Evaluating at Three Scales the Hydraulic Conductivity in an Unconfined and Stratified Alluvial Aquifer

The values of hydraulic conductivity (K) were evaluated at three scales in a stratified alluvial aquifer. The small scale is that of hundreds of soil samples for which K was estimated using predictive methods. A first estimate assumed that each sample was homogeneous. A second estimate proceeded with the modal decomposition for the grain-size distribution curve: this quantified the existing and visually confirmed stratification before predicting K. The medium scale is that of hundreds of variable-head (slug) permeability tests in monitoring wells. The large scale is that of 16 pumping tests in steady-state conditions. The aquifer heterogeneity was quantified with the K values distribution curves for small and medium scales and their modal decompositions. The large data sets provided an excellent opportunity to check the lognormal assumption for the K distributions. Large-scale K values were predicted from the small-scale K distribution with assumed stratification and also from medium-scale K distribution: these predicted values were found to be equal to the mean K value of pumping tests. Therefore, if the grain-size distributions are correctly interpreted and the field permeability tests are correctly performed and interpreted, the distribution curves for the small-scale and medium-scale K values explain the large-scale K values of pumping tests, and there is no need to invoke any scale effect.