Interpretation of local scouring at bridge piers and abutments with the phenomenological theory of turbulence

Abstract

The phenomenological theory of turbulence is here applied to the scouring phenomenon at bridge piers and abutments. In the last ve decades many researches have been devoted to the development of predictive formulae able to quantify the maximum scour depth for both design and risk assessment needs of hydraulic structures. Owing to the complexity of the problem, most of the proposed formulae were developed on an empirical basis, which made them susceptible to scale issues and not fully consistent with the physics underpinning the scouring phenomenon. Recently, some studies of Gioia & Bombardelli (2005), Bombardelli & Gioia (2006), Manes & Brocchini (2015) and Ali & Dey (2018) have proposed a di erent approach, which exploits a theory to derive scaling relations between the equilibrium scour depth and non-dimensional parameters. Their work presented the phenomenological theory of turbulence and the paradigms of the sediment incipient motion theory assuming rough ow conditions, meaning that the momentum transport near the sediment-water interface was dominated by eddies belonging to the turbulent energy spectrum inertial range and scaling with the sediment diameter. In order to provide more general models and on the basis of the ndings of Bonetti et al. (2017), the present work relaxes this as sumption by exploring the scaling of the equilibrium scour depth in cases where momentum transport is a ected by eddies belonging to the dissipation and production range. This improvements were applied to the scouring phenomenon at bridge piers, to derive a predictive formula for the maximum scour depth, and to the scouring phenomenon at bridge abutments, to derive a scaling law that does not allow a directly assessment of the maximum scour depth, but provides new avenues for the development of general predictive formulae that are founded more on physical than empirical bases. In both cases, the proposed theory includes the relevant non-dimensional parameters controlling the scouring process and, contrary to commonly employed empirical formulae, it is free from scale issues.