Aeolian windblown sand saltation: an application of copulae for the estimation of threshold shear velocity

Windblown sand interacts with both human activities and civil structures and infrastructures in arid environments. This makes windblown sand a key issue to tackle for engineering disciplines. Windblown sand transport results from soil erosion and implies sand sedimentation around any obstacle. Railway infrastructures are particularly sensitive to this issue because of their extent and their technical complexity. The periodic removal of sedimented sand is fundamental to avoid both serviceability issues and failures. Saltation is the main sand transport mechanism in terms of transported mass. If the wind shear velocity is higher than the threshold shear velocity, sand grains are entrained into the lower part of the atmospheric boundary layer and saltation occurs. A number of deterministic models to assess the threshold shear velocity have been proposed in the literature so far. Microscopic models discuss the equilibrium of forces acting on the single particle interacting with the sand bed. Semi-empirical macroscopic models derive the threshold shear velocity as a function of the particle diameter. Recent probabilistic microscopic models aim at including random variables describing the moments induced by the forces acting on grains. On the one hand they need a sound probability distribution for each random variable. On the other hand it is not straightforward conceiving a model inclusive of all the random variables affecting threshold shear velocity. Indeed, threshold shear velocity suffers the effect of a number of uncertainties, both aleatory and epistemic ones. In the design perspective and within a probabilistic approach to design, the engineer is interested in relating a sand erosion or transport condition to a low probability of exceedance, i.e. high percentile. Triggered by this motivation, this study aims at contributing to shed some light on such issue. The deterministic approach is critically reconsidered in the light of a wide collection of experimental measurements. Then, a purely statistical approach based on copula modelling is proposed. This allows to comprehensively merge all kinds of uncertainty sources and recognize the dependence of the threshold shear velocity on the grains diameter not only in terms of mean value, but also referring to higher statistical moments and percentiles.