It is well known that scouring is one of the most common causes of bridge failures and this has motivated scientists to devote significant efforts to find formulas for predicting scouring depths and hence to provide guidelines for proper pier-foundation design (Ettema et al. 2011). The enormous amount of research carried out on clear water scouring in the past 60 years resulted in the development of over 30 formulas, which predict the scour depth around a bridge pier for given flow, sediment and pier-geometry conditions. These formulas have been derived mainly with an empiri cal approach supported by dimensional analysis, which involves making hypothesis regarding the relevant non dimensional groups influencing the scouring process and testing these hypotheses over experimental data obtained from extensive laboratory investigations. Experimental data are then fit with equations that contain some free parameters usually in the form of scaling exponents of the non-dimensional groups. Recently, the scaling of one of these dimensionless groups, namely the relative coarseness (i.e. ald, where a is the pier diameter and d the characteristic diameter of sediments), has been the focus of extensive research because there is large consensus on the fact that one of the causes of discrepancy between field scour observations and predictions based on laboratory data is due to a poor understanding of the relation between y_s/a and a/d (where y, is the scour depth of equilibrium). On the basis of large-scale laboratory experiments spanning a wide range of a/d values, a general agreement on the relation between y_s/a and a/d has recently been reached (Sheppard et al. 2004,Lee and Sturm 2009, Lan?a et al. 2013). However, the physical mechanisms underlying the observed relation are still a matter of debate. This paper intends to contribute to the debate with a novel approach. A new formula to predict the scour depth of equilibrium under clear water conditions is derived using principles pertaining to the phenomenological theory of turbulence. The derivation suggests that, if the sediment diameter d lies within the range of turbulent inertial length scales of the flow, then y_s/K(a/d)~(2/3) (where K is the kinetic head of the approach flow). This result was tested against an extensive set of laboratory measurements showing good agreement between theory and data. The relation between y_s/K and a/d is also discussed for two limiting conditions of d approaching the integral and the Kolmogorov length scale. It is finally suggested that the relation between the normalized scour depth and the relative coarseness is a result of the relative positioning of d within the range of length scales pertaining to the spectrum of turbulent energy.
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