A Global Optimization Method to Calculate Water Retention Curves

Water retention curves (WRC) have a key role for the hydraulic characterization of soils and rocks. The behaviour of the medium is defined by relating the unsaturated water content to the matric potential. The experimental determination of WRCs requires an accurate and detailed measurement of the dependence of matric potential on water content, a time-consuming and error-prone process, in particular for rocky media. A complete experimental WRC needs at least a few tens of data points, distributed more or less uniformly from full saturation to oven dryness. Since each measurement requires to wait to reach steady state conditions (i.e., between a few tens of minutes for soils and up to several hours or days for rocks or clays), the whole process can even take a few months. The experimental data are fitted to the most appropriate parametric model, such as the widely used models of Van Genuchten, Brooks and Corey and Rossi-Nimmo, to obtain the analytic WRC. We present here a new method for the determination of the parameters that best fit the models to the available experimental data. The method is based on differential evolution, an evolutionary computation algorithm particularly useful for multidimensional real-valued global optimization problems. With this method it is possible to strongly reduce the number of measurements necessary to optimize the model parameters that accurately describe the WRC of the samples, allowing to decrease the time needed to adequately characterize the medium. In the present work, we have applied our method to calculate the WRCs of sedimentary carbonatic rocks of marine origin, belonging to 'Calcarenite di Gravina' Formation (Middle Pliocene - Early Pleistocene) and coming from two different quarry districts in Southern Italy. WRC curves calculated using the Van Genuchten model by simulated annealing (dashed curve) and differential evolution (solid curve). The curves are calculated using 10 experimental data points randomly extracted from the full experimental dataset. Simulated annealing is not able to find the optimal solution with this reduced data set.