A numerical model for wind-borne compact debris trajectory estimation: Part 1 – Probabilistic analysis of trajectory in the proximity of tall buildings

Abstract

This paper describes the development of a numerical algorithm for investigating the probability of wind-borne compact debris, impacting on the vertical façade of tall buildings. A uniform wind field with constant velocity was employed; turbulence effects were neglected.The trajectory of compact debris was estimated by solving the three-dimensional (3D) equations of motion of the object, immersed in uniform wind field; simulation results were compared to experimental data, derived from literature. Random parameters were selected to estimate the trajectory and to derive “Iso-probability Impact Contours”, using Monte Carlo simulation. These contours describe the probability associated with “randomly flying” debris, as they impact against a cladding on the vertical façade, conditional on the initial position of the object relative to the structure. These contours were developed for two different cases, “Quasi-2D” and “Fully 3D”, to account for wind directionality.Moreover, a “Universal Probability Curve”, describing the probability of impact for compact objects against the façade of a benchmark tall building, was developed in two-dimensional (2D). It was proven that this curve is universal and can be used independently of wind velocity.