Simultaneous Prediction of Saturated Hydraulic Conductivity and Drainable Porosity Using the Inverse Problem Technique

The saturated hydraulic conductivity $K$ and the effective porosity $f$ are two important input parameters needed for lateral drain spacing design, as well as some other applications. The technical and economic justification, of most drainage projects, is mainly connected to these two parameters. The current design procedure is based upon calculation of the lateral spacing, using some average values of $K$ and $f$ within the drainage area. The objectives of this study were to introduce a new method for simultaneous estimation of $K$ and $f$ parameters using the inverse problem technique, and to evaluate five different unsteady drainage analytical models of the Boussinesq equation, suggested by different researchers for simultaneous prediction of the parameters. Consequently, five different analytical models for predicting water table profiles were solved, using the inverse problem technique. Each model was then evaluated. A physical drainage model of $2.2\mathrm{m}$ length, $0.3\mathrm{m}$ width, and $0.5\mathrm{m}$ height was established in the laboratory and carefully packed with a sandy loam soil. A perforated drainage pipe of $4.5\mathrm{cm}$ in diameter was installed at the bottom end of the model. Many piezometers were inserted in the soil for spatial and temporal water table monitoring. Different data sets from the experiments and literature were used for model calibration. The newly proposed approach that is based upon measuring water table profiles, at different times, was then evaluated with both constant and variable $f$ . The predicted values of the proposed approach indicated reasonable agreement with the measured data. With variable effective porosity, the method was even more accurate to predict the water table profiles. Using the inverse problem technique, all the analytical models provided good agreement with the measured data. Among these, however, the Topp and Moody model predicted more accurate results than other models.