A theoretical analysis of the fluid-solid interactions governing the removal of woody debris jams from cylindrical bridge piers

This paper proposes a theoretical model to describe previous laboratory observations of the dynamics of debris accumulations around bridge piers of cylindrical shape. The model is based on the assumption that the observed dynamics is mainly governed by dynamic changes of the point of application of the drag force exerted on the solid body formed by debris accumulated around the pier. A phase plane analysis of the resulting non-linear system of ODEs shows that the model captures the main patterns observed in previous laboratory experiments, including an oscillatory motion and the removal of debris from the pier by the flow. The model provides a theoretical basis for the analysis of the conditions required for debris jams to remain stable over long periods of exposure to impinging flow. Namely, the model indicates that stability of debris accumulations primarily depends on geometrical asymmetry and on the length of the extension downstream of the pier. The former induces the torque required to rotate the jam about the pier, while the latter produces a stabilising effect after the body rotates.