Dimensional analysis of backward erosion piping phenomena

Backward erosion piping (BEP) is a mechanism of internal erosion that leads to the formation of shallow erosion channels in the sandy foundation of river embankments, or other water-retaining structures, at the interface with a more impervious layer. Under ultimate conditions this process may result in the failure of the earthen structure. Physical modelling enables the reproduction and study of this phenomenon in a controlled environment, thereby identifying the main variables involved in the process. To build a model capable of accurately reproducing the phenomenology at different scales, the achievement of dynamic similarity between the model and the real system, which in turn implies geometric and kinematic similarities, is crucial. Nonetheless, the requirement for dynamic similarity is generally difficult to achieve. In this context, dimensional analysis is of paramount importance, as it enables to define dimensionless groups of significant relevance for the physical problem under study. In this work, after a brief introduction to the BEP process, the theoretical approach required for dimensional analysis is applied to the results of physical model tests from the scientific literature, as well as to those obtained from the experimental apparatus recently implemented at the University of Bologna. Despite the dispersion of the results, which is certainly related to an insufficiently homogeneous experimental database, this preliminary study emphasizes the importance of the dimensional analysis tool and confirms the complex nature of BEP.