A Simplified Analytical Modeling of the Hole Erosion Test

Abstract

Problem statement: Internal erosion occurs in soils containing fine particles under the action of high pressure gradients that could result from water discharge. This phenomenon can yield in its final stage to the formation of piping which constitutes a real threat for hydraulics infrastructures as it can precipitate their entire rupture in very short time. In order to mitigate this insidious hazard, it is important to characterize piping dynamics. In this context, the Hole Erosion Test was introduced to assess the erosive features of soils by means of two parameters, the erosion rate and the critical shear stress indicating the beginning of erosion. Modeling this test can enable to understand more comprehensibly the piping phenomenology. Approach: A simplified analytical modeling of the Hole Erosion Test was considered in this study. A closed form solution of erosion taking place during piping was derived without resorting to the habitual cumbersome developments that are needed to achieve complete solution of the rational equations describing this highly coupled problem. This was achieved by assuming formal analogy between the erosive shear stress and the friction shear that develops at a cylindrical piping wall under an axial viscous flow. The flow was assumed to be uniform along the tube. Results: A closed form analytical formula describing erosion dynamics associated to piping was derived. Theoretical predictions were compared with experimental results and the simplified model was found to predict accurately the increase of flow rate that results from piping erosion. Conclusion/Recommendations: The one-dimensional modeling that was proposed for the Hole Erosion Test under strong simplifying assumptions was found to yield the same features as those obtained in the literature by using other approaches. It gives furthermore the dynamics as function of the fluid regime existing inside the tube. In order to get further insight regarding the flowing flow action, which could be non uniform during erosion, more advanced modeling is needed.