# Research on Snow Load Characteristics on a Complex Long-Span Root Based on Snow-Wind Tunnel Tests
## 2 Validation of Experimental Approach
### Similarity Criterion

Table 1: Prototype drifting parameters. Figure 3: Wind speed \(U_{\mathrm{h}}\) and direction \(\theta_{\mathrm{h}}\) at 1.0 m height for the entire measuring period on SN09 [18]. The selected model scale of 1/2 satisfied the blockage effects. The vertical profiles of the flow field identified over the snow mantle in the test section were similar to these over the measured field in Sapporo. In order to assess the modeling reliability, the results of the typical similarity numbers for both the prototype and model are summarized in Table 3. The experimental wind velocity (2.3 m/s at the height of the model top) used for calculating the scaled model values was determined according to Equation (1). Requirement 2 in Table 3 represents the geometric similarity of both model and prototype. The correct modeling of the ejection process of particles is realized by satisfying requirements 3, 4, and 5. Requirement 5 is a roughness-height Reynold number, where \(\
u\) is the fluid's kinematic viscosity. The basic requirements of dynamic similarity could be measured with densimetrical Froude numbers 6 and 7 (ratio between the inertia force and gravity force), and similarity number 8. In order to model the fully rough saltation flow, it is desirable to guarantee the lower limit of the Reynolds number \(U^{3}/2g\
u>30\). If the saltation mechanism occurs, the fully rough flows will be satisfied if \(U_{\mathrm{t}}^{3}/2g\
u>30\)[16]. This lower limit was satisfied in this experimental case as shown in Table 3. Except for this, the noticeable mismatches are found in the particle ejection process scaling and dynamic similarity. For the particle ejection scaling, the gravitational force is overestimated in requirement 4 with a greater particle density, which is also observed in requirement 8 with a higher snowfall velocity. This indicates that the trajectory of the artificial snow particle is smaller than the natural snow particle one [19]. However, a higher particle/air density ratio is usually required [19] and the saltation trajectory for the scale model is small in comparison with the actual snowdrift observed [20]. For the dynamic similarity, the particulate Froude number weighted by the density ratio (requirement 7) is the parameter that allows for assessing the similarity of the transport mechanism of suspended particles [12]. The evaluation of the particulate Froude number based on the threshold friction velocity (requirement 6) is linked to surface transport. According to comparisons of requirement 6 and requirement 7, the saltation mechanism, which has been identified as the major particle transport process, is better reproduced than other transport processes [12]. The prototype snowstorm duration was assumed to be 24 h according to the observation duration [18]; whereas, the experimental snowstorm duration was set to approximately 8 h according to the definition for the dimensionless time used by [PERSON] [12]. As the experiment would have been excessively lengthy, the test was divided into four stages to allow the fan to rest and refill the snow particles into the feeder. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Particle Parameters** & **Values** & **Particle Parameters** & **Values** \\ \hline Particle diameter \(D_{\mathrm{P}}\) & 100 to 150 \(\mathrm{\SIUnitSymbolMicro m}\) & Threshold friction velocity \(U_{\mathrm{t}}^{*}\) & 0.3 to 0.6 m/s \\ Snowfall velocity \(W_{\mathrm{f}}\) & 2.0 to 2.4 m/s & Accumulated snow density \(\rho_{\mathrm{P}}\) & 386 to 447 kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters relating to the physical properties of artificial snow. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dimensionless Parameters** & **Prototype Value** & **Model Value** & **Number** \\ \hline \(D_{\mathrm{P}}/L\) & \(1.5\times 10^{-4}\) to \(2\times 10^{-4}\) & \(2\times 10^{-4}\) to \(3\times 10^{-4}\) & (2) \\ \(U/U_{\mathrm{t}}^{*}\) & 4.7 to 11.3 & 3.8 to 7.7 & (3) \\ \(\rho_{\mathrm{P}}/\rho\) & 41 to 574 &