Dam sites in soluble rocks: a model of increasing leakage by dissolutional widening of fractures beneath a dam

Abstract

Water flowing through narrow fissures and fractures in soluble rock, e.g. limestone and gypsum, widens these by chemical dissolution. This process, called karstification, sculptures subterranean river systems which drain most of their catchment. Close to dam sites, unnaturally high hydraulic gradients are present to drive the water impounded in the reservoir downstream through fractures reaching below the dam. Under such conditions, the natural process of karstification is accelerated to such an extent that high leakage rates may arise, which endanger the operation of the hydraulic structure. Model simulations of karstification below dams by coupling equations of dissolutional widening to hydrodynamic flow are presented. The model scenario is a dam 100 m wide in limestone or gypsum. The modelling domain is a two-dimensional slice 1 m wide directed perpendicular to the dam. It extends 375 m vertically and 750 m horizontally. The dam is located in its center. This domain is divided by fractures and fissures into blocks of 7.5×7.5×1 m. The average aperture width of the fractures is 0.02 cm. We performed model runs on standard scenarios for a dam site in limestone with the height H of impounded water 150 m, a horizontal impermeable apron of width W=262 m and a grouting curtain reaching down to a depth of G=97 m. In a second scenario, we changed these construction features to G=187 m and W=82 m. To calculate widening of the fractures, well-established experimental data on the dissolution of limestone and gypsum have been used as they occur in such geochemical settings. All model runs show similar characteristic behaviour. Shortly after filling, the reservoir exhibits a small leakage of about 0.01 m 3 s −1, which increases steadily until a breakthrough event occurs after several decades with an abrupt increase of leakage to about 1 m 3 s −1 within the short time of a few years. Then, flow in the fractures becomes turbulent and the leakage increases to 10 m 3 s −1 in a further time span of about 10 years. The widths of the fractures are visualized in various time steps. Small channels propagate downstream and leakage rises slowly until the first channel reaches the surface downstream. Then breakthrough occurs, the laminar flow changes to turbulent and a dense net of fractures which carry flow is established. We performed a sensitivity analysis on the dependence of breakthrough times on various parameters, determining breakthrough. These are the height of impounded water H, the depth G of grouting, the average aperture width a 0 of the fractures and the chemical parameters, which are c eq the equilibrium concentration of Ca with respect to calcite and the Ca-concentration c in of the inflowing water. The results show that the most critical parameter is a 0. At fracture aperture widths of 0.01 cm, breakthrough times are above 500 years. For values of a 0>0.02 cm, however, breakthrough times are within the lifetime of the structure. We have also modelled dam sites in gypsum, which exhibit similar breakthrough times. However, after breakthrough, owing to the much larger dissolution rates of gypsum, the time until unbearable leakage is obtained, is only a few years. The modelling can be applied to complex geological settings, as phreatic cave conduits below the dam, or a complex stratigraphy with varying properties of the rock with respect to hydraulic conductivity and solubility. A few examples are given. In conclusion, our results support the assumption that increasing leakage of dam sites may be caused by dissolutional widening of fractures.