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24. Dale, J., Gamble, S., Brooks, A., *Design snow load refinement using modeling and analysis techniques*, Proceedings of the Canadian Society for Civil Engineering 4th International Structural Specialty Conference, May 28-31, Halifax, NS, p. CST-88-1, 2014.

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# CFD simulation of drift snow loads for an isolated gable-roof building

Yoshihide Tominaga<fnref n="1" />,ª, Tsubasa Okaze<fnref n="2" /> and Akashi Mochida<fnref n="3" />

**Abstract.** Unbalanced snow accumulation on an isolated gable-roof building with different roof pitches was modeled using computational fluid dynamics (CFD). First, we confirmed CFD prediction accuracy for the velocity and pressure fields around the building by comparing simulated results with results obtained in prior wind tunnel experiments. Next, the unbalanced roof snow accumulation was predicted for different wind velocities using a snowdrift model previously proposed by the authors. The predicted drift coefficients were compared with observational data and resultant design codes developed by ISO4355. Finally, we confirmed that the observational data could generally be reproduced using the proposed CFD simulation method.

## 1 Introduction

When predicting snow loads on building roofs, unbalanced snow accumulation due to wind flow is a difficult problem. Accumulation occurs because of a complex interaction between snow particle motion and fluid flow affected by building geometry. Through field observations, much has been learned about this phenomenon [1–3]. Observation of specific cases in which impacts of various parameters on snow accumulations can be considered under controllable conditions (e.g., wind or water tunnels) has also been effective in advancing the knowledge [4–6]. Although these efforts have greatly contributed to improvements in building design [7, 8], their applicability has been limited to specific geometries and weather conditions. Recently, computational fluid dynamics (CFD) has been applied to model snowdrift around buildings [9]. However, few studies have applied CFD to model roof snow. This et al. [10, 11] predicted snow distribution on a sports hall with a curved roof located in Oslo, Norway, and compared the simulated results with field measurements. They focused primarily on reproducing the snow distributions observed on the actual building caused by the specific weather conditions. Few prior studies have applied CFD to model snowdrifts with a generic configuration.

This study aimed to clarify the fundamental performance and limitations of CFD in roof snow prediction. First, we confirmed the prediction accuracy of CFD on the flowfield by comparing simulation results with experimental wind tunnel results for a gable roof with different pitches. Next, we applied a proposed snowdrift model to predict snow distribution on the roof. For this application, drift coefficient data measured in Norway [2, 3]—the data used for snow load design by the ISO4355 ‘Bases for design of structures - Determination of snow loads on roofs’ [8]—was compared with the simulated results.

<figure><img src="image_388.png" /><figcaption>**Figure 1.** Field observation of unbalanced roof snow on gable roofs: (a) courtesy of Dr. T. Tomabechi, (b, c) courtesy of Dr. T. Thisi [7]</figcaption></figure>

<figure><img src="image_389.png" /><figcaption>**Figure 2.** Snow depth for 5:10 roof pitch obtained by field observation (modified from [12])</figcaption></figure>

<figure><img src="image_390.png" /></figure>

<footnote n="1">¹Niigata Institute of Technology, 1719 Fujihashi, Kashiwazaki, Japan</footnote>

<footnote n="2">²Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama, Japan</footnote>

<footnote n="3">³Tohoku University, 6-6-11 Aoba, Sendai, Japan</footnote>

<footnote>ª Corresponding author: tominaga@abe.niit.ac.jp</footnote>
## 2 Snow accumulation on gable roofs

Gables are a common roof shape for single-family residences, garages, barns, etc. Figure 1 shows examples of unbalanced snow accumulations on various gable roofs. Snow blown by incoming flow on the windward side of the roof can accumulate on the leeward side of the roof, where the wind velocity is sufficiently low allowing snow to settle out and form a drift. As a result, the snow load on the leeward side is larger than the snow load elsewhere on the roof and, in some cases, is even larger than the ground snow load [7].

Figure 2 shows accumulated snow depth on a gable roof with a 5:10 roof pitch obtained by field observation [12]. The larger snow accumulations on the leeward side of the roof are clearly demonstrated. O'Rourke and Auren [13] suggested that roof slope, roof width, and ground snow load are key parameters affecting drift size on gable roofs. The American Society of Civil Engineers (ASCE) [14] considered uniform surcharges that extend downwind from the roof ridge for some specified distance (related to the eave-to-ridge fetch distance and the roof slope) and noted a smaller downwind extent for shorter fetch distances and steeper roof slopes. Measurements obtained by Høibø [2, 3] indicated that both the mean and standard deviation of the differences and drift coefficients increase with roof slope [7]. Therefore, gable roofs with different roof pitches that experience unbalanced snow accumulations are good candidates for investigating the complex interaction between snow particle motion and fluid flow affected by building geometry. This roof type is deemed suitable to validate the CFD numerical methods proposed in this study.

<figure><img src="image_391.png" /><figcaption>**Figure 4.** Plan and cross-sectional grid overlay for the building model (5:10 roof pitch)</figcaption></figure>

<figure><img src="image_392.png" /><figcaption>**Figure 5.** Inflow boundary conditions (actual scale)</figcaption></figure>

## 3 CFD simulation method

### 3.1 Building configuration

Figure 3 provides a schematic view of the building model used in this study. An isolated gable-roof building, with an eave height ($H_e$) of 6 m and a width (W) of 6.6 m, was placed perpendicular to the approaching wind flow. The model singularly considered three different roof pitches: 3:10 (16.7°), 5:10 (26.6°), and 7.5:10 (36.9°). The eave height ($H_e$) was constant for the three model scenarios. Tominaga et al. [15] performed a detailed investigation on

<figure><img src="image_393.png" /><figcaption>**Figure 3.** Schematic view of building model</figcaption></figure>

<figure><img src="image_394.png" /><figcaption>**Figure 6.** Comparison of simulated and measured (a) mean streamwise velocity ($U_1$) and (b) turbulent kinetic energy ($k$) (5:10 roof pitch)</figcaption></figure>
CFD prediction accuracy for this type of configuration.

## 3.2 Numerical methods

### 3.2.1 Flowfield

The ANSYS FLUENT 14.5 commercial software was used to perform steady-state Reynolds-averaged Navier-Stokes (RANS) equation computations based on a control volume approach for solving the flow equations.

Grid generation is an important consideration when applying CFD to predict roof snow. If structured grids consisting of rectangular cells are used for slanted roofs (such as a gable), prediction of friction velocity and snow distribution on the roof surface may be inaccurate. Tetrahedral and pyramid cells are superior in reproducing complicated shapes, but controlling appropriate grid resolution to ensure accurate prediction of surface velocity and calculation convergence is difficult. In this study, special care was taken to allocate an adequate number of hexahedral cells along the oblique roof to preclude tetrahedral and pyramid cells. Figure 4 shows example grid resolutions for the plan-view building and ground surfaces, and for the building cross section for the 5:10 roof pitch. One side of each roof pitch was divided into approximately 20 cells. For the 5:10 roof pitch domain, the computational grid comprised 2,355,280 cells; other roof pitches had similar grid sizes. In a prior study [15], a grid-sensitivity analysis showed that grid refinement did not significantly affect the results. The realizable $k-\epsilon$ model [16] was used as the turbulence model.

The computational conditions used in this study were based on guidelines from the Architectural Institute of Japan (AIJ) [17]. The computational domain comprised a volume measuring 16 H (x-axis) × 12 H (y-axis) × 7 H (z-axis). For the flowfield validation study, the profiles of the streamwise velocity ($U_l$) and turbulent kinetic energy ($k$) were imposed at the inlet, based on experimental data. For the snowdrift study, a power law profile with an index of 0.20 was assumed for $U_l$; the profile for $k$ was determined using a turbulent intensity equation proposed by the AIJ [18]. Figure 5 shows the $U_l$ and $k$ profiles for the snowdrift study. The $\epsilon$ values were determined from the local equilibrium assumption, $P_k = \epsilon$, where $P_k$ is the production term in the $k$ equation.

### 3.2.2 Drifting snow field

The snowdrift model previously proposed by the authors [9] was implemented in CFD code as a user-defined function. To model suspension, the transport equation for snowdrift density ($\Phi$) [kg/m³] was solved, where $W_f$ is the snowfall settling velocity assumed to be - 0.5 m/s.

$$ \frac{\partial \Phi}{\partial t} + \frac{\partial U_l \Phi}{\partial x_l} + \frac{\partial W_f \Phi}{\partial x_3} = \frac{\partial}{\partial x_l} \left( \frac{v_t}{\sigma_s} \frac{\partial \Phi}{\partial x_l} \right) \quad (1) $$

The snowdrift density at the inflow and top boundaries ($\Phi_{in}$) was $7.5 \times 10^{-4}$ kg/m³, calculated using the amount of

snowfall per unit time and snowfall velocity ($W_f$). The turbulent Schmidt number ($\sigma_s$) was 0.7 [19].

The deposition flux on the snow surface ($q_{dep}$) [kg/m²s] and the erosion flux on the snow surface ($q_{ero}$) [kg/m²s] are determined as follows using Eqs. (2) and (3):

$$ q_{dep} = W_f \Phi_P \left( \frac{U_{*t}^2 - U_{*s}^2}{U_{*t}^2} \right) \quad (U_* \le U_{*t}) \quad (2) $$

$$ q_{ero} = -A_e \rho_t U_* \left(1 - \frac{U_{*t}^2}{U_*^2}\right) \quad (U_* > U_{*t}) \quad (3) $$

where $\Phi_P$ is the drift density at the first grid adjacent to the snow surface, $U_*$ is the friction velocity at the snow surface, $U_{*t}$ is the threshold friction velocity (0.2 m/s), $A_e$ is a proportional constant ($1.0 \times 10^{-5}$), and $\rho_t$ is the density of ice. This model differs from the prior study's model [9] because friction velocity effects on the snow surface were included in not only erosion but also deposition fluxes [20]. The net deposition flux ($q_{total}$) [kg/m²s] is given by Eq. (4).

$$ q_{total} = q_{dep} + q_{ero} \quad (4) $$

When erosion occurs ($U^* > U_t^*$), $q_{ero}$ is given as the surface boundary condition for the $\Phi$ transport equation.

Friction velocity ($U^*$) was calculated using a generalized log law adopted in CFD code [21] as follows:

$$ U_*^2 = \frac{\kappa C_{\mu}^{1/4} k_P^{1/2} U_P}{\ln \left( \frac{E C_{\mu}^{1/4} k_P^{1/2} y_P}{\nu} \right)} \quad (5) $$

where

$U_P$ is mean velocity of the fluid at point P

$k_P$ is the turbulent kinetic energy at point P

$y_P$ is the distance from point P to the wall

$\nu$ is the kinematic viscosity of the fluid

$E = 9.793$

$\kappa = 0.4187$

$C_\mu = 0.09$

### 3.2.3 Snow accumulation

In this study, snow depth was not calculated directly. The snow depth ratio was defined as the ratio between the standard deposition flux ($q_{sta} = \Phi_{in} \times W_f$) and net deposition flux ($q_{total}$). The drift coefficient (described later in Section 4.3) was calculated using the net deposition flux at the reference point, which was not affected by the building.

The snowdrift analysis was performed using steady-state CFD, in which the flowfield is unaffected by snow accumulation. Thus, the results of this analysis express the potential for snow deposition or erosion due to the flowfield determined by the building geometry without snow. Although, surface change effects can be considered using sequential predicted snow surface levels and grid deformation [10, 11, 22, 23], such an approach is time-consuming and complicated. In this study, the applicability of the one-way method that does not consider the influence of surface change on the flowfield was examined from a practical viewpoint.

In steady-state CFD simulation, a mean wind velocity is applied as a boundary condition. In a real environment,
<figure><img src="image_395.png" /><figcaption>Figure 7. Snow depth ratio for different wind velocities</figcaption></figure>

wind velocity fluctuates over time during snowdrift formation; erosion and deposition do not occur continually. This real phenomenon is difficult to reproduce accurately using steady-state CFD. In this study, a simplified method to reproduce this process was proposed for steady-state CFD. Specifically, the weighted average of prediction results for different wind velocities were used to obtain the snowdrift result at a specific reference velocity. In this study, the occurrence frequency of the wind velocities was assumed to follow normal distribution. Accordingly, the occurrence probabilities of $U_{ave}$, $U_{ave} \pm 1$ m/s, and $U_{ave} \pm 2$ m/s were assumed as 40%, 25%, and 5%, respectively, to obtain the averaged snowdrift result for $U_{ave}$ at the eave height.

# 4 Results and discussion

## 4.1 Velocity field validation

Figure 6 compares the vertical distributions of the mean streamwise velocity ($U_1$) and the turbulent kinetic energy ($k$) obtained using CFD simulation with the measured results obtained from the wind tunnel experiment [15] for 5:10 roof pitches. The agreement between the simulated and experimental results is generally good. Similar agreement was observed for the other roof pitches

considered. Generally, the steady RANS CFD results agreed well with the measured data for $U_1$ and $k$, although the predicted values were overestimated near the windward roof and ridge of the building [15]. The average deviation between the simulated and measured results was typically less than 10%; the deviation increased to 30% in the lower wind speed region behind the building.

## 4.2 Roof snow accumulation

Figure 7 indicates the contours of the snow depth ratio ($q_{total}/q_{sta}$) on the roof and ground for three different roof pitches and different wind velocities. Results for $U_H = 1.0$ m/s are omitted in Figure 7 because only very small undulations were observed. Figure 8 compares the snow depth at the vertical center section on the various roof pitches for different wind velocities. For $U_H = 2.0$ m/s, erosion occurred only near the ridges of each roof pitch. Large snow depths were observed near the middle of the windward side of the roof for $U_H = 3.0$ m/s. For $U_H \ge 4.0$ m/s, the windward side of the roofs were eroded and snow depths converged to 0 for each roof pitch. Concurrently, snowdrifts were formed on the leeward side of the roof. For the 5:10 roof pitch, an extraordinarily sharp peak of snow depth was observed on the leeward side of the ridge for $U_H = 4.0$ and 5.0 m/s.
This snow depth overestimation is likely caused by the standing vortex behind the ridge specific to this roof pitch that is attributed to the failure of the turbulence model.

Figure 8 also shows results using the weighted averages of $U_{ave} = 2.0$ and $3.0$ m/s. The results from these averaged velocities were consistent with other observed results; snow depth on the leeward side of the roof tended to increase with increasing wind velocity and roof pitch. Results were also consistent with snow load codification [8, 18]. Therefore, the efficacy of the simplified averaging method proposed in this study was confirmed. Further, the superiority of CFD simulation over traditional experimental approaches was demonstrated through the unique visual display of detailed snow depth distributions shown previously in Figure 7.

### 4.3 Drift coefficient comparison

Table 1 lists the drift coefficients ($C_d$) calculated using Eq. (6) as follows:

$$C_d = \frac{S_l - S_w}{S_g} \qquad (6)$$

where $S_w$ and $S_l$ are the snow load on the windward and leeward sides, respectively, and $S_g$ is the ground snow load, which is unaffected by the building. Only values at the center section were used, along with wind direction, for averaging each side of the roof. In the CFD simulation, these snow loads were replaced by the net deposition fluxes at each position.

<table><caption>Table 1. Drift coefficient ($C_d$) at different wind velocities</caption><thead><tr><th></th><th>3:10 pitch</th><th>5:10 pitch</th><th>7.5:10 pitch</th></tr></thead><tbody><tr><td>U<sub>H</sub> = 1.0 m/s</td><td>0.02</td><td>0.05</td><td>0.04</td></tr><tr><td>U<sub>H</sub> = 2.0 m/s</td><td>0.15</td><td>0.27</td><td>0.23</td></tr><tr><td>U<sub>H</sub> = 3.0 m/s</td><td>0.41</td><td>0.79</td><td>0.74</td></tr><tr><td>U<sub>H</sub> = 4.0 m/s</td><td>0.90</td><td>2.07</td><td>2.00</td></tr><tr><td>U<sub>H</sub> = 5.0 m/s</td><td>*</td><td>*</td><td>*</td></tr><tr><td>U<sub>ave</sub> = 2.0 m/s</td><td>0.18</td><td>0.35</td><td>0.32</td></tr><tr><td>U<sub>ave</sub> = 3.0 m/s</td><td>0.39</td><td>0.82</td><td>0.77</td></tr></tbody></table>

The results listed in Table 1 further confirm observations made in Figures 7 and 8; the drift coefficient increases with increasing wind velocity and roof pitch. Drift coefficients for the 5:10 pitch are larger than coefficients for the 7.5:10 pitch. The relative differences in drift coefficient magnitude for roof pitches remain similar for different wind velocities.

Figure 9 shows the predicted drift coefficients ($C_d$) for $U_H = 1.0$ m/s, $U_H = 2.0$ m/s, and $U_{ave} = 2.0$ m/s (from Table 1) plotted against a scatter plot of observational results [7]. The observational data comprised approximately 1,300 examples of snowdrift formation on gable roofs in Norway [2, 3]. This data also supported development of various models (normal, sheltered, exposed) in ISO 4355 Bases for Design of Structures— Determination of Snow Loads on Roofs [3]. For $U_{ave} = 2.0$ m/s (▲), simulation results generally corresponded well with the ISO model (exposed), but values for the 5:10 pitch were overestimated. Deviations from ISO model were within 5% for the 3:10 and 7.5:10 roof pitches, and were approximately 40% for the 5:10 roof

<figure><img src="image_396.png" /><figcaption>Figure 8. Normalized snow depth along roof centerline</figcaption></figure>

<figure><img src="image_397.png" /><figcaption>Figure 9. Comparison of CFD simulated drift coefficients with measured and ISO model results</figcaption></figure>

pitch. Comparatively, the ISO model (normal) corresponded well to intermediate values between $U_H = 1.0$ m/s (♦) and $U_H = 2.0$ m/s (■). Values with $U_H = 2.0$ m/s at the eave height are somewhat smaller than the established threshold velocity for drifting snow. This difference may be caused by overestimation of turbulent kinetic energy (k) as an intrinsic defect of the turbulence model used. Furthermore, the validity of the existing

<footnote>*Not calculated due to zero net deposition flux on the ground</footnote>
threshold friction velocity ($U_{*i}$) for slanting snow surfaces (such as gable roofs) is unconfirmed and should be considered for future study.

## 5 Conclusions

In this study, CFD simulations of unbalanced snow accumulation on roofs were conducted for an isolated gable-roof building. The simulated results were compared with observational data.

As a result of this work, the following conclusions can be drawn:

- The proposed CFD simulation method was generally able to reproduce observational results. Consistent with prior results, the model showed that the snow depth on the leeward side of the roof increases with increasing wind velocity and roof pitch.

- Further, snow depth distributions can be visually captured and displayed using CFD simulation; such visualization is not provided in traditional experimental approaches.

- A prediction method, in which results obtained for different wind velocities are combined assuming a normally distributed occurrence frequency for wind velocities, was proposed and verified.

- For $U_{ave} = 2.0$ m/s, the predicted drift coefficients generally corresponded well with the ISO Model (Exposed) [3], but values for the 5:10 pitch were overestimated. Deviations from the ISO Model were within 5% for the 3:10 and 7.5:10 roof pitches, and were approximately 40% for the 5:10 roof pitch.

The current study has the following limitations that will be addressed in future work:

- Although three different roof pitches were used, this study considered only an isolated gable-roof building. Applicability of the proposed CFD method should be examined for other configurations, such as flat and step roofs.

- The validity of the model parameters, such as threshold friction velocity and snowfall settling velocity, should also be examined and optimized for various conditions.

- This study considered wind direction only perpendicular to the windward facade. The effect of wind direction variations should be considered.

## Acknowledgements

The first author would like to express his gratitude for the financial support provided through the Grants-in-Aid for Scientific Research in Japan (No. 16H04467).

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# Analysis of snow drifts on arch roofs

Michael O'Rourke<fnref n="1" />,<fnref n="2" />, Jan Potac<fnref n="2" /> and Thomas K. Thiis<fnref n="3" />

**Abstract.** ASCE provisions for unbalanced loads on arch roofs have remained nominally unchanged since the 1982 predecessor to ASCE 7. This was due to the lack of snow load case histories for these iconic roof shapes. Fortunately, drift load case histories for three large arch roofs in Norway have recently become available. In this paper, the observed arch roof snow drifts will be compared to unbalanced load provisions in current model codes and load standards in Europe and North America, specifically the ASCE 7 load standard, ISO and NBCC.

## 1. Introduction

Due to their structural efficiency and ability to economically span large distances, arches are frequently the preferred roof shape for large indoor sports facilities. They are particularly effective for symmetric loads (e.g. nominally uniform snow loads from eave to eave). Arches are not as efficient for asymmetric or unbalanced loads. Examples of asymmetric loads include across-the-ridge drift loads and differential sliding resulting from one side directly facing towards the sun. Furthermore, the shorter structural components which span between arches are particularly sensitive to localized drift surcharge loads.

In the U.S., drift loads in general and unbalanced loads for common gable roofs shapes have undergone modification and improvement based upon analysis of case histories. Provisions for unbalanced loads on arch roofs however have remained nominally unchanged since the 1982 predecessor to ASCE 7. This was due to the lack of snow load case histories for these iconic roof shapes. Fortunately drift load case histories for three large arch roofs in Norway have recently become available.

In this paper, the observed arch roof snow drifts will be compared to unbalanced load provisions in current model codes and load standards in Europe and North America, specifically the ASCE 7 load standard, ISO and NBCC.

## 2. Study sites and analysis

Potac (2013) measured snow drift accumulation on several roofs over a period of several years. In this study the snow drift loads on three arch roofs are analyzed. An overview of the roofs in the study is given in Figure 1. A total of 9 measurements were made at the Vallhall Arena over 4 winter seasons. The roof itself is a quarter cylinder with a radius of 198.5 ft (60.5 m) and a 45° roof slope at the eaves. Two measurements were made at Ekeberghallen during the 2009-10 winter. The roof was also a quarter cylinder (i.e., roof slope of 45° at the eaves). The arch roof radius at Ekeberghallen was 105.6

ft (32.2 m). Finally one measurement was made at Byggmakker (arch roof radius = 59.7 ft (18.2 m)) during the 2009-10 winter. Although the Byggmakker structure consisted of three arches, only data from the windward arch (arch #1) is analyzed herein.

<figure><img src="image_398.png" /><figcaption>**Figure 1.** The three buildings in the study a) Ekeberghallen sports hall, b) Vallhall sports hall and c) Byggmakker shopping mall.</figcaption></figure>

<figure><img src="image_399.png" /></figure>

<footnote n="1">¹ Rensselaer Polytechnic Institute, New York, USA</footnote>

<footnote n="2">² Multiconsult ASA, Tromsø, Norway</footnote>

<footnote n="3">³ Norwegian University of Life Sciences, Norway</footnote>

<footnote>a Corresponding author: orourm@rpi.edu</footnote>
Figure 2 is a sample of the arch measurements. They consisted of a plot of roof snow depth (in meters) as a function of the horizontal distance (in meters) from the top (ridgeline) of the arch.

The snow load atop the downwind portion of the arch is taken to be a nominally uniform (balanced) load plus a drift surcharge. The depth of the balanced load is taken to be 70% of the ground snow depth at a nearby location on the date of the measurement. In some cases the snow load at the ridgeline was zero, increasing with location downwind. In such cases, the location of the start of the surcharge is taken to be the location where the roof snow depth first reaches $0.7 h_g$.

<figure><img src="image_400.png" /><figcaption>**Figure 2.** Roof snow depth measurements for Vallhall on 1/7/08</figcaption></figure>

Since the three circular arch roofs had different radii, and the location of the peak roof snow depth moves during development of the snow drift (Thiis et al., 2009), the nominally triangular drift surcharge will be characterized by 4 angles as sketched in Figure 3. The first is the angle $\theta_1$ from vertical to the start of the drift surcharge (thought to be the initial flow separation point). The second is the angle $\theta_2$ to the end of the drift surcharge (thought to be the drifted snow angle of repose, or the angle corresponding to snow sliding). The next angle $\beta$ is the initial slope of the top surface of the drift surcharge (thought to correspond to the top of the aerodynamic shade region downwind of the ridge). While the final angle characterizing the surcharge geometry, $\theta_p$, is the angle from vertical to the location of the peak roof snow depth. Furthermore, the angle $\theta_p$ also corresponds to the flow separation point for a roof with a developed drift surcharge. At the start of the drift accumulation process, the angle $\theta_p$ equals $\theta_1$ and moves further downwind as the drift surcharge grows.

<figure><img src="image_401.png" /><figcaption>**Figure 3.** Four angles characterizing the arch roof drift surcharge.</figcaption></figure>

Table 1 presents the location, measurement date and the 2 snow depth measurements for the Norwegian arches. Table 2 presents the 4 angles for the 12 sets of measurements. The ground snow depth $h_g$ ranged from 0.59 to 1.64 ft (0.18 to 0.5 m) with an average of 0.98 ft (0.3 m). The peak roof depth $h_{max}$ (balanced plus surcharge) ranged from 1.15 to 3.94 ft (0.35 to 1.2 m) with an average of 2.52 ft (0.77 m). The location of the start of the drift surcharge, $\theta_1$, ranged from 4.7 to 14.4° with an average of 8°. The peak drift location, $\theta_p$, ranged from 20.9 to 29.7° with an average of 24.5°. The end point of the surcharge, $\theta_2$, (point where the roof snow depth returned to $0.7 h_g$) ranged from 25.8 to 34° with an average of 28.6°. Finally, the initial slope of the top surface of the drift ranged from 2.4 to 16.9° with an average of 13.6°.

<table><caption>**Table 1.** Norwegian Arch Depth Measurements</caption><thead><tr><th>No.</th><th>Location</th><th>Date</th><th>Ground Snow Depth h<sub>g</sub> [ft] ([m])</th><th>Peak Roof Snow Depth d<sub>max</sub> [ft] ([m])</th></tr></thead><tbody><tr><td>1</td><td>Vallhall</td><td>2/27/07</td><td>0.66 (0.20)</td><td>2.46 (0.75)</td></tr><tr><td>2</td><td>Vallhall</td><td>1/7/08</td><td>0.59 (0.18)</td><td>1.15 (0.35)</td></tr><tr><td>3</td><td>Vallhall</td><td>1/20/09</td><td>0.89 (0.27)</td><td>1.48 (0.45)</td></tr><tr><td>4</td><td>Vallhall</td><td>1/25/09</td><td>0.59 (0.18)</td><td>2.95 (0.90)</td></tr><tr><td>5</td><td>Vallhall</td><td>2/8/09</td><td>1.44 (0.44)</td><td>2.79 (0.85)</td></tr><tr><td>6</td><td>Vallhall</td><td>2/23/09</td><td>1.64 (0.50)</td><td>2.63 (0.80)</td></tr><tr><td>7</td><td>Vallhall</td><td>1/5/10</td><td>0.72 (0.22)</td><td>1.80 (0.55)</td></tr><tr><td>8</td><td>Vallhall</td><td>2/5/10</td><td>0.95 (0.29)</td><td>2.30 (0.70)</td></tr><tr><td>9</td><td>Vallhall</td><td>2/23/10</td><td>1.02 (0.31)</td><td>3.44 (1.05)</td></tr><tr><td>10</td><td>Ekeberg</td><td>1/12/10</td><td>0.89 (0.27)</td><td>2.30 (0.70)</td></tr><tr><td>11</td><td>Ekeberg</td><td>2/5/10</td><td>1.21 (0.37)</td><td>2.95 (0.90)</td></tr><tr><td>12</td><td>Byggmakker</td><td>2/8/10</td><td>1.18 (0.36)</td><td>3.94 (1.20)</td></tr></tbody></table>
<table><caption>**Table 2.** Norwegian Arch Angle Measurements</caption><thead><tr><th>No.</th><th>θ₁ [°]</th><th>θₚ [°]</th><th>θ₂ [°]</th><th>β [°]</th></tr></thead><tbody><tr><td>1</td><td>9.5</td><td>27.6</td><td>34.0</td><td>16.8</td></tr><tr><td>2</td><td>11.0</td><td>23.4</td><td>29.7</td><td>16.9</td></tr><tr><td>3</td><td>4.7</td><td>24.4</td><td>29.7</td><td>13.9</td></tr><tr><td>4</td><td>14.4</td><td>26.5</td><td>29.7</td><td>17.0</td></tr><tr><td>5</td><td>4.74</td><td>23.4</td><td>27.0</td><td>14.4</td></tr><tr><td>6</td><td>4.74</td><td>21.8</td><td>27.0</td><td>12.0</td></tr><tr><td>7</td><td></td><td></td><td></td><td></td></tr><tr><td>8</td><td>9.5</td><td>24.4</td><td></td><td>15</td></tr><tr><td>9</td><td>9.5</td><td>29.7</td><td></td><td>17.5</td></tr><tr><td>10</td><td>5.34</td><td>21.9</td><td>25.8</td><td>10.4</td></tr><tr><td>11</td><td>10.7</td><td>25.8</td><td></td><td>13.9</td></tr><tr><td>12</td><td>6.3</td><td>20.9</td><td>26.1</td><td>2.4</td></tr></tbody></table>

Since the overall objective is to investigate arch loads for design purposes, particular attention was paid to the larger drifts. The drifts were subdivided into three groups based upon relative drift size, specifically the ratio of peak snow depth to balanced depth,

$$RDS = \frac{h_{max}}{0.7 h_g} \qquad (1)$$

For group A, the ratio was less than 3. For group B the ratio was between 3 and 4, while for group C the ratio was greater than 4, as shown in Table 3.

<table><caption>**Table 3.** Relative Drift Size classes</caption><thead><tr><th>A</th><th>B</th><th>C</th></tr></thead><tbody><tr><td>RDS &lt; 3</td><td>3 &lt; RDS &lt; 4</td><td>RDS &gt; 4</td></tr></tbody></table>

The starting angle, $θ₁$, was found to be an increasing function of relative drift size. The value chosen for $θ₁$ was 9.2°, the average for groups B and C. Similarly the peak location, $θₚ$, was found to be an increasing function of relative drift size. The value chosen for $θₚ$ was 25.1°, again the average for groups B and C. On the other hand, there was no apparent variation of $θ₂$ or $β$ with relative drift size. For these parameters, the average of all three groups was chosen that is $θ₂ = 28.6°$ and $β = 13.6°$.

The cross-sectional area of the drift surcharge and the location of the surcharge center of gravity were determined from the surcharge geometry given above. The drift surcharge area $A_d$ was

$$A_d = 0.00416 R^2 \qquad (2)$$

and the location of the surcharge center of gravity was

$$\chi = 0.354 R \qquad (3)$$

where R is the radius of the circular roof. Note that the values in (2) and (3) are based on circular arch roofs with the radius roughly in the 65.6 to 196.85 ft (20 to 60 m) range. One expects for a given amount of wind, the percentage of the upwind snow that is transported onto the leeward side (hence eligible for drift formation) is a decreasing function of roof radius. That is, one expects that the constant 0.00416 in (2) would be larger for smaller radius roofs and smaller for larger radius roofs.

The size and location of the observed drift surcharge is quantified by (2) and (3). Since the size is provided as an area, one needs a snow density to convert into load. Herein the ASCE 7 empirical relation between snow density $γ$ (lb/ft³) and ground snow load $p_g$ (lb/ft²) is used

$$\gamma = 0.13 p_g + 14 \qquad (4) \\ \text{in SI: } \gamma = 0.426 p_g + 2.2$$

For a quarter cylinder roof (eave roof slope = 45°) the total downwind load (lb/ft) from (2) thru (4) is presented in Table 4 for four values of the roof radius $R$ and the ground snow load $p_g$. Also presented in Table 4 is the location of the center of gravity $χ$ of the total (balanced plus surcharge) downwind (ridge to eave) load. These parameters, the total snow load on the downwind side of the arch and its center of gravity would be needed for the structural design of the arch spanning from eave to eave. However, for the in-fill beams which span between adjacent arches, the peak localized load is the key parameter. Based upon the Norwegian measurements, this peak pressure occurs at $θₚ$ (25.1°). The drift surcharge depth at this peak load location is 0.026 $R$ based upon geometry.

<table><caption>**Table 4.** Total downwind load and center of gravity (distance from ridge) based upon Norwegian observed geometry.</caption><thead><tr><th rowspan="3">Arch radius<br>R [ft]<br>([m])</th><th colspan="3">Total Downwind Load [lb/ft]<br>([kN/m])</th><th rowspan="3">χ [ft]<br>([m])</th></tr><tr><th>p<sub>g</sub> = 20<br>lb/ft<sup>2</sup><br>(1<br>kN/m<sup>2</sup>)</th><th>p<sub>g</sub> = 50<br>lb/ft<sup>2</sup><br>(2.4<br>kN/m<sup>2</sup>)</th><th>p<sub>g</sub> = 100<br>lb/ft<sup>2</sup><br>(4.8<br>kN/m<sup>2</sup>)</th></tr><tr><th></th><th></th><th></th></tr></thead><tbody><tr><td>20<br>(6.1)</td><td>226<br>(3.3)</td><td>529<br>(7.7)</td><td>1035<br>(15.1)</td><td>7.1<br>(2.2)</td></tr><tr><td>50<br>(15.2)</td><td>668<br>(9.8)</td><td>1452<br>(21.2)</td><td>2756<br>(40.2)</td><td>17.7<br>(5.4)</td></tr><tr><td>100<br>(30.5)</td><td>1681<br>(25.5)</td><td>3328<br>(48.6)</td><td>6073<br>(88.6)</td><td>35.4<br>(10.8)</td></tr><tr><td>200<br>(61)</td><td>4741<br>(69.2)</td><td>8361<br>(122)</td><td>14380<br>(210)</td><td>70.8<br>(21.6)</td></tr></tbody></table>

Table 5 presents the peak localized pressure (surcharge plus balanced) for various values of $R$ and $p_g$. Note in this regard that for the Norwegian observations,
the ratio of the peak roof snow depth to the ground depth for the 12 measurements in Table 1 ranged from 1.6 to 5.0 with an average of 2.71.

<table><caption>**Table 5.** Peak Localized Pressure (drift surcharge plus balanced) based upon observed geometry of Norwegian Arches.</caption><thead><tr><th rowspan="2">Arch radius<br>R [ft] ([m])</th><th colspan="3">Peak Pressure [lb/ft²] ([kN/m²])</th></tr><tr><th>p<sub>g</sub> = 20<br>lb/ft²<br>(1 kN/m²)</th><th>p<sub>g</sub> = 50<br>lb/ft²<br>(2.4 kN/m²)</th><th>p<sub>g</sub> = 100<br>lb/ft²<br>(4.8 kN/m²)</th></tr></thead><tbody><tr><td>20 (6.1)</td><td>22.6 (1.1)</td><td>45.7 (2.2)</td><td>84.0 (4.0)</td></tr><tr><td>50 (15.2)</td><td>35.6 (1.7)</td><td>61.7 (2.9)</td><td>105.1 (5.0)</td></tr><tr><td>100 (30.5)</td><td>57.2 (2.7)</td><td>88.3 (4.2)</td><td>140.2 (6.7)</td></tr><tr><td>200 (61)</td><td>100.3 (4.8)</td><td>141.6 (6.8)</td><td>210.0 (10.1)</td></tr></tbody></table>

### 3. Comparison to ASCE 7 provisions

ASCE 7-10 (ASCE 2010) provides curved roof unbalanced loads for three groups of roof slope at the eave. Specifically the unbalanced load for an eave roof slope of 45°, corresponding to the quarter cylinder roofs in the Norwegian measurement program, is shown in Figure 4. The roof snow load at the ridge is half the so-called flat roof snow load $0.5 p_f$, while the load at the 30° roof slope point is $2 p_f C_s^*/C_e$ and $2 p_f C_s^* / C_e$ at the eave (45° roof slope point). In ASCE 7 the flat roof load is a function of the structures importance factor $I_s$, the roof exposure factor $C_e$, and the roof thermal factor $C_t$. Herein it is assumed that the roof is of ordinary importance ($I_s = 1.0$), has normal wind exposure ($C_e = 1.0$) and is heated ($C_t = 1.0$). For these conditions, the flat roof load is $0.7 p_g$ where $p_g$ is the ground snow load with a 50 year mean recurrence interval.

<figure><img src="image_402.png" /><figcaption>**Figure 4.** Unbalanced load in ASCE 7 for an arch roof with eave slope of 45°.</figcaption></figure>

$C_s^*$ is the slope factor at the 30° point and $C_s^*$ is the slope factor at the eave (45° point for our quarter cylinder roofs). For slippery roof surfaces, corresponding to the Norwegian arches with plastic membrane roof material, the slope factors at 30 and 45° are 0.615 and 0.385 respectively. As such the load at the ridge is $0.35 p_g$ while the loads at the 30° point and the eave are 0.861 $p_g$ and 0.53 $p_g$.

The total downwind load from the ASCE 7 provisions is shown in Table 6 for an arch radius ranging from 20 to 200 ft (6.1 to 61 m), and a ground snow load ranging from 20 to 100 lb/ft² (1 kN/m² to 4.8 kN/m²). A comparison of the total loads in Table 4 and Table 6 show that the ASCE 7 load is smaller than that suggested by the observed geometry of the Norwegian arch measurements. The ratio of ASCE 7/Norwegian observed ranged from 38% to 86% with the lowest percentage (38% - most unconservative) occurring for the low ground snow loads (20 lb/ft² (1 kN/m²)) and large arch radius (200 ft (61 m)). The highest ratio (86% - slightly unconservative) occurs for the high ground snow loads (100 lb/ft² (4.8 kN/m²)) and small arch radius (20 ft (6.1 m)).

<table><caption>**Table 6.** Total Downwind Load and center of gravity (distance from ridge) based upon ASCE 7 provisions.</caption><thead><tr><th rowspan="2">Arch radius<br>R [ft] ([m])</th><th colspan="3">Total Downwind Load [lb/ft] ([kN/m])</th><th rowspan="2">χ [ft] ([m])</th></tr><tr><th>p<sub>g</sub> = 20<br>lb/ft²<br>(1 kN/m²)</th><th>p<sub>g</sub> = 50<br>lb/ft²<br>(2.4 kN/m²)</th><th>p<sub>g</sub> = 100<br>lb/ft²<br>(4.8 kN/m²)</th></tr></thead><tbody><tr><td>20 (6.1)</td><td>179<br>(2.6)</td><td>447<br>(6.5)</td><td>894<br>(13.1)</td><td>7.7<br>(2.4)</td></tr><tr><td>50 (15.2)</td><td>447<br>(6.5)</td><td>1118<br>(16.3)</td><td>2235<br>(32.6)</td><td>19.3<br>(5.9)</td></tr><tr><td>100 (30.5)</td><td>894<br>(13.1)</td><td>2235<br>(32.6)</td><td>4470<br>(65.2)</td><td>38.6<br>(11.8)</td></tr><tr><td>200 (61)</td><td>1788<br>(26.1)</td><td>4470<br>(65.2)</td><td>8940<br>(130)</td><td>77.2<br>(23.5)</td></tr></tbody></table>

In terms of the location of the total unbalance load, the Norwegian measurements suggest that the center of gravity is at 0.354 R from the ridge, while the ASCE 7 provisions have the center of gravity at 0.386 R - a difference of 9%.

For the design of the in-fill beams which span between adjacent arches, the peak localized pressure as per the ASCE 7 provisions is 0.86 $p_g$ or 17.2, 43.1 and 86.1 lb/ft² for $p_g$= 20, 50 and 100 lb/ft² respectively. In comparison to the peak local pressures in Table 4, the ASCE pressures are arguably reasonable for an arch radius of 20 ft (6.1 m) but are low by roughly a factor of 2 to 5 for an arch radius of 200 ft (61 m).

In relation to the location of the peak localized pressures the Norwegian measurement program suggests it occurs at $θ_p$ = 25.1°, while the peak localized pressure in the ASCE 7 provisions occurs at 30° or a difference of about 20%.
## 4. Comparison with ISO 4355 provisions

Provisions in the International Standards Organization (ISO 4355) provide unbalanced snow loads for curved roofs, pointed arches, and domes. For a quarter cylinder (circular arch with eave slope of 45°), the unbalanced snow load is

$$s_d = s_0 \mu_b \mu_d(x) \quad (5)$$

where $s_0$ is the 50 year design ground snow load, $\mu_b$ is a slope coefficient and $\mu_d(x)$ is a drift coefficient given by

$$\mu_d(x) = \begin{cases} 2x/x_{30} & x \le x_{30} \\ 2 & x \ge x_{30} \end{cases} \quad (6)$$

where $x$ is the horizontal distance from the ridge and $x_{30}$ is the horizontal distance to the location where the roof slope is 30°.

The slope coefficient for a slippery roof surface over a heated space (i.e., characteristics for the Norwegian Arches) is shown in Figure 5.

<figure><img src="image_403.png" /><figcaption>**Figure 5.** Slope Coefficient in ISO 4355 for slippery roof surface over a heated space</figcaption></figure>

As such, the unbalanced snow load in the ISO provisions for a quarter cylinder roof increases from zero at the ridge to $2s_0$ at the 30° roof slope point and then decreases to $s_0$ at the eave (45° roof slope point). This unbalanced load is sketched in Figure 6.

<figure><img src="image_404.png" /><figcaption>**Figure 6.** Unbalanced Snow Load for Quarter Cylinder Arch in ISO</figcaption></figure>

The total downwind snow load in Figure 6 is $0.8R \ s_0$ and its center of gravity is at 0.437 R from the ridge.

Table 7 presents the total downwind load and location of the center of gravity for the ISO provisions for the

same range of arch radius and ground snow loads as Table 4 and Table 6.

<table><caption>**Table 7.** Total Downwind Load and center of gravity (distance from ridge) based upon ISO provisions</caption><thead><tr><th rowspan="2">Arch radius<br>R [ft]<br>([m])</th><th colspan="3">Total Downwind Load<br>[lb/ft] ([kN/m])</th><th rowspan="2">χ [ft]<br>([m])</th></tr><tr><th>p<sub>g</sub> = 20<br>lb/ft<sup>2</sup><br>(1<br>kN/m<sup>2</sup>)</th><th>p<sub>g</sub> = 50<br>lb/ft<sup>2</sup><br>(2.4<br>kN/m<sup>2</sup>)</th><th>p<sub>g</sub> =<br>100<br>lb/ft<sup>2</sup><br>(4.8<br>kN/m<sup>2</sup>)</th></tr></thead><tbody><tr><td>20 (6.1)</td><td>320<br>(4.7)</td><td>800<br>(11.7)</td><td>1600<br>(23.4)</td><td>8.74<br>(2.7)</td></tr><tr><td>50 (15.2)</td><td>800<br>(11.7)</td><td>2000<br>(29.2)</td><td>4000<br>(58.4)</td><td>21.90<br>(6.7)</td></tr><tr><td>100 (30.5)</td><td>1600<br>(23.4)</td><td>4000<br>(58.4)</td><td>8000<br>(117)</td><td>43.70<br>(13.3)</td></tr><tr><td>200 (61)</td><td>3200<br>(46.7)</td><td>8000<br>(117)</td><td>16000<br>(234)</td><td>87.40<br>(26.6)</td></tr></tbody></table>

In terms of total downwind load, the ISO provisions provide a much better match to the observed Norwegian values (Table 4) than the ASCE 7 provisions (Table 6). For most combinations of R and $s_0$ (i.e. $p_g$), the ISO loads are larger than the observed with ISO overestimating the observed by roughly 55% for the case of small arch radius (R = 20 ft (6.1 m)) and large ground snow load ($p_g = s_0 = 100$ lb/ft$^2$ (4.8 kN/m$^2$)). For a large arch radius (R = 200 ft (61 m)) and small ground snow loads ($p_g = s_0 = 20$ lb/ft$^2$), the ISO underestimate the expected (Table 4) loads by roughly 50%.

In terms of the location of the center of gravity, the Norwegian measurements suggest that the center of gravity, $\chi$, is at 0.36 R while the ISO provisions yield $\chi$ at 0.44 R, roughly a 20% difference.

Finally, in terms of the peak pressure need for design of the in-fill beams which span between arches, the ISO provisions specify a peak pressure of $2s_0$ (twice the design ground snow load). In comparison to the observed Norwegian values in Table 5, the ISO values overestimate the peak pressures for eight of the 12 combinations of R and $p_g$. The worst underestimation is for $p_g = 20$ lb/ft$^2$ (1 kN/m$^2$) and R = 200 ft (61 m), for which the peak pressure based upon the observed Norwegian geometry is about 2.5 times larger.

## 5. Comparison with NBCC provisions

The National Building Code of Canada (NBCC, 2010) provides unbalanced snow load provisions for arch roofs, curved roofs and domes. For a quarter cylinder arch of ordinary importance, the unbalanced load is
$$S = C_b C_w C_s C_a S_s \quad (7)$$

where $C_b$ is the basic snow factor, $C_w$ is the wind exposure factor specified as 1.0 for the unbalanced case, $C_a$ is shape factor, $C_s$ is the slope factor, and $S_s$ (i.e., $p_g$) in the 50 year ground snow load. In the Canadian provisions, the product $C_b C_a$ is identical to the ISO drift coefficient $\mu_d(x)$ in (5). The slope factor $C_s$ in NBCC for unobstructed slippery surfaces is similar to the ISO $\mu_b$ shown in Figure 5, except that the transition from flat to sloped (uniform to linearly decreasing) occurs at the 15° roof slope location.

As a result, the unbalanced snow load in NBCC for a quarter cylinder arch with a slippery unobstructed roof surface is as sketched in Figure 7.

<figure><img src="image_405.png" /><figcaption>**Figure 7.** Unbalanced Snow Load for Quarter Cylinder Arch in NBCC</figcaption></figure>

The total downward load in Figure 7 is 0.618 $S_s^* R$ (roughly 75% of that in ISO), while the center of gravity is located at 0.408 $R$ from the ridge. Table 8 presents the total downward load and location of the center of gravity for the same range of roof and ground load parameters as Table 4.

<table><caption>**Table 8.** Total Downwind Load and center of gravity based upon NBCC provisions.</caption><thead><tr><th rowspan="2">Arch radius<br>R<br>[ft]<br>([m])</th><th colspan="3">Total Downwind Load [lb/ft]<br>([kN/m])</th><th rowspan="2">χ[ft]<br>([m])</th></tr><tr><th>S<sub>s</sub> = 20<br>lb/ft<sup>2</sup><br>(1<br>kN/m<sup>2</sup>)</th><th>S<sub>s</sub> = 50<br>lb/ft<sup>2</sup><br>(2.4<br>kN/m<sup>2</sup>)</th><th>S<sub>s</sub> = 100<br>lb/ft<sup>2</sup><br>(4.8<br>kN/m<sup>2</sup>)</th></tr></thead><tbody><tr><td>20 (6.1)</td><td>247<br>(3.6)</td><td>617 (9.0)</td><td>1236<br>(18.0)</td><td>8.2<br>(2.5)</td></tr><tr><td>50<br>(15.2)</td><td>618<br>(9.0)</td><td>1545<br>(22.6)</td><td>3090<br>(45.1)</td><td>20.4<br>(6.2)</td></tr><tr><td>100<br>(30.5)</td><td>1236<br>(18.0)</td><td>3090<br>(45.1)</td><td>6180<br>(90.2)</td><td>40.8<br>(12.4)</td></tr><tr><td>200<br>(61)</td><td>2472<br>(36.1)</td><td>6180<br>(90.2)</td><td>12360<br>(180)</td><td>81.6<br>(24.9)</td></tr></tbody></table>

Fifty percent of the downwind load values in Table 8 are larger than the Norwegian values in Table 4. Like the ASCE 7 (Table 6) and ISO (Table 7), the worst performance is for low ground snow loads and large arch radius (NBCC load ~50% of expected load at $S_s$ (i.e., $p_g$) of 20 lb/ft$^2$ (1 kN/m$^2$) and R of 200 ft (61 m)).

Considering the design load for in-fill beams, the peak local pressure on the roof for the NBCC provisions is 1.33 $S_s$ or 26.6, 66.5, and 133 lb/ft$^2$ for $S_s$ of 20, 50 and 100 lb/ft$^2$ respectively (1.33, 3.19, and 6.38 kN/m$^2$ for $S_s$ of 1.0, 2.4, and 4.8 kN/m$^2$ respectively). In comparison to Table 5, NBCC underestimated the peak local pressure for seven of the twelve radius and ground load combinations. This performance (7 of 12 underestimated) was better than ASCE 7 (11 of 12 underestimated, but not as good as ISO (4 of 12 underestimated)).

## 6. Conclusions

A series of full scale measurements on circular arch roofs in Norway were analyzed to determine the downwind snow surcharge corresponding to the unbalanced load case. The Norwegian arches were quarter cylinders (constant radius, 45° roof slope at the eaves) with roof radius ranging from 60 to 198.5 ft (18.2 to 60.5 m). The drift surcharge typically began at 9.2° and terminated at 28.6° with the peak surcharge occurring at 25.5°. The initial slope of the drift surcharge had a slope of 13.6°.

Based upon the observed geometry, the expected load for a series of quarter cylinder arches were determined and compared to current provisions in ASCE 7, ISO 4355 and NBCC.

Unbalanced loads from the ASCE 7 provisions generally underestimated the magnitude of the leeward load. The poorest performance occurred for a low ground snow load and a large arch radius where the expected load was more than 2.5 times the load prescribed by the ASCE 7 provision.

The ISO provisions faired much better in comparison to the Norwegian observation. In about 66% of the comparisons the ISO loads were larger than those based upon the Norwegian observations. However, like the ASCE 7 provisions, ISO underestimated the expected loads for low ground snow loads and large arch radii.

In relation to the peak roof pressure needed to design the in-fill beams which span between arches, ISO again did a better job than ASCE. However, all these sets of provisions performed poorly in relation to the expected peak pressure for arches with a large radius in a low ground load location.

The NBCC provisions resulted in larger loads (better performance) than the ASCE 7 provisions but lower loads (poorer performance) than the ISO provisions.

Finally, the Norwegian measurements were for arch roofs with arch radius ranging from 60 to 198.5 ft (18.2 to 60.5 m). The ground snow depths ranged from 0.59 to 1.64 ft (0.18 to 0.5 m). Since the unbalanced load case is the result of snow drifting, one expects that the
normalized drift size as characterized by the ratio of peak
roof snow depth to ground snow depth (d<sub>max</sub>/h<sub>g</sub> ranged
from 1.6 to 5.0 with an average of 2.71) would decrease
for larger values of the arch radius and increase for
smaller values of the arch radius. Similarly, one also
expects that the d<sub>max</sub>/h<sub>g</sub> ratio will decrease for larger
values of the ground snow load and increase for smaller
values of the ground snow load.

References

"ASCE (American Society of Civil Engineers) (2010)" Minimum design loads for buildings and other structures (ASCE/SEI 7-10). American Society of Civil Engineers, Reston, VA, USA.

ISO (International Standards Organization) (2013), “ISO 4355 Bases for design of structures, Determination of snow loads on roofs”.

NRCC (National Research Council of Canada) (2010)
"National Building Code of Canada," Institute for
Research in Construction, Ottawa, Ontario, Canada.

Potac, J. (2013) Field measurements and numerical simulations of snow transport and deposition around structures and into ventilation intakes. PhD Thesis Norwegian University of Life Sciences ISSN 1503-1667 ISBN 978-82575-1180-7

Thiis, T.K., Potac, J., Ramberg, J.F. 3D numerical simulations and full scale measurements of snow deposition on a curved roof. 5th European and African conference on Wind engineering, EACWE 5, Florence, Italy, 2009

http://www.iawe.org/Proceedings/5EACWE/104.pdf
# Falling snow and ice from buildings and structures: risk assessment and mitigation – two case studies

Stefan Margreth¹,ᵃ

¹WSL Institute for Snow and Avalanche Research SLF, 7260 Davos Dorf, Switzerland

**Abstract.** Falling snow and ice from buildings can be extremely dangerous for pedestrians or traffic. This paper describes the factors contributing to hazardous snow and ice accumulations and shows how the risks can be assessed. Two case studies are presented to demonstrate how the adverse effects of snow and ice accumulations on buildings are identified and minimized. An important conclusion is to involve snow experts in an early planning stage of complex buildings in snowy areas.

## 1 Introduction

Snow loads on buildings, including the load of snow overhangs, are comprehensively regulated in different standards (e.g. Swiss Code 261 [1]). Few documents, however, exist concerning how to handle the risk of falling ice and snow from buildings or facades. Falling snow and ice from buildings can be extremely dangerous for pedestrians or traffic [2]. Even a small piece of ice can be dangerous if it hits a sensitive area such as a person's eye [3]. Snow accumulates not only on roofs but also to some extent on exterior architectural features such as window sills, solar shades or fins especially in snowy areas. Deposited snow can become unstable and meltwater can contribute to ice accumulations [4]. The normal approach to handle the risk of falling ice and snow is to specify safety zones covering the endangered areas or to optimize the design of the structure. The latter includes, for example, adaptations of the roof geometry, minimizing horizontal structural features such as window sills where snow can accumulate, reducing the size of drift areas or improving drainage systems to prevent dripping of meltwater. Sometimes the risk can be minimized with the installation of mitigation measures such as snow fences, snow barriers, snow drift measures or heating systems. Building designers are often not aware of the danger of falling snow or ice leading to expensive, post-construction design modifications.

## 2 Assessment of risk

The amount of snow and ice which accumulates on a building depends mainly on the geographic location, climate, wind exposure, geometry and structure of building, solar exposure and heat losses. Whether accumulated snow stays stable or not depends on many factors, such as strength of snow, width of snow overhang, relation of snow thickness to supporting surface or inclination and surface roughness. A chunk of snow typically falls if overhanging snow breaks off (case 1, Figs. 1 and 2) or if a mass of snow becomes unstable (case 2, Figs. 1 and 4). Case 1 occurs often in snowdrift situations if the weight of the overhanging snow mass is greater than its strength. Case 2 is especially relevant if the height of

the accumulated snow is greater than the width of the supporting surface or if the supporting surface is inclined and smooth. The equilibrium of an accumulated snow mass can become unstable due to unfavourable deformation processes because of settlement of the snow and melting processes which reduce friction.

<figure><img src="image_406.png" /><figcaption>**Figure 1.** Hazard scenarios for falling and sliding snow masses from tunnel entrances.</figcaption></figure>

<figure><img src="image_407.png" /></figure>

<footnote>ᵃ Corresponding author: margreth@slf.ch</footnote>
If a tunnel portal is sloped snow can slide off like an avalanche (case 3, Figs. 1 and 5) and hit the road. Snow can slide directly on the structure if the surface roughness is low. This case is mostly decisive if the slope of the structure is relatively low [5]. In snowy climates and on steep surfaces snowslides can release as well on or in between the snow cover (Fig. 5). Such snowslides happen especially during snow storms and warming periods if the stability of the snow cover is very poor.

The resulting risk of falling snow depends mainly on the likelihood that a snow accumulation breaks off or slides, the weight of the falling chunk of snow, the drop height, the width of the danger zone and the presence of persons and objects. Very crucial is the geometry of the structure and conditions of the area where snow can accumulate. The annual snowfall controls the risk. For a structure located at high elevation with a great annual snowfall (see case study A) the risk of falling snow is much higher compared to a low elevation with a small annual snowfall.

Icicles typically form on buildings because of freezing or dripping water. The roof or facade of a building can warm up because of heat transfer or solar radiation. Deposited snow melts and dripping water freezes if the air temperature is below 0 °C. The growth of an icicle on a building is a complicated process, which is very sensitive to the atmospheric conditions and the water flux. The growth is faster if the air temperature is below -5 °C than if the air temperature is between 0 °C and -5 °C. The growth rate is increasing with strong winds and low melting water flux [6]. For Switzerland maps exist which show the frequency of meteorological icing at 10 and 100 m height above ground [7]. For the Central Plateau, the meteorological icing frequency at a height of 10 m is low, about 4 days/year. The maximum simulated icing frequency at a height of 10 m is found in the area of the Central Alps and is about 100 days/year. These icing maps were elaborated with focus on ice accretion on powerlines and wind turbines.

Little information is available on the problem of icing on buildings because of dripping water or melted snow. We tried to quantify the probability of potential icing and formation of icicles by analysing the combination of days per winter with a snow height of more than 10 cm and mean negative temperatures. We named such a day an "icicle day". Because a single "icicle day" is often not sufficient to form a large icicle we looked as well at the number of "icicle periods". We named a time period an "icicle period" if the snow height is more than 10 and 20 cm respectively and the mean air temperature is lower than 0 °C during three consecutive days and lower than -5 °C respectively during two consecutive days. We think that the number of "icicle days" and "icicles periods" per winter allows to assess for a certain location the potential risk of icing and icicle formation. An icicle breaks off when its weight is greater than its strength. This occurs typically if the air temperature is above 0 °C or if the structural component where the icicle is fixed warms up. Strong winds combined with warm temperatures increase the risk that an icicle falls. The risk is reduced if the air temperature is below -5 °C [4]. Icicles do not build without dripping water. The risk of icicle formation can be

minimized by preventing the snow from melting (e.g. cold roof), by draining melting water with structural adaptations (e.g. rain pipes) or by installing combined heating and drain systems.

The following two case studies on risk and mitigation of falling snow and ice from buildings and structures are based on consulting mandates we recently completed.

## 3 Case study A: Tunnel entrances along San Bernardino highway (Switzerland)

The San Bernardino national highway is 58 km long and connects eastern Switzerland with the Canton of Ticino. The highway is the second most important transit axis, after the Gotthard route, crossing the Swiss Alps for freight and private transport. The culmination of the highway is a 6.6 km long road tunnel at an elevation of 1650 m a.s.l. On 1 February 2014, strong southerly winds on the San Bernardino national highway led to the formation of snow drifts at different tunnel entrances. The new snow height in the area was about 35 cm. In the late afternoon, a chunk of snow weighing approximately 10 kg broke off from the northern entrance of the San Bernardino tunnel and struck a passing car with an approximate impact force of 900 N.

<figure><img src="image_408.png" /><figcaption>**Figure 2.** North entrance of the San Bernardino tunnel on 1 February 2014 with the fractured snow overhang (Photo Tiefbauamt Graubünden).</figcaption></figure>

<figure><img src="image_409.png" /><figcaption>**Figure 3.** Damaged front shield of a car hit by a falling chunk of snow on San Bernardino national highway, on 1 February 2014 (Photo Kantonspolizei Graubünden).</figcaption></figure>
We calculated the impact force as a function of the falling snow mass, the drop height, the velocity of the car and the deceleration time [8]. Although the impact caused heavy damage to the vehicle, the passengers were unharmed (Figs. 2 and 3). The maintenance personnel checked the portal two hours before the accident without spotting a dangerous snow overhang. A similar accident happened in 2012 at the southern entrance of the Cassanawald tunnel when a chunk of snow weighing approximately 15 kg hit the windshield of a passing car. Luckily there was also only material damage. A survey in Switzerland showed that no other similar incidents are documented.

<figure><img src="image_410.png" /><figcaption>**Figure 4.** Entrance of the Cassanawald tunnel with portal collar in winter 2014, San Bernardino national highway. The width of the portal collar is 50 cm and the depth of the accumulated snow is about 80 cm.</figcaption></figure>

The SLF was asked to investigate how and where dangerous snow overhangs form on tunnel entrances and to evaluate possible measures for avoiding accidents in the future. The analysis of snow data shows that the 100-year snow height varies along the San Bernardino national highway between 90 cm at an elevation of 400 m a.s.l. and 340 cm at an elevation of 1650 m a.s.l. The return period of a snowfall of 40 cm varies between 4 and 50 years. Based on a daily traffic of 5000 vehicles, a vehicle velocity of 70 km/h and the assumption that every winter five times a snow chunk breaks off we calculated an occurrence probability of 0.03 per year that a vehicle is hit along the San Bernardino national highway. With the assumption that every tenth hit ends deadly the risk of death of a commuter who travels the road four times a day is $2.4 \times 10^{-6}$ which is a little lower than the threshold value of $1 \times 10^{-5}$ accepted in Switzerland [9].

We analysed the geometry and design, the local amount of snow and the exposure to snowdrift of 38 tunnel entrances for the risk assessment and the possible planning of mitigation measures. Five of the tunnel entrances which are all situated above an elevation of 1500 m a.s.l. were found to be particularly endangered due to high exposure to snowdrift and portal collars where snow accumulations can get easily unstable (Figs. 1 and 4).

<figure><img src="image_411.png" /><figcaption>**Figure 5.** South entrance of the San Bernardino tunnel in winter 2014. The snow cover was removed around the sloped tunnel portal. Snow drift accumulations or new snow can easily slide (see case 3, Fig. 1). The old snow cover is stabilized by knee pines which are overfilled with snow.</figcaption></figure>

The normal procedure to prevent the formation of dangerous snow accumulations on tunnel portals is to visually check the situation within the scope of the winter maintenance and to remove manually hazardous snow masses if necessary. At some tunnel portals up to 30 clearing operations were performed in the snow rich winter 2013/14. The maintenance personnel climb on the portals and remove the snow with shovels. Such operations can be very dangerous and time consuming. We recommended in particular that access for maintenance personnel be improved with fixed installed ladders and guardrails. Furthermore, we proposed installing heating bands on the portal collars at three critical entrances (Fig. 6). The heating band prevents the accumulation of snow by continuous melt. Heating bands worked well on a portal collar with a width of 50 cm in winter 2014.

<figure><img src="image_412.png" /><figcaption>**Figure 6.** North entrance of the Cassanawald tunnel, San Bernardino national highway. In fall 2014 an electrical trace heating system was installed on the portal collar to prevent hazardous snow accumulations. A fixed installed ladder and guardrails allow an easier access to the roof of the tunnel and safer work conditions to remove snow accumulations.</figcaption></figure>
<figure><img src="image_413.png" /></figure>

**Figure 7.** Snowdrift fence on the north entrance of the San Bernardino tunnel (Fig. 2). The fence which is anchored on prefabricated concrete slabs is made out of wooden boards and trusses. The snowdrift fence can relatively easily be displaced if necessary. In addition, guardrails were installed to allow a safe removal of snow overhangs.

The northern portal of the San Bernardino tunnel has a 40 m long horizontal roof. Southerly winds transport snow towards the portal. We proposed to build a snowdrift fence with a height of 2.5 m and a length of 12 m to prevent dangerous snowdrift accumulations (Fig. 7). The goal of a snowdrift fence is to restrain the wind so that the force of the wind on the snow surface is reduced allowing moving snow particles to come to rest [10]. Most of the drifted snow is deposited on a limited area on the downwind side of the fence. The fence should be oriented perpendicular to the predominant wind direction. We proposed a porosity of the fence of 30% and a bottom gap of 30 cm. The fence was designed on a wind force of 1.6 kN/m². So far not much experience on the effectiveness of the installed snow fence could be gained because the winters 2015 and 2016 were not very rich in snow.

## 4 Case study B: Facades of a planned four-story office building in St. Gallen (Switzerland)

The planned building, resting on two mighty cones, forms the main entrance to the Helvetia Insurance building complex (Fig. 8). The building is the last stage of three similar extensions which were as well planned by the architects Herzog & de Meuron and completed in 2004. The facades of the buildings consist of room-height windows, mounted with a slight twist from their vertical or horizontal axis (Fig. 9). The window boxes overhang the facade by 20 to 30 cm.

Observations demonstrate that dangerous snow and ice accumulations can form on the window boxes and roof parapets. On 10 February 2015 the snow height in St. Gallen varied between 20 and 30 cm. About 20 cm of snow accumulated on the roof and the top most window boxes (Fig. 10). The snow masses accumulated in the facade were about ten times smaller compared to the roof.

<figure><img src="image_414.png" /></figure>

**Figure 8.** The planned new west wing of the Helvetia Insurance building complex in St. Gallen towers above the main entrance (planning architects Herzog & de Meuron, Basel, Switzerland). Falling snow and ice from the 17 m high building can be a risk. The identity of the entire complex is shaped by the uniform facade treatment of all four extensions (Visualisation Herzog & de Meuron).

<figure><img src="image_415.png" /></figure>

**Figure 9.** Snow accumulations on the window boxes of the existing Helvetia building on 10 February 2015.
<figure><img src="image_416.png" /><figcaption>**Figure 10.** Snow accumulations on the window boxes of the existing Helvetia building on 10 February 2015. The snow height is about 20 to 40 cm.</figcaption></figure>

<figure><img src="image_417.png" /><figcaption>**Figure 11.** Formation of small icicles on the window boxes of the existing Helvetia building on 10 February 2015.</figcaption></figure>

A chunk of snow weighing approximately 10 to 20 kg broke off from a window box and hit the ground. Our evaluation showed that the break off was caused by tipping of the snow mass due to uneven melting (case 2, Fig. 1). Solar radiation considerably warms the facade and window boxes. This can cause additional meltwater which can refreeze as ice accumulations or icicles (Fig. 11). The cover of each window box is designed with a slight slope towards the outer facade. Rain water and meltwater drops uncontrolled along the facade. Falling snow chunks or icicles were so far not a problem because green areas surrounded the buildings. However, the newly planned main entrance will be situated directly below the facade.

The SLF was mandated to evaluate the risk of falling snow and ice masses and to propose mitigation measures for the planned new west wing to decrease the risk. The 50-year snow height in St. Gallen (776 m a.s.l.) is 90 cm. The 50-year snow height on the roof of the planned building is estimated to be 70 cm. The maximum recorded new snow depth in 24 hours is 60 cm and the 50-year total new snow sum is 375 cm. The long-term average number of ice days with maximum temperatures below 0 °C is 35. The number of “icicle days” is 28 with a mean temperature below 0 °C and a snow height of 10 cm or 14 with a snow height of 20 cm (Fig. 12). Furthermore, we evaluated the number of “icicle periods”. On average, 2 to 3 “icicle

periods” per winter with a minimal snow height of 10 cm and a length of 7 days must be expected in St. Gallen. Our analysis demonstrated that nearly every winter dangerous snow and ice accumulations have to be expected on the planned office building. We concluded that the risk of falling snow and ice is unacceptable without further structural adaptations and mitigation measures. Without such measures the access to the building would have to be closed every winter for certain time periods.

<figure><img src="image_418.png" /><figcaption>**Figure 12.** Number of “icicle days” per winter in St. Gallen, 776 m a.s.l.</figcaption></figure>

The installation of a porch roof above the main entrance would be the most simple and most effective mitigation measure. However such a porch roof was out of the question because of the architectural design concept of the whole building complex. The uniform shape of the facade could not be changed. Therefore we proposed comprehensive mitigation measures which include heating systems on all window boxes above the entrance area and the roof parapets, heated rain pipes and an enlargement of the roof parapets to 65 cm (Fig. 13). Furthermore, we recommended planning the ledges of the facade to be inclined towards the roof to prevent that snow masses slide outward and endanger the entrance area. In addition, we suggested to connect the drainage of the window boxes with continuous heated rain pipes over the whole width of the entrance area. The heat capacity should be planned so that about 10 cm of new snow with a density of 150 kg/m³ can be melted per hour.

We concluded that the risk of falling snow and ice is acceptable with the proposed mitigation measures for a normal winter scenario with an estimated return period of 50 years. Additional temporary measures such as closures or snow and ice removal were considered to be only necessary in exceptional meteorological situations. We proposed to inspect the completed new building after ice and snow events to verify the performance of the proposed measures.
<figure><img src="image_419.png" /><figcaption>**Figure 13.** Facade and roof parapet of the planned new west wing building with the proposed mitigation measures for the new building.</figcaption></figure>

## 5 Conclusions

The risk of falling snow and ice accumulations depends strongly on the building design and the snow climate. It is very important to involve snow experts in an early planning stage. If problematic accumulation surfaces for snow such as small ledges, window sills or roof parapets are identified their adverse effect can be often minimized with small adaptations to the design. An important point is to inspect a completed building after ice and snow events to verify the performance of the proposed measures. According to experience it is much more complex and costly to improve the design of an existing building or structure. The quantification of the adverse effect of snow and ice accumulations is very difficult and has to be assessed mostly by expert judgment. Therefore the documentation of incidents or interesting winter observations is very valuable for a better understanding of the interaction between snow, ice and buildings.

## References

1. SIA, *Actions on structures*, Swiss Code 505 261 (2014).

2. M. Carter, R. Stangl, *Increasing Problems of Falling Ice and Snow on Modern Tall Buildings*. CTBUH Journal 2012 Issue IV. 24-28 (2012).

3. C.J. Williams, M. Carter, F. Hochstenbach and T. Lovlin. *Sliding snow and ice on buildings: a balance of risk, cost and aesthetics*. Proceedings of the Fifth International Conference on Snow Engineering, 5-8 July 2004, Davos, Switzerland. Edited by E. Adams, P. Bartelt, R. Sack, A. Sato, and M. Christen. Taylor & Francis 2004, 59–66 (2004).

4. A. Nielsen, *Snow, Ice and icicles on Roofs – Physics and Risks*, Sixth Nordic Conference on Building Physics in the Nordic Countries, Reykjavik, 562-569 (2005).

5. D.A. Taylor, *Sliding Snow on Sloping Roofs*. Canadian Building Digest (1983).

6. L. Makkonen, *A model of icicle growth*. J. Glaciol. **34**, 64-70 (1988).

7. T. Grünewald, S. Dierer, R. Cattin, P. Steiner, W. Steinkogler, F. Fundel and M. Lehning. *Mapping frequencies of icing on structures in Switzerland*. J. Wind Eng. Ind. Aerodyn. **107-108**, 76-82 (2012).

8. R. Perla, T. Beck and J. Banner, *Impact Force of Snow*. NHRI Paper No. **2**, IWD Sci. Ser. No. 97. Natl. Hydrology Research Institute, Ottawa, Canada (1979).

9. Federal Roads Office FEDRO, *Natural hazards on national roads: Risk concept. Methodology for risk-based assessment, prevention and response to gravitative natural hazards on national roads*. ASTRA 89001 (2012).

10. R.D. Tabler, *Snow fence guide*. SHRP-W/FR-91-106 (1991).
# Capture of windward drift snow

Jan Potac <fnref n="1" />,ᵃ, Michael O'Rourke <fnref n="2" /> and Thomas K. Thiis <fnref n="3" />

**Abstract.** A new taller building adjacent to an existing building with a lower roof is a relatively common situation. The new building provides a snow source area, which results in snow drift atop the lower roof which likely was not anticipated in its original design. Since it is usually difficult to retrofit the existing roof structure, a solid wall can be considered to capture the expected snow transport on the upper roof. Using field measurement on snowdrift development, ASCE 7 provisions and Drift Ratio parameter, two approaches based on average or conservative values are studied to determine the required height of the solid wall.

## 1. Introduction

Building roofs are generally designed to carry snow loads prescribed in snow load standards. Shape factors have been used to describe the snow distribution for various roof shapes. However, a snow drift load not anticipated in original design can appear, for example, in case of a new higher building adjacent to an existing lower roof building, as show in Figure 1. In this example, the uniform distribution on the lower roof would alter to the triangular distribution due to the effect of the upwind building. It is difficult to retrofit the existing roof, in general. Therefore, to avoid the snowdrift on the lower roof, a solid wall could be erected on the upper roof to capture the expected upwind snow and thus avoid the snowdrift built-up on the lower roof.

<figure><img src="image_420.png" /><figcaption>**Figure 1.** Scheme of load situation</figcaption></figure>

In this paper, two approaches are evaluated to determine the relation between the upper roof fetch, and the solid wall height to capture the snow on the upper roof. Potac [1] conducted measurements on snowdrift development around solid fences of various heights and shapes. This experimental data and data on drift loads from Cocca and O'Rourke [3] together with ASCE 7 provisions [2] are utilized to evaluate the required height of the solid wall.

## 2. Method

The snow load is commonly considered to consist of balanced and drifted components. Therefore, the minimum wall height $h_w$ that would capture the expected upwind snow can be expressed as the sum of the heights of the balanced and drifted snow $h_b$ and $h'_d$, respectively.

In addition, one needs to consider a height characterizing the required freeboard $h_s$ (distance from top of the drift to top of wall) to avoid snow particles hopping over the wall. Therefore, an expression for $h_w$ can be written as

$$h_w = h_b + h'_d + h_s \quad (1)$$

The height of balanced drift $h_b$ can be obtained using the expression for flat surface loads and snow density as

$$h_b = \frac{0.7p_g}{\gamma} \quad (2)$$

Where $p_g$ is the ground snow load and $\gamma$ (lb/ft<fnref n="3" />) is the snow density determined as

$$\begin{array}{l} \gamma = 0.13p_g + 14 \\ \text{in SI: } \gamma = 0.426p_g + 2.2 \end{array} \quad (3)$$

To evaluate the drift component $h'_d$, two approaches are introduced. The first, Approach 1, adopts the ASCE 7 relation for a leeward drift of characteristic slope $s = 0.25$ (rise to run of 1:4). Furthermore, it is assumed that the trapping efficiency, which lead to the drift is 0.5. That is, the total amount of snow transport is twice the area of the ASCE 7 leeward drift. Comparing the area of the ASCE 7 drift with the area of measured drifts, one can obtain the drift height $h'_d$ as a function of $h_d$ defined in ASCE 7 as

$$h_d = 0.43\sqrt[3]{l_u^4}\sqrt{p_g + 10 - 1.5} \quad (4)$$

where $l_u$ is the length of the roof upwind the drift.

The second approach utilizes Drift Ratio (DR) [3], which is defined as a percentage of the snow in the snow source area that contributes to drift formation. Drift Ratio can be expressed as

$$DR = \frac{L_d}{p_g l_u} \quad (5)$$

where $L_d$ is the annual maximum drift load. Similarly to Approach 1 above, trapping efficiency of 0.5 is assumed. Then, the annual maximum drift load $L_d$ is compared to the load from drift measurements. As a result, a relation for drift height $h'_d$ is obtained as a function of DR, $p_g$ and $l_u$.

<figure><img src="image_421.png" /></figure>

<footnote n="1">¹Multiconsult AS, Tromsø, Norway</footnote>

<footnote n="2">²Rensselaer Polytechnic Institute, Troy, NY USA</footnote>

<footnote n="3">³Norwegian University of Life Sciences, Ås, Norway</footnote>

<footnote>ᵃ Corresponding author: jan.potac@gmail.com</footnote>
The height characterizing the required freeboard $h_s$ should correspond to a height when snow particles are not able to hop over the wall. Its value is to be determined from measurements. In both approaches, average or maximum (conservative) values of drift parameters and Drift Ratio are considered.

## 3. Field data

Three solid wall fences (I) and two solid wall fence with lee-overhang (Γ) are analyzed. The schematic overview of the geometries studied is given in Figure 2.

<figure><img src="image_422.png" /><figcaption>**Figure 2.** Snow fence geometries</figcaption></figure>

The measurements show that the snowdrift starts developing first on the windward side of the fence. When the windward side is partially filled, the leeward snowdrift starts developing, as shown in Figure 3.

<figure><img src="image_423.png" /><figcaption>**Figure 3.** Snowdrift development [1]</figcaption></figure>

The geometry of windward snowdrift is characterized by four parameters: solid wall height $h_0$, windward drift height for no leeward drift $h_1$, windward drift height for substantial leeward drift $h_2$, and slope parameter for windward drift $s$. The height parameters are summarized in Table 1.

<table><caption>**Table 1.** Snowdrift parameters</caption><thead><tr><th>Fence type</th><th><i>h</i><sub>0</sub><br>[ft] ([m])</th><th><i>h</i><sub>1</sub><br>[ft] ([m])</th><th><i>h</i><sub>2</sub><br>[ft] ([m])</th></tr></thead><tbody><tr><td>I</td><td>2.07 (0.63)</td><td>0.98 (0.30)</td><td>1.57 (0.48)</td></tr><tr><td>I</td><td>2.95 (0.90)</td><td>—</td><td>1.87 (0.57)</td></tr><tr><td>I</td><td>4.26 (1.30)</td><td>2.36 (0.72)</td><td>2.36 (0.72)</td></tr><tr><td>Γ</td><td>2.3 (0.70)</td><td>1.31 (0.30)</td><td>1.31 (0.40)</td></tr><tr><td>Γ</td><td>3.44 (1.05)</td><td>1.97 (0.52)</td><td>1.97 (0.60)</td></tr></tbody></table>

Since the snow transport along a surface is primarily given via saltation, one expects that the odds that a saltating snow particle will hop over the wall is related to the height difference. Height difference obtained from the measurements is shown in Table 2.

Later on in this study two sets of slope $s$ and height difference $h_s = h_0 - h_1$ are employed. While Approach 1 uses average values, the second, Approach 2 uses maximum, thus conservative values.

<table><caption>**Table 2.** Height difference</caption><thead><tr><th>Fence type</th><th><i>s</i><br>[-]</th><th><i>h</i><sub>0</sub> - <i>h</i><sub>1</sub><br>[ft] ([m])</th><th><i>h</i><sub>0</sub> - <i>h</i><sub>2</sub><br>[ft] ([m])</th></tr></thead><tbody><tr><td>I</td><td>0.14</td><td>1.08 (0.33)</td><td>0.49 (0.15)</td></tr><tr><td>I</td><td>0.09</td><td>—</td><td>1.08 (0.33)</td></tr><tr><td>I</td><td>0.08</td><td>1.90 (0.58)</td><td>1.90 (0.58)</td></tr><tr><td>Γ</td><td>0.06</td><td>1.31 (0.40)</td><td>0.98 (0.30)</td></tr><tr><td>Γ</td><td>0.16</td><td>1.74 (0.53)</td><td>1.48 (0.45)</td></tr><tr><td>Avg.</td><td>0.107</td><td>1.51 (0.46)</td><td>1.19 (0.36)</td></tr><tr><td>Max.</td><td>0.16</td><td>1.90 (0.58)</td><td>1.90 (0.58)</td></tr></tbody></table>

## 4. Analysis

In the section above, the minimum wall height was derived as a function of two parameters: $p_g$ and $l_u$. Therefore, for further analysis we consider the following ranges of $p_g = 10, 20, 50, 100 \text{ lb/ft}^2$ and $l_u = 50, 100, 250, 500$ and $1000 \text{ ft}$.

### 4.1. Approach 1

As described in 2, using this approach, the minimum solid wall height is determined using ASCE 7 drift area, trapping efficiency of 50% and drift height $h_d$, in comparison to geometric properties of the snowdrift from measurements. For further analysis average values of geometrical properties of measured drifts, i.e. $s = 0.1$ and height difference $h_s = h_0 - h_1 = 1.5 \text{ ft} (0.46 \text{ m})$ are considered. Comparing the ASCE 7 drift area with the area of drift measurements, one obtains the relation for $h'_d$ as

$$h'_{d}^{2} = \frac{4}{5} h_{d}^{2} \Rightarrow h'_{d} = 0.90 h_{d} \quad (6)$$

Employing Equation 2, 3, 4 and 6 into Equation 1 together with the average value of $s$ and $h_s$, the minimal wall height $h_w$ for given ranges of ground snow load and fetch is calculated in Table 3.

<table><caption>**Table 3.** Minimum wall height, Approach 1</caption><thead><tr><th rowspan="2"></th><th rowspan="2">h<sub>w</sub><br>[ft]<br>([m])</th><th colspan="5">l<sub>u</sub> [ft] ([m])</th></tr><tr><th>50<br>(15.2)</th><th>100<br>(30.5)</th><th>250<br>(76.2)</th><th>500<br>(152.4)</th><th>1000<br>(304.8)</th></tr></thead><tbody><tr><td rowspan="4">p<sub>g</sub><br>[lb/ft<sup>2</sup>]<br>([kN/m<sup>2</sup>])</td><td>10<br>(0.5)</td><td>3.62<br>(1.10)</td><td>4.41<br>(1.34)</td><td>5.76<br>(1.76)</td><td>7.10<br>(2.17)</td><td>8.79<br>(2.68)</td></tr><tr><td>20<br>(1)</td><td>4.33<br>(1.32)</td><td>5.20<br>(1.58)</td><td>6.70<br>(2.04)</td><td>8.18<br>(2.49)</td><td>10.05<br>(3.06)</td></tr><tr><td>50<br>(2.4)</td><td>5.83<br>(1.78)</td><td>6.86<br>(2.09)</td><td>8.64<br>(2.63)</td><td>10.41<br>(3.17)</td><td>12.63<br>(3.85)</td></tr><tr><td>100<br>(4.8)</td><td>7.36<br>(2.24)</td><td>8.56<br>(2.61)</td><td>10.64<br>(3.24)</td><td>12.69<br>(3.87)</td><td>15.28<br>(4.66)</td></tr></tbody></table>

Values from Table 3 are visualized in Figure 4. It is shown that for given parameters of $l_u$ and $p_g$ the minimal wall height ranges from 3.62 ft to 12.69 ft for ground snow load 10 lb/ft$^2$ and fetch 50 ft, and 100 lb/ft$^2$ and 500 ft, respectively.
<figure><img src="image_424.png" /><figcaption>Figure 4. Minimum wall height, Approach 1</figcaption></figure>

## 4.2. Approach 2

Cocca and O'Rourke [3] present plots of DR as a function of ground snow load for upwind fetches 50, 250, 500 and 1000 ft. These figures can be used to establish conservative DR values for Approach 2. Table 4 shows conservative values of DR assigned to upwind fetches according to the plots in Cocca and O'Rourke.

<table><caption>Table 4. Fetch and conservative DR values</caption><thead><tr><th>l<sub>u</sub> [ft] ([m])</th><th>DR [-]</th></tr></thead><tbody><tr><td>50 (15.2)</td><td>0.35</td></tr><tr><td>250 (76.2)</td><td>0.30</td></tr><tr><td>500 (152.4)</td><td>0.25</td></tr><tr><td>1000 (304.8)</td><td>0.20</td></tr></tbody></table>

Furthermore, conservative values of slope and height difference from measurements are considered, i.e. $s = 0.16$ and $h_s = 2$ ft. Then, the annual maximum drift load $L_d$ can be obtained from Equation 5 and equated to load calculated from trapping efficiency 50%, conservative drift parameters and snow density $\gamma$. Hence, the expression for the drift height $h'_d$ is obtained as

$$h'_{d} = \sqrt[2]{\frac{2 DR p_g l_u}{3 \gamma}} \quad (7)$$

Then, considering the conservative value of $h_s$, the minimum wall height can be determined from Equation 1. Calculated values are shown in Table 5 and plotted in Figure 5.

<table><caption>Table 5. Minimum wall height, Approach 2</caption><thead><tr><th rowspan="2">h<sub>w</sub><br/>[ft]<br/>([m])</th><th colspan="4">l<sub>u</sub> [ft] ([m])</th></tr><tr><th>50<br/>(15.2)</th><th>250<br/>(76.2)</th><th>500<br/>(152.4)</th><th>1000<br/>(304.8)</th></tr></thead><tbody><tr><td rowspan="4">p<sub>g</sub><br/>[lb/ft<sup>2</sup>]<br/>([kN/m<sup>2</sup>])</td><td>10<br/>(0.5)</td><td>5.22<br/>(1.59)</td><td>8.17<br/>(2.49)</td><td>9.84<br/>(3.00)</td><td>11.79<br/>(3.59)</td></tr><tr><td>20<br/>(1)</td><td>6.59<br/>(2.01)</td><td>10.60<br/>(3.23)</td><td>12.86<br/>(3.92)</td><td>15.52<br/>(4.73)</td></tr><tr><td>50<br/>(2.4)</td><td>9.04<br/>(2.76)</td><td>14.75<br/>(4.50)</td><td>17.96<br/>(5.48)</td><td>21.74<br/>(6.63)</td></tr><tr><td>100<br/>(4.8)</td><td>11.17<br/>(3.40)</td><td>18.20<br/>(5.55)</td><td>22.16<br/>(6.75)</td><td>26.81<br/>(8.17)</td></tr></tbody></table>

<figure><img src="image_425.png" /><figcaption>Figure 5. Minimum wall height, Approach 2</figcaption></figure>

Comparing values of $h_w$ for both approaches, Figure 4 with Figure 5, values of approximately 30% larger are obtained using Approach 2 than by Approach 1.

Since the second approach uses both conservative (i.e. “not likely to be exceeded”) values for DR and for drift parameters, it is found that Approach 2 arguably provides unrealistically large values for $h_w$.

Hence, two other scenarios are considered. First scenario combines conservative values for DR (Table 6) and average windward drift parameters. Alternately, the second combination uses average value of DR and conservative windward drift parameters. The larger of these two combinations is expected to provide reasonably safe values for $h_w$.

<table><caption>Table 6. Conservative (maximum) values of DR</caption><thead><tr><th rowspan="2">DR [-]</th><th colspan="4">l<sub>u</sub> [ft] ([m])</th></tr><tr><th>50<br/>(15.2)</th><th>250<br/>(76.2)</th><th>500<br/>(152.4)</th><th>1000<br/>(304.8)</th></tr></thead><tbody><tr><td rowspan="3">p<sub>g</sub><br/>[lb/ft<sup>2</sup>]<br/>([kN/m<sup>2</sup>])</td><td>10<br/>(0.5)</td><td>0.37</td><td>0.30</td><td>0.25</td><td>0.20</td></tr><tr><td>20<br/>(1)</td><td>0.25</td><td>0.20</td><td>0.20</td><td>0.20</td></tr><tr><td>40<br/>(1.9)</td><td>0.25</td><td>0.22</td><td>0.20</td><td>0.18</td></tr></tbody></table>

Similarly to previous calculation, using the average value of $s = 0.106$, drift density, trapping efficiency of 50%, the drift load can be compared to the load obtained by using conservative values of DR (Table 6), which results in expression for $h'_d$ as

$$h'_{d} = \sqrt[2]{0.377 \frac{DR p_g l_u}{\gamma}} \quad (8)$$

Using the average value of $h_0 - h_1$ and $h_0 - h_2$ from Table 2 $h_s = 1.33$ ft, the minimum wall height is obtained from Equation 1 and shown in Table 7.

<table><caption>Table 7. Minimum wall height, Approach 2, combination 1</caption><thead><tr><th rowspan="2">h<sub>w</sub><br/>[ft]<br/>([m])</th><th colspan="4">l<sub>u</sub> [ft] ([m])</th></tr><tr><th>50<br/>(15.2)</th><th>250<br/>(76.2)</th><th>500<br/>(152.4)</th><th>1000<br/>(304.8)</th></tr></thead><tbody><tr><td rowspan="3">p<sub>g</sub><br/>[lb/ft<sup>2</sup>]<br/>([kN/m<sup>2</sup>])</td><td>10<br/>(0.5)</td><td>3.92<br/>(1.2)</td><td>6.09<br/>(1.86)</td><td>7.34<br/>(2.24)</td><td>8.81<br/>(2.68)</td></tr><tr><td>20<br/>(1)</td><td>4.56<br/>(1.39)</td><td>6.94<br/>(2.11)</td><td>8.91<br/>(2.72)</td><td>11.70<br/>(3.57)</td></tr><tr><td>40<br/>(1.9)</td><td>5.92<br/>(1.8)</td><td>9.36<br/>(2.85)</td><td>11.65<br/>(3.55)</td><td>14.68<br/>(4.47)</td></tr></tbody></table>
In second combination, maximum value of height difference $h_s=1.90$ ft (0.58m) is employed together with the maximum slope $s=1.6$. Comparing the measured drift load with the load obtained using DR, and assuming trapping efficiency 50%, the drift height $h'_d$ can be calculated as

$$h'_d = \sqrt[2]{0.63 \frac{DR p_g l_u}{\gamma}} \quad (9)$$

The resulting values of minimal wall height $h_w$ are shown in Table 8.

<table><caption>**Table 8.** Minimum wall height, Approach 2, combination 2</caption><thead><tr><th rowspan="2">h<sub>w</sub><br/>[ft]<br/>([m])</th><th colspan="4">l<sub>u</sub> [ft] ([m])</th></tr><tr><th>50<br/>(15.2)</th><th>250<br/>(76.2)</th><th>500<br/>(152.4)</th><th>1000<br/>(304.8)</th></tr></thead><tbody><tr><td rowspan="3">p<sub>g</sub><br/>[lb/ft<sup>2</sup>]<br/>([kN/m<sup>2</sup>])</td><td>10<br/>(0.5)</td><td>4.55<br/>(1.39)</td><td>6.31<br/>(1.92)</td><td>7.14<br/>(2.18)</td><td>8.47<br/>(2.58)</td></tr><tr><td>20<br/>(1)</td><td>5.23<br/>(1.59)</td><td>7.33<br/>(2.23)</td><td>8.61<br/>(2.62)</td><td>10.05<br/>(3.06)</td></tr><tr><td>40<br/>(1.9)</td><td>6.30<br/>(1.92)</td><td>9.39<br/>(2.86)</td><td>11.48<br/>(3.5)</td><td>12.25<br/>(3.73)</td></tr></tbody></table>

Table 9 show maximum values of minimum wall height from Table 7 and Table 8. Values are plotted in Figure 6.

The combination of average and conservative values of drift parameters and DR shows more realistic values than in the case of conservative values only. The minimum wall height in this case are close to values obtained by Approach 1, that is based on average values of drift parameters and ASCE 7 drift.

<table><caption>**Table 9.** Minimum wall height, Approach 2, maximum of combination 1 and combination 2</caption><thead><tr><th rowspan="2">h<sub>w</sub><br/>[ft]<br/>([m])</th><th colspan="4">l<sub>u</sub> [ft] ([m])</th></tr><tr><th>50<br/>(15.2)</th><th>250<br/>(76.2)</th><th>500<br/>(152.4)</th><th>1000<br/>(304.8)</th></tr></thead><tbody><tr><td rowspan="3">p<sub>g</sub><br/>[lb/ft<sup>2</sup>]<br/>([kN/m<sup>2</sup>])</td><td>10<br/>(0.5)</td><td>4.55<br/>(1.39)</td><td>6.31<br/>(1.92)</td><td>7.34<br/>(2.24)</td><td>8.81<br/>(2.68)</td></tr><tr><td>20<br/>(1)</td><td>5.23<br/>(1.59)</td><td>7.33<br/>(2.23)</td><td>8.91<br/>(2.72)</td><td>11.7<br/>(3.57)</td></tr><tr><td>40<br/>(1.9)</td><td>6.30<br/>(1.92)</td><td>9.39<br/>(2.86)</td><td>11.65<br/>(3.55)</td><td>14.68<br/>(4.47)</td></tr></tbody></table>

<figure><img src="image_426.png" /><figcaption>**Figure 6.** Minimum wall height, Approach 2, maximum of combination 1 and combination 2</figcaption></figure>

Comparison of all three sets of calculation for ground snow load of 20 lb/ft² (1 kN/m²) is shown in Figure 7. It shows that the minimum wall height values are relatively similar for Approach 1 and Approach 2 using combinations of average and conservative parameters.

<figure><img src="image_427.png" /><figcaption>**Figure 7.** Summary of all three approaches for ground snow load of 20 lb/ft²</figcaption></figure>

## 5. Conclusions

Field measurements of snowdrift around solid snow fences were analyzed, and characteristic drift properties (slope and height difference) were determined. For further analysis, average and conservative values were considered. In first set of calculations, average drift parameters $s=0.1$ and $h_s=1.5$ ft (0.46 m) were compared to ASCE 7 drift relation resulting in minimum wall height ranging from 4.33 ft (1.32 m) to 10.05 ft (3.06 m) for a location with ground snow load of 20 lb/ft² (1 kN/m²) and fetch of 50 ft (15.24 m) and 1000 ft (304.8 m) respectively.

The second set of calculations employs conservative values of drift parameters ($s=0.16$ and $h_s=2$ ft (0.58 m)) and conservative values of Drift Ratio DR. This approach leads to arguably unrealistic large values. The minimum wall height ranged from 6.59 ft (2.01 m) to 15.52 ft (4.73 m) for a location with ground snow load of 20 lb/ft² (1 kN/m²) and fetch of 50 ft (15.24 m) and 1000 ft (304.8 m) respectively. It is approximately 30% lagrer than values obtained from first set of calculations.

Finally, two combinations of average and conservative values of DR and drift parameters are considered. Resulting values of minimum wall height lead to more realistic values ranging from 5.23 ft (1.59 m) to 11.7 ft (3.57 m) for a location with ground snow load of 20 lb/ft² (1 kN/m²) and fetch of 50 ft (15.24 m) and 1000 ft (304.8 m) respectively. These values are relatively similar to values obtained using by Approach 1.

## 6. References

1. Potac, J. (2013) Field measurements and numerical simulations of snow transport and deposition around structures and into ventilation intakes. PhD Thesis Norwegian University of Life Sciences ISSN 1503-1667 ISBM 978-82575-1180-7

2. American Society of Civil Engineers (2013) Minimum Design Loads for Buildings and Other Structures ASCE 7-10, New York, NY

3. Cocca, J. and O'Rourke, M. (2008) Mathematical Simulation of 50-Year Snow Drift Loads. Structures Congress 2008: pp. 1-9. doi: 10.1061/41016(314)150
# Wind tunnel tests and analysis of snow load distribution on three different large size stadium roofs

Andrzej Flaga<fnref n="1" />, Łukasz Flaga<fnref n="2" />

**Abstract.** The article contains comparison and analysis of snow load tunnel tests for three different roofs of sport facilities. Tests were performed in a wind tunnel with boundary layer modelling. Snow precipitation and redistribution tests were performed using powdered polystyrene foam as artificial snow. The results of snow load distributions were presented as dimensionless roof shape factor of snow load for both the precipitation and redistribution simulations.

## 1 Introduction

The paper deals with snow load tunnel tests for three different roof constructions of sport facilities. Test were performed for: Municipal Stadium in Łódź, Poland [1] (study case L), Municipal Stadium in Poznań, Poland [2] (study case P), and multi-purpose sports and entertainment hall in Krakow (study case K) [3] (comp. Fig. 1, 2 & 3).

<figure><img src="image_428.png" /></figure>

<figure><img src="image_429.png" /></figure>

<figure><img src="image_430.png" /></figure>

**Figure 1.** Model of the: Municipal Stadium in Łódź, Poland (a), Municipal Stadium in Poznań, Poland (b) and multi-purpose sports and entertainment hall in Krakow, (Poland) (c) in working section of the wind tunnel [1, 2, 3]

Experimental works were made in a boundary layer wind tunnel, which allowed proper creation of natural wind speed and turbulence profile. Wind tunnel facility belongs to the Wind Engineering Laboratory at the Cracow University of Technology. Main goal of the paper is to compare and analyse results of snow load tunnel tests for three geometrically different roofs of sport facilities.

The geometry of each roof shape as well as its construction is different (comp. Fig. 2). It is obvious that the unique shape of the roof substantially affect the shape of the snow cover. Key differences in the form of roof structures are: study case L – concave membranes (comp Fig. 2 a); study case P – convex membrane (comp Fig. 2 b); study case K – dome – (comp Fig. 2 c). Comparison between influences of snow load distribution schemes on each construction was not a part of this article. Initially, for each of tested cases similarity criteria were elaborated. The powdered polystyrene foam was used to simulate snow for each study case (P, L & K). It was powdered on a belt sander. Detailed description of the adopted similarity criteria and bases for experimental works are presented in [4, 5, 6].

## 2 Experimental setup

### 2.1 Wind tunnel

The flow structure inside working section of the tunnel was established using floor blocks, spires and fence (Fig. 3). Wind speed was measured in several vertically aligned points with the use of hotwire thermometers. From the regression of the mean speed measurement, exponent of the power-law wind speed profile in model situation was obtained for both precipitation and redistribution experiments.

<figure><img src="image_431.png" /></figure>

<footnote n="1">¹Prof.D.Sc.Eng. Andrzej Flaga, Wind Engineering Laboratory, Faculty of Civil Engineering, Cracow University of Technology, Poland</footnote>

<footnote n="2">²Ph.D.Eng.Arch. Łukasz Flaga, Faculty of Civil Engineering, Department of Technology of Building and Materials Processes, Częstochowa University of Technology, Poland</footnote>

<footnote>a Corresponding author: lukasz.flaga@interia.pl</footnote>
<figure><img src="image_432.png" /><figcaption>**Figure 2.** Key differences in the form of roof structures: study case L – concave membranes (a), study case P – convex membranes (b), study case K – dome (c) [1, 2, 3]</figcaption></figure>

## 2.2 Artificial snow

Substance: grinded styrofoam (Fig. 4):

* $\rho_c$ – particle bed density: ~10 kg/m³

* $d$ – mean particle diameter: 0,43 mm

* $v_t$ – terminal speed: 0,3 m/s

* $\chi$ – kinematical cohesion: 0 m²/s²

Density was measured with help of laboratory scales and cylinder. Diameter was measured with help of 100x microscope. Terminal speed was obtained by measurement of artificial snow falling time from 1m height. Because artificial snow is a loose material the kinematical cohesion is nearly zero.

<figure><img src="image_433.png" /><figcaption>**Figure 4.** A sample of "artificial snow" made of styrofoam (numbers on the scale denote centimetres) [5]</figcaption></figure>

## 2.3 Artificial snow supply (feeder)

A feeder is presented in Figure 5. The device consists of stable sieve – steel frame 108x220 cm, with perforated bottom 6x20 mm and movable sieve – steel frame 100x210 cm, identical perforated bottom. Movable sieve is suspended on slide bearing. Sieve is moved by a motor with continuous regulation of speed. It is possible to stop the sieve in closed position.

<figure><img src="image_434.png" /><figcaption>**Figure 3.** Experiment implementation [4]</figcaption></figure>
## 2.4 Photogrammetry method

The measurement of snow cover thickness was done by a single frame photogrammetry method for case study P and K. For the case study L an optical scanning method was used. The results were elaborated as diagrams that can be used during design process. Scheme of photogrammetry arrangement schematic diagrams and method used in experiments are presented in Figure 6 (a) and (b).

a)

<figure><img src="image_435.png" /></figure>

<figure><img src="image_436.png" /><figcaption>Figure 5. Experimental setup – feeder [5]</figcaption></figure>

## 2.5 Tests algorithm

In snow load tunnel tests following algorithm was assumed:

- Model preparation;

- Setting the direction of inflowing air;

- Setting a proper wind speed;

- Precipitation;

- Measurement of thickness of snow cover after precipitation;

- Setting a proper wind speed for redistribution:

- Redistribution;

- Measurement of thickness of snow cover after redistribution;

- Removing layer of artificial snow.

# 3 Comparison of setup parameters values

## 3.1 Precipitation simulation

The main similarity criteria numbers according to [4, 5] for each of model situations are as follows:

$$ \Pi_t = \frac{v_{ref}}{v_t}; \quad Stk = \frac{\frac{v_t}{g}}{\frac{v_{ref}}{L}} = \frac{v_t v_{ref}}{g L}, \quad (1) $$

where: $\Pi_t$ - speed ratio similarity number; $Stk$ - Stokes number; $v_{ref}$ - average reference horizontal flow speed (at $z_{ref}$); $z_{ref}$ - reference height; $v_t$ - terminal velocity of powdered polystyrene foam particle (dispersion terminal speed); $g$ - acceleration due to gravity; $L$ - reference length;

a)

<figure><img src="image_437.png" /></figure>

b)

<figure><img src="image_438.png" /></figure>

$$ k = \frac{y_b}{\cos \varepsilon + b \cdot \sin \varepsilon \cdot \tan \varphi} $$

<figure><img src="image_439.png" /><figcaption>Figure 6. Experimental setup – photogrammetry (a) and photogrammetry algorithm diagram (b) [5]</figcaption></figure>
These two quantities are called “ballistic” because they describe airborne particles behavior. The $Π_t$ is responsible for the particle movement in the free fall state. The Stk is responsible for the dispersion particles inertial movement. It is a ratio of the particle movement characteristic time to the fluid flow characteristic time. Comparison of setup parameters values for precipitation situation is given in Table 1.

<table><caption>**Table 1.** Comparison of setup parameters values for precipitation situation</caption><thead><tr><th rowspan="2"></th><th colspan="2">Study case L</th><th colspan="2">Study case P</th><th colspan="2">Study case K</th></tr><tr><th>(M)</th><th>(P)</th><th>(M)</th><th>(P)</th><th>(M)</th><th>(P)</th></tr></thead><tbody><tr><td>scale</td><td>1:200</td><td>-</td><td>1:200</td><td>-</td><td>1:150</td><td>-</td></tr><tr><td>a</td><td>-</td><td>-</td><td>0,22</td><td>0,19 - 0,24</td><td>0,224</td><td>0,19 - 0,24</td></tr><tr><td>z<sub>ref</sub></td><td>12,5 cm</td><td>20 m</td><td>40 cm</td><td>80 m</td><td>27,2 cm</td><td>40,8 m</td></tr><tr><td>Π<sub>t</sub></td><td>3,13</td><td>3,13</td><td>3,0</td><td>3,0</td><td>3,05</td><td>3,05</td></tr><tr><td>v<sub>ref</sub> [m/s]</td><td>0,94</td><td>4,7</td><td>0,9</td><td>4,5</td><td>0,914</td><td>4,6</td></tr><tr><td>v<sub>10</sub> [m/s]</td><td>-</td><td>3,83</td><td>-</td><td>2,85</td><td>-</td><td>3,38</td></tr><tr><td>I<sub>u</sub> [%]</td><td>25,8</td><td>23,8 - 33,4</td><td>12,6</td><td>17,9 - 22,8</td><td>14,0</td><td>20,4 - 27,0</td></tr></tbody></table>

where: (M) – Model; (P) – Prototype; $α$ – velocity profile power law coefficient; $I_u$ – intensity of turbulence.

Eight precipitation tests were conducted for different wind angle in 45° interval. For each test after establishing steady flow, 60 litres of powdered polystyrene foam was poured into the working section of the wind tunnel from a sieve-like feeder during 5 minutes (comp. Figure 5). The particle cover reference height samples were collected from the wind tunnel floor and the height of the particle cover on the model roof was measured with photogrammetry method. The particle cover shape factor $μ_{pre}$ was determined as dimensionless height of the cover.

## 3.2 Redistribution simulation

For each wind direction, redistribution test of particle cover was performed. The reference flow velocity was increased in regard to precipitation simulation up to $v_{ref}$. Tests at this velocity were performed until equilibrium state was obtained after about 20 minutes. Assuming the air density $ρ_f = 1.23$ kg m⁻³, following similarity numbers according to [4, 5, 6] are as follows:

$$ \Pi_g = \frac{(\rho_c - \rho_f) \cdot d_{cl} \cdot g}{v_{ref}^2 \cdot \rho_f}; \quad \Pi_\chi = \frac{\chi \cdot \rho_c}{v_{ref}^2 \cdot \rho_f} \quad (2) $$

where: $Π_g$ – particle bed gravitational number; $Π_χ$ – particle bed cohesive number; $χ$ – “kinematical” cohesion of the particle bed; $ρ_c$ – particle cover density, $ρ_f$ – fluid (air) density; $d_{cl}$ – mean “cluster” diameter (or simply, mean particle diameter); $g$ – acceleration due to gravity; Comparison of setup parameters values for redistribution situation is given in Table 2.

<table><caption>**Table 2.** Comparison of setup parameters values for redistribution situation.</caption><thead><tr><th></th><th>Π<sub>t</sub></th><th>Π<sub>g</sub></th><th>v<sub>ref</sub></th></tr></thead><tbody><tr><td>Study case L (M)</td><td>4,95</td><td>0,0137</td><td>1,48 m/s</td></tr><tr><td>Study case P (M)</td><td>8,33</td><td>0,00482</td><td>2,5 m/s</td></tr><tr><td>Study case K (M)</td><td>5,67</td><td>0,0104</td><td>1,7 m/s</td></tr></tbody></table>

## 4 Snow load distribution formulation

<figure><img src="image_440.png" /><figcaption>**Figure 7.** Wind rose for the study case L (a), study case P (b), study case K (c) localization [1, 2, 3]</figcaption></figure>
Procedure of assembling results from wind-tunnel experiments into recommended load distributions took into account different wind directions. So called “base scheme” (Fig. 7) was obtained by determining the weighted mean from precipitation simulation results for different wind directions:

$$ \mu_{base} = \sum p_i \mu_{i,pre} \quad (3) $$

where $\mu_{base}$ is shape factor for base scheme, $p_i$ is probability of the wind from $i^{th}$ direction (obtained from local wind rose, comp. Fig. 7), $\mu_{pre}$ is shape coefficient obtained from single precipitation simulation. Resultant redistribution patterns were calculated for each direction from the formula:

$$ \mu_{i,drift} = \mu_{base} + \Delta \mu_{i,drift} = \mu_{base} + (\mu_{i,red} - \mu_{i,0}) \quad (4) $$

where $\mu_{i,drift}$ is the drift scheme shape factor for $i^{th}$ wind direction, $\mu_{i,red}$ is the shape coefficient obtained from single redistribution simulation, $\mu_{i,0}$ is the initial shape factor for redistribution test.

## 5 Comparison of selected experimental results

Selected examples of basic snow load distributions - $\mu_{base}$ shape factor of snow load for precipitation and redistribution simulation for each study case is presented in Fig. 8 - 15.

<figure><img src="image_441.png" /><figcaption>Figure 8. Basic snow load distribution - $\mu_{base}$ shape factor of snow load for precipitation simulation for the study case L: (a) whole model; (b) close-ups of selected roof parts [1]</figcaption></figure>

<figure><img src="image_442.png" /><figcaption>Figure 9. Characteristic basic snow load distribution [kN/m²] with use of - $\mu_{base}$ shape factor for structure division into fields, in which an averaging process has been done [1]</figcaption></figure>

<figure><img src="image_443.png" /><figcaption>Figure 10. Snow load distribution - $\mu_{drift}$ shape factor of snow load for the 90° redistribution simulation for the study case L: (a) whole model; (b) close-ups of selected roof parts [1]</figcaption></figure>
<figure><img src="image_444.png" /></figure>

<figure><img src="image_445.png" /></figure>

<figure><img src="image_446.png" /></figure>

<figure><img src="image_447.png" /><figcaption>**Figure 10.** Characteristic snow load distribution [kN/m²] with use of - *μ*<sub>drift</sub> shape factor of snow load (for structure division into fields, in which an averaging process has been done) for the study case L for the: 90° (a), 0° (b), 45° (c),135° (d) redistribution simulation [1]</figcaption></figure>

<figure><img src="image_448.png" /></figure>

<figure><img src="image_449.png" /></figure>

<figure><img src="image_450.png" /><figcaption>**Figure 11.** Snow load distribution - μ<sub>pre</sub> shape factor of snow load for the study case P for the: 0° (a), 225° (b), 270° (c) precipitation simulation [2]</figcaption></figure>
<figure><img src="image_451.png" /><figcaption>**Figure 12.** Snow load distribution - *μ<sub>drift</sub>* shape factor of snow load for the study case P for the: 0° (a), 315° (b), 225° (c), 270° (d) redistribution simulation [2]</figcaption></figure>

<figure><img src="image_452.png" /><figcaption>**Figure 13.** Example of basic snow load distribution - *μ<sub>base</sub>* shape factor of snow load for precipitation simulation for the study case K</figcaption></figure>

<figure><img src="image_453.png" /><figcaption>**Figure 14.** Snow load distribution - *μ<sub>drift</sub>* shape factor of snow load for the study case K for the: 0° (a), 45° (b), redistribution simulation [3]</figcaption></figure>
<figure><img src="image_454.png" /><figcaption>**Figure 15.** Snow load distribution - *μ<sub>drift</sub>* shape factor of snow load for the study case K for the: 135° (a), 90° (b) redistribution simulation [3]</figcaption></figure>

**6 General conclusions**

All presented snow load distributions, both in the
precipitation and redistribution simulations, differ
significantly each other. Roof shapes of selected cases
differ as well. So, in such cases no convergence features
were noticed. Each case should be treated separately with
respect to local conditions.

Shape factor distribution results are reasonable.
These distributions diverge substantially from results
which could be obtained by extrapolation of rough shape
factor distribution in Eurocode [8] for cylindrical and
abutting roofs. Peak values of obtained shape factors are
lower than ones that could be derived from
abovementioned code schemes.

**7 References**

1. A. Flaga, G. Bosak, G. Kimbar, R. Kłaput, Ł. Flaga, P. Matys, *Wind tunnel tests of snow load distribution and wind action on the roof of the municipal stadium in Łódź, Kraków* (in Polish) (2012)

2. A. Flaga, G. Kimbar, *Wind tunnel tests for snow load prediction on the roof of the Municipal Stadium in Łódź, Kraków* (in Polish) (2012)

Poznań, Snow Engineering VI, Whistler, Canada,
Conference Proceedings. (2008)

3. A. Flaga, G. Bosak, G. Kimbar, R. Kłaput, Ł. Flaga, P. Matys, *Study work: Wind tunnel tests of snow load distribution on the roof of the New Krakow Arena*. Cracow University of Technology, Kraków (2009).

4. G. Kimbar, A. Flaga, *A new approach to similarity criteria for predicting a snow load In wind tunnel experiments*, Snow Engineering VI, Whistler, Canada, Conference Proceedings. (2008)

5. G. Kimbar, A. Flaga, *Similarity criteria of snow precipitation and redistribution and snow load simulation in wind tunnel*, 6th International Symposium on Environmental effects on buildings and people Actions, influences, interactions, discomfort, EEBP VI, Tomaszowie near Cracow, Poland, (2010)

6. A. Flaga, *Wind engineering – bases and applications* (in Polish), Arkady, Warsaw (2008)

7. M. Mellor, *Cold regions Science and Engineering Part III, Section A3c: Blowing Snow*; Cold Regions Research & Engineering Laboratory, Hanover New Hampshire (1965)

8. PN-EN 1991-1-4: Actions on structures - General actions - Part 1-4: Wind actions (in Polish)
# Comparison of physical snow accumulation simulation techniques

Albert Brooks¹, a, Scott Gamble¹, Jan Dale¹ and Jill Bond¹

¹Rowan Williams Davies and Irwin (RWDI), Guelph, Ontario, CA

**Abstract.** Simulated snow accumulation patterns are presented using two methods: scale model testing in a water flume and wind tunnel testing of a model combined with numerical simulations of snow accumulation and depletion. The results of these two approaches are compared using a calibration building with features that demonstrate the complexity of building aerodynamics and resulting snow accumulation patterns. This paper identifies the strengths and limitations of each method and provides recommendations for future research initiatives.

## 1 Introduction

The ability to predict the distribution of snow accumulations on a structure is important for determining structural requirements and to address building serviceability challenges in cold regions.

Simulations using a water flume or a wind tunnel have been preferred methods since the 1970s for investigating snow drifting using scale models of an existing or proposed building or development. Where problematic snow accumulations are observed, remedial solutions can be readily developed.

However, these simulation approaches can be limited due to the challenge of directly simulating the effects of multiple meteorological events that occur in succession over a winter. More recently, simulation methods using the combination of numerical modelling and wind tunnel testing or computational fluid dynamics (CFD) have been developed, such as the finite area element (FAE) method.

These approaches, while accounting for the varying nature of snow accumulation, are more computationally intensive and may not account for the iterative time-varying aerodynamic changes that result during the accumulation of drifting snow.

This paper compares the snow accumulation patterns obtained using water flume and FAE simulation methods with partial scale field observations. Strengths and limitations of each approach are identified from the perspectives of structural snow load design and building serviceability.

## 2 Snow simulation methods

### 2.1 Simulation scaling

A great deal of detailed, fundamental research has been conducted to assess the applicability of scale model testing within wind tunnels and water flumes. Although scaling laws are important, exact matching is difficult so the summation of similitude relationships for saltation drifting may be simplified down the variable of particle trajectory length to the selected model scale. Most model scales used by researchers and industry have been derived through qualitative methods such as the visual comparison of drift patterns on simple model geometries

like building roof steps, snow fence accumulation patterns and through experience.

Tests conducted within wind tunnels have used glass spheres or sodium borate simulation materials at scales of around 1:20 [1, 2, and 3]. Successful tests have been conducted using water as the working fluid and crushed walnut shells at 1:30 [4], and using sand at 1:300 model scales in literature [5, 6, and 7]. Table 1 provides a summary of historical simulate materials, simulation methods, and approximate geometric model scales.

Model scale studies conducted in both air and water have provided valuable snow accumulation distribution information to researchers and designers. However, the applicability of testing models of larger scales, for example 1:10 to 1:20, for large commercial structures is of limited practicality due to the physical size of the models and test facilities required, and the overall volume of simulation material needed to conduct a test. As a result, smaller model scale testing is required, placing greater demand on matching the simulated particle trajectory length to the model scale. For these types of structures, testing within water using a sand particle or in a wind tunnel with a heavier particle with a shorter particle trajectory length carries great appeal, even if all similitude requirements are not strictly met.

<table><caption>**Table 1.** Simulation modelling materials and scale.</caption><thead><tr><td>Simulate Material</td><td>Simulation Method</td><td>Approx. Model Scales</td></tr></thead><tbody><tr><td>Real/Artificial Snow</td><td>Field, Wind Tunnel [1,8]</td><td>1:1 - 1:150</td></tr><tr><td>Borax</td><td>Wind Tunnel [1,3]</td><td>1:20 - 1:50</td></tr><tr><td>Glass Spheres</td><td>Wind Tunnel [1]</td><td>1:20 - 1:50</td></tr><tr><td>Crushed Glass</td><td>Water Flume [5,6,7]</td><td>1:200 - 1:500</td></tr><tr><td>Crushed Walnut Shells</td><td>Water Flume [4]</td><td>1:30</td></tr></tbody></table>

### 2.2 Water flume simulation

Scale model simulation of snow drifting and accumulations using a water flume has a long history in snow engineering, having many practical design uses

<figure><img src="image_455.png" /></figure>

<footnote>a Corresponding author: Albert.Brooks@rwdi.com</footnote>
including the identification of snow drift patterns at ground level, unusual roof drifts, and snow infiltration problems [2, 5, 6, 7, and 9].

Although the strict requirements for dynamic similarity are not met, it appears that in many cases, the main features of full scale drifts are adequately represented on a model [1, 2, and 4].

The water flume simulations described in this paper were conducted with building models at a 1:300 model scale. Snow drifting is simulated using finely crushed glass particles with sizes ranging from 60 through 120 sieve size, which is commonly used as a sand blasting material in industry. The crushed glass particles carried by the water simulate snow particles saltated by the wind over the actual site. Like drifting at full scale, the drifting particles are deposited in regions of flow deceleration on a scale model building. Snow simulation depths and patterns can be varied by modifying the application rate of crushed glass snow simulate material and water flow rates. These settings are commonly varied on a case-by-case basis to account for differences in local meteorological climates, or to provide greater volumes of simulated snow to calibrate to building code or field measurement based drift accumulations [7].

## 2.3 Finite Area Element (FAE) method

The FAE method numerically simulates the hour-by-hour deposition, drifting, and melting of snow and absorption of rain and melt water into a snow pack within a grid system that divides the roof into a large number of finite areas. Entire winters are simulated on an hour-by-hour basis using historical meteorological data, including the cumulative effects of successive storms, drifting events and melting periods.

As part of the simulation process, physical scale models are instrumented and tested within a boundary layer wind tunnel to obtain the aerodynamic flow patterns that are required as an input into the snow flux, redistribution and melting models used within the FAE numerical simulation [5, 11, and 13].

# 3 Simulation of roof step surcharge accumulation

Of the snow loads recommended by building codes and standards, snow accumulations located within roof steps tend to govern the design of a structural system for many buildings.

Generically speaking, most commercial building stock contains large flat roof surfaces on the order of 10s of metres in roof length and width, with roof steps on the order of 3000 mm in height or greater. A simple building roof step described by Brooks et al., 2016 has dimensions that are considered representative of commercial buildings, and is illustrated in Figure 1 [13].

<figure><img src="image_456.png" /></figure>

<figure><img src="image_457.png" /><figcaption>**Figure 1.** Plan and elevation views of the roof step model. Dimensions are given in full-scale millimetres. Wind tunnel velocity sensor locations are indicated by the dark blue circles.</figcaption></figure>

Field observations of snow drifts on a simple roof step model of comparable geometry are described in detail by Tsuchiya et al., 2002 [14]. Valuable snow drift geometry information was obtained for both upwind and downwind drift formations on a roof step 4500 mm in total width, 1800 mm high and 5400 mm long with a roof step height of 900 mm. It is assumed that these dimensions were selected due to practical construction and measurement reasons. As this roof step is much smaller than typically seen on commercial buildings, the model used by Tsuchiya et al 2002 may be considered a 1:3 scale model for practical application. The findings described by Tsuchiya et al., 2002 will serve as a point of reference for each of the modelling techniques further described in this paper. Two roof step models were used to illustrate downwind and upwind roof step drifts by orienting the buildings perpendicular to prevailing winds.

## 3.1 Reference meteorological events

Meteorological data recorded in Sapporo, Hokkaido Prefecture, Japan covering the period of record described by Tsuchiya et al., 2002 is used as a reference climate for comparison purposes. An analysis of winter winds determined that the predominate direction and frequency of winds in January and February are from the west through west-northwest and southeast through northeast directions. The snowfall and resulting snow drift patterns were recorded following events on January 31st, February 20, and February 25, 2001, resulting in uniform snow accumulation depths on the ground of 70 mm, 150 mm and 200 mm, respectively over the duration of each event. During these events, winds were blowing from the northwest. Each test event started with the model cleared of snow. This represents a limited meteorological data set, and does not include the effects of multiple successive snowfall, drifting, rain and melting events over the course of the winter. Most of these events are also of relatively small snowfall amounts and low wind speed (between 2.9 and 3.5 m/s being referenced). Of this data set, the 200 mm snowfall event on February 25, 2001 is considered most valuable for comparison purposes.

## 3.2 Water flume simulation

Water flume simulations were conducted using the 1:300 scale models described in Figure 1 with roof step heights of 3000 mm, 9000 mm and 30000 mm, respectively, at full scale. Although the model roof described in Figure 1
is much larger than that described by Tsuchiya et al., 2002, the aerodynamic wind flow patterns are expected to be similar for winds perpendicular to the step.

Photographs of snow accumulation and scour patterns are shown in Figure 2 for each roof step model when winds approach from over the upper roof and when winds approach from over the lower roof. Wind flow is from left to right in each photograph.

A great deal of useful design information can be gleaned through inspection and comparison of scour and deposition patterns for each image. For example, as the upper roof height is increased, wind exposure and scour unsurprisingly increased. Step accumulation patterns vary with roof step height as well. When winds flow over the upper roof, a downwind drift is formed within the roof step. As the step height is increased, the resulting accumulation patterns indicate that there is greater turbulent mixing within the downwind flow, leading to more uniform and smaller accumulation depths. Within the lower 3000 mm roof step, localized wind accelerations and scour patterns can be seen at the outer edges of the lower roof at the vertical wall of the roof step. Review of these patterns indicates that although the geometry of the model is simple, the simulated wind flow patterns at work are not.

When wind flows over the lower roof toward the step face, snow deposition patterns are equally complex, with evidence of strong flow separations and recirculation patterns on both the lower and upper roof surfaces. Greater downwash and recirculating wind flows tend to relocate snow to the middle of the lower roof surface in a roll back drift, with greater snow movement and localized drift accumulation with greater roof step heights.

<figure><img src="image_458.png" /><figcaption>**Figure 2.** Snow accumulation patterns when winds approach from over the upper roof (top images) and over the lower roof (bottom images).</figcaption></figure>

## 3.3 Finite Area Element (FAE) method

### 3.3.1 Ground snow accumulation simulation

24-hour meteorological data from the Sapporo reference winter of 2000-2001 was used to simulate the ground snow load. The resulting time history of snow accumulation and depletion for the winter has been plotted in Figure 3 with the corresponding snow and rainfall rates plotted on the secondary axis. The snow load is presented in kilopascals (kPa) and precipitation in millimetres (mm/hr) of water equivalent. The maximum simulated snow load for this year occurred on March 18, 2001 and corresponds to a ground snow load of 3.5 kPa. As can be seen, the peak snow load is the result of numerous freezing precipitation events with little opportunity for melting earlier in the winter.

Tsuchiya et al., 2002 identified three significant snowfall and drifting events occurring on January 31st, February 20 and February 25, 2001 with uniform ground snow depths of 70 mm, 150 mm and 200 mm, respectively occurring over the course of each event. These events have been identified in Figure 3.

Of these events, the February 25th event has been selected for comparison as it features the largest snow accumulation when winds occurred from a narrow range of directions. The increase in simulated ground snow accumulation over the February 24/25 event was 0.17 kPa using the FAE procedure, suggesting an average storm snow density of 0.85kN/m³.

<figure><img src="image_459.png" /><figcaption>**Figure 3.** Example simulated ground snow load for the winter of 2000-2001 with the reference snowfall events identified.</figcaption></figure>

### 3.3.2 Roof step snow accumulation - Single event simulation

Identical physical and numerical models of the roof steps presented in Figure 1 and Figure 2 were created using the FAE methodology. This required each model to be instrumented and tested within a boundary layer wind
tunnel. A standard suburban wind velocity and turbulence profile was used to obtain the required aerodynamic flow patterns.

Figure 4 and Figure 5 illustrate the distribution of area averaged snow load in kilopascals for each area element after the February 25th event beginning with a bare roof. These distributions of snow loads represent single instances in time during the event, as the peak snow load in each element can vary due to the meteorological history and building roof step aerodynamics. For the 3000 mm step, the FAE method predicted an accumulation of load within the first row of area elements as indicated in Figure 4. With higher roof steps, similar to the water flume simulations, the load was more distributed over the lower roof surface.

<figure><img src="image_460.png" /><figcaption>**Figure 4.** FAE-predicted snow accumulation patterns when winds approach from over the upper roof (top images) and over the lower roof (bottom images).</figcaption></figure>

The snow distribution for the 3000 mm roof step when winds flow over the upper roof are illustrated in the top and bottom images in Figure 5 when simulated using the FAE and water flume, respectively. In this wind flow and drifting scenario, the FAE method predicts an accumulation of load within each element located closest to the roof step. The distribution in load along the width of this zone appears to vary, with the greatest loading occurring closer to the outer ends of the roof. The corresponding water flume simulations provide evidence of similar accumulation patterns, where localized wind flow recirculation has drawn snow towards the ends of the roof step region.

When winds flow over the lower roof, the FAE method results indicate smaller drift loads within the roof step regions than when winds flow over the upper roof using the reference meteorological data. These simulations also indicate that increasing the roof step height leads to an increase in snow redistribution on the lower roof, with evidence of a localized increase in accumulation in the middle of the roof, similar to the trends observed within the water flume simulations.

<figure><img src="image_461.png" /><figcaption>**Figure 5.** Comparison of FAE simulated of snow load (top) with water flume pattern (bottom).</figcaption></figure>

## 3.4 Comparison of simulation methods

The plots in Figure 6 and Figure 7 contain the geometric distribution of snow within the simple building roof step for each of the snow simulation methods including field observations [14], and via water flume and FAE simulation methods. The direct geometric comparison of simulated snow accumulations required rescaling of the field measurements to the 3000 mm roof step height. The geometry of the snow accumulations obtained from field observations and each simulation method are presented as normalized ratios where s is the measured depth or load, and Sd is the uniform depth or load on the ground.
<figure><img src="image_462.png" /><figcaption>**Figure 6.** Normalized field measurements of snow accumulation (s/Sd) [14] and predictions from water flume and FAE simulation techniques for when wind blows over the upper roof.</figcaption></figure>

As indicated in Figure 6, snow accumulation depths are greatest using the water flume technique. In addition, some subtleties in the cross-section of the downwind accumulation have not been explicitly captured, such as the small trough and second peak moving away from the vertical wall. When winds flow over the lower roof, Figure 7, field observations provided evidence of a strong recirculation zone which swept snow into a tight roll back drift with a high angle of repose removed from the vertical wall of the roof step. The results of the water flume simulations indicate the presence and location of these flow patterns, but at a lower magnitude and angle of repose of the drift.

Two distribution geometries have been presented in Figure 6 for the loads predicted by the FAE: one as a uniform accumulation as predicted by the FAE, and one as a tapering snow load by redistributing the area averaged load as a triangular load over the width of the area element. In general, the magnitude and distribution in load appear to be within reason when compared to the field observations. However, when winds blow over the lower roof, Figure 7, the FAE method predicted a uniform distribution in snow load and misses the formation of the roll back drift for the single event scenario.

This may be due to the meteorological data used within the simulation, and the assumptions in local site exposure. The tendency to form greater loads in the middle of the roof is however captured with increased step heights as illustrated in Figure 4. It is suspected that the roll back drift in the 3000 mm step was not captured for this particular case due to the implementation of a fixed threshold velocity for drifting that was perhaps not appropriate for the specific snow characteristics of the chosen event. An event with a slightly higher wind speed is expected to have produced the roll back drift.

Review of the simulated distributions in snow for the entire reference year containing a variety of snow events more faithfully illustrates the roll back drift for the 3000 mm step model (see Section 3.5).

<figure><img src="image_463.png" /><figcaption>**Figure 7.** Normalized field measurements of snow accumulation (s/Sd) [14] and predictions from water flume and FAE simulation techniques for when wind blows over the lower roof.</figcaption></figure>

For the simple case of a building roof step, the water flume method captured a great deal of high resolution information regarding wind flow patterns and the bulk movement and deposition of snow, as evidenced by the photographs in Figure 2 and Figure 5, although snow distribution patterns show some variability as compared with field data. The inability to physically simulate successive meteorological events, such as winds from multiple approaching directions, represents a significant practical limitation to the direct application of this modelling technique to providing snow loads.

The FAE method provides reasonable estimations of the transport and accumulation of snow, but lacks the high resolution and visual nature of a physical simulation, such as the subtleties in drift shape that may be provided by the water flume modelling technique. However, the FAE approach overcomes the limitations of a single wind direction event simulation technique by accounting for the time-varied nature of snow accumulation and depletion.

These simulation approaches can therefore be considered synergistic, where each method can be used to overcome some of the shortcomings and uncertainties inherent in snow simulation. Despite some limitations in modelling, it should be noted that each simulation technique represents an extremely powerful tool for modelling snow. These tools can and should be used for researchers and designers as they provide a great deal of information and insight that is currently beyond building code recommendations [5, 7, 11, 12, and 13].

## 3.5 Multiple event simulation

Within most cold climate regions, the peak snow load is seldom the result of a single storm event, as illustrated by the increase and depletion of snow load within the simulated 2000-2001 time history shown in Figure 3. Exposure to successive events can cause snow to be scoured and relocated when in a drivable state.

Figure 8 presents the distribution in snow load at a single instance in time when the peak load is at its greatest. Review of the distribution of snow load when the upper roof surface is oriented to the northwest indicates the presence of a large roof step accumulation. When the upper roof is oriented towards the southeast,
prevailing winter winds from the northwest appear to create strong flow recirculation which result in a roll back drift. A comparison with the loads presented in Figure 4 indicates that the trends in snow accumulation patterns are similar, although more redistribution in snow has occurred, which is likely the result of multiple wind events. This is due to the highly directional nature of winds around Sapporo; however this is not the case for many other snow-prone regions of the world.

<figure><img src="image_464.png" /><figcaption>**Figure 8.** Peak snow accumulation patterns as a result of numerous successive precipitation events for the winter of 2000-2001 when the upper roof surface is oriented towards the northwest (top) and to the southeast (bottom).</figcaption></figure>

# 4 SPACE model simulations

The tests conducted using a building roof step provides a good geometry for evaluating simulation methods. However, for a simulation approach to be robust and applicable, it must be able to simulate the deposition and scour of snow on complex building geometries that are likely to be encountered in practice.

To test and refine various simulation approaches, the authors created the Snow Precipitation and Accumulation Calibration Experiment (SPACE) model, as illustrated in Figure 9. This building includes geometries that result in complex building aerodynamics and resulting snow accumulation patterns. A detailed description of the SPACE model and the water flume simulation method can be found in Brooks et al, 2015 and Brooks et al 2016 [7, 13].

## 4.1 Water flume simulation

The top two images shown in Figure 10 are photographs taken from above the SPACE model, where the simulated snow drifts can be seen on and surrounding the scale model. A heavy drifting scenario was performed to provide greater visual detail.

<figure><img src="image_465.png" /><figcaption>**Figure 9.** Plan and elevation views of the SPACE model building. Dimensions are given in full-scale millimetres (Brooks et al, 2015).</figcaption></figure>

The distribution of simulated snow on the SPACE model is shown in Figure 10 when winds are from the northwest. Wind flow flows from left to right in the top image. The bottom photograph in Figure 10 is a close up of the roof step located mid-span of the arched roof.

Regions of interest to practitioners may include the well exposed upper roof, regions of wind flow acceleration and scour across the arched roof and the corresponding location of snow on the arched roof.

Also of interest is the location and relative magnitude of roof step surcharges, as these types of accumulations are highly dependent on wind directionality [13]. It should also be noted that most of these snow accumulation patterns are not well addressed by current building codes and standards.
As can be seen in Figure 10, the water flume simulation provides a very detailed picture of the wind flow patterns across the structure, with well exposed areas being scoured of snow and depositions where wind flows decelerate. Visual comparison between the wind velocity vectors obtained through the boundary layer wind tunnel testing shown in Figure 11 and the regions of scour and deposition show good agreement.

<figure><img src="image_466.png" /><figcaption>**Figure 10.** Photograph of the SPACE model when winds were approaching from the northwest direction (top). Distribution of snow in the roof step region of the arched roof (bottom).</figcaption></figure>

## 4.2 Finite Area Element (FAE) simulation

The FAE simulation method required detailed wind flow velocity information. This information was obtained through boundary layer wind tunnel testing of a 1:300 scale model identical in geometry to the water flume model (top photograph in Figure 11). Velocity data (magnitude and direction) were measured with a high degree of spatial resolution using 253 surface velocity vector (SVV) sensors [11] (middle photograph in Figure 11). A standard suburban wind and turbulence profile

was used for each of the 24 equally incremented test directions.

The velocity at each sensor was linearly interpolated to each of the nodes of the area elements used to define the geometry of the model. An example of the direction and relative magnitude of wind flows are presented in the bottom image in Figure 11 when winds are from the northwest (315°).

<figure><img src="image_467.png" /><figcaption>**Figure 11.** SPACE model within a boundary layer wind tunnel (top) instrumented wind tunnel model with surface velocity vector (SVV) sensors (middle) and resulting wind velocity vector field when wind is from the northwest (bottom).</figcaption></figure>

### 4.2.1 Single event accumulation distributions

The distribution of snow load using the FAE method using meteorological data encompassing the February 25th snowfall event in Sapporo, Hokkaido Prefecture, Japan can be seen in Figure 12. Visual comparison of the distribution patterns of snow between Figure 10 and
Figure 12, indicate that the water flume and FAE simulations are in quite good agreement.

Areas of uniform snow depth are consistent, for example the snow accumulations along the lower roof surface at the northeast corner of the building, and within the wake region west of the tower. Regions with greater accumulation are also well replicated, such as the tapering drift accumulation on the leeward side of the arched roof, and the accumulations within roof step areas.

However, there are some minor differences between the simulations; the FAE model illustrates the presence of uniform snow loads at the northeast corner of tower, where the water flume simulations indicate the presence of a roll back drift at the base of the tower. It is expected that these minor differences are primarily the result of the discretized nature of the FAE approach and due to area averaging of the loads, removing the localized minimums and maximums that normally occur due to the aerodynamic shape of drifts.

<figure><img src="image_468.png" /><figcaption>**Figure 12.** Plan view of the SPACE model building illustrating the distribution of snow load using meteorological data from February 24-25, 2001. Loads presented in kilopascals (kPa) for February 25 at 23:00 hours. Prevailing approaching wind direction is indicated by the arrow at top-left in the image.</figcaption></figure>

### 4.2.2 Multiple event accumulation distributions

As previously discussed, peak snow accumulations in most cold climate zones are the result of multiple successive events. The simulation presented in Figure 13 is the result of the hour by hour simulation of the winter of 2000-2001 using the meteorological data described in Section 3.3.3. To illustrate the range of various wind directions and speeds within this data set, an analysis of the directional distribution of winds was performed, which are presented in the wind rose (bottom image of Figure 13).

Within this meteorological data set, the majority of strong winds occur from the west through north, with weaker winds occurring from the southeast through south-southeast. Inspection of the snow drift patterns with those presented in Figure 10 and Figure 12 clearly illustrate that the majority of scour and redistribution is the result of these northwest winds.

<figure><img src="image_469.png" /><figcaption>**Figure 13.** Snow accumulation distribution using meteorological data from the winter of 2000-2001 (top). Accumulations presented in kilopascals (kPa) on March 8 at 02:00 hours. Directional distribution of winds (blowing from) as recorded in Sapporo, Hokkaido Prefecture, Japan of the months of November through April for the winter or 2000-2001(bottom).</figcaption></figure>

The effect of variable wind directionality can be better illustrated through the use of a climate other than the Sapporo, Japan, such as Toronto, Canada. Figure 14 illustrates the predicted distribution of snow while accounting for a climate where winds occur from many directions. As can be seen within the wind rose, winds in this example winter occur from a wide variety of directions and are quite strong. As a result, snow drift and scour zones are more varied, with drifts occurring within multiple roof step zones in patterns very different than the patterns driven by the highly directional wind climate of Sapporo.

Currently, accounting for the time varying nature of snow drifting when approaching winds occur from a variety of directions is not practical within a wind tunnel or water flume. Although individual test directions provide excellent information regarding aerodynamics and snow accumulation geometry, the use of the FAE method provides additional advantages, particularly for these more challenging meteorological climates.
<figure><img src="image_470.png" /><figcaption>**Figure 14.** Snow accumulation distribution using meteorological data from the winter of 1970-1971 (top). Accumulations presented in kilopascals (kPa) on February 23, 1971 at 23:00 hours. Directional distribution of winds (blowing from) as recorded at Pearson International Airport in Toronto, Canada for the months of November through April for the winter of 1970-1971 (bottom).</figcaption></figure>

**5 Conclusions and recommendations**

Predicting the accumulation, movement and depletion of snow on a building is a very complex process that is a challenge to model despite decades of continued research. The findings presented in this paper illustrate some of the many physical and numerical simulation challenges. Principal findings and recommendations for future work include:

* When comparing field observations on a partial scale model to water flume simulations, the resulting drift accumulations tend to be varied in predicting snow accumulation depths. The large scale features of the drift patterns are well represented, such as regions of scour and deposition. Therefore, water flume simulations provide invaluable wind flow information, as well as useful information regarding the geometry of resulting snow accumulations.

* Water flume simulations provide excellent information to designers regarding wind flows and resulting snow redistributions for a single wind direction at a time. This can provide reasonable approximations within a highly directional climate, but cannot simulate the time history of numerous wind and precipitation events.

* The trends in the distribution in snow load agree well between water flume, FAE and field observations. However, the detailed geometry of the FAE-generated snow accumulations is generally of lower

resolution due to area averaging within each simulation element. For the purpose of structural design, such small scale geometries are generally not as significant since a structural system is not as sensitive to point loads due to load sharing. Some drift accumulations may not be predicted due to the size of the elements, or when sufficient wind velocity information is not available.

* The FAE method can simulate the time history of entire winters and can account for the effects of multiple wind events from different directions, temperature variables, heat loss and the driftability of snow.

* Where the FAE method lacks the ability to determine the geometry of a drift at high resolution, the water flume simulation technique can provide some of this information, while compensating for the inability of the water flume technique to simulate multiple events. These approaches should be considered synergistic and should be applied together to determine the most efficient and applicable estimations for snow distribution on a building.

* Advancing the science of snow accumulation techniques for structures requires validation through partial and full scale field observations. Models should include a simplified roof step of various heights and a more complicated geometry such as the SPACE model. Not only should the geometry of snow accumulation be studied, but also the time history of the increase and decrease in structural load. To provide a more robust data set, a long term monitoring and data collection program should be initiated for a variety of climate zones.

**Acknowledgments**

The authors would like to thank Anne McIntosh, Perry Tuchlinsky and Josh Ward for their efforts in constructing physical and graphic models used in this paper.

**References**

1. J.D. Iverson. Drifting-snow similitude – transport-rate and roughness modelling. Journal of Glaciology. Vol. 26, no. 94 (1980).

2. J.D. Iversen. Development of Small-Scale Snowdrift Simulation. Western Snow Conference. Reno, NV, USA, (1982) 112-119.

3. R.W. Gerdel, G.H Strom. Wind Tunnel Studies with Scale Model Simulated Snow.

4. M. O'Rourke, A. DeGaetano, J.D. Tokarczyk. Snow Drifting Transport Rates from Water Flume Simulation. Journal of Wind Engineering and Industrial Aerodynamics. 92, (2004) 1245-1264.

5. P.A. Irwin, C.J. Williams. Application of snow simulation model tests to planning and design. 40th Eastern Snow Conference. Toronto, Ontario, Canada. (1983) 118-130.
6. C.J. Williams. Field Observations of Wind Deflection Fins to Control Snow Accumulations on Roofs. Proc. 1st Int. Conf. on Snow Eng., Santa Barbara, California, USA, (1986) 307-314.

7. A.J. Brooks, J.C. Dale, S.L. Gamble, S. F. Kriksic. The Rapid Assessment of Snow Drifting Conditions using Physical Model Simulations. American Society of Civil Engineers Cold Regions Conference. Salt Lake City, UT (2015).

8. R.B. Haehnel, CPT., J.H. Wilkinson, J.H. Lever. Snowdrift Modeling in the CRREL Wind Tunnel. 50th Eastern Snow Conference. 61st Western Snow Conference. Quebec City (1993).

9. J.D. Iverson. Development of snow-scale snowdrift simulation. Western Snow Conference (1982).

10. A.J. Brooks, S.L. Gamble, J.C. Dale, M.P. Gibbons. Determining Snow Loads on Buildings with Solar Arrays. CSCE 2014 4th International Structural Specialty Conference. Halifax, NS (2014).

11. S.L. Gamble, W.W. Kochanski, P.A. Irwin. Finite Area Element Snow Loading Prediction – Applications and Advancements. Journal of Wind Engineering and Industrial Aerodynamics, 41(1992)

12. P.A. Irwin, S.L. Gamble, D.A. Taylor, D.A. Effects of Roof Size, Heat Transfer, and Climate on Snow Loads: Studies for the 1995 NBC. Canadian Journal of Civil Engineering. 22 (1995).

13. A.J. Brooks, J.V. Bond, J.C. Dale, S.L. Gamble. Parametric Simulation of Roof Structural Snow Loads. Canadian Society of Civil Engineers. CSCE2016 Resilient Infrastructure Specialty Conference. London, ON (2016).

14. M. Tsuchiya, T. Tomabechi, T. Hongo, H. Ueda. Wind effects on snowdrift on stepped flat roofs. Journal of Wind Engineering and Industrial Aerodynamics, 90(2002) 1881-1892.
# Snowdrifts on two-level building roofs and modeling of snow density at Harbin

Guolong Zhang <fnref n="1" />,<fnref n="2" />, Yu Zhang <fnref n="1" />,<fnref n="2" /> and Feng Fan <fnref n="1" />,<fnref n="2" />

**Abstract.** Outdoors measurements on snowdrifts on two-level building roofs and an equation for predicting snow density by the use of meteorological data are presented. The measurement was undertaken within the campus of Harbin Institute of Technology (HIT), during the period 2014-2015. The models were two-level buildings, with angles of the upper roof being 0°, 15°, 30° and 45°. The observations were undertaken directly after snowfall. The results show that the critical angle of the upper roof that affects the snow distribution on lower roofs is 30°. In addition, the critical angle that causes snow sliding from upper roofs is 30°. The snow density and meteorology measurements for the period 2010-2013 were taken by authors. With an analysis of variance, a relationship of snow density with various predictor variables was explored, That is, the snow depth and temperature have a significant effect on the snow density, while velocity, humidity and precipitation have a weak influence. Based on the various predictor variables, a fitting equation of snow density was developed with a coefficient of determination equaling 0.90.

## 1 Introduction

Snow load on building roofs is calculated based on the snow distribution and the regional mean snow density. For many years, lots of research has been carried out on both issues.

In the aspect of the snow distribution. Thiis [1] investigated the snowdrifts around three different model buildings in a valley in Spitsbergen, Norway. The different roof designs proved to have a significant influence on the size of the snowdrifts produced. A flat roof gives a larger snowdrift than a single pitch roof, and a single pitch roof, tilted upstream the wind, gives a larger snowdrift than a single pitch roof tilted downstream the wind. Oikawa [2] explored the snowdrift around a cubic model on open ground. The results showed that a deep snowdrift was encountered windward of the cube, followed by large snowdrifts on each lateral side and leeward of the cube. Strong erosion areas were observed nearly surrounding the cube. Beyers [3] evaluated the snowdrift characteristics surrounding the research station of the South African National Antarctic Expedition, SANAE IV. In this research, a 1:25 scale model of the research station was constructed and mounted on a large flat snow covered area. The wind profiles of the prevailing winds were measured with a 6-m wind mast positioned near the model. The characteristic surface roughness and shear velocity functions were derived and analyzed. From the results, a new velocity profile function was established with additional parameters to account for the effects of surface roughness and saltating snow.

In the aspect of the snow density. Meløysund [4] presented a simple method for predicting snow density using weather data, and pointed out that the snow density values suggested in the Norwegian code are, in most cases, overestimated. Bruland [5] modified Sturm's model of snow density by extending predictor variables. The final model improved the snow density predictions

Corresponding author: zhanggl_hit@126.com

for the Norwegian data, compared to the model of Sturm, by up to 50%. McCreight [6] developed a new model of the bulk density for a daily time step, and demonstrated its improved accuracy over existing models.

Although many researches on snow distributions on building roofs have been carried out, more details need determinations, like the critical angles, the amount of sliding snow from upper roofs, the relationship between the angle and the distribution coefficient, etc. Furthermore, the snow load on building roofs, in China, is calculated based on the regional mean snow density, which may cause a doubtful estimated load. Therefore, an accurate estimation equation for snow density is needed.

## 2 Outdoor experiments of snow distributions on building roofs

### 2.1 Study site and setup

The outdoor experiments were undertaken on an open flat base within the campus of Harbin Institute of Technology (HIT), China (Figure 1). It was part of a large snow engineering program. The wind pattern in this area has been previously found to be constant during the winter (Figure 2). The uniform wind direction makes this area ideal for snowdrift experiments.

<figure><img src="image_471.png" /><figcaption>Figure 1. Location where outdoor experiments were conducted</figcaption></figure>

<figure><img src="image_472.png" /></figure>

<footnote n="1">¹School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China</footnote>

<footnote n="2">²Key Lab of Structures Dynamic Behavior and Control of China Ministry of Education, Harbin Institute of Technology, Harbin 150090, China</footnote>
<figure><img src="image_473.png" /><figcaption>**Figure 2.** Wind frequency diagram in the winter of 2012-2013</figcaption></figure>

The models were two-level buildings, with angles of the upper roof being 0°, 15°, 30° and 45°. The snow distribution on each roof was observed right after snowfall (Figure 3).

<figure><img src="image_474.png" /><figcaption>**Figure 3.** Photos of snow distribution on two-level roofs</figcaption></figure>

The models were installed on December 15th on flat bare ground. In the following 3 months. The wind speed and direction were measured at 1.8 m on a PC-4 automatic weather station and the sampling interval was 1min.

## 2.2 Results

The two-level buildings had four kinds of upper roofs, namely, 0°, 15°, 30° and 45° slopes. Each slope pattern was made twice, and positioned face to face to investigate the snow distribution windward and leeward. The measurements on lower roofs were untaken simultaneously with those on upper single pitch roofs.

The results on 2014/12/29 have been selected for this investigation. The incidence angle of wind was 22.5° on the windward wall. The mean wind speed in dominant direction was approximately 0.7m/s (at 1.8m) and the maximum was 1.6m/s, as indicated in Figure 4.

<figure><img src="image_475.png" /><figcaption>**Figure 4.** Wind speed and rose map for the whole period on 2014/12/29 at Harbin</figcaption></figure>

<figure><img src="image_476.png" /><figcaption>a) Snow profiles on the lower roofs in windward</figcaption></figure>

<figure><img src="image_477.png" /><figcaption>b) Snow profiles on the lower roofs in leeward</figcaption></figure>

<caption>**Figure 5.** Snow profiles on the lower roofs with four upper slope roofs in windward and leeward on 2014/12/29</caption>

Figure 5 gives a thickness-profile for different upper slopes. In the windward condition, deposition occurs close to the foot of the upper wall, then erosion extends along the width direction, due to the strong vortex at the corner of the upper wall. In the leeward condition, the snow distribution has a gradual rising pattern along the width side. Instead of the deposition next to the wall, there exists a slight erosion.

The results presented in Figure 5 and Figure 6 illustrate that, when the slope of upper roofs is less than 30°, its influence on the snow distribution can be neglected. Furthermore, a similar pattern exists with a higher thickness value, when the upper slope exceeds 30°. In addition, the critical angle that causes snow sliding from upper roofs is 30°.

<figure><img src="image_478.png" /><figcaption>**Figure 6.** Profiles of model snowdrift formed on two-level roofs with sliding snow on 2015/01/02</figcaption></figure>

# 3 Analyses of snow density

## 3.1. Data

The snow density and meteorological data were measured directly after each snowfall. No measurements were undertaken when the maximum snow depth on the ground was less than 5mm. Snow density measurements
were undertaken using a sharp-edged tube with an internal cross-section of 1135mm². The snow inside the tube was weighed and the density calculated. The meteorological data were measured by a PC-4 automatic weather station. Air temperature and humidity were measured at 1.5 m above the ground, with an accuracy of 0.1 °C and 0.1%, respectively. Precipitation (mm water equivalent) was measured with fresh snow. Snow depth

was measured using a yardstick simultaneously with snow density. This was a measure of the accumulated snow depth (not only precipitation as snow was present since the last measurement). In the period 2012-2013, a total of eight sets of data were collected. The mean temperatures, mean wind velocities, precipitations and maximum snow depths during the measurement period are given in Table 1.

<table><caption>**Table 1.** Snow and meteorological data for the measurement period of 2012–2013</caption><thead><tr><th>Time</th><th>Temperature (°C)</th><th>Humidity (%)</th><th>Wind velocity (m/s)</th><th>Precipitation (mm)</th><th>Snow depth (mm)</th><th>Snow density (kg/m³)</th></tr></thead><tbody><tr><td>2012/11/26</td><td>-12.0</td><td>79.8</td><td>2.0</td><td>7.0</td><td>7.3</td><td>86.6</td></tr><tr><td>2012/11/27</td><td>-8.5</td><td>80.2</td><td>2.7</td><td>51.0</td><td>57.8</td><td>106.4</td></tr><tr><td>2012/12/03</td><td>-13.9</td><td>82.5</td><td>2.3</td><td>37.0</td><td>94.0</td><td>136.4</td></tr><tr><td>2012/12/15</td><td>-17.1</td><td>78.1</td><td>1.8</td><td>40.0</td><td>133.2</td><td>150.8</td></tr><tr><td>2012/12/21</td><td>-20.1</td><td>71.5</td><td>1.8</td><td>20.0</td><td>149.6</td><td>156.4</td></tr><tr><td>2012/12/29</td><td>-19.4</td><td>78.3</td><td>2.4</td><td>24.0</td><td>173.6</td><td>144.7</td></tr><tr><td>2013/01/23</td><td>-12.5</td><td>79.5</td><td>2.0</td><td>18.0</td><td>185.8</td><td>154.6</td></tr><tr><td>2013/02/28</td><td>-10.0</td><td>58.2</td><td>1.3</td><td>100.0</td><td>267.4</td><td>154.6</td></tr></tbody></table>

## 3.2 Analyses and result

Analysis of variance (ANOVA) is a procedure for assigning sample variance to different sources and deciding whether the variation arises within or among different population groups. ANOVA can be used to identify sources of variability in a response variable Y and determine which factors affect the output in a design of experiment (DOE). This method contains One-Way ANOVA, Two-Way ANOVA and N-Way ANOVA. The model of Two-Way ANOVA may be described by the linear equation:

$$Y_{ijk} = \mu + \tau_{i} + \beta_{j} + (\tau\beta)_{ij} + \varepsilon_{ijk} \begin{cases} i = 1, 2, \dots, a \\ j = 1, 2, \dots, b \\ k = 1, 2, \dots, n \end{cases}$$

Here, $\mu$ is the overall mean effect, $\tau_i$ is the effect of the i th level of factor A, $\beta_j$ is the effect of the j th level of factor B, $(\tau\beta)_{ij}$ is the effect of the interaction between A and B. $\varepsilon_{ijk}$ is a random error component, having a normal distribution with mean zero and variance $\sigma^2$. The ANOVA was used to identify qualitatively the effect of meteorological variables on snow density.

Each variable had two levels, i.e. H (High) and L (Low). Three variables were selected in each analysis, because of the limited amount of data. As the snow depth and the temperature are the main contribution factors proposed in literature, the analyses were divided into three groups, as shown in Table 2.

<table><caption>**Table 2.** The group information of meteorological variables in each analysis</caption><thead><tr><th rowspan="3">Level</th><th colspan="9">meteorological variable</th></tr><tr><th colspan="3">Group 1</th><th colspan="3">Group 2</th><th colspan="3">Group 3</th></tr><tr><th>Depth</th><th>Temperature</th><th>Velocity</th><th>Depth</th><th>Temperature</th><th>Humidity</th><th>Depth</th><th>Temperature</th><th>Precipitation</th></tr></thead><tbody><tr><td></td><td>L</td><td>L</td><td>L</td><td>L</td><td>L</td><td>L</td><td>L</td><td>L</td><td>L</td></tr><tr><td></td><td>H</td><td>L</td><td>L</td><td>H</td><td>L</td><td>L</td><td>H</td><td>L</td><td>L</td></tr><tr><td></td><td>L</td><td>H</td><td>L</td><td>L</td><td>H</td><td>L</td><td>L</td><td>H</td><td>L</td></tr><tr><td></td><td>L</td><td>L</td><td>H</td><td>L</td><td>L</td><td>H</td><td>L</td><td>L</td><td>H</td></tr><tr><td></td><td>H</td><td>H</td><td>L</td><td>H</td><td>H</td><td>L</td><td>H</td><td>H</td><td>L</td></tr><tr><td></td><td>H</td><td>L</td><td>H</td><td>H</td><td>L</td><td>H</td><td>H</td><td>L</td><td>H</td></tr><tr><td></td><td>L</td><td>H</td><td>H</td><td>L</td><td>H</td><td>H</td><td>L</td><td>H</td><td>H</td></tr><tr><td></td><td>H</td><td>H</td><td>H</td><td>H</td><td>H</td><td>H</td><td>H</td><td>H</td><td>H</td></tr></tbody></table>

Note: H denotes high; L denotes low.

<table><caption>**Table 3.** The results of ANOVA</caption><thead><tr><th rowspan="2">Variable</th><th colspan="3">p-value (%)</th></tr><tr><th>Group 1</th><th>Group 2</th><th>Group 3</th></tr></thead><tbody><tr><td>Dep.</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>Tem.</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>Var.</td><td>0.67</td><td>0.48</td><td>0.12</td></tr><tr><td>Dep.&Tem.</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>Dep.&Var.</td><td>0.24</td><td>0.97</td><td>0.00</td></tr><tr><td>Tem.&Var.</td><td>0.00</td><td>0.08</td><td>0.23</td></tr></tbody></table>

Note: Dep. denotes snow depth; Tem. denotes temperature; Var. denotes velocity, humidity and precipitation respectively in Group 1, 2 and 3

The results of ANOVA are shown in Table 3. According to this method, the effect is significant with a lower p value. If the significance level is 0.05, the snow depth and temperature have a significant effect, while velocity, humidity and precipitation have a weak influence. Considering interaction effects, depth & temperature, depth & precipitation and temperature & velocity, all have obvious influences. Furthermore, the
effect of temperature & humidity is relatively high. Therefore, snow depth, temperature, depth & temperature, depth & precipitation, temperature & velocity and temperature & humidity are chosen for the regression analysis.

### 3.3 Multiple regression analyses

Multiple regression analyses are suitable for predicting snow density by the use of meteorological data. The parameters investigated as predictors in this study are those discussed in 3.2. The analyses were performed using the statistical software program MATLAB. During the period of 2012-2013, there were 50 observations. If the significance level is set to 0.05, the function is as follows with a high coefficient of determination equaling 0.90:

$$ \rho = 45.02 + 0.88D - 0.01D^2 - 2.97T + 0.02D \cdot T + 0.30T \cdot V - 0.01T \cdot H $$

Here, $\rho$ is the snow density. D is the snow depth. T is the air temperature. V is the wind velocity. H is the humidity.

## 4 Conclusions

This study has investigated the characteristics of drifting snow on some typical roofs and developed a method for estimating snow density using meteorological data. The following results have been obtained:

1) For two-level roofs, when the angle of the upper roof is smaller than 30°, its influence on the snow distribution on the low roof can be neglected. In addition, the critical angle that causes snow sliding from the upper roof is 30°.

2) In the aspect of influence factors of the snow density, Snow depth and temperature are the main influencing factors. In the aspect of the effect of the interaction, depth & temperature, depth & precipitation and temperature & velocity also have an obvious influence. Furthermore, the regression equation, presented in 3.3, could predict the snow density accurately with a high coefficient of determination equaling 0.90.

## References

1. T. K. Thiis, Y. Gjessing. J. Cold Reg. Sci. Technol. 30, 175 (1999)

2. S. Oikawa. J. J. of Snow Eng. of Japan. 5, 3 (2000)

3. J.H.M. Beyers, T.M. Harms. J. J. Wind Eng. Ind. 91, 551 (2003)

4. V. Meløysund, B. Leira, K. V. Høiseth, K. R. Lisøa. J. Meteorol. Appl. 14, 413 (2007)

5. O. Bruland, Å. Færevåg, I. Steinsland, G. E. Liston. J. HYDROL RES. 46, 494 (2015)

6. J. L. McCreight, E. E. Small. J. TC. 8, 521 (2014)
# Advantages and features of four different snow utilizing facilities

Seiji Kamimura<fnref n="1" />, a, Yoshiomi Ito<fnref n="2" /> and Junki Zen<fnref n="3" />

**Abstract.** In the summer of 2014, the air-conditioning performance of four different snow-utilizing facilities in Niigata and Nagano Prefectures in Japan were evaluated. Systems with a snow storeroom, a rice depot and spa resort, showed the advantages of stable and flexible air temperature control with high deodorizing and dedusting effects. The investment will be earned back in less than 10 years. The system with a snow mound, shiitake mushroom greenhouses, showed that the annual cost is cheaper than that of the heat pump unit. A highway lavatory with daily snow delivery was not cost effective.

## 1 Introduction

In Japan, the northwestern region bordering the Sea of Japan receives heavy snows not seen in other locations worldwide. Therefore, a traditional but unique culture using natural snow for daily life and industry has developed. From the late 1980s, traditional snow utilization applications and facilities have been upgraded with modern technology and revitalized in Japan. Currently, more than 150 facilities are utilizing snow and/or ice in Japan<fnref n="1" />).

In Niigata Pref., two trials were conducted in 1998¹): a refrigerated vegetable warehouse in Tokamachi City was covered with snow and a residential house in Uonuma City was cooled by deposited snow sliding down from a roof. These challenging applications showed many advantages, such as much lower energy consumption, greater and longer crop freshness, high comfort, and so on. Government support since 2002 has also helped with the development of snow-utilizing facilities, and their applications have been diversifying.

From the late 1980s to the early 1990s, the first stage of snow utilization was to verify the technical possibilities and to develop the basic technologies. After that, snow utilization was applied as alternatives to air-conditioners and refrigerators. The second stage, from the late 1990s to the early 2000s, concentrated on the energy saving effect. The authors assume that we are now in the third stage, which focuses on the advantages of snow, such as an extremely stable temperature of around 0 °C, high relative humidity of around 100%, and high absorptivity of odor and dust<fnref n="2" />, <fnref n="3" />). In this third stage, many effects have been demonstrated in succession: taste improvement of root vegetables, maintaining freshness of green-leaved crops and fruit, and high-quality aging of meat, coffee, sake, wine, and so on. There are now a wide range of applications for snow storage⁴).

Snow cooling/refrigerating systems mainly consist of three sections: snow storing, cold heat extraction and delivery, and snow use. The methods for storing snow are classified into two types: snow mound and snow storeroom. In the snow mound, naturally accumulated snow is collected and piled up outside, then covered with special insulation material, such as rice shells, wood

chips/bark or an industrial insulation sheet. The initial cost of a snow mound is relatively low, but a snow mound has some disadvantages, such as poor insulation performance, slightly higher running cost and larger space requirements, as compared to a snow storehouse⁵).

Two major methods are used to extract and deliver cold heat to the cooling target: cold-air circulation and cold-water circulation. In the cold-air circulation method, dust, odor and humidity in the circulating air are expected to be removed as they contact the wet snow surface. The water-circulation method offers no air-purifying effect, but it only requires piping with a small diameter and does not transmit noise through this piping.

The most simple and inexpensive way to use snow is the snow/ice house method, which puts both snow and stored goods in a room. The natural convection of air results in a temperature of about 5 °C and a humidity of 70 to 100%. The air-circulation and water-circulation systems can produce any temperature condition if the control equipment is well designed.

Now, the number of snow-utilizing facilities is over 150 in Japan and the application of snow utilization has diversified for various purposes and industries. In 2014, we had an opportunity to investigate four snow-utilizing

<figure><img src="image_479.png" /><figcaption>**Figure 1.** Locations of snow-utilizing facilities. (Numeral is number of facilities in each municipality)</figcaption></figure>

<figure><img src="image_480.png" /></figure>

<footnote n="1">¹Nagaoka University of Technology, Department of Mechanical Engineering, 1603-1 Kamitomioka, Nagaoka, Japan</footnote>

<footnote n="2">²Yuki-daruma (snowman) Foundation, 722-3 Yasuzuka, Jo-etsu, Niigata 942-0411, Japan</footnote>

<footnote n="3">³Nagaoka University of Technology, Graduate School of Engineering, 1603-1 Kamitomioka, Nagaoka, Japan</footnote>

<footnote>a Seiji Kamimura: kami@nagaokaut.ac.jp</footnote>
facilities in Niigata and Nagano Prefectures, Japan. The facilities are shown in **Figure 1**. Temperature, humidity, amount of heat used, and the air purifying effect of all the facilities were observed during the entire summer of 2014. In this study, the advantages, characteristics, performance, and stability of these four snow-utilizing facilities were evaluated.

# 2 Facilities and evaluation

## 2.1 Outline of facilities

The four snow-utilizing facilities are as follows: (1) a rice depot having a snow storeroom with cold-air circulation, (2) a spa resort having a snow storeroom with cold-water circulation, (3) shiitake mushroom greenhouses having a snow mound covered by rice shells with cold-water circulation, and (4) a highway service area (SA) lavatory with daily snow delivery from a snow mound covered by wood chips with a simplified cold-water circulation unit. A summary of these systems is listed in **Table 1**. Schematic layouts and pictures of the systems are shown in **Figures 2, 3, 4, and 6**.

## 2.2 Rice depot having a snow storeroom with cold-air circulation

The rice depot was constructed in Aga town, Niigata Pref. in January 2014 and utilizes snow for cooling. The depot has two rice storage rooms of different temperatures, 5 and 15 °C, for paddy rice and brown rice, respectively. The storage room for the paddy rice (PR room) has the following dimensions: width 13 m, depth 15 m and height 8 m. The PR room can store 4,000 bales of paddy rice (1 bale is equal to 60 kg). The storage room for brown rice (BR room) has dimensions 15 x 20 x 8 m. The BR room can store 6,000 bales of brown rice. The snow storeroom has dimensions of 10 x 7 x 8 m and can store 545 tons of snow, as calculated from the capacity multiplied by the packing rate of 0.8 under the assumption that the average snow density is 0.5 t/m³. Snow collecting/throwing is combined with the snow removal operation for parking lots neighboring the facility.

The aim of storing rice in a cooling room less than 15 °C is to suppress infestation by insects and microbes, and to lower the physical activity to keep the rice fresh. A lower temperature may give better results but a control temperature of 15 °C is normally chosen to reduce operating costs. In the case of the snow-cooling room, a lower temperature, such as 5 or 10 °C, can easily be realized and, moreover, it can avoid the temperature fluctuations associated with electric coolers. Such temperature fluctuations may increase the fatty acid content. For the above reasons, the control temperature of the rice depot with the snow storeroom is set to 5 °C for the paddy rice room for long-term storage and to 15 °C (12°C from 1 May to 11 July) for the brown rice room based on demand/supply regulations.

The depot has two sets of blowers (send and return) and electric dampers (send, return and bypass). The output of the blowers is 1.5 and 3.7 kW for the PR room and the BR room, respectively. All blowers are generally operating all the time, while the dampers are controlled to maintain a predetermined room temperature. The snow-cooling system began on 16 April 2014 for the BR room, then the PR room was added from 1 May to 19 Nov. 2014.

<figure><img src="image_481.png" /><figcaption>**Figure 2.** Snow-cooling system for the rice depot.</figcaption></figure>

<table><caption>**Table 1.** Outline of four snow-utilizing facilities.</caption><thead><tr><th></th><th>Cooling space<br>[m³]</th><th>Set temperature<br>[°C]</th><th>Purpose</th><th>Snow storage<br>[tons]</th><th>Extraction of<br>cold heat</th><th>Operating period</th></tr></thead><tbody><tr><td>(1) Rice depot<br>for paddy rice<br>for brown rice</td><td>1,560<br>2,400</td><td>5<br>12, 15</td><td>Refrigeration</td><td>545<br>in storeroom</td><td>Cold-air<br>circulation</td><td>5 months</td></tr><tr><td>(2) Spa resort<br>lounge and<br>cafeteria</td><td>741<br>716</td><td>25<br>25</td><td>Space<br>cooling</td><td>263<br>in storeroom</td><td>Cold-water<br>circulation</td><td>3 months</td></tr><tr><td>(3) Mushroom<br>greenhouses</td><td>1,463</td><td>10–20 (budding)<br>20–30 (growing)</td><td>Space<br>cooling</td><td>1,000<br>mound covered with<br>rice shells</td><td>Cold-water<br>circulation</td><td>3 months</td></tr><tr><td>(4) Highway SA<br>lavatory</td><td>289 / 289<br>for M and F</td><td>No control<br>(25)</td><td>Space<br>cooling</td><td>1,000<br>mound covered with<br>wooden chips</td><td>Daily delivery,<br>Cold-water<br>circulation</td><td>1 months</td></tr></tbody></table>
## 2.3 Spa resort having snow storeroom with cold-water circulation

The spa resort facility was reconstructed in Nozawa-onsen village, Nagano Pref. in July 2014. At that time, the space-cooling system utilizing snow was added to the facilities. The site is a very famous ski area in winter, but few tourists visit in summer because skiing is the main attraction. Therefore, snow cooling is expected to be a summer tourist resource. The resort lounge of 741 m³ and the cafeteria of 716 m³ are cooled by fan coil units (FCUs) connected to the snow storeroom through a pipeline.

The resort has two heat exchanging circuits, which are primary and secondary. In the primary circuit of water, warm water sprays onto the snow, then the resulting cooler water, including melt water, flows down to the water reservoir, and then is pumped up to the heat exchanger (HE) and returns to the snow storeroom. In the secondary circuit, warm water returned from the FCUs release heat at the HE, and then is sent to the FCUs again.

The snow storeroom has dimensions of 15 x 10 x 5 m, and can store 241 tons of snow, as calculated from the capacity multiplied by the packing rate of 0.7. Snow collecting/throwing work is combined with the snow removal operation for a parking lot neighboring the facility. The volumes of the lounge and cafeteria are 741 and 716 m³, respectively. The experiment ran from 16 June to 2 Sept. 2014. The FCUs during this time were manually operated by the users.

<figure><img src="image_482.png" /><figcaption>**Figure 3.** Snow-cooling system for a spa resort.</figcaption></figure>

## 2.4 Shiitake mushroom greenhouse having snow mound covered by rice shells with cold-water circulation

A farmers association in Minami-Uonuma City in Niigata Pref. is cultivating shiitake mushrooms in greenhouses (GHs) in a year-round operation. To cultivate mushrooms all through the year, the temperature in the GHs must be kept constant, and so they require heating in winter and cooling in summer. The annual cost of heating and cooling is about 500,000 yen/y (approx. 4,600 USD) for a greenhouse. In particular, the electricity cost for cooling accounts for two-thirds of the whole energy cost. Therefore, reduction of the cooling cost is very effective for improving profitability. Since summer 2011, farmers

have tried to use a snow mound system for GH cooling. After trial and error for three seasons, a practical way to use snow for the GHs was established. The snow mound shown in **Figure 4** was heaped up by using a rotary snow blower of 10 horsepower for one day. After forming a snow mound of about 1000 tons, rice shells partly mixed with snow were also blown up to the snow surface to a thickness of 20 to 30 cm. Finally, an anti-scattering net was put on the surface.

The bed of the snow mound is 30 x 30 m with a water gradient. **Figure 5** shows the layout of the snow mound, pipeline, and GHs. Melt water in the reservoir pit from the snow mound is pumped up and sent through a PVC pipe to the FCUs in the GHs and then heat is exchanged and cold air is blown in. The warmed-up water returns to the upper end of the snow mound and is cooled down again under the snow mound. FCUs are installed in GHs Nos. 3, 4, 5 and 6 of the six GHs. In addition, the No. 3 GH only has two FCUs due to its large room volume. Because each GH is also equipped with an electric cooler unit, the snow-cooling system is constantly working for the base demand in the summer. The electric coolers are controlled by room temperature to adapt to the fluctuating demand.

The snow-cooling system operation for Nos. 3, 4, and 5 started on 6 June 2014 and ran until 9 Sept., while No. 6 started on 11 July. The control temperatures in the room were between 10 to 20 °C for cultivating the mushroom beds, and 20 to 30 °C for the development.

<figure><img src="image_483.png" /><figcaption>**Figure 4.** Snow-cooling system for the shiitake mushroom Greenhouse.</figcaption></figure>

<figure><img src="image_484.png" /><figcaption>**Figure 5.** Layout of a snow mound, GHs and piping.</figcaption></figure>
## 2.5 Highway SA lavatory with daily snow delivery from a snow mound covered by wooden chips with simplified cold-water circulation unit

A trial experiment of snow cooling for a lavatory of a highway service area (SA) was conducted in July and Aug. 2014 in Kawaguchi, Niigata Pref. Figure 6 shows delivery procedure from the snow mound to lavatory. Because the

<figure><img src="image_485.png" /><figcaption>Figure 6. Snow cooling system for Highway SA lavatory.</figcaption></figure>

<figure><img src="image_486.png" /><figcaption>Figure 7. Simple Snow Cooling Unit (SSCU).</figcaption></figure>

<figure><img src="image_487.png" /><figcaption>Figure 8. Plan view of snow mound and Service Area building.</figcaption></figure>

highway SA has a large parking lot, much of the SA budget in winter is snow removal, and the resulting piles of snow take up a large area. In addition, a sudden increase of melt water containing antifreezing salt from the snow piles in the spring may adversely affect the neighboring rice paddy.

For three days in the middle of March, 2014, a snow mound was shaped into a pyramid in a back area of the SA by using a backhoe. For two days after shaping, the mound was covered by crushed chips of wood. The mass of the snow mound was estimated to be 866 t, as calculated from the measured volume of 1732 m³ under the assumed snow density of 0.5 t/m³. The stored snow was also used for an event in the summer.

Because the snow mound was 50 m away from the lavatory, we decided to deliver 1 ton of snow every morning from the snow mound to a simple snow-cooling unit (SSCU), which was newly designed and assembled for the project, as shown in Figure 7. The SSCU (2.5 x 1.3 x 1.6 m) was composed of an insulated chassis, a filtering tank (bag of crushed shells), a melt-water reservoir, and a cold water outlet. In addition, it had a mesh container (1.7 x 1.1 x 1.4 m) inside for storing the snow. The amount of snow packed in the mesh container was about 0.9 tonnes, which was estimated from the volume of 2.05 m³ under the assumed snow density of 0.5 t/m³ and packing factor of 0.9. Every morning, an operator brought snow down from the snow mound with a backhoe and then packed snow into the mesh container. The container packed with snow was transported by a dump truck with a crane and stored in the SSCU.

The cold water outlet of the SSCU was connected to an insulated PVC pipeline and pump, and the melt water was sent to the FCUs in both the men's and women's lavatories, and then returned to the SSCU again. The FCUs were placed around the entrance of each lavatory. The pump operated 24 hours a day from 18 July to 20 Aug. 2014. On average, 1 ton of snow was carried at 8 am and remained until approximately 8 pm.

## 3 Evaluation of facilities

The cooling performance of these facilities was evaluated by the coefficient of performance (COP) calculated from the amount of cold heat extracted from the stored snow (GJ), Q, and the electric power consumption for system operation (GJ), P, as follows:

$$COP = Q/P.$$

Q is calculated by the following equation,

$$Q = \int \rho C_p (T_{out} - T_{in}) G dt$$

where ρ is the density of circulating fluid (kg/m³), C_p is the isobaric specific heat (kJ/kg*K), T_in and T_out are the fluid temperature of the supply and return, respectively, and G is the mass flow rate of fluid (m³/s). P is the sum of the products of electric current I and electric voltage V:

$$P = \int I V dt.$$

The profitability of these facilities is discussed with the simple cost calculation denoted in the following equation,

$$C_a = \frac{C_i}{L} + C_r$$
<table><caption>Table 2. Observation items.</caption><thead><tr><th></th><th>(1) Rice depot</th><th>(2) Spa resort</th><th>(3) Mushroom GH</th><th>(4) SA lavatory</th></tr></thead><tbody><tr><td>Room temp. & humid.</td><td>○</td><td>○</td><td>○</td><td></td></tr><tr><td>Blowing air temp.</td><td></td><td></td><td>○</td><td>○</td></tr><tr><td>Fluid temp. of inlet</td><td>○</td><td>○</td><td>○</td><td>○</td></tr><tr><td>Fluid temp. of outlet</td><td>○</td><td>○</td><td>○</td><td>○</td></tr><tr><td>Fluid velocity</td><td>○</td><td>○</td><td>○</td><td></td></tr><tr><td>Calories</td><td></td><td>○</td><td></td><td>○</td></tr><tr><td>Electric current</td><td></td><td></td><td>○</td><td>○</td></tr><tr><td>Electric power</td><td>○</td><td></td><td></td><td></td></tr><tr><td>Snow-room temp.</td><td></td><td>○</td><td></td><td></td></tr><tr><td>Water tank temp.</td><td></td><td>○</td><td></td><td></td></tr><tr><td>Outside temp. & humid.</td><td>○</td><td>○</td><td>○</td><td>○</td></tr><tr><td>Dust concentration</td><td>○</td><td></td><td></td><td></td></tr><tr><td>Odor level</td><td>○</td><td></td><td></td><td></td></tr></tbody></table>

where $C_a$ is the annual cost of the system, $C_i$ and $C_r$ are the initial and running costs, respectively. L is the lifetime of the components of the system. The cost of these facilities is compared with a commercial air-coupled heat pump system, and then the break-even point is discussed.

# 4 Experimental result

## 4.1 Rice depot having a snow storeroom with cold-air circulation

Figure 9 shows the observed outdoor temperatures and room temperatures. The temperature in the BR room was followed well at the pre-set temperature of 12 °C from 1 March to 11 July and 15 °C after 12 July. The standard deviation for the BR room was 0.4 °C even in the middle of summer. The temperature in the PR room varied around 7 °C after the end of May despite the pre-set temperature of 5 °C. The reason for the higher temperature difference after the beginning of June is considered to be the lower heat exchanging efficiency in the snow storeroom due to the short circuit of the air flow. The standard deviation from the pre-set temperature for the PR room was 2.1 °C. After mid-September, the temperature varied widely because it was the harvesting season and the door was often opened. The humidity in both rooms had been kept at about 70% and the standard deviations were 4.4% and 3.5% for the PR room and the BR room, respectively.

In the case of the air-circulation system, it is known that the effect of air-purifying and deodorizing is promising. Figure 10 shows the dust concentration in the PR room. The suspended dust concentration was far below the environmental standard of 0.10 mg/m³. The odor level was about 160, which corresponds to that of a kitchen or laundry machine and is less than that in a factory of plastic products. This beneficial effect was confirmed by a facility operator's comment that "There is no rice bran smell."

## 4.2 Spa resort having snow storeroom with cold-water circulation

Figure 11 shows the air temperature of the lounge and cafeteria of the spa resort. The snow cooler operated from 9 am to 8 pm, so the air temperature was quite low in the daytime and relatively high in the night time. Therefore, the following analysis takes into account the daytime result. The temperature in the lounge and cafeteria was kept in the range between 20 to 25 °C even when the outside temperature exceeded 30 °C. Especially, the

<figure><img src="image_488.png" /><figcaption>Figure 9. Observation result of temperature in the rice depot.</figcaption></figure>

<figure><img src="image_489.png" /><figcaption>Figure 10. Concentration of suspended dust in the PR room.</figcaption></figure>
cafeteria temperature sometimes reached 22 °C, so the snow cooler was shown to be effective. The snow cooler operated until the end of Sep., when the outside temperature became lower than the room temperature.

<figure><img src="image_490.png" /><figcaption>Figure 11. Observed temperature of the spa resort.</figcaption></figure>

## 4.3 Shiitake mushroom greenhouses having snow mound covered by rice shells with cold-water circulation

Figure 12 shows the water temperatures of the inlet and outlet of the FCU in the No. 4 GH. The daily fluctuation of the curve corresponds to the outdoor temperature. The temperature difference, which corresponds to the amount of heat released at the FCU from the beginning of Aug. to the beginning of Sept. was around 5 °C in the daytime, so this shows that the snow-cooling system worked well. After 10 Sept. the volume of the snow mound shrank and the heat exchange at the snow mound did not work well. The average temperature differences for the whole period were 3.4, 4.1, 3.1 and 2.2 for Nos. 3, 4, 5 and 6 GHs, respectively.

<figure><img src="image_491.png" /><figcaption>Figure 12. Observed temperature of the No. 4 GH.</figcaption></figure>

Some problems were explained by the experiment in 2014. For the GHs except No. 4, which was the closest to the snow mound, the flow rate of the circulated water was insufficient, because the piping design of the distribution to that branch was inappropriate and two filters often had troubles. In addition, the storage capacity of the snow mound was too small, because two FCUs were added to

the No. 3 and No. 6 GHs, even though the volume of the snow mound in 2014 was the same as in the previous year. The number of FCUs in the 2013 season was three each for the Nos. 3, 4 and 5 GHs, while it increased to five each in the 2014 season.

The maximum cooling energy per day extracted from the snow mound was 3.0 GJ, which is equal to 9.1 tons of snow. By assuming no filter problems, the total cooling energy was estimated as 219 GJ, which corresponds to 654 tons of snow. This estimate suggests that 65% of the stored energy from a snow mound of 1000 tons can be used.

## 4.4 Highway SA lavatory with daily snow delivery from a snow mound covered by wooden chips with simplified cold-water circulation unit

Figure 13 shows the wind temperature at an FCU outlet at the SA lavatory. The average temperatures were 17.3, 22.5 and 26.1 °C for the men's lavatory, the women's lavatory, and the outside air, respectively. The temperature of the women's lavatory was about 5 °C higher than the temperature of the men's lavatory. The assumed reason is the length of piping was 1.5 times longer and was affected by solar radiation and heat convection from the outside hot air.

<figure><img src="image_492.png" /><figcaption>Figure 13. Wind temperature at FCU outlet of SA lavatory.</figcaption></figure>

# 5 Consideration

## 5.1 Cool energy utilization

The effective cool energy used for the facility was estimated from the temperature difference, flow rate of circulation and specific heat of the media. The amounts of electricity consumed for the snow-cooling system operations are summarized in Table 3.

In the rice depot, the COP of the PR room was 5.3, which is somewhat better than that of a commercial electric cooling unit of equivalent capacity, whereas the COP of the BR room was 2.5, which is about that of an ordinary electric cooler that has a COP of 3. The values of P in parentheses in Table 3 are for the snow-cooling operations and do not consider the electricity consumption for air circulation. As shown, the 4.9 GJ in Table 3 lead to an improved COP of 7.3 in the snow-cooling operation.