Use of Referential Coordinates in Deforming Soils
- Philippe Baveye ,
- Charles W. Boast and
- Juan V. Giráldez
Analysis of hydrological processes in deforming soils generally involves use of some form of a referential, or material, coordinate transformation. In the most commonly used of these relationships, there appear two macroscopic soil mass density factors, that associated with the configuration of the soil at a reference time t = 0, and that associated with its configuration at a later (arbitrary) time. In some previous work, the assumption was made that these bulk densities could be evaluated at the same space-fixed point. In an illustrative application to dual-energy gamma-ray data on the swelling of a clay loam during infiltration, this approximation is shown here to predict vertical displacement values that are as much as 7 mm in excess of values obtained without the approximation. Moreover, the approximation fails to satisfy macroscopic mass balance. It is also shown that the direction, downward or upward, of the vertical displacement of macroscopic body-points depends on the boundary condition used in the integration of the referential coordinate transformation; i.e., depends on whether the integration begins at the soil surface or at a point below the wetting front. Since these two integration pathways are mathematically equivalent, it is argued that a systematic comparison between results obtained using them can serve a useful purpose in detecting occurrences of lateral expansion or systematic errors in the experimental data.
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