Current Canadian and U.S. Approaches to Snow Drift Loads

Snow drift procedures in Canada and the U.S. are compared and evaluated.

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 W₂ (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/ft³) given by

 γ = 0.13 p_g + 14 ≤ 30 lb/ft³ (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, W₂ 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. W₂ 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 W₂ to the 0.85 power, W₂^0.85.

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_up_g. If the wind is out of the North 50% of the time, then L_d = 0.5 l_up_g.

 L_d is proportional to l_up_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 W₂ 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.