# Snow Load Shape Coefficients and Snow Prevention Method for Stepped Flat Roofs
## 4 Results and Discussion
### Snow Accumulation Processes for Stepped Flat Roofs  
Based on the correspondences between the measurement results and codes, differences can be noted in the snow load shape coefficient values on stepped flat roofs. To explore the reasons, Figure 14 compares the snow accumulation processes on the stepped flat roof and flow fields around the roof at different times. The simulation time is 780 s, which is the same as the field-measured time. The dimensionless length of the erosion zone is defined as \(L_{e}\), and the time \(t\) of the snow accumulation is nondimensionalized to \(T=t/780\). Correspondingly, \(T=1\) represents the time when the snow evolved into its final form. The snow shape on the lower roof was almost rectangular at \(T_{1}=0.064\), and the erosion and the deposition of snow were not obvious at this time. However, via the flow field analysis, it can be observed that a vortex with a dimensionless length of about 2 was formed on the lower roof, from which it can be inferred that this area was the erosion region. When the snow developed to \(T_{2}=0.128\), obvious erosion was observed due to the vortex on the lower roof. The dimensionless range of the erosion length was about 0\(\sim\)1. Over time, the erosion region gradually shrank. The vortex scale and the erosion length decreased to 0.5 at \(T_{3}=0.256\). The reverse flow on the lower roof disappeared at \(T_{4}=0.385\) when erosion was also not observed. It was concluded that erosion could be observed at \(T_{2}=2T_{1}\), and the erosion length was reduced by half at \(T_{3}=4T_{1}\). This indicates a linear relationship between the erosion length \(L_{e}\) and the time \(T\) of the snow accumulation on stepped flat roofs; that is, \(L_{e}=\mathrm{CT}\), where C is the proportional coefficient. The snow accumulation reached the final pattern at \(T_{5}=1\). In the processes of snow accumulation, a flow separation preventing deposition occurred at the end of the lower roof, which verifies the results observed in the measurement.  
The simulation results of snow development are compared with the measurement results [12; 14; 22], as shown in Figure 15. The dotted lines indicate the numerical simulation results at different dimensionless times, while the solid lines represent the measurement results. The relative results are marked with the same color.  
\begin{table}
\begin{tabular}{c c c} \hline
**Code or Equation** & **Maximum \(\mu\)** & **Dimensionless Unbalanced Length (\(x/\mathrm{H}\))** \\ \hline AlJ & 1 & 2 \\ ASCE & 2 & 0.5 \\ NBCC & 2.7 & 1 \\ EN & 2.5 & 2 \\ GB & 2.5 & 2 \\ Equation (20) & 3.44 & 1.6 \\ Equation (21) & 3.44 & 2 \\ \hline \end{tabular}
\end{table}
Table 4: Comparison of the maximum snow load shape coefficients and the unbalanced length of snow.  
Figure 14: Snow accumulation and flow field distribution on stepped flat roofs.  
Figure 15 indicates that the simulation results are consistent with the field measurement results, and the erosion area and the peak depth of snow are reflected in the simulation results. Further comparison illustrates that different snow distributions in the literature correspond to different moments of snow accumulation on stepped flat roofs. Moreover, the corresponding times are all less than one-third of the snow accumulation time. This also proves that it is difficult for the snow on prototype structures to reach a stable state due to the influence of the measurement time and the environment.