On the reliability of mathematical modelling of capillary barriers

Abstract

The problem of the reliability of capillary-barriers' modelling is studied making use of tipping trough measurements. In its fi rst part, the article describes laboratory mea surements of saturated hydraulic conductivities and retention curves of four materials of two different capillary barriers. Both the main branches of the retention curves were measured, and the unsaturated hydraulic conductivities and capacity functions were determined. The second part of the article describes numerical modelling of two tipping trough experiments. The obtained results are compared with the measured data. The comparison shows a good agreement that is presented and discussed. It is concluded that, in the case of capillary barrier materials, the laboratory measurements made on samples and the subsequent math- ematical modelling can substitute for the tipping trough experiments. The capillary barrier is a simple device frequently used to cover landfi lls. It consists of two inclined layers: the overlying fi ne grained layer called the capillary layer and the underlying coarse grained layer called the capillary block. The capillary layer consists of fimaterial, usually a fi ne to medium grained sand, while the capillary block consists of signifi cantly coarser material usually a uniform coarse-grained sand or figravel. The insulating effect of the barrier is based on the fact that, under suffi ciently low values of pressure head, the hydraulic conductivity of the upper layer is signifi cantly, at least one order, higher than that of the capillary block. The infi ltrating water comes from above into the capillary layer and fl ows along it downwards rather than to cross the interface (the capillary interface) and to enter the capillary block, see e.g. Ross (1) or Abdolahzadeh et al. (2). Several laboratory experiments testing two capillary barriers were carried out at the Ruhr University in Bochum. A large tipping trough containing the barriers was used for the exper- iments (3). A measured time-dependent infi ltration into the capillary layer was applied and the responding discharge from both layers of the tested barriers was measured as a function of time. The results made it possible to fi nd out critical values of infi ltration intensity and cumulative infi ltration causing water fl ow through the capillary interface into the capil- lary block (3) and (4). The tested barriers were built up of well-defi ned standard materials and, moreover, several physical characteristics of the materials were measured in Bochum. Numerical simulations of water behaviour in capillary barriers are based on numerical solutions of the Richards equation describing water fl ow in unsaturated media. As the equa- tion contains two unknown functions, the pressure head h and the water content 0, it is necessary to make use of the material's soil-moisture retention curve either in the form