, and initial bedrock porosity. It is attested that the water flowing in the fracture remains undersaturated with respect to silica over very long timescales (in the order of 105 years) and over very long flow paths. In turn, this suggests that the extremely slow reaction between quartz and water is the keyfactor for the formation of subterranean karst-like features in quartz sandstone, otherwise silica saturation would be reached after short distances and deep weathering in this lithology would be prevented. Finally, the model outcomes were compared to field data from the Gran Sabana caves (Venezuela) and other quartz sandstone weathering landforms elsewhere, showing that dissolution/diffusion in the rock matrix is a reliable mechanism for the formation of these peculiar karst-like features.