Measurement of retention functions with hysteresis using ground-penetrating radar
The non-invasive measurement of water retention functions employing geophysical methods involves the determination of the timely variation of water content using parametrized petrophysical models. Over the last two decades several methods have been published, which are based on the dielectric constant derived from ground-penetrating radar measurements and their relation to the water content. While it is error-prone to ascertain true radar traveltimes from radar reflection data, ground wave or diffraction analysis, transmission measurements are quite accurate. Soil water content is classically estimated by a simple equation or a mixing law derived from small-scale laboratory analysis, which may deny clarification of hydraulic constraints. However, the application of these relationships for the in situ determination of retention functions from water content may lead to non-representative results. For this reason, the aim of this study was to measure non-invasively representative retention functions including their hysteresis of large sand samples using radar transmission data. Experiments were conducted in a two metre high rectangular Plexiglas© tank with a sample volume of 0.6 m³, being the main component of the set up. Implemented radar transmission measurements provided profiles of the dielectric constant across the transition between the water saturated zone and unsaturated soil zone. The spatiotemporal variations of water content induced by the multi-step-outflow/ inflow method were monitored with fixed transmitter-receiver-positions. A new petrophysical model, applicable to sand and incorporating the dielectric effect of hydraulic residual water, was developed to transform radar traveltimes into volumetric water content. This model can be easily calibrated on the basis of the monitored water contents at a fixed site because it includes the defined hydraulic conditions of fully gravitational drainage and full water saturation. Even the consideration of just two water phases with different dielectric properties allowed a satisfactory fitting. Following from the study, a complete retention function was obtained for each sand sample and characterized by a set of van-Genuchten-parameters. The work demonstrated that if a reference level of the water table is known from independent measurements, it is possible to determine retention functions reliably. Despite the fact, however, that further experiments are required, the results of this investigation offer a powerful tool for in situ determination of retention functions and the estimation of van-Genuchten parameters with radar measurements, either in boreholes or from the surface.