# Research on Snow Load Characteristics on a Complex Long-Span Root Based on Snow-Wind Tunnel Tests
## 2 Validation of Experimental Approach
### Similarity Criterion  
The snowdrift phenomenon can be explained as solid particle transport. Depending on whether the friction velocity reaches a threshold, three particle transport mechanisms can be observed: creep, saltation, and suspension. Creep is a phenomenon in which snow particles move by rolling, sliding, or creeping at the surface; saltation is a process in which snow particles move with repeated leaping up or jumping and colliding with a snow surface; and at a higher wind velocity, particles are transported upwards by turbulent eddies and transported far downwind. Among the mechanisms, saltation has been identified as the major particle transport process, which causes approximately 67% of the total drifting mass [12]. For reliable modeling of these transport mechanisms, a reasonable similarity criterion is necessary for reduced-scale experiments. As the similarity criterions are incompatible with one another, compromises have to be made according to their relevance [12; 16]. Even so, none of the models cited in the literature are able to provide a satisfying interpretation of experimental results. Figure 1: Schematic view of the experimental facility. Figure 2: Snowfall simulator: (**a**) artificial snow particles; (**b**) snow particle feeder. In this study, considering that the experimental modeling was focused on the reliable preproduction of snowdrift on a long-span roof, the similarity number based on the similarity of the drifting snow flux in the saltation layer was selected. These similarity criteria were first introduced by [PERSON] [17] and also adopted by [PERSON] [12]. The similitude criterion based on the drifting flux is shown in Equation (1). \[\big{(}\rho/\rho_{\mathrm{P}}\big{)}\big{(}U^{2}/2g\big{)}(1-U_{0}/U) \tag{1}\]  
where \(\rho\) and \(\rho_{\mathrm{P}}\) are the air and particle densities, respectively; \(U\) and \(U_{0}\) are the reference wind velocity and threshold reference velocity, respectively; and \(g\) is the gravitational acceleration. Furthermore, similarity criteria related to geometric, dynamic, and kinetic criteria were also considered. To validate the similarity criterion, snowdrift around a surface-mounted cubic model, employed in detailed field measurements carried out by [PERSON] et al. [18] in Sapporo, Hokkaido, Japan, was adopted as the analyzed prototype. The snowdrift was observed for only one day by cleaning up the snow around the model following each drifting snow event. The model was 1.0 m on each edge. The averaged wind velocity was approximately 1.7 m/s at a 1.0 m height, and the maximum wind velocity was close to 4.3 m/s (Figure 3). The snow depth at a reference point was 20 cm. The other measurement parameters are summarized in Table 1. The smallest undulation of snowdrift due to the weak wind velocity and the large snowfall make it the most suitable measurement data for validation of the similarity criteria. The artificial snow particles were selected for the validation experiment. The air/water ratio in the snowmaker was set to make sure the artificial snow was dry enough to prevent the particles from sticking together. The accumulated snow density was measured with a scale and cylinder; whereas, the particle diameter was measured with a microscope. The snowfall velocity was obtained by measuring the artificial particle falling times from 1.0 m height [8]. The threshold friction velocity was estimated according to an empirical formula [1]. The parameters of the artificial snow particles are summarized in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Particle Parameters** & **Values** & **Particle Parameters** & **Values** \\ \hline Particle diameter \(D_{\mathrm{P}}\) & 150 to 200 \(\mu\)m & Threshold friction velocity \(U_{\mathrm{t}}^{*}\) & 0.15 to 0.36 m/s \\ Snowfall velocity \(W_{\mathrm{f}}\) & 0.2 to 0.5 m/s & Accumulated snow density \(\rho_{\mathrm{P}}\) & 50 to 700 kg/m\({}^{3}\) \\ Air density \(\rho\) & 1.22 kg/m\({}^{3}\) & Repose angel & 30\({}^{\circ}\) to 50\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}