*To view the figures and tables associated with this article, please refer to the flipbook above.*

Historically, the snow drift provisions in the early editions of ASCE 7 were adopted from Canadian practice. Although there are similarities between practices in the United States and Canada, the current U.S. snow drift provisions differ in significant ways from the current Canadian provisions.

The objective of this article is to identify and discuss these differences to provide structural engineers with a better understanding of snow drifting in general and of specific differences for those with projects in Canada. The comparison is restricted to the simple leeward roof step drift load, which is arguably the most important snow load since it results in more snow-related structural performance issues. Specifically, simple geometry refers to nominally flat upper and lower-level roof surfaces, no upwind or downwind parapets on the upper-level roof, and a step size that does not impact the lower-level roof drift size. Also, the roof elevation difference at the step is less than 16.5 ft. (5 meters) since the Canadian code allows a reduction in drift load for larger step sizes.

## U.S. Snow Loads

In the current U.S. provisions as defined by the American Society of Civil Engineers Standard *Minimum Design Loads and Associated Criteria for Buildings and Other Structures*, ASCE/SEI 7-22, the drift height is a function of the ground snow load p_{g} (in pounds per square foot), the length of roof upwind of the drift (or “fetch”) l_{u} (in feet) and a winter wind parameter W_{2} (dimensionless). Specifically, the leeward roof step surcharge drift height, h_{d} (in feet), is given by

h_{d} = 1.5 (1)

where γ is the snow density (lb/ft^{3}) given by

γ = 0.13 p_{g} + 14 ≤ 30 lb/ft^{3} (2)

Equation 1 was developed using multiple regression analysis of numerically simulated maximum annual snow drift loads for 10 upwind fetch distances over a 35-year period at 46 sites across the U.S.

A general discussion of each of these variables follows.

**Ground Snow Load:** As one would expect, the drift height is an increasing function of the ground snow load. The larger the ground snow load, the more snow that is available for drift formation. Table 1 presents the drift height in ASCE 7-22 as a function of p_{g}, normalized by the drift height for p_{g} = 40 psf. As shown, h_{d} is nominally proportional to p_{g} to the 0.3 power, p_{g}^{0.3}.

**Upwind Fetch:** Similar to the influence of p_{g}, the drift heights in the current ASCE 7-22 provisions are an increasing function of upwind fetch distance l_{u}. From Equation 1, h_{d} is proportional to the fetch to the 0.35 power (l_{u})^{0.35}.

**Winter Wind Parameter:** In ASCE 7-22, W_{2} is the percent of time the wind speed exceeds 10 miles per hour during October through April; values for the lower 48 states are presented in ASCE7-22 map, Figure 7.6-1. W_{2} values vary from 0.25 in the Intermountain West to 0.65 in parts of the Midwest. As shown in Equation 1, h_{d} is proportional to W_{2} to the 0.85 power, W_{2}^{0.85}.

Canadian Snow Loads

The snow load, S, in the 2020 version of the National Building Code of Canada (NBCC) is as shown in Equation 3.

S = I_{s} [S_{s} (C_{b} C_{w} C_{s} C_{a}) + S_{r}] (3)

where I_{s} is the importance factor for snow loads which equals 1.0 for the roofs of ordinary importance considered herein; S_{s} is the 50-year ground snow load (in kilopascals), C_{b} is the basic roof snow load factor; C_{w} is the wind exposure factor which equals 1.0 for roofs involving snow drift accumulation; C_{s} is the slope factor which equals 1.0 for the flat roofs considered herein; C_{a} is an accumulation factor, and S_{r} is the 50-year associated rain load (in kilopascals). Note that, somewhat surprisingly, the design roof snow load in Canada is not a function of the roof’s thermal condition.

As shown above, the Canadians have chosen to include rain with their snow load. Herein, the rain contribution will be neglected, as the focus of this article is loading due to drifted snow.

The C_{b} factor is the Canadian version of the ASCE ground-to-roof conversion factor of 0.7, which is a function of the C_{w} factor and a characteristic length of the upper or lower roof, l_{c}. The characteristic roof length l_{c} (m) is defined as

l_{c} = 2 w – (4)

where w is the smaller plan dimension for the roof and l is the larger plan dimension. Defining the aspect ratio A_{r} as l/w, l_{c} becomes

l_{c} = (5)

The C_{b} factor is 0.8 for a characteristic roof length l_{c} of 230 ft. (70 m) or less and increases non-linearly to 1.0 for l_{c} of about 1400 ft. (440 m) or more. This factor accounts for the inability of wind to remove snow from very large roofs.

**Drift Loads:** NBCC accounts for drift loads via the accumulation factor C_{a}. The drift atop the lower-level roof at the step is given by the parameter C_{ao}. For the case considered herein, where the leeward step size does not influence the drift size

C_{ao} = (6)

Where for the case considered herein with no parapets,

F = 0.35β + C_{b} ≤ 5 (7)

where γ is the snow density (same as the ASCE 7 relation in Equation 2) and β =1.0 for leeward drifts. (β is a factor that is dependent upon the direction of the wind, whether leeward or windward.) Note that the first part of Equation 7 corresponds to the surcharge drift while the second term (i.e., C_{b}) corresponds to the balanced snow load atop the lower-level roof. Since C_{ao} is multiplied by dimensionless factors (i.e., I_{s}, C_{b}, C_{w}, and C_{s}) and S_{s} in Equation 3, it is a load with units of psf or kPa. As such, for comparisons with the drift surcharge height h_{d} in ASCE 7-22, one needs to divide by the snow density.

Hence, the relation for drift height as per the NBCC, (h_{d})_{NBCC}, absent the rain load, is

(h_{d})_{NBCC} = I_{s} S_{s} (C_{w} C_{s}) /γ (8)

with I_{s} = C_{w} = C_{s} = 1.0. That is

(h_{d})_{NBCC} is proportional to (9)

Hence, in relation to the ground snow load, (h_{d})_{NBCC} is proportional to the square root of S_{s} divided by the snow density γ. The influence of the ground snow load upon the NBCC drift height is shown in Table 3, normalized by that for

S_{s} = 40 psf.

Note that (h_{d})_{NBCC} is nominally proportional to S_{s}^{0.38}.

In relation to the fetch distance, (h_{d})_{NBCC} is proportional to the square root of the characteristic roof length l_{c}. However, to facilitate comparisons with ASCE 7-22, it can be shown that for a given A_{r} ratio, (h_{d})_{NBCC} is proportional to the traditional upwind fetch l_{u} to the 0.5 power, (l_{u})^{0.5}.

## Theoretical Consideration

Although the h_{d} relations in ASCE 7-22 were based on multiple regression analysis of numerically simulated drift data, one can estimate the expected influence of l_{u} and p_{g} from theoretical considerations. The drift load (half the drift height times drift width times snow density with units of lbs./ft.) is the snow transfer from the upper-level roof times a trapping efficiency. For the simulated drifts, the trapping efficiency was taken to be a constant, 50%. The snow transfer, due mainly to snow saltation (wind-driven snow particles bouncing along the snow surface), is a function of the wind speed to a power and the fetch distance. The snow transport is proportional to the square root of the fetch for l_{u} ≤ 750 ft. For larger fetch distances, the transport rate is constant for a given wind speed. That is, for l_{u} of 750 ft. and larger, we have the “infinite fetch” transport rate.

In relation to fetch distances, for the ASCE 7-22 relationship, the simulated drift database had 10 fetch distances ranging from 25 to 1000 ft. There was only one fetch equal to or larger than the transport rate transition fetch distance of 750 ft. That is, 90% of the simulated drift database upon which the ASCE 7-22 drift relation was based had a l_{u} of 750 ft. or less. Based upon this, it will be assumed herein that the upwind fetch distance is 750 ft. or less. Specifically, the transport rate will be assumed proportional to the square root of the fetch distance (l_{u})^{0.5}.

The drift formation process stops when either a) the wind stops blowing, or the speed is less than the drift threshold of 10 MPH, or b) the driftable snow has been blown off the upper-level roof.

The theoretical influence of l_{u} and p_{g} upon the drift height is based upon two scenarios.

**High Wind Scenario:** In this scenario, the wind speed is large enough to completely remove driftable snow from the upper-level roof after each snowfall event. For this scenario, the drift load L_{d} (lbs/ft) on the lower-level roof would be proportional to the upwind fetch and the ground snow load. For example, consider an upper-level roof north of the lower-level roof. If the wind is out of the north 100% of the time, then L_{d} = l_{u}p_{g}. If the wind is out of the North 50% of the time, then L_{d} = 0.5 l_{u}p_{g}.

L_{d} is proportional to l_{u}p_{g}

For a large roof step, the drift width is typically 4h_{d} (drift slope of 1:4). Hence, the drift height h_{d} is proportional to the square root of the drift load L_{d} divided by the snow density. Using the ASCE 7 relation for snow density.

h_{d} is proportional to

Hence, for the High Wind Scenario, the drift height is proportional to the upwind fetch to the 0.5 power, l_{u}^{0.5}. It can be shown that the influence of p_{g} upon the drift height for the high wind scenario is nominally the same as in Table 1. That is, for the high wind scenario, h_{d} is nominally proportional to the ground snow load to the 0.3 power, p_{g}^{0.3}.

**Low Wind Scenario:** In this scenario, the wind speed is low enough that some snow remains atop the upper-level roof and does not contribute to drift accumulation on the lower-level roof. For this scenario, the drift load L_{d} is proportional to the transport rate, which in turn is proportional to the square root of the fetch.

L_{d} proportional to

As such, the drift height is proportional to the upwind fetch l_{u} to the 0.25 power, (l_{u})^{.25}.

h_{d} proportional to

The influence of P_{g} upon the drift height for the Low Wind Scenario is presented in Table 4.

Notice that for the low wind scenario, the ground snow load has little or no influence.

## Comparisons to Theory

**ASCE 7-22:** In relation to the ASCE 7-22 provisions, the drift height h_{d} is nominally proportional to the ground snow load p_{g} to the 0.3 power and proportional to the upwind fetch to the 0.35 power. Hence, the influence of both parameters is consistent with the expected behavior in the low and high wind scenarios. That is, for the ground snow load, p_{g}^{0.3} is within the theoretical range of p_{g}^{0.0} (low wind) to p_{g}^{0.3} (high wind). Similarly, for the upwind fetch, l_{u}^{0.35} is within the theoretical range of l_{u}^{0.25} (low wind) to l_{u}^{0.5} (high wind). These comparisons are presented in Table 5.

**NBCC:** In relation to the NBCC provision, the drift height is nominally proportional to the ground snow load to the 0.38 power and proportional to the traditional fetch l_{u} to the 0.5 power. Hence, the influence of l_{u} is consistent with theory; that is, l_{u}^{0.5} is within the range of l_{u}^{0.35} (low wind) to l_{u}^{0.5} (high wind). However, using the NBCC approach, the influence of ground snow load, p_{g}^{0.38}, is outside the expected range of p_{g}^{0.0} (low wind) to p_{g}^{0.3} (high wind). As a result, the NBCC provisions would tend to underpredict drifts for low-ground snow load sites and over-predict for high-ground snow load sites.

The NBCC provision does not utilize a winter wind parameter in its drift load procedures. Hence, a US/Canadian comparison of the influence of the W_{2} parameter in ASCE 7-22 is not possible.

Similarly, a US/Canadian comparison of the influence of the NBCC snow source aspect ratio A_{r} is not possible since ASCE 7-22 does not utilize that parameter. However, it is possible to estimate from theoretical considerations the expected relative influence of the NBCC characteristic length l_{u} and the corresponding aspect ratio A_{r}. As noted above, the NBCC characteristic length cleverly decreases the fetch for upper roof snow sources that are long in the along-wind direction and short in the cross-wind direction l_{c} ≤ l_{u} (l parallel to l_{u}), while increasing the fetch for the reverse (i.e., (l_{c} ≥ l_{u}) for w parallel to l_{u}. If the aspect ratio is 3.0 or 5.0, the NBCC drift height is 74% or 60%, respectively, of that for A_{r} = 1.0 if w is perpendicular to l_{u}. If w is parallel to l_{u}, the NBCC drift height is 29% or 34% (for an aspect ratio of 3.0 or 5.0, respectively) larger than that for A_{r} =1.0.

In theory, the aspect ratio has two potential influences upon the drift height. As sketched in Figure 1, the first potential influence is the fact that the along wind fetch distance AB is somewhat larger than the traditional fetch l_{u}. However, it can be shown that the resulting expected increase in the drift height at B is effectively negated by the corresponding increase in the new drift surcharge width on the lower-level roof, which would now likely be parallel to AB.

The second potential influence of the aspect ratio upon leeward drift size is that a larger or smaller number of wind directions could contribute to significant drift formation atop the lower-level roof. That is, in Figure 1, wind parallel to AB, CB, or DB could contribute to leeward drift formation. Wind along line AE could cause snow transport from the upper-level roof. However, it is unlikely that, that snow will end up atop the lower-level roof. Hence, in Figure 1, wind direction within plus or minus θ of north is assumed herein to potentially contribute to leeward drift formation. Table 6 presents θ as a function of aspect ratio A_{r} as well as θ normalized by that for A_{r} = 1.0. That is, for a roof with l parallel to l_{u} (l_{c} ≤ l_{u}) and an aspect ratio of 5 (l = 5w), the wind directions potentially contributing to drift formation are 21 percent of those for A_{r} = 1.0. For a roof with w parallel to l_{u} (l_{c} ≥ l_{u}) and A_{r} = 5, wind directions potentially contributing to drift formation are about 2.6 times that for A_{r} = 1.0.

Table 6 also shows the relative influence of aspect ratio as per the NBCC provisions mentioned above.

## Conclusion

In summary, Table 5 shows that the influence of l_{u} and p_{g} in the ASCE 7-22 drift load provisions is consistent with that from theoretical considerations. Table 5 also shows that the influence of the traditional upwind fetch in the NBCC provisions is consistent with that from theoretical considerations. In contrast, the influence of the ground snow load (p_{g}^{0.38} versus a range of p_{g}^{0.0} to p_{g}^{0.3}) is close. Table 6 suggests that the influence of aspect ratio in the NBCC provisions has the expected trend but is not consistent with a theory that drift size is proportional to the range of contributing wind direction. As such, it is the authors’ opinion that the ASCE 7-22 provisions for snow drift loading are, in general, more consistent with expected behavior than the NBCC provisions.■

## References

O’Rourke, M., and J. Cocca., 2019. “Improved snow drift relations.” *J. Struct. Eng. *145 (5): 04019027

Tabler, R., 1994. “Design guidelines for the control of blowing and drifting snow.” Rep. SHRP-H-381. Washington, DC: National Research Council.