Resumen de Upscaling of water flow and mass transport in a tropical soil: numerical, laboratory and field studies
Numerical models are becoming fundamental tools to predict a range of complex problems faced by geotechnical and geo-environmental engineers. However, to render the model reliable for future predictions, the model input parameters must be determined with consideration of the scale effects. In this context, this thesis focuses on upscaling of water flow and mass transport in a tropical soil by means of numerical, laboratory and field studies. This thesis is organized in four parts.
First, the heterogeneity, correlation and cross-correlation between solute transport parameters (dispersivity, ¿, and partition coefficient, Kd) and soil properties were studied in detail. In this part, it was verified that the hydraulic conductivity (K) and solute transport parameters are highly heterogeneous, while soil properties not. Spatial correlation of ¿, K, and statistically significant variables were studied, and it would probably improve the estimation only in a small-scale study, since the spatial correlation were only observed up to 2.5 m. This study was a first attempt to evaluate the spatial variation in the correlation coefficient of transport parameters of a reactive and a nonreactive solute, indicating the more relevant variables and the one that should be included in future studies.
In the second part, scale effect on K, dispersivity and partition coefficient of potassium and chloride is studied experimentally by means of laboratory and field experiments. The purpose of was to contribute to the discussion about scale effects on K, ¿ and Kd and understanding how these parameters behave with the change in the scale of measurement. Results shows that K increases with scale, regardless of the method of measurement. Dispersivity trends to increases exponentially with the sample height. Partition coefficient, tend to increase with sample length, diameter and volume. These differences in the parameters according to the scale of measurement must be considered when these observations are later used as input to numerical models, otherwise the responses can be misrepresented.
Third, stochastic analysis of three-dimensional hydraulic conductivity upscaling was performed using a simple average and the Laplacian-with-skin methods for a variety of block sizes using real K measurements. In this part it was demonstrated the errors that can be introduced by using a deterministic upscaling using simple averages of the measured K without accounting for the spatial correlation. The application shows that K heterogeneity can be incorporated in the daily practice of the geotechnical modeler. The aspects to consider when performing the upscaling were also discussed. Finally, the dependence of the exponent of the p-norm as a function of the block size was analyzed.
In the last part, an application of stochastic upscaling of hydrodynamic dispersion coefficient (D) and retardation factor (R) was performed using real data aiming to reduce the lack in experimental upscaling of reactive solute transport research. Upscaling of D was done using macrodispersion method. Simple average method based on p-norm was used to perform R upscaling. A good propagation of the uncertainties was achieved. Simple upscaling methods can be incorporated to the modeling practice using commercial transport codes and properly reproduce de transport at coarse scale but may require corrections to reduce smoothing of the heterogeneity caused by the upscaling procedure.
